U.S. patent application number 12/814269 was filed with the patent office on 2011-08-04 for polarization-modulating optical element.
This patent application is currently assigned to Carl Zeiss SMT AG. Invention is credited to Markus Deguenther, Damian Fiolka.
Application Number | 20110188019 12/814269 |
Document ID | / |
Family ID | 37678720 |
Filed Date | 2011-08-04 |
United States Patent
Application |
20110188019 |
Kind Code |
A1 |
Fiolka; Damian ; et
al. |
August 4, 2011 |
POLARIZATION-MODULATING OPTICAL ELEMENT
Abstract
The invention relates to a projection system, comprising a
radiation source, an illumination system operable to illuminate a
structured mask, and a projection objective for projecting an image
of the mask structure onto a light-sensitive substrate, wherein
said projection system comprises an optical system comprising an
optical axis or a preferred direction given by the direction of a
light beam propagating through the optical system; the optical
system comprising a temperature compensated polarization-modulating
optical element described by coordinates of a coordinate system,
wherein one preferred coordinate of the coordinate system is
parallel to the optical axis or parallel to said preferred
direction; said temperature compensated polarization-modulating
optical element comprising a first and a second
polarization-modulating optical element, the first and/or the
second polarization-modulating optical element comprising solid
and/or liquid optically active material and a profile of effective
optical thickness, wherein the effective optical thickness varies
at least as a function of one coordinate different from the
preferred coordinate of the coordinate system, in addition or
alternative the first and/or the second polarization-modulating
optical element comprises solid and/or liquid optically active
material, wherein the effective optical thickness is constant as a
function of at least one coordinate different from the preferred
coordinate of the coordinate system; wherein the first
polarization-modulating optical element comprises optically active
material with a specific rotation of opposite sign compared to the
optically active material of the second polarization-modulating
optical element.
Inventors: |
Fiolka; Damian; (Oberkochen,
DE) ; Deguenther; Markus; (Aalen, DE) |
Assignee: |
Carl Zeiss SMT AG
Oberkochen
DE
|
Family ID: |
37678720 |
Appl. No.: |
12/814269 |
Filed: |
June 11, 2010 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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12201767 |
Aug 29, 2008 |
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12814269 |
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11440475 |
May 25, 2006 |
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12201767 |
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PCT/EP2005/000320 |
Jan 14, 2005 |
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11440475 |
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60684607 |
May 25, 2005 |
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60537327 |
Jan 16, 2004 |
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Current U.S.
Class: |
355/71 ; 355/67;
359/492.01; 362/19; 362/257; 362/296.09; 362/317 |
Current CPC
Class: |
G03F 7/70191 20130101;
G03F 7/70341 20130101; G03F 7/70566 20130101; G02B 27/286 20130101;
G03B 27/72 20130101; G03F 7/70966 20130101; G02B 7/008 20130101;
G03F 7/70891 20130101 |
Class at
Publication: |
355/71 ; 362/257;
362/296.09; 362/19; 355/67; 359/492.01; 362/317 |
International
Class: |
G03B 27/72 20060101
G03B027/72; F21V 7/00 20060101 F21V007/00; F21V 9/14 20060101
F21V009/14; G03B 27/54 20060101 G03B027/54; G02B 5/30 20060101
G02B005/30 |
Claims
1. (canceled)
2. An apparatus which illuminates a surface to be illuminated with
radiation from a radiation source, the apparatus comprising: an
optical member having a first portion of a first thickness along an
optical axis direction of the apparatus and a second portion of a
second thickness along the optical axis direction of the apparatus,
wherein the first and second portion thicknesses are different from
each other, and the optical member is made of an optical material
with optical activity.
3. The apparatus according to claim 2, wherein the optical member
includes a first basic element and a second basic element.
4-7. (canceled)
8. The apparatus according to claim 3, wherein the first and second
basic elements are arranged in a plane in an illumination path of
the apparatus.
9-14. (canceled)
15. The apparatus according to claim 3, wherein the first basic
element and the second basic element are integrally formed.
16. (canceled)
17. The apparatus according to claim 2, further comprising: a first
optical unit including a first optical axis; a second optical unit
including a second optical axis which crosses the first optical
axis, the first optical unit arranged in an illumination path
between the radiation source and the second optical unit; a third
optical unit including a third optical axis which crosses the
second optical axis, and the third optical unit is arranged in an
illumination path between the second optical unit and the surface
to be illuminated, wherein the second optical unit includes the
optical member.
18. The apparatus according to claim 17, wherein the optical member
includes a first basic element and a second basic element.
19-21. (canceled)
22. The apparatus according to claim 17, wherein the first basic
element and the second basic element are integrally formed.
23. The apparatus according to claim 17, wherein the third optical
unit includes a folding mirror.
24. The apparatus according to claim 17, wherein the second optical
unit includes a polarization state converter.
25-26. (canceled)
27. The apparatus according to claim 2, wherein a polarization
state of the beam from the optical member is set based on an
influence of a second optical member in an illumination path
between the light source and a substrate arranged surface.
28-75. (canceled)
76. An apparatus which illuminates a surface to be illuminated with
radiation from a radiation source, the apparatus comprising: a
polarization state converter arranged in an illumination path; a
first crystal optical element having a first thickness along an
optical axis direction; and a second crystal optical element having
a second thickness along an optical axis direction; wherein the
first and second crystal optical elements are arranged in a plane
disposed in an illumination path of the apparatus.
77-91. (canceled)
92. An exposure apparatus comprising the apparatus as defined in
claim 76, wherein the exposure apparatus illuminates a
predetermined pattern, and projects an image of the predetermined
pattern onto a photosensitive substrate on the surface to be
illuminated.
93. The exposure apparatus according to claim 92, wherein an
illumination pupil distribution on or near an illumination pupil of
the apparatus is a distribution in at least a part of a
predetermined annular region centered around an optical axis of the
apparatus.
94. The exposure apparatus according to claim 92, wherein a
polarization state of the beam from the first and second crystal
optical elements is set based on an influence of an optical member
disposed in an illumination path between the light source and the
photosensitive substrate on the surface to be illuminated.
95. (canceled)
96. The exposure apparatus according to claim 92, wherein a
polarization state of the beam at an illumination pupil is set so
that light illuminating the photosensitive substrate is in a
polarization state in which a principal component is s-polarized
light.
97-108. (canceled)
109. An apparatus which illuminates a surface to be illuminated
with radiation from a radiation source, the apparatus comprising:
an optical element made of an optical material with optical
activity, an optic axis of the optical material of the optical
element being aligned along an optical axis of the apparatus.
110-114. (canceled)
115. The apparatus according to claim 110, wherein the first and
second basic elements are arranged in a plane which is disposed in
an illumination path of the apparatus.
116-122. (canceled)
123. An exposure apparatus comprising the apparatus as defined in
claim 109, which illuminates a predetermined pattern and projects
the predetermined pattern onto a photosensitive substrate.
124. The exposure apparatus according to claim 123, wherein an
illumination pupil distribution on or near an illumination pupil of
the apparatus is a distribution in at least a part of a
predetermined annular region, which is a predetermined annular
region centered around an optical axis of the apparatus.
125. The exposure apparatus according to claim 124, wherein a
polarization state of the beam at the illumination pupil is set
based on an influence of an optical member disposed in an optical
path between the light source and the photosensitive substrate.
126. (canceled)
127. The exposure apparatus according to claim 124, wherein a
polarization state of the beam at the illumination pupil is set so
that light illuminating the photosensitive substrate is in a
polarization state in which a principal component is s-polarized
light.
128-219. (canceled)
220. A polarization transforming element used in an illumination
optical apparatus that illuminates a predetermined pattern on the
basis of a beam from a light source, comprising: a plurality of
optical members with different thicknesses, each optical member
made of an optical material with optical activity, wherein each of
the plurality of optical member provides a predetermined
polarization state on a predetermined surface according to the
thickness of the optical member.
221. The polarization transforming element according to claim 220,
wherein the predetermined surface is an illumination pupil plane of
the illumination optical apparatus or a plane near the illumination
pupil plane.
222. The polarization transforming element according to claim 221,
wherein a predetermined light intensity distribution of an annular
shape or a multipole shape positioned in a predetermined annular
region formed on the predetermined surface, and wherein the
predetermined annular region is centered around a predetermined
point on the predetermined surface.
223. (canceled)
224. The polarization transforming element according to claim 221,
wherein the predetermined polarization state has a polarization
state in which a principal component is linearly polarized light
having a direction of polarization along a circumferential
direction of a predetermined annular region, which is a
predetermined annular region centered around a predetermined point
on the predetermined surface.
225. (canceled)
226. The polarization transforming element according to claim 224,
wherein the optical members are made of crystalline quartz.
227. (canceled)
228. The polarization transforming element according to claim 220,
wherein the optical members are made of an optical material with
optical activity.
229. An illumination optical apparatus for illuminating a surface
to be illuminated, based on a beam from a light source, comprising:
the polarization transforming element as defined in claim 220, for
transforming the beam from the light source in order to form a
predetermined polarization distribution on or near an illumination
pupil of the illumination optical apparatus.
230-231. (canceled)
232. The illumination optical apparatus according to claim 229,
wherein the polarization state of the beam from the polarization
transforming element is so set that light illuminating the surface
to be illuminated is in a polarization state in which a principal
component is s-polarized light.
233-238. (canceled)
239. The beam transforming element according to claim 145, wherein
an optical axis of the optical material of the first basic element
is aligned along a traveling direction of the incident beam, and
wherein an optical axis of the optical material of the second basic
element is aligned along the traveling direction of the incident
beam.
240. (canceled)
241. The polarization transforming element according to claim 220,
wherein each optical axis of the optical material of the optical
member is aligned along a traveling direction of the incident
beam.
242. The apparatus of claim 2, further comprising a light source
and one or more optical elements arranged to direct radiation from
the light source to the surface to be illuminated during operation
of the apparatus, the one or more optical elements defining a pupil
plane between the light source and the surface to be illuminated,
wherein the optical member is arranged at the pupil plane.
243. The apparatus of claim 76, further comprising a light source
and one or more optical elements arranged to direct radiation from
the light source to the surface to be illuminated during operation
of the apparatus, the one or more optical elements defining a pupil
plane between the light source and the surface to be illuminated,
wherein the first and second crystal optical elements are arranged
at the pupil plane.
244. The apparatus of claim 109, further comprising a light source
and one or more additional optical elements arranged to direct
radiation from the light source to the surface to be illuminated
during operation of the apparatus, the one or more optical elements
defining a pupil plane between the light source and the surface to
be illuminated, wherein the optical element made of an optical
material with optical activity is arranged at the pupil plane.
245. An illumination optical apparatus that illuminates a
predetermined pattern, comprising: a light source; one or more
optical elements; and the polarization transforming element of
claim 220, wherein the one or more optical elements define a pupil
plane between the light source and the predetermined pattern and
the polarization transforming element is arranged at the pupil
plane.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. application Ser.
No. 12/201,767, Aug. 29, 2008, which is a continuation application
of U.S. application Ser. No. 11/440,475, filed May 25, 2006, which
is a Continuation-In-Part of, and claims priority under 35 U.S.C.
.sctn.120 to, International Application PCT/EP2005/000320, having
an international filing date of Jan. 14, 2005, which claimed the
benefit of U.S. Ser. No. 60/537,327, filed on Jan. 16, 2004. This
application also claims the benefit under 35 U.S.C. .sctn.119 of
U.S. Ser. No. 60/684,607, filed on May 25, 2005. Each of these
applications is incorporated herein by reference.
FIELD OF THE INVENTION
[0002] The invention relates to an optical element that affects the
polarization of light rays. The optical element has a thickness
profile and consists of or comprises an optically active crystal
with an optical axis.
BACKGROUND
[0003] In the continuing effort to achieve structures of finer
resolution in the field of microlithography, there is a parallel
pursuit of substantially three guiding concepts. The first of these
is to provide projection objectives of very high numerical
aperture. Second is the constant trend towards shorter wavelengths,
for example 248 nm, 193 nm, or 157 nm. Finally, there is the
concept of increasing the achievable resolution by introducing an
immersion medium of a high refractive index into the space between
the last optical element of the projection objective and the
light-sensitive substrate. The latter technique is referred to as
immersion lithography.
[0004] In an optical system that is illuminated with light of a
defined polarization, the s- and p-component of the electrical
field vector, in accordance with Fresnel's equations, are subject
to respectively different degrees of reflection and refraction at
the interface of two media with different refractive indices. In
this context and hereinafter, the polarization component that
oscillates parallel to the plane of incidence of a light ray is
referred to as p-component, while the polarization component that
oscillates perpendicular to the plane of incidence of a light ray
is referred to as s-component. The different degrees of reflection
and refraction that occur in the s-component in comparison to the
p-component have a significant detrimental effect on the imaging
process.
[0005] This problem can be avoided with a special distribution of
the polarization where the planes of oscillation of the electrical
field vectors of individual linearly polarized light rays in a
pupil plane of the optical system have an approximately radial
orientation relative to the optical axis. A polarization
distribution of this kind will hereinafter be referred to as radial
polarization. If a bundle of light rays that are radially polarized
in accordance with the foregoing definition meets an interface
between two media of different refractive indices in a field plane
of an objective, only the p-component of the electrical field
vector will be present, so that the aforementioned detrimental
effect on the imaging quality is reduced considerably.
[0006] In analogy to the foregoing concept, one could also choose a
polarization distribution where the planes of oscillation of the
electrical field vectors of individual linearly polarized light
rays in a pupil plane of the system have an orientation that is
perpendicular to the radius originating from the optical axis. A
polarization distribution of this type will hereinafter be referred
to as tangential polarization. If a bundle of light rays that are
tangentially polarized in accordance with this definition meets an
interface between two media of different refractive indices, only
the s-component of the electrical field vector will be present so
that, as in the preceding case, there will be uniformity in the
reflection and refraction occurring in a field plane.
[0007] Providing an illumination with either tangential or radial
polarization in a pupil plane is of high importance in particular
when putting the aforementioned concept of immersion lithography
into practice, because of the considerable negative effects on the
state of polarization that are to be expected based on the
differences in the refractive index and the strongly oblique angles
of incidence at the respective interfaces from the last optical
element of the projection objective to the immersion medium and
from the immersion medium to the coated light-sensitive
substrate.
SUMMARY
[0008] In one aspect, the invention generally features a
microlithography optical system that includes an illumination
system, a projection objective and a temperature compensated
polarization-modulating optical element in the illumination system.
The temperature compensated polarization-modulating optical element
includes a first polarization-modulating optical element that
includes an optically active material. The first
polarization-modulating optical element has a first specific
rotation with a sign. The temperature compensated
polarization-modulating optical element also includes a second
polarization-modulating optical element comprising optically active
material. The second polarization-modulating optical element has a
second specific rotation with a sign opposite to the sign of the
first specific rotation.
[0009] In another aspect, the invention generally features using
the system described in the preceding paragraph to manufacturing a
micro-structured semiconductor component.
[0010] In a further aspect, the invention generally features an
optical element that includes a temperature compensated
polarization-modulating element. The temperature compensated
polarization-modulating element includes a first
polarization-modulating optical element having a first thickness.
The first polarization-modulating element includes an optically
active material with a first specific rotation having a sign. The
temperature compensated polarization-modulating element also
includes a second polarization-modulating optical element having a
second thickness different from said first thickness. The second
polarization-modulating optical element includes an optically
active material with a second specific rotation having a sign
opposite the sign of the first specific rotation.
[0011] In an additional aspect, the invention generally a
microlithography optical system that includes an illumination
system, a projection objective and the optical element described in
the preceding paragraph. The optical element is in the illumination
system.
[0012] In another aspect, the invention generally features using
the system described in the preceding paragraph to manufacturing a
micro-structured semiconductor component.
[0013] In a further aspect, the invention generally features an
optical system that has an optical axis. The optical system
includes a first plane plate and a second plane plate. The first
plane plate includes optically active quartz, and the first plane
plate has a first thickness in the direction of the optical axis.
The second plane plate includes optically active quartz. The second
plane plate has a second thickness in the direction of the optical
axis, and the second thickness being different from the first
thickness.
[0014] In an additional aspect, the invention generally features a
system that includes an illumination system, a projection objective
and an optical system having an optical axis. The optical system
includes a first plane plate and a second plane plate. The first
plate includes optically active quartz. The first plane plate has a
first thickness in the direction of the optical axis. The second
plane plate includes optically active quartz. The second plane
plate has a second thickness in the direction of the optical axis,
and the second thickness being different from the first
thickness.
[0015] In one aspect, the invention generally features an optical
element that includes a support plate comprising optically active
material, and at least two planar-parallel portions. Each of the at
least two planar-parallel portions includes optically active
material. When a first linearly polarized light ray passes through
the optical element, a plane of oscillation of the first linearly
polarized light ray is rotated by a first angle. When a second
linearly polarized light ray passes through the optical element, a
plane of oscillation of the second linearly polarized light ray is
rotated by a second angle different from the first angle.
[0016] In another aspect, the invention generally features a
microlithography optical system that includes an illumination
system, a projection objective and the optical element described in
the preceding paragraph. The optical element is in the illumination
system.
[0017] In a further aspect, the invention generally features using
the system described in the preceding paragraph to manufacturing a
micro-structured semiconductor component.
[0018] In an additional aspect, the invention generally features an
optical arrangement that includes a polarization-modulating optical
element that includes a first optically active material having a
first specific rotation with a sign. The polarization-modulating
optical element has a first optical axis, and the
polarization-modulating element has a first thickness profile that,
as measured in the direction of the first optical axis, is
variable. The optical arrangement also includes a compensation
plate that includes a second optically active material having a
second specific rotation with a sign opposite the sign of the first
specific rotation. The compensation plate has a second thickness
profile configured so that, when radiation passes through the
optical arrangement, the compensation plate substantially
compensates for angle deviations of the radiation that are caused
by the polarization-modulating optical element.
[0019] In another aspect, the invention generally features a
microlithography optical system that includes an illumination
system, a projection objective and the optical arrangement
described in the preceding paragraph. The optical arrangement is in
the illumination system.
[0020] In a further aspect, the invention generally features using
the system described in the preceding paragraph to manufacturing a
micro-structured semiconductor component.
[0021] In certain embodiments, a polarization-modulating optical
element is provided, which--with a minimum loss of
intensity--affects the polarization of light rays in such a way
that from linearly polarized light with a first distribution of the
directions of the oscillation planes of individual light rays, the
optical element generates linearly polarized light with a second
distribution of the directions of the oscillation planes of
individual light rays.
[0022] In some embodiments, an optical system is provided that has
improved properties of the polarization-modulating optical element
regarding thermal stability of the second distribution of
oscillation planes (polarization distribution), and/or minimized
influence of additional optical elements in the optical system to
the polarization distribution after the light rays have passed
these elements.
[0023] In some embodiments, a polarization-modulating optical
element is provided which consists of or comprises an optically
active crystal and which is shaped with a thickness profile that
varies in the directions perpendicular to the optical axis.
[0024] A polarization-modulating optical element can have the
effect that the plane of oscillation of a first linearly polarized
light ray and the plane of oscillation of a second linearly
polarized light ray are rotated, respectively, by a first and a
second angle of rotation, with the first angle of rotation being
different from the second angle of rotation. The
polarization-modulating optical element can be made of an optically
active material.
[0025] In some embodiments, one or more of the following desirable
features can be provided.
[0026] In order to generate from linearly polarized light an
arbitrarily selected distribution of linearly polarized light rays
with a minimum loss of intensity, an optically active crystal with
an optical axis is used as raw material for the
polarization-modulating optical element. The optical axis of a
crystal, also referred to as axis of isotropy, is defined by the
property that there is only one velocity of light propagation
associated with the direction of the optical axis. In other words,
a light ray travelling in the direction of an optical axis is not
subject to a linear birefringence. The polarization-modulating
optical element has a thickness profile that varies in the
directions perpendicular to the optical axis of the crystal. The
term "linear polarization distribution" in this context and
hereinafter is used with the meaning of a polarization distribution
in which the individual light rays are linearly polarized but the
oscillation planes of the individual electrical field vectors can
be oriented in different directions.
[0027] If linearly polarized light traverses the
polarization-modulating optical element along the optical axis of
the crystal, the oscillation plane of the electrical field vector
is rotated by an angle that is proportional to the distance
traveled inside the crystal. The sense of rotation, i.e., whether
the oscillation plane is rotated clockwise or counterclockwise,
depends on the crystal material, for example right-handed quartz
vs. left-handed quartz. The polarization plane is parallel to the
respective directions of the polarization and the propagation of
the light ray. In order to produce an arbitrarily selected
distribution of the angles of rotation, it is advantageous if the
thickness profile is designed so that the plane of oscillation of a
first linearly polarized light ray and the plane of oscillation of
a second linearly polarized light ray are rotated, respectively, by
a first and a second angle of rotation, with the first angle of
rotation being different from the second angle of rotation. By
shaping the element with a specific thickness at each location, it
is possible to realize arbitrarily selected angles of rotation for
the oscillation planes.
[0028] Different optically active materials have been found
suitable dependent on the wavelength of the radiation being used,
specifically quartz, TeO.sub.2, and AgGaS.sub.2.
[0029] In an advantageous embodiment, the polarization-modulating
optical element has an element axis oriented in the same direction
as the optical axis of the crystal. In relation to the element
axis, the thickness profile of the optical element is a function of
the azimuth angle .theta. alone, with the azimuth angle .theta.
being measured relative to a reference axis that intersects the
element axis at a right angle. With a thickness profile according
to this design, the thickness of the optical element is constant
along a radius that intersects the element axis at a right angle
and forms an azimuth angle .theta. with the reference axis.
[0030] In a further advantageous embodiment, an azimuthal section
d(r=const., .theta.) of the thickness profile d(r,.theta.) at a
constant distance r from the element axis is a linear function of
the azimuth angle .theta.. In the ideal case, this azimuthal
section has a discontinuity at the azimuth angle .theta.=0. The
linear function d(r=const., .theta.) at a constant distance r from
the element axis has a slope
m = 180 .degree. .alpha. .PI. r ##EQU00001##
wherein .alpha. stands for the specific rotation of the optically
active crystal. At the discontinuity location for .theta.=0, there
is an abrupt step in the thickness by an amount of
360.degree./.alpha.. The step at the discontinuity location can
also be distributed over an azimuth angle range of a few degrees.
However, this has the result of a non-optimized polarization
distribution in the transition range.
[0031] In a further advantageous embodiment, an azimuthal section
d(r=const., .theta.) of the thickness profile d(r,.theta.) at a
constant distance r from the element axis is a linear function of
the azimuth angle .theta. with the same slope m but, in the ideal
case, with two discontinuities at the azimuth angles .theta.=0 and
.theta.=180.degree., respectively. At each discontinuity location,
there is an abrupt step in the thickness by an amount of
180.degree./.alpha.. The two abrupt steps at the discontinuity
locations can also be distributed over an azimuth angle range of a
few degrees. However, this has the result of a non-optimized
polarization distribution in the transition range.
[0032] In a further advantageous embodiment, an azimuthal section
d(r=const., .theta.) of the thickness profile d(r,.theta.) at a
constant distance r from the element axis and in a first azimuth
angle range of 10.degree.<.theta.<170.degree. is a linear
function of the azimuth angle .theta. with a first slope m, while
in a second azimuth angle range of
190.degree.<.theta.<350.degree., the azimuthal section is a
linear function of the azimuth angle .theta. with a second slope n.
The slopes m and n have the same absolute magnitude but opposite
signs. The magnitude of the slopes m and n at a distance r from the
element axis is
m = n = 180 .degree. .alpha. .PI. r . ##EQU00002##
With this arrangement, the thickness profile for all azimuth
angles, including .theta.=0 and .theta.=180.degree., is a
continuous function without abrupt changes in thickness.
[0033] In a further advantageous embodiment, the
polarization-modulating optical element is divided into a large
number of planar-parallel portions of different thickness or
comprises at least two planar-parallel portions. These portions can
for example be configured as sectors of a circle, but they could
also have a hexagonal, square, rectangular, or trapezoidal
shape.
[0034] In a further advantageous embodiment, a pair of first
plan-parallel portions are arranged on opposite sides of a central
element axis of said polarization-modulating optical element, and a
pair of second plan-parallel portions are arranged on opposite
sides of said element axis and circumferentially displaced around
said element axis with respect to said first plan-parallel
portions, wherein each of said first portions has a thickness being
different from a thickness of each of said second portions.
[0035] In a further advantageous embodiment, a plane of oscillation
of linearly polarized light passing through the
polarization-modulating optical element is rotated by a first angle
of rotation .beta..sub.1 within at least one of said first
plan-parallel portions and by a second angle of rotation
.beta..sub.2 within at least one of said second plan-parallel
portions, such that .beta..sub.1 and .beta..sub.2 are approximately
conforming or conform to the expression
|.beta..sub.2-.beta..sub.1|=(2n+1)90.degree., with n representing
an integer.
[0036] In an advantageous embodiment, .beta..sub.1 and .beta..sub.2
are approximately conforming or conform to the expressions
.beta..sub.1=90.degree.+p180.degree., with p representing an
integer, and .beta..sub.2=q180.degree., with q representing an
integer other than zero. As will discussed below in more detail,
such an embodiment of the polarization modulating optical element
may be advantageously used in affecting the polarization of
traversing polarized light such that exiting light has a
polarization distribution being--depending of the incoming
light--either approximately tangentially or approximately radially
polarized.
[0037] The pair of second plan-parallel portions may particularly
be circumferentially displaced around said element axis with
respect to said pair of first plan-parallel portions by
approximately 90.degree..
[0038] In a further advantageous embodiment, said pair of first
plan-parallel portions and said pair of second plan-parallel
portions are arranged on opposite sides of a central opening or a
central obscuration of said polarization-modulating optical
element.
[0039] Adjacent portions of said first and second pairs can be
spaced apart from each other by regions being opaque to linearly
polarized light entering said polarization-modulating optical
element. Said portions of said first and second group can
particularly be held together by a mounting. Said mounting can be
opaque to linearly polarized light entering said
polarization-modulating optical element. The mounting can have a
substantially spoke-wheel shape.
[0040] In a further advantageous embodiment, the
polarization-modulating optical element comprises a first group of
substantially planar-parallel portions wherein a plane of
oscillation of traversing linearly polarized light is rotated by a
first angle of rotation .beta..sub.1, and a second group of
substantially planar-parallel portions wherein a plane of
oscillation of traversing linearly polarized light is rotated by a
second angle of rotation, such that .beta..sub.1 and .beta..sub.2
are approximately conforming or conform to the expression
|.beta..sub.2-.beta..sub.1|=(2n+1)90.degree., with n representing
an integer.
[0041] In a further advantageous embodiment, .beta..sub.1 and
.beta..sub.2 are approximately conforming to the expressions
.beta..sub.1=90.degree.+p180.degree., with p representing an
integer, and .beta..sub.2=q180.degree., with q representing an
integer other than zero.
[0042] In a further advantageous embodiment, the thickness profile
of the polarization-modulating optical element has a continuous
surface contour without abrupt changes in thickness, whereby an
arbitrarily selected polarization distribution can be generated
whose thickness profile is represented by a continuous function of
the location.
[0043] To ensure an adequate mechanical stability of the optical
element, it is preferred to make the minimal thickness d.sub.min of
the polarization-modulating optical element at least equal to 0.002
times the element diameter D.
[0044] If the optically active material used for the optical
element also has birefringent properties as is the case for example
with crystalline quartz, the birefringence has to be taken into
account for light rays whose direction of propagation deviates from
the direction of the optical crystal axis. A travel distance of
90.degree./.alpha. inside the crystal causes a linear polarization
to be rotated by 90.degree.. If birefringence is present in
addition to the rotating effect, the 90.degree. rotation will be
equivalent to an exchange between the fast and slow axis in
relation to the electrical field vector of the light. Thus, a total
compensation of the birefringence is provided for light rays with
small angles of incidence if the distance traveled inside the
crystal equals an integer multiple of 180.degree./.alpha.. In order
to meet the aforementioned requirement for mechanical stability
while simultaneously minimizing the effects of birefringence, it is
of advantage if the polarization-modulating optical element is
designed with a minimum thickness of
d min = N 90 .degree. .alpha. , ##EQU00003##
where N represents a positive integer.
[0045] From a manufacturing point of view, it is advantageous to
provide the optical element with a hole at the center or with a
central obscuration.
[0046] For light rays propagating not exactly parallel to the
optical crystal axis, there will be deviations of the angle of
rotation. In addition, the birefringence phenomenon will have an
effect. It is therefore particularly advantageous if the maximum
angle of incidence of an incident light bundle with a large number
of light rays within a spread of angles relative to the optical
crystal axis is no larger than 100 mrad, preferably no larger than
70 mrad, and with special preference no larger than 45 mrad.
[0047] In order to provide an even more flexible control over a
state of polarization, an optical arrangement is advantageously
equipped with a device that allows at least one further
polarization-modulating optical element to be placed in the light
path. This further polarization-modulating optical element can be
an additional element with the features described above. However,
it could also be configured as a planar-parallel plate of an
optically active material or an arrangement of two half-wavelength
plates whose respective fast and slow axes of birefringence are
rotated by 45.degree. relative to each other.
[0048] The further polarization-modulating optical element that can
be placed in the optical arrangement can in particular be designed
in such a way that it rotates the oscillation plane of a linearly
polarized light ray by 90.degree.. This is particularly
advantageous if the first polarization-modulating element in the
optical arrangement produces a tangential polarization. By
inserting the 90.degree.-rotator, the tangential polarization can
be converted to a radial polarization.
[0049] In a further embodiment of the optical arrangement, it can
be advantageous to configure the further polarization-modulating
optical element as a planar-parallel plate which works as a
half-wavelength plate for a half-space that corresponds to an
azimuth-angle range of 180.degree.. This configuration is of
particular interest if the first polarization-modulating optical
element has a thickness profile (r=const., .theta.) that varies
only with the azimuth angle .theta. and if, in a first azimuth
angle range of 10.degree.<.theta.<170.degree., the thickness
profile (r=const., .theta.) is a linear function of the azimuth
angle .theta. with a first slope m, while in a second azimuth angle
range of 190.degree.<.theta.<350.degree., the thickness
profile is a linear function of the azimuth angle .theta. with a
second slope n, with the slopes m and n having the same absolute
magnitude but opposite signs.
[0050] The refraction occurring in particular at sloped surfaces of
a polarization-modulating element can cause a deviation in the
direction of an originally axis-parallel light ray after it has
passed through the polarization-modulating element. In order to
compensate this type of deviation of the wave front which is caused
by the polarization-modulating element, it is advantageous to
arrange a compensation plate in the light path of an optical
system, with a thickness profile of the compensation plate designed
so that it substantially compensates an angular deviation of the
transmitted radiation that is caused by the polarization-modulating
optical element. Alternatively, an immersion fluid covering the
profiled surface of the polarization-modulating element could be
used for the same purpose.
[0051] Principally, in order to achieve the effect of compensating
for the deviation in the direction of an originally axis-parallel
light ray due to the polarization-modulating element, it would be
possible to use a non-birefringent material such as CaF.sub.2 or
fused silica as raw material for the compensation plate. However,
significant drawbacks of such an optical arrangement are as
follows: CaF.sub.2 is relatively difficult to handle during the
manufacturing of the compensation plate, which usually makes it
necessary to enhance its thickness e.g. up to 5 mm to achieve
sufficient mechanical stability, leading to an enhancement of the
space needed in the optical design. Fused silica is relatively
sensitive to thermal compaction leading to local variations of the
density and non-deterministic birefringence properties, which
inadvertently modifies or destroys the polarization distribution
after the optical arrangement. Furthermore, since the refraction
indices of CaF.sub.2 or fused silica, on the one hand, and the
optically active material of the polarization-modulating element,
on the other hand, are not the same, the slopes in the thickness
profiles of the compensation plate and the polarization-modulating
element (or the "wedge angles") in these elements, have to be
different. With other words, the distance between the curved
surfaces of these elements is not constant, which leads to a
non-symmetric ray displacement for a light ray passing through the
arrangement.
[0052] In order to avoid the above drawbacks while achieving a
compensation for the deviation in the direction of an originally
axis-parallel light due to the polarization-modulating element, an
optical arrangement according to a further aspect of the present
invention comprises
[0053] a polarization-modulating optical element having a first
thickness profile and comprising a first optically active material
with a first optical axis, wherein said first thickness profile, as
measured in the direction of said optical axis, is variable,
[0054] and a compensation plate being arranged in the light path of
the optical system and having a second thickness profile configured
to substantially compensate for angle deviations of transmitted
radiation which are caused by said polarization-modulating optical
element,
[0055] wherein said compensation plate comprises a second optically
active material with a specific rotation of opposite sign compared
to said first optically active material.
[0056] Like in the embodiments of the polarization-modulating
element discussed above, the first and second optically active
materials could be solid or liquid optically active materials.
[0057] In an advantageous embodiment, the polarization-modulating
optical element and the compensation plate are made of optical
isomers. In a particular advantageous embodiment, the
polarization-modulating optical element and the compensation plate
are made of optically active crystalline quartz with clockwise and
counterclockwise specific rotation. With other words, if the
polarization-modulating optical element is made of R-quartz, the
compensation plate is preferably made of L-quartz and vice versa.
In such a combination of optically active materials with a specific
rotation of opposite sign, a net change in the polarization
direction of any linear polarized light ray will still occur, but
is now depending on the value of the difference in the respective
thicknesses being passed in these optically active materials. Such
an embodiment has, in particular, the following advantageous
effects: [0058] a) Since the refractive indices in the R-quartz and
the L-quartz are substantially the same, the slopes in the
thickness profiles of the compensation plate and the
polarization-modulating element (or the "wedge angles" in these
elements) may also be the same. In particular, both elements may be
in direct contact to each other with their respective inclined or
curved surface, in order to effectively forming a common or single
optical element having the shape of a substantially plan-parallel
plate. Alternatively, the compensation plate and the
polarization-modulating element may also be arranged spaced apart
from each other such that the distance between the inclined or
curved surfaces of these elements is constant. As a consequence,
any ray displacement that occurs for a light ray passing through
the arrangement of the compensation plate and the
polarization-modulating element will be symmetric. [0059] b) Any
parts of the polarization-modulating element and the corresponding
counter-part of the compensation plate can be substantially
identical in geometry, making it possible to identically perform
the corresponding manufacturing process (i.e. with the same
programming of the tools used for the manufacturing procedure).
[0060] c) Since the polarization-modulating optical element and the
compensation plate are turning the direction of polarization of
linear polarized light into opposite directions,
temperature-induced modifications of the effective rotation of
polarization in these elements will be at least partially
compensated. In particular, any offset thickness of the
compensation plate or the polarization-modulating element,
respectively, will be without influence with regard to temperature
changes, since the accompanying temperature-induced modifications
of the effective rotation in one of the elements will be
compensated by the opposed effective rotation in the other element.
[0061] d) Since both the polarization-modulating optical element
and the compensation plate are providing optical activity with a
variable thickness profile, the respective slopes in the thickness
profiles of the compensation plate and the polarization-modulating
element may be reduced for each of these elements, if compared to
the case where only the polarization-modulating optical element is
made of optically active material. In particular, in the specific
case where both the compensation plate and the
polarization-modulating element have a substantially wedge-shaped
cross-section, a tangential polarization distribution can be
achieved with substantially half of the slope of the inclined
surface of the compensation plate or the polarization-modulating
element, respectively, if compared to the case where only the
polarization-modulating optical element is made of optically active
material. As a consequence of these reduced slopes, the space
needed in the optical design is reduced and the manufacturing
process is simplified due to less effort in the abrasive treatment
of the respective raw materials used for making the compensation
plate and the polarization-modulating element.
[0062] Polarization-modulating elements of the foregoing
description, and optical arrangements equipped with them, are
advantageously used in projection systems for microlithography
applications. In particular, polarization-modulating elements of
this kind and optical arrangements equipped with them are well
suited for projection systems in which the aforementioned immersion
technique is used, i.e., where an immersion medium with a
refractive index different from air is present in the space between
the optical element nearest to the substrate and the substrate.
[0063] According to a further aspect of the present invention, a
polarization-modulating optical element is provided,
[0064] wherein a plane of oscillation of a first linearly polarized
light ray and a plane of oscillation of a second linearly polarized
light ray are rotated, respectively, by a first angle of rotation
and a second angle of rotation in such a way that said first angle
of rotation is different from said second angle of rotation;
[0065] wherein said polarization-modulating optical element
comprises at least two planar-parallel portions that consist of an
optically active material; and
[0066] wherein said planar-parallel portions are arranged on a
support plate that consists of an optically active material.
[0067] As a consequence of making the support plate--like the at
least two planar-parallel portions which are arranged thereon--of
an optically active material, an enhanced durability of a
wringing-connection between the support plate and said
planar-parallel portions can be achieved, in particular under
varying temperature conditions. The enhanced stability or
durability of the wringing-connection particularly results from the
fact that the support plate may be made from the same material and
even with the same crystal orientation. Physical properties as the
refraction numbers or expansion coefficients of the optically
quartz material in the support plate and the plan-parallel portions
can be made rotational symmetric with regard to the respective
optical crystal axis. In particular, it can be achieved that the
thermal expansion coefficients of the support plate and the
plan-parallel portions (e.g. sector-shaped parts) are identical.
Therefore, if the temperature changes in the direct environment of
the contact region between the support plate and the
planar-parallel portions (e.g. due to laser irradiation during the
microlithography process or during applying antireflection
coatings), the temperature increase and the thermal expansion are
the same in the support plate and the planar-parallel portions, so
that the risk of a temperature- or stress-induced loose of contact
between these element is significantly reduced or eliminated, if
e.g. compared to the use of a support plate made of CaF.sub.2 or
fused silica (SiO.sub.2). A further advantage is that the use of an
optical active material such as crystalline quartz avoids
compaction effects as occurring e.g. in fused silica.
[0068] According to a further aspect the present invention relates
to a projection system, comprising a radiation source, an
illumination system operable to illuminate a structured mask, and a
projection objective for projecting an image of the mask structure
onto a light-sensitive substrate,
[0069] wherein said projection system comprises an optical system
comprising an optical axis or a preferred direction given by the
direction of a light beam propagating through the optical
system,
[0070] the optical system comprising a temperature compensated
polarization-modulating optical element described by coordinates of
a coordinate system, wherein one preferred coordinate of the
coordinate system is parallel to the optical axis or parallel to
said preferred direction;
[0071] said temperature compensated polarization-modulating optical
element comprising a first and a second polarization-modulating
optical element, the first and/or the second
polarization-modulating optical element comprising solid and/or
liquid optically active material and a profile of effective optical
thickness, wherein the effective optical thickness varies at least
as a function of one coordinate different from the preferred
coordinate of the coordinate system, in addition or alternative the
first and/or the second polarization-modulating optical element
comprises solid and/or liquid optically active material, wherein
the effective optical thickness is constant as a function of at
least one coordinate different from the preferred coordinate of the
coordinate system;
[0072] wherein the first polarization-modulating optical element
comprises optically active material with a specific rotation of
opposite sign compared to the optically active material of the
second polarization-modulating optical element.
[0073] Due to the presence of two polarization-modulating optical
elements comprising optically active materials having specific
rotations of opposite sign, the temperature effects in both these
elements at least partially compensate each other, so that the
combined system of these two elements has a reduced temperature
dependence regarding the change of the polarization. Consequently,
even under conditions of temperature variation, a change of the
polarization state of light passing both elements is reduced, or
the polarization state even remains unchanged. As a consequence of
said compensation effect, a detrimental effect of temperature
variations on the polarization state of light passing through said
system can be reduced or avoided even with relatively large
thicknesses (e.g. of several mm) of said elements.
[0074] The above compensation concept may particularly be used in a
system of two plane plates with a first and a second thickness in
the direction of the propagating light beam, said plates being made
of optically active quartz with clockwise and counterclockwise
specific rotation. Furthermore, according to the present invention
said plane plates may have either substantially the same thickness
or different thicknesses. In the case of substantial identical
thicknesses of the two plane plates, a resulting effect of the
whole arrangement of the two plates may be avoided, so that such
arrangement is particularly suited e.g. as a polarization-neutral
support of a micro-optical element such as a DOE. In the case of
different thicknesses of the two plane plates, a resulting effect
of the whole arrangement of the two plates can be achieved to
provide a polarization-modulating arrangement having, due to the
partial compensation effect mentioned before, a relatively weak
sensitivity to temperature variations even if relatively large
thicknesses for the plane plates are used in view of manufacturing
aspects.
[0075] Therefore, according to a further aspect the present
invention relates to an optical system comprising an optical axis
or a preferred direction given by the direction of a light beam
propagating through the optical system,
[0076] the optical system comprising a temperature compensated
polarization-modulating optical element described by coordinates of
a coordinate system, wherein one preferred coordinate of the
coordinate system is parallel to the optical axis or parallel to
said preferred direction;
[0077] said temperature compensated polarization-modulating optical
element comprising a first and a second polarization-modulating
optical element, the first and/or the second
polarization-modulating optical element comprising solid and/or
liquid optically active material and a profile of effective optical
thickness, wherein the effective optical thickness varies at least
as a function of one coordinate different from the preferred
coordinate of the coordinate system, in addition or alternative the
first and/or the second polarization-modulating optical element
comprises solid and/or liquid optically active material, wherein
the effective optical thickness is constant as a function of at
least one coordinate different from the preferred coordinate of the
coordinate system; wherein the first polarization-modulating
optical element comprises optically active material with a specific
rotation of opposite sign compared to the optically active material
of the second polarization-modulating optical element;
[0078] wherein said first and second polarization-modulating
optical elements are plane plates with a first and a second
thickness in the direction of the propagating light beam, said
plates being made of optically active quartz with clockwise and
counterclockwise specific rotation; wherein the first and the
second thickness are different from each other.
[0079] Preferably, the absolute value of the difference of the
first and the second thickness is smaller than the thickness of the
smaller plate.
[0080] According to a further aspect the present invention relates
to an optical system having an optical axis, the optical system
comprising a first plane plate with a first thickness in the
direction of the optical axis and a second plane plate with a
second thickness in the direction of the optical axis, wherein said
first and second plane plates are made of optically active quartz
with specific rotations opposite to each other; and wherein the
first and the second thickness are different from each other.
[0081] According to a further aspect the present invention relates
to a projection system comprising a radiation source, an
illumination system operable to illuminate a structured mask, and a
projection objective for projecting an image of the mask structure
onto a light-sensitive substrate, wherein said projection system
comprises an optical system having an optical axis, the optical
system comprising a first plane plate with a first thickness in the
direction of the optical axis and a second plane plate with a
second thickness in the direction of the optical axis; wherein said
first and second plane plates are made of optically active quartz
with specific rotations opposite to each other.
[0082] Further advantageous aspects can be gathered from the
following description and the appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0083] The invention will hereinafter be explained in more detail
with reference to the attached drawings, wherein:
[0084] FIG. 1 illustrates a polarization-modulating optical element
with a thickness profile;
[0085] FIG. 2 schematically illustrates how the plane of
oscillation is rotated when a linearly polarized light ray
propagates along the optical axis in an optically active
crystal;
[0086] FIG. 3 illustrates a first exemplary embodiment of a
polarization-modulating optical element;
[0087] FIG. 4a schematically illustrates a second exemplary
embodiment of a polarization-modulating optical element;
[0088] FIG. 4b illustrates the thickness profile as a function of
the azimuth angle in the embodiment of the polarization-modulating
optical element of FIG. 4a;
[0089] FIG. 4c illustrates the thickness profile as a function of
the azimuth angle in a further embodiment of the
polarization-modulating optical element;
[0090] FIG. 4d illustrates the thickness profile as a function of
the azimuth angle in the embodiment of the polarization-modulating
optical element of FIG. 3;
[0091] FIG. 4e illustrates the thickness profile as a function of
the azimuth angle in a further embodiment of the
polarization-modulating optical element;
[0092] FIG. 4f schematically illustrates a further exemplary
embodiment of a polarization-modulating optical element;
[0093] FIG. 4g-h schematically illustrate a further exemplary
embodiment of a polarization-modulating optical element in a plan
view (FIG. 4g) and a front-side view (FIG. 4h);
[0094] FIG. 5 schematically illustrates the polarization
distribution of a bundle of light rays before and after passing
through the polarization-modulating optical element with the
thickness profile according to FIG. 3 or 4d;
[0095] FIG. 6 schematically illustrates the polarization
distribution of a bundle of light rays before and after passing
through an optical arrangement with the polarization-modulating
optical element with the thickness profile according to FIG. 3 and
a further polarization-modulating optical element;
[0096] FIG. 7a schematically illustrates the polarization
distribution of a bundle of light rays before and after passing
through an optical arrangement with the polarization-modulating
optical element with the thickness profile according to FIG. 4e and
a planar-parallel plate, one half of which is configured as a
half-wave plate;
[0097] FIG. 7b shows a plan view of a planar-parallel plate, one
half of which is configured as a half-wave plate;
[0098] FIG. 8 schematically illustrates a microlithography
projection system with a polarization-modulating optical
element;
[0099] FIG. 9 schematically shows a parallel plane plate of optical
active material used as a polarization-modulating element by
adjusting its temperature and/or temperature profile;
[0100] FIG. 10 shows a combination of a parallel plate of optical
active material with a plate made of birefringent material;
[0101] FIG. 11 shows schematically a temperature compensated
polarization-modulating optical element for the application in an
optical system;
[0102] FIG. 12-13 show schematically temperature compensated
optical elements according to further embodiments of the present
invention;
[0103] FIG. 14a-b are schematic illustrations to demonstrate the
effect of a temperature compensated optical element according to a
further embodiment of the present invention;
[0104] FIG. 15-16 are schematic illustrations of a temperature
compensated grey filter (FIG. 15) and a temperature compensated
diffractive optical element (FIG. 16) according to further
embodiments of the present invention;
[0105] FIGS. 17a-d show different views on a combination of a
polarization-modulating optical element with a compensation plate
in a preferred embodiment of the present invention; and
[0106] FIGS. 18a-c show thickness profiles as a function of the
azimuth angle for different combinations of a
polarization-modulating optical element with a compensation
plate.
DETAILED DESCRIPTION
[0107] FIG. 1 illustrates a polarization-modulating optical element
1 of an optically active material. Particularly well suited for
this purpose are optically active crystals with at least one
optical crystal axis which are transparent for the wavelength of
the light being used. For example TeO.sub.2 works in a range of
wavelengths from 1000 nm down to 300 nm, AgGaS.sub.2 works from 500
nm to 480 nm, and quartz from 800 nm down to 193 nm. The
polarization-modulating optical element 1 is designed so that the
element axis is oriented parallel to the optical crystal axis. In
order to produce a selected polarization distribution, the optical
element 1 is designed with a thickness profile (measured parallel
to the element axis EA) which varies in the directions
perpendicular to the element axis EA, also comprising variations in
thickness of the optical element in an azimuth direction .theta.
(see FIG. 3) at e.g. a fixed distance of the element axis EA.
[0108] FIG. 2 will serve to explain the function of optically
active crystals, and in particular of polarization-modulating
elements made from such crystals, in more detail.
[0109] Optically active crystals have at least one optical axis OA
which is inherent in the crystal structure. When linearly polarized
light travels along this optical axis OA, the plane of oscillation
of the electrical field vector 206 is rotated by an angle .beta. of
proportionate magnitude as the distance d traveled by the light
inside the crystal 202. The proportionality factor between distance
d and angle of rotation is the specific rotation .alpha.. The
latter is a material-specific quantity and is dependent on the
wavelength of the light rays propagating through the crystal. For
example in quartz, the specific rotation at a wavelength of 180 nm
was measured as about .alpha.=(325.2.+-.0.5).degree./mm, at 193 nm
.alpha.=323.1.degree./mm at a temperature of 21.6.degree. C.
[0110] It is also important for the present invention, applying
optically active materials in an illumination system and/or an
objective of a projection optical system of e.g. a projection
apparatus used in microlithography, that also the temperature
dependency of the specific rotation is considered. The temperature
dependency of the specific rotation .alpha. for a given wavelength
is to a good and first linear approximation given by
.alpha.(T)=.alpha..sub.0(T.sub.0)+.gamma.*(T-T.sub.0), where
.gamma. is the linear temperature coefficient of the specific
rotation .alpha.. In this case .alpha.(T) is the optical activity
coefficient or specific rotation at the temperature T and
.alpha..sub.0 is the specific rotation at a reference temperature
T.sub.0. For optical active quartz material the value .gamma. at a
wavelength of 193 nm and at room temperature is .gamma.=2.36
mrad/(mm*K).
[0111] Referring again to FIG. 2, in particular, light that
propagates inside the crystal 202 along the optical axis OA is not
subject to a linear birefringence. Thus, when a linearly polarized
light ray traverses an optically active crystal 202 along the
optical axis OA, its state of polarization remains the same except
for the change in the spatial orientation of the plane of
oscillation of the electrical field vector 206 which depends on the
distance d traveled by the light ray inside the crystal 202.
[0112] Based on this property of an optically active crystal, it is
possible to produce an arbitrarily selected linear polarization
distribution by designing the polarization-modulating optical
element 1 of FIG. 1 with a thickness profile that varies dependent
on the location. The thickness profile is designed to have the
effect that the directions of polarization of parallel linearly
polarized light rays are rotated by an angle that varies dependent
on the location where the light ray traverses the optical
element.
[0113] More general, alternative or in addition to the variation of
the thickness d=d(x,y) of the polarization-modulating element, the
specific rotation .alpha. may itself be dependent on the location
within the modulating element such that a becomes an .alpha.(x,y,z)
or .alpha.(r,.theta.,z), where x,y or r,.theta. are Cartesian or
polar coordinates in a plane perpendicular to the element axis EA
(or alternative to the optical axis OA) of the
polarization-modulating element, as shown e.g. in FIG. 1, where z
is the axis along the element axis EA. Of course also a description
in spherical-coordinates like r,.theta.,.phi., or others is
possible. Taking into account the variation of the specific
rotation .alpha., the polarization-modulating optical element in
general comprises a varying profile of the "optical effective
thickness D" defined as D(x,y)=d(x,y)*.alpha.(x,y), if there is no
dependency of .alpha. in z-direction. In the case that .alpha. may
also depend on the z-direction (along the optical axis or element
axis EA, or more general along a preferred direction in an optical
system or a direction parallel to the optical axis of an optical
system) D has to be calculated by integration
D(x,y)=.intg..alpha.(x,y,z) dz(x,y), along the
polarization-modulating optical element. In general, if a
polarization-modulating optical element is used in an optical
system, having an optical axis or a preferred direction defined by
the propagation of a light beam through the optical system, the
optical effective thickness D is calculated by integrating the
specific rotation .alpha. along the light path of a light ray
within the polarization-modulating optical element. Under this
general aspect the present invention relates to an optical system
comprising an optical axis or a preferred direction given by the
direction of a light beam propagating through the optical system.
The optical system also comprises a polarization-modulating optical
element described by coordinates of a coordinate system, wherein
one preferred coordinate of the coordinate system is parallel to
the optical axis of the optical system or parallel to the preferred
direction. As an example, in the above case this preferred
direction was the z-coordinate which is the preferred coordinate.
Additionally the polarization-modulating optical element comprises
optical active material and also a profile of effective optical
thickness D as defined above, wherein the effective optical
thickness D varies at least as a function of one coordinate
different from the preferred coordinate of the coordinate system
describing the polarization-modulating optical element. In the
above example the effective optical thickness D varies at least as
a function of the x- or y-coordinate, different from the
z-coordinate (the preferred coordinate). There are different
independent methods to vary the effective optical thickness of an
optical active material. One is to vary the specific rotation by a
selection of appropriate materials, or by subjecting the optically
active material to a non-uniform temperature distribution, or by
varying the geometrical thickness of the optically active material.
Also combinations of the mentioned independent methods result in a
variation of the effective optical thickness of an optical active
material.
[0114] FIG. 3 illustrates an embodiment of the
polarization-modulating optical element 301 which is suited
specifically for producing a tangential polarization. A detailed
description will be presented in the context of FIGS. 4d and 5. The
embodiment illustrated in FIG. 3 will serve to introduce several
technical terms that will be used hereinafter with the specific
meanings defined here.
[0115] The polarization-modulating optical element 301 has a
cylindrical shape with a base surface 303 and an opposite surface
305. The base surface 303 is designed as a planar circular surface.
The element axis EA extends perpendicular to the planar surface.
The opposite surface 305 has a contour shape in relation to the
element axis EA in accordance with a given thickness profile. The
optical axis of the optically active crystal runs parallel to the
element axis EA. The reference axis RA, which extends in the base
plane, intersects the element axis at a right angle and serves as
the reference from which the azimuth angle .theta. is measured. In
the special configuration illustrated in FIG. 3, the thickness of
the polarization-modulating optical element 301 is constant along a
radius R that is perpendicular to the element axis EA and directed
at an angle .theta. relative to the reference axis RA. Thus, the
thickness profile in the illustrated embodiment of FIG. 3 depends
only on the azimuth angle .theta. and is given by d=d (.theta.).
The optical element 301 has an optional central bore 307 coaxial
with the element axis EA. In another preferred embodiment of the
polarization-optical element the thickness may vary along the
radius R such that the thickness profile is d=d(R,.theta.). In a
further more generalized preferred embodiment the thickness profile
shown in FIG. 3 is not representing the geometrical thickness d of
the polarization-optical element, as described above, but the
profile represents the optical effective thickness
D=D(R,.theta.)=D(x,y), depending on the used coordinate system. In
this case also any profile of the specific rotation like e.g.
.alpha.=.alpha.(x,y)=.alpha.(R,.theta.) or
.alpha.=.alpha.(x,y,z)=.alpha.(R,.theta.,z) is considered in the
profile of the polarization-modulating optical element which is
effective for a change in the direction of the polarization plane
of a passed light beam.
[0116] In addition it should be mentioned that the
polarization-modulating optical element 301 not necessary need to
comprise a planar base surface 303. This surface in general can
also comprise a contour shaped surface e.g. similar or equal to the
surface as designated by 305 shown in FIG. 3. In such a case it is
of advantage to describe the contour surfaces 303 and 305 relative
to a plane surface perpendicular to the optical axis or element
axis.
[0117] FIG. 4a schematically illustrates a further embodiment of
the polarization-modulating optical element 401. The element axis
EA through the center of the polarization-modulating optical
element 401 in this representation runs perpendicular to the plane
of the drawing, and the optical crystal axis of the crystal runs
parallel to the element axis. Like the embodiment of FIG. 3, the
polarization-modulating optical element 401 has an optional central
bore 407. The polarization-modulating optical element 401 is
divided into a large number of planar-parallel portions 409 in the
shape of sectors of a circle which differ in their respective
thicknesses. Alternative embodiments with different shapes of the
portions 409 are conceivable. They could be configured, e.g., as
hexagonal, square, rectangular or trapeze-shaped raster
elements.
[0118] As described in connection with FIG. 3, the embodiment
according to FIG. 4a can be modified such that the different
thicknesses of the sectors should be understood as different
effective optical thicknesses D. In this case the specific rotation
.alpha. may vary from one segment to the other too. To manufacture
such an embodiment, the polarization-modulating optical element can
e.g. have a shape as shown in FIG. 4a in which the sectors 409 are
at least partly exchanged e.g. by any optical inactive material,
which is the simplest case to vary the specific rotation .alpha. to
zero. Also as a further embodiment the sectors 409 may be replaced
by cuvettes or cells which are filed with an optical active or
optical inactive liquid. In this case the polarization-modulating
optical element may comprise optical active and optical inactive
sections. If the sectors 409 are only party replaced by cuvettes or
if at least one cuvette is used in the polarization-modulating
optical element 401, a combination of e.g. optical active crystals
with e.g. optical active or optical inactive liquids in one element
40 is possible. Such an optical system according to the present
invention may comprise a polarization-modulating optical element
which comprises an optically active or an optically inactive liquid
and/or an optically active crystal. Further, it is advantageously
possible that the polarization-modulating optical element of the
optical system according to the present invention comprises
clockwise and counterclockwise optically active materials. These
materials could be solid or liquid optically active materials.
Using liquids in cuvettes has the advantage that by changing the
liquids, or the concentration of the optical active material within
the liquid, the magnitude of the change in polarization can be
easily controlled. Also any thermal changes of the specific
rotation .alpha. due to the thermal coefficient .gamma. of the
specific rotation .alpha. can be controlled e.g. by temperature
control of the optical active liquid such that either the
temperature is constant within the cuvette, or that the temperate
has predefined value T such that the specific rotation will have
the value .alpha.(T)=.alpha..sub.0(T.sub.0)+.gamma.*(T-T.sub.0).
Also the formation of a certain temperature distribution within the
liquid may be possible with appropriate heating and/or cooling
means controlled by control means.
[0119] The optical systems in accordance with the present invention
advantageously modify respective planes of oscillation of a first
linearly polarized light ray and a second linearly polarized light
ray. Both light rays propagating through the optical system, and
being at least a part of the light beam propagating through the
optical system. The light rays are also passing the
polarization-modulating optical element with different paths, and
are rotated by a respective first and second angle of rotation such
that the first angle is different of the second angle. In general
the polarization-modulating optical element of the optical systems
according to the present invention transforms a light bundle with a
first linear polarization distribution, which enters said
polarization-modulating optical element, into a light bundle
exiting said polarization-modulating optical element. The exiting
light bundle has a second linear polarization distribution, wherein
the second linear polarization distribution is different from the
first linear polarization distribution.
[0120] FIG. 4b shows the thickness profile along an azimuthal
section d(r=const., .theta.) for the polarization-modulating
optical element 401 divided into sectors as shown in FIG. 4a. The
term azimuthal section as used in the present context means a
section traversing the thickness profile d(.theta.,r) along the
circle 411 marked in FIG. 4a, i.e., extending over an azimuth angle
range of 0.degree..ltoreq..theta..ltoreq.360.degree. at a constant
radius r. In general the profile shows the optical effective
thickness D=D(.theta.) along a circle 411.
[0121] An azimuthal section of a polarization-modulating optical
element 401 that is divided into sector-shaped portions has a
stair-shaped profile in which each step corresponds to the
difference in thickness d or optical effective thickness D between
neighbouring sector elements. The profile has e.g. a maximum
thickness d.sub.max and a minimum thickness d.sub.min. In order to
cover a range of 0.ltoreq..beta..ltoreq.360.degree. for the range
of the angle of rotation of the oscillation plane of linearly
polarized light, there has to be a difference of
360.degree./.alpha. between d.sub.max and d.sub.min. The height of
each individual step of the profile depends on the number n of
sector elements and has a magnitude of 360.degree./(n.alpha.). At
the azimuth angle .theta.=0.degree., the profile has a
discontinuity where the thickness of the polarization-modulating
optical element 401 jumps from d.sub.min to d.sub.max. A different
embodiment of the optical element can have a thickness profile in
which an azimuthal section has two discontinuities of the
thickness, for example at .theta.=0.degree. and
.theta.=180.degree..
[0122] In an alternative embodiment the profile has e.g. a maximum
optical effective thickness D.sub.max and a minimum optical
effective thickness D.sub.min, and the geometrical thickness d is
e.g. constant, resulting in a variation of the specific rotation
.alpha. of the individual segments 409 of the element 401. In order
to cover a range of 0.ltoreq..beta..ltoreq.360.degree. for the
range of the angle of rotation of the oscillation plane of linearly
polarized light, there has to be a difference of 360.degree./d
between .alpha..sub.max and .alpha..sub.min. The change of the
specific rotation of each individual step of the profile depends on
the number n of sector elements 409 and has a magnitude of
360.degree./(nd). At the azimuth angle .theta.=0.degree., the
profile has a discontinuity regarding the optical effective
thickness where it jumps from D.sub.min to D.sub.max. It should be
pointed out, that advantageously in this embodiment there is no
discontinuity in the geometrical thickness d of the
polarization-modulating element 401. Also the thickness profile of
the optical effective thickness in which an azimuthal section has
two discontinuities of the optical effective thickness can easily
be realized, for example at .theta.=0.degree. and
.theta.=180.degree.. To realize the defined changes in magnitude of
the specific rotation of .DELTA..alpha.=360.degree./(nd) (if there
a n angular segments 409 to form the element 401), the individual
sector elements 409 are preferably made of or comprises cuvettes or
cells, filled with an optical active liquid with the required
specific rotation .alpha.. As an example, for the m-th sector
element the specific rotation is
.alpha.(m)=.alpha..sub.min+m*360.degree./(nd), and
0.ltoreq.m.ltoreq.n. The required specific rotation e.g. can be
adjusted by the concentration of the optical active material of the
liquid, or by changing the liquid material itself.
[0123] In a further embodiment the segments 409 of a
polarization-modulating optical element 401 may comprise components
of solid optically active material (like crystalline quartz) and
cells or cuvettes filled with optically active material, and these
components are placed behind each other in the light propagation
direction. Alternative or in addition the cuvette itself may
comprise optically active material like crystalline quartz.
[0124] The polarization-modulating optical element of the foregoing
description converts linearly polarized incident light into a
linear polarization distribution in which the oscillation planes of
linearly polarized light rays are rotated by an angle that depends
on the thickness (or optical effective thickness) of each
individual sector element. However, the angle by which the
direction of polarization is rotated is constant over an individual
sector element. Thus, the distribution function for the directions
of the oscillation planes of the individual field vectors takes
only certain discrete values.
[0125] A continuous distribution of linear polarizations can be
achieved with an optical element that has a continuously varying
thickness (optical effective thickness) profile along an azimuthal
section.
[0126] An example of a continuously varying thickness profile is
illustrated in FIG. 4c. The azimuthal section 411 in this
embodiment shows a linear decrease in thickness (in general optical
effective thickness) with a slope m=-180.degree./(.alpha..pi.) over
an azimuth-angle range of 0.ltoreq..theta..ltoreq.360.degree.. Here
the slope is defined a slope of a screw. Alternatively the slope
can be defined by m=-180.degree./(.alpha.*.pi.*r) where r is the
radius of a circle centred at the element axis EA. In this case the
slope depends on the distance of the element axis, e.g. if the
polarization-modulating optical element 301 has a given constant
screw-slope (lead of a screw).
[0127] The symbol .alpha. in this context stands for the specific
rotation of the optically active crystal. As in the previously
described embodiment of FIG. 4b, the thickness profile of FIG. 4c
has likewise a discontinuity at the azimuth angle
.theta.=0.degree., the thickness of the polarization-modulating
optical element 401 jumps from d.sub.min to d.sub.max by an amount
of approximately 360.degree./.alpha..
[0128] A further embodiment of a polarization-modulating optical
element which is shown in FIG. 4d has a thickness profile (in
general optical effective thickness profile) which is likewise
suitable for producing a continuous distribution of linear
polarizations, in particular a tangentially oriented polarization.
This thickness profile corresponds to the embodiment shown in FIG.
3, in which the angle .theta. is measured in counterclockwise
direction. The azimuthal section 411 in this embodiment is a linear
function of the azimuth angle .theta. with a slope
m=-180.degree./(.alpha..pi.) over each of two ranges of
0<.theta.<180.degree. and
180.degree.<.theta.<360.degree.. The thickness profile has
discontinuities at .theta.=0.degree. and .theta.=180.degree. where
the thickness rises abruptly from d.sub.min to d.sub.max by an
amount of 180.degree./.alpha..
[0129] FIG. 4e represents the thickness profile (in general optical
effective thickness profile) along an azimuthal section for a
further embodiment of the polarization-modulating optical element
401. The azimuthal section is in this case a linear function of the
azimuth angle .theta. with a first slope m for
0<.theta.<180.degree. and with a second slope n for
180.degree.<.theta.<360.degree.. The slopes m and n are of
equal absolute magnitude but have opposite signs. The respective
amounts for m and n at a distance r from the element axis are
m=-180.degree./(.alpha..pi.r) and n=180.degree./(.alpha..pi.r).
While the difference between the minimum thickness d.sub.min and
the maximum thickness d.sub.max is again approximately
180.degree./.alpha., i.e., the same as in the embodiment of FIG.
4d, the concept of using opposite signs for the slope in the two
azimuth angle ranges avoids the occurrence of discontinuities.
[0130] Additionally it is mentioned that for certain special
applications clockwise and counterclockwise optically active
materials are combined in a polarization-modulating optical
element.
[0131] As the slope of the thickness profile along an azimuthal
section increases strongly with smaller radii, it is advantageous
from a manufacturing point of view to provide a central opening 407
or a central obscuration in a central portion around the central
axis of the circular polarization-modulating optical element.
[0132] It is furthermore advantageous for reasons of mechanical
stability to design the polarization-modulating optical element
with a minimum thickness d.sub.min of no less than two thousandths
of the element diameter. It is particularly advantageous to use a
minimum thickness of d.sub.min=N90.degree./.alpha., where N is a
positive integer. This design choice serves to minimize the effect
of birefringence for rays of an incident light bundle which
traverse the polarization-modulating element at an angle relative
to the optical axis.
[0133] FIG. 4f schematically illustrates a further embodiment 421
of the polarization-modulating optical element. As in FIG. 4a, the
element axis EA through the center of the polarization-modulating
optical element 421 runs perpendicular to the plane of the drawing,
and the optical crystal axis runs parallel to the element axis.
However, in contrast to the embodiments of FIGS. 3 and 4a where the
polarization-modulating optical elements 301, 401 are made
preferably of one piece like in the case of crystalline material
like crystalline quartz, the polarization-modulating optical
element 421 comprises of four separate sector-shaped parts 422,
423, 424, 425 of an optically active crystal material which are
held together by a mounting device 426 which can be made, e.g., of
metal and whose shape can be described as a circular plate 427 with
four radial spokes 428. The mounting is preferably opaque to the
radiation which is entering the polarization-modulating optical
element, thereby serving also as a spacer which separates the
sector-shaped parts 422, 423, 424, 425 from each other. Of course
the embodiment of the present invention according to FIG. 4f is not
intended to be limited to any specific shape and area of mounting
device 426, which may also be omitted.
[0134] According to an alternate embodiment not illustrated in FIG.
4f, incident light which is entering the polarization-modulating
optical element can also be selectively directed onto the
sector-shaped parts, e.g. by means of a diffractive structure or
other suitable optical components.
[0135] The sector-shaped parts 422 and 424 have a first thickness
d1 which is selected so that the parts 422 and 424 cause the plane
of oscillation of linearly polarized axis-parallel light to be
rotated by 90.degree.+p180.degree., where p represents an integer.
The sector-shaped parts 423 and 425 have a second thickness d2
which is selected so that the parts 423 and 425 cause the plane of
oscillation of linearly polarized axis-parallel light to be rotated
by q180.degree., where q represents an integer other than zero.
Thus, when a bundle of axis-parallel light rays that are linearly
polarized in the y-direction enters the polarization-modulating
optical element 421, the rays that pass through the sector-shaped
parts 423 and 425 will exit from the polarization-modulating
optical element 421 with their plane of oscillation unchanged,
while the rays that pass through the sector-shaped parts 422 and
424 will exit from the polarization-modulating optical element 421
with their plane of oscillation rotated into the x-direction. As a
result of passing through the polarization-modulating optical
element 421, the exiting light has a polarization distribution
which is exactly tangential at the centrelines 429 and 430 of the
sector-shaped parts 422, 423, 424, 425 and which approximates a
tangential polarization distribution for the rest of the
polarization-modulating optical element 421.
[0136] When a bundle of axis-parallel light rays that are linearly
polarized in the x-direction enters the polarization-modulating
optical element 421, the rays that pass through the sector-shaped
parts 423 and 425 will exit from the polarization-modulating
optical element 421 with their plane of oscillation unchanged,
while the rays that pass through the sector-shaped parts 422 and
424 will exit from the polarization-modulating optical element 421
with their plane of oscillation rotated into the y-direction. As a
result of passing through the polarization-modulating optical
element 421, the exiting light has a polarization distribution
which is exactly radial at the centrelines 429 and 430 of the
sector-shaped parts 422, 423, 424, 425 and which approximates a
radial polarization distribution for the rest of the
polarization-modulating optical element 421.
[0137] Of course the embodiment of the present invention according
to FIG. 4f is not intended to be limited to the shapes and areas
and the number of sector-shaped parts exemplarily illustrated in
FIG. 4f, so that other suitable shapes (having for example but not
limited to trapeze-shaped, rectangular, square, hexagonal or
circular geometries) as well as more or less sector-shaped parts
422, 423, 424 and 425 can be used. Furthermore, the angles of
rotation .beta..sub.1 and .beta..sub.2 provided by the
sector-shaped parts 422, 423, 424, 425 (i.e. the corresponding
thicknesses of the sector-shaped parts 422, 423, 424, 425) may be
more generally selected to approximately conform to the expression
|.beta..sub.2-.beta..sub.1|=(2n+1)90.degree., with n representing
an integer, for example to consider also relative arrangements
where incoming light is used having a polarization plane which is
not necessarily aligned with the x- or y-direction. With the
embodiments as described in connection with FIG. 4f it is also
possible to approximate polarization distributions with a
tangential polarization.
[0138] In order to produce a tangential polarization distribution
from linearly polarized light with a wave length of 193 nm and a
uniform direction of the oscillation plane of the electric field
vectors of the individual light rays, one can use for example a
polarization-modulating optical element of crystalline quartz with
the design according to FIGS. 3 and 4d. The specific rotation
.alpha. of quartz for light with a wavelength of 193 nm is in the
range of (325.2.+-.0.5).degree./mm, which was measured at a
wavelength of 180 nm, or more precise it is 321.1.degree./mm at
21.6.degree. C. The strength and effect of the optical activity is
approximately constant within a small range of angles of incidence
up to 100 mrad. An embodiment could for example be designed
according to the following description: An amount of 276.75 .mu.m,
which approximately equals 90.degree./.alpha., is selected for the
minimum thickness d.sub.min, if crystalline quartz is used.
Alternatively, the minimum thickness d.sub.min can also be an
integer multiple of this amount. The element diameter is 110 mm,
with the diameter of the optically active part being somewhat
smaller, for example 105 mm. The base surface is designed as a
planar surface as illustrated in FIG. 3. The opposite surface has a
thickness profile d(r,.theta.) in accordance with FIG. 4d. The
thickness profile is defined by the following mathematical
relationships:
D ( r , .theta. ) = 276.75 + 180 .degree. - .theta. 180 .degree.
553.51 .mu.m ##EQU00004## for 0 .ltoreq. .theta. .ltoreq. 180
.degree. and ##EQU00004.2## r > 10.5 2 mm ##EQU00004.3## D ( r ,
.theta. ) = 276.75 + 360 .degree. - .theta. 180 .degree. 553.51
.mu.m ##EQU00004.4## for 180 .ltoreq. .theta. .ltoreq. 360 .degree.
and ##EQU00004.5## r > 10.5 2 mm ##EQU00004.6## D ( r , .theta.
) = 0 for r .ltoreq. 10.5 2 mm ##EQU00004.7##
[0139] The above mentioned data are based exemplarily for a
specific rotation a of (325.2.+-.0.5).degree./mm. If the specific
rotation .alpha. changes to 321.1.degree./mm, the value at 193 nm
and at a temperature of 21.6.degree. C., the thickness profile will
change as follows:
D ( r , .theta. ) = 278.6 + 180 .degree. - .theta. 180 .degree. 557
.mu.m for 0 .ltoreq. .theta. .ltoreq. 180 .degree. and r > 10.5
2 mm ##EQU00005## D ( r , .theta. ) = 278.6 + 360 .degree. -
.theta. 180 .degree. 557 .mu.m for 180 .ltoreq. .theta. .ltoreq.
360 .degree. and ##EQU00005.2## r > 10.5 2 mm ##EQU00005.3## D (
r , .theta. ) = 0 for r .ltoreq. 10.5 2 mm ##EQU00005.4##
[0140] The polarization-modulating optical element according to
this embodiment has a central opening 407 with a diameter 10.5,
i.e., one-tenth of the maximum aperture. The thickness maxima and
minima, which are found at the discontinuities, are 830.26 .mu.m
and 276.75 .mu.m, respectively for the first given example.
[0141] The embodiment of the foregoing description can be produced
with a robot-polishing process. It is particularly advantageous to
produce the polarization-modulating element from two wedge-shaped
or helically shaped half-plates which are seamlessly joined
together after polishing. If the element is produced by
half-plates, it is easy and in some applications of additional
advantage to use one clockwise and one counterclockwise optically
active material like clockwise crystalline and counterclockwise
crystalline quartz (R-quartz and L-quartz).
[0142] FIGS. 4g and 4h schematically show a further preferred
embodiment of a polarization-modulating element 450 in a plan-view
(FIG. 4g) and a front-side view (FIG. 4h). The
polarization-modulating element 450 of FIG. 4g comprises a support
plate 451 and two sector-shaped parts 452 and 453 which are fixed,
by means of wringing, on said support plate 451.
[0143] The embodiment of FIG. 4g,h is characterized in that the
support plate 451 is made of optically active crystalline quartz,
with the optical crystal axis being perpendicular to the surface of
the support plate 451, i.e. parallel to the z-direction in the
coordinate system also shown in FIG. 4g,h. The direction of the
optical crystal axis in the support plate 451 is also shown in FIG.
4h and referenced with "oa-1". Furthermore, and like in the
embodiment described with reference to FIG. 4f, the sector-shaped
parts 452 and 453 are also made of optically active crystalline
quartz, with the optical crystal axis being perpendicular to their
surface, i.e. also parallel to the z-direction. The direction of
the optical crystal axis in the sector-shaped parts 452 and 453 is
also shown in FIG. 4h and referenced with "oa-2".
[0144] The thickness d.sub.2 of the sector-shaped parts 452 and 453
is such that the orientation of polarization of linearly polarized
light with normal incidence on the light entrance side of the
polarization-modulating element 450 is rotated by an angle of
90.degree.. The thickness d.sub.1 of the support plate 451 is such
that the orientation of polarization of linearly polarized light
with normal incidence on the light entrance side of the support
plate 451 is rotated by an angle of q*180.degree., with q being an
integer larger than zero. For use of synthetic, optically active
crystalline quartz having a specific rotation of 323.1.degree./mm
for a wavelength of 193 nm and a temperature of 21.6.degree. C.,
this condition means that the thickness d of the support plate is
d.sub.1.apprxeq.q*557 .mu.m. As a consequence, the support plate
451 behaves neutral with respect to the effect of the
polarization-modulating element 450 in the sense that the
polarization distribution of light entering the light entrance side
of the support plate 451 with normal incidence is identical to the
polarization distribution of this light after having passed the
support plate 451, i.e. at the light exit side of the support plate
451.
[0145] A significant advantage of this embodiment using the
above-described support plate 451 made of optically active quartz
is that an enhanced durability of the wringing-connection between
the support plate 451 and sector-shaped parts 452 and 453 can be
achieved, in particular under varying temperature conditions. The
enhanced stability or durability of the wringing-connection is a
result from the fact that the support plate 451 and the
sector-shaped parts 452 and 453 are not only made from the same
material, but also have, in addition to the identity of materials,
the same crystal orientation. In the crystal orientation according
to the configuration shown in FIGS. 4g and 4h, physical properties
as the refraction numbers or expansion coefficients of the
optically active quartz material in the support plate 451 and the
sector-shaped parts 452 and 453 are rotational symmetric with
regard to the respective optical crystal axis. In particular, the
thermal expansion coefficients of the support plate 451 and the
sector-shaped parts 452 and 453 are identical. Therefore, if the
temperature changes in the direct environment of the contact region
between the support plate 451 and the sector-shaped parts 452 and
453 (e.g. due to laser irradiation during the microlithography
process or during applying antireflection coatings), the
temperature increase and the thermal expansion are the same in the
support plate 451 and the sector-shaped parts 452 and 453, so that
the risk of a temperature- or stress-induced loose of contact
between these element is significantly reduced or eliminated, if
e.g. compared to the use of a support plate made of CaF.sub.2 or
fused silica.
[0146] In the embodiment illustrated in FIGS. 4g and 4h, the
support plate 451 and the sector-shaped parts 452 and 453 are all
made of right-handed optically active quartz. The invention is
however not limited thereto. Alternatively, the support plate 451
and the sector-shaped parts 452 and 453 can be made of left-handed
optically active quartz. In a further preferred embodiment, the
support plate 451 is made of right-handed optically active quartz,
and the sector-shaped parts 452 and 453 are made of left-handed
optically active quartz, or vice versa. An advantage of the use of
both R-quartz and L-quartz is that the sector-shaped parts 452 and
453 (or the combined system of the support plate 451 and the
sector-shaped parts 452 and 453) will have a reduced temperature
dependence regarding the change of polarization, since the
temperature dependence of the polarization state becomes partly
compensated. This advantageous effect is explained in more detail
below with respect to FIG. 11.
[0147] Furthermore, although in the embodiment as shown in FIGS. 4g
and 4h the thicknesses of the sector-shaped parts 452 and 453 and
the support plate 451 are such that the orientation of polarization
of linearly polarized light with normal incidence on the light
entrance side of the polarization-modulating element 450 is rotated
by an angle of 90.degree. in the sector-shaped parts 452 and 453,
and by an angle of 180.degree. in the support plate 451, the
invention is not limited thereto. In an alternate embodiment, the
thicknesses d.sub.1, d.sub.2 of the sector-shaped parts 452 and 453
and the support plate 451 may e.g. be such that the orientation of
polarization of linearly polarized light with normal incidence on
the light entrance side of the polarization-modulating element 450
is rotated by an angle of 180.degree. in the sector-shaped parts
452 and 453, and by an angle of 90.degree. (or more generally an
angle of 90.degree.+k*180.degree., with k being an
integer.gtoreq.0) in the support plate 451. In a further, more
general embodiment, the thickness of the support plate 451 may be
such that the orientation of polarization of linearly polarized
light with normal incidence on the light entrance side of the
polarization-modulating element 450 is rotated by an angle of
k*90.degree..
[0148] In FIG. 4g, the directions of polarization of light that
exits from the polarization-modulating element 450 (and which has
entered the polarization-modulating element 450 as linear polarized
light with polarization along the y-axis) are referenced with
double-arrows "P1" to "P4". It can be seen that the embodiment as
shown in FIGS. 4g and 4h may be used to approximate a tangential
polarization direction for the exiting light bundle. However,
although in the embodiment according to FIGS. 4g and 4h the
polarization-modulating element 450 comprises two sector-shaped
parts 452 and 453 being arranged on the support plate 451, the
invention is not limited to the shapes and areas and the number of
sector-shaped parts. Other suitable shapes (having for example but
not limited to trapeze-shaped, rectangular, square, hexagonal or
circular geometries) as well as more or less sector-shaped parts
can be used in the embodiment of FIGS. 4g and 4h in order to create
a desired polarization distribution.
[0149] FIG. 5 schematically illustrates how a
polarization-modulating optical element 501 with a thickness
profile according to FIGS. 3 and 4d converts the polarization
distribution of an entering light bundle 513 with a uniformly
oriented linear polarization distribution 517 into a tangential
polarization 519 of an exiting light bundle 515. This can be
visualized as follows: A linearly polarized light ray of the
entering light bundle 513 which traverses the
polarization-modulating optical element at a location of minimum
thickness, for example at .theta.=180.degree., covers a distance of
90.degree./.alpha. inside the optically active crystal. This causes
the oscillation plane of the electrical field vector to be rotated
by 90.degree.. On the other hand, a linearly polarized light ray
traversing the polarization-modulating optical element 501 at a
location with .theta.=45.degree. covers a distance of
135.degree./.alpha. inside the optically active crystal, thus the
oscillation plane of the electrical field vector of this ray is
rotated by 135.degree.. Analogous conclusions can be drawn for each
light ray of the entering light bundle 513.
[0150] FIG. 6 schematically illustrates how an optical arrangement
with a polarization-modulating optical element 601 with a thickness
profile according to FIGS. 3 and 4d in combination with a further
polarization-modulating element 621 converts the polarization
distribution of an entering light bundle 613 with a uniformly
oriented linear polarization distribution 617 into a radial
polarization 623 of an exiting light bundle 615. As explained in
the context of FIG. 5, the polarization-modulating optical element
601 produces a tangential polarization distribution. A tangential
polarization distribution can be converted into a radial
polarization distribution by a 90.degree.-rotation of the
respective oscillation plane of each individual linearly polarized
ray of the light bundle. There are several different possibilities
to accomplish this with an optical arrangement according to FIG. 6.
One possible concept is to arrange a planar-parallel plate of an
optically active crystal as a further polarization-modulating
element 621 in the light path, where the thickness of the plate is
approximately 90.degree./.alpha..sub.p with .alpha..sub.p
representing the specific rotation of the optically active crystal.
As in the polarization-modulating element 601, the optical crystal
axis of the planar parallel plate runs likewise parallel to the
element axis. As another possible concept, the further
polarization-modulating element 621 can be configured as a
90.degree.-rotator that is assembled from two half-wave plates. A
90.degree.-rotator consists of two half-wave plates of birefringent
crystal material. Each plate has a slow axis associated with the
direction of the higher refractive index and, perpendicular to the
slow axis, a fast axis associated with the direction of the lower
refractive index. The two half-wave plates are rotated relative to
each other so their respective fast and slow axes are set at an
angle of 45.degree. from each other.
[0151] Of course further possible embodiments for producing a
radial polarization distribution are conceivable within the scope
of the invention. For example, the further polarization-modulating
optical element 621 can be connected to the polarization-modulating
optical element 601. To allow a fast change-over from tangential to
radial polarization, one could provide an exchange device that
allows the further polarization-modulating element 621 to be placed
in the light path and to be removed again or to be replaced by
another element.
[0152] A tangential polarization distribution can also be produced
with a polarization-modulating optical element that has a thickness
profile in accordance with FIG. 4e. The thickness profile in this
embodiment of the invention has no discontinuities. As visualized
in FIG. 7a, the uniformly oriented polarization distribution 717 of
the entering light bundle 713 is first transformed by the
polarization-modulating optical element 701 into a linear
polarization distribution 727 of an exiting light bundle 715. The
one-half of the entering light bundle 713 that passes through the
polarization-modulating optical element 701 in the azimuth range
0.ltoreq..theta..ltoreq.180.degree. of the thickness profile shown
in FIG. 4e is converted so that the corresponding one-half of the
exiting light bundle has a tangential polarization distribution.
The other half, however, has a different, non-tangential
polarization distribution 727. A further polarization-modulating
optical element is needed in the light path in order to completely
convert the polarization distribution 727 of the light bundle 715
exiting from the polarization-modulating optical element 701 into a
tangential polarization distribution 719. The further
polarization-modulating optical element is in this case configured
as a planar-parallel plate 725 with a first half 729 and a second
half 731. A plan view of the planar-parallel plate 725 is shown in
FIG. 7b. The first half 729 is made of an isotropic material that
has no effect on the state of polarization of a light ray, while
the second half 731 is designed as a half-wave plate. The
planar-parallel plate 725 in the optical arrangement of FIG. 7a is
oriented so that a projection RA' of the reference axis RA of the
polarization-modulating optical element 701 onto the
planar-parallel plate runs substantially along the separation line
between the first half 729 and the second half 731. The slow axis
LA of the birefringence of the half-wave plate is perpendicular to
this separation line. Alternatively tangential polarization can
also be achieved with a polarization-modulating optical element,
having a thickness profile as given by FIG. 4e, if the element is
composed of two half wedge-shaped or helically shaped elements of
crystalline quartz, wherein the optical activity of one element is
clockwise and that of the other is counterclockwise. In this case
no additional plane-parallel plate 725 is necessary, as it is in
the embodiment of FIG. 7a. In this embodiment preferably each
wedge-shaped element has a constant screw-slope, but the slopes
have different directions as shown in the profile of FIG. 4e.
Further, it is not necessary that the slopes of the geometrical
thickness d have the same absolute values, it is sufficient if the
slopes D of the optical effective thicknesses have the same
absolute values. In this case the specific rotations .alpha. are
different regarding absolute values for the two wedge-shaped
elements which form the polarization-modulating optical
element.
[0153] FIG. 8 schematically illustrates a microlithography
projection system 833 which includes the light source unit 835, the
illumination system 839, the mask 853 which carries a
microstructure, the projection objective 855, and the substrate 859
that is being exposed to the projection. The light source unit 835
includes a DUV- or VUV-laser, for example an ArF laser for 192 nm,
an F.sub.2 laser for 157 nm, an Ar.sub.2 laser for 126 nm or a
Ne.sub.2 laser for 109 nm, and a beam-shaping optical system which
produces a parallel light bundle. The rays of the light bundle have
a linear polarization distribution where the oscillation planes of
the electrical field vectors of the individual light rays are
oriented in a uniform direction. The principal configuration of the
illumination system 839 is described in DE 195 20 563 A1 (U.S. Pat.
No. 6,285,433 B1). The parallel light bundle falls on the
divergence-increasing optical element 837. As a
divergence-increasing optical element, one could use for example a
raster plate with an arrangement of diffractive or refractive
raster elements. Each raster element generates a light bundle whose
angle distribution is determined by the dimension and focal length
of the raster element. The raster plate is located in or near the
object plane of an objective 840 that follows downstream in the
light path. The objective 840 is a zoom objective which generates a
parallel light bundle with a variable diameter. A
direction-changing mirror 841 directs the parallel light bundle to
an optical unit 842 which contains an axicon (i.e., a rotationally
symmetric prism arrangement) 843. The zoom objective 840 in
cooperation with the axicon 843 generates different illumination
profiles in the pupil plane 845, depending on the setting of the
zoom and the position of the axicon elements. A
polarization-modulating optical element 801, for example of the
kind shown in FIG. 3, is arranged in the pupil plane 845. The
polarization-modulating optical element 801 is followed in the
light path by a compensation plate 847 which has a thickness
profile designed to compensate the angle deviations which the
polarization-modulating optical element causes in the light rays
that pass through it. The optical unit 842 is followed by a
reticle-masking system (REMA) 849. The REMA Objective 851 projects
an image of the reticle-masking system 849 onto the
structure-carrying mask (reticle) 853, whereby the illuminated area
of the reticle 853 is delimited. The projection objective 855
projects the image of the structure-carrying mask 853 onto the
light-sensitive substrate 859. The space between the last optical
element 857 of the projection objective and the light-sensitive
substrate 859 contains an immersion liquid 861 with a refractive
index different from air.
[0154] An additional advantage of the present invention is that
polarization-modulating optical elements or the optical system
according to the present invention can be used for adjusting the
polarization distribution and also for temperature compensation of
the polarization distribution in a microlithography projection
system as described in FIG. 8. Advanced microlithography projection
systems require in some applications a predefined polarization
distribution at the reticle 853 with an accuracy of about 5.degree.
or even better, in some cases even better than 1.degree..
[0155] Since the polarization distribution at the reticle is
influenced by the various optical elements by e.g. tension-induced
birefringence, or by undefined or uncontrolled changes of the
temperature of individual optical elements, the polarization
distribution can unpredictably or uncontrollably change over time.
To correct such changes the temperature dependency of the specific
rotation .alpha. of the polarization-modulating optical element can
be used to control the magnitude of the polarization angles. The
optical system according to an embodiment of the present invention
preferably comprises a polarization control system for controlling
the polarization distribution of the light beam which is
propagating through the optical system. The polarization
distribution of interest is at a predefined location in the optical
system. The polarization control system comprises at least one
heating or cooling device to modify the temperature and/or the
temperature distribution of the polarization-modulating optical
element to affect the polarization distribution of the light beam
at the predefined location. Here the polarization-modulating
optical element may have a varying or constant effective optical
thickness.
[0156] In the case of a constant effective optical thickness the
optical system comprises an optical axis or a preferred direction
given by the direction of a light beam propagating through the
optical system. The optical system additionally comprises a
polarization-modulating optical element described by coordinates of
a coordinate system, wherein one preferred coordinate of the
coordinate system is parallel to the optical axis or parallel to
said preferred direction. The polarization-modulating optical
element comprises solid and/or liquid optically active material,
wherein the effective optical thickness is constant as a function
of at least one coordinate different from the preferred coordinate
of the coordinate system. The optical system comprises further a
polarization control system for controlling the polarization
distribution of the light beam (propagating through the optical
system) at a predefined location in the optical system, and the
polarization control system comprises at least one heating or
cooling device to modify the temperature and/or the temperature
distribution of the polarization-modulating optical element to
affect the polarization distribution of the light beam at the
predefined location.
[0157] As an example, if the polarization-modulating optical
element (as used e.g. in the optical system according to the
present invention) is made of synthetic (crystalline) quartz,
comprising a parallel plate or formed as a parallel plate, a
thickness of 10 mm of such a plate will result in a change of
polarization of 23.6 mrad/.degree. C. or 23.6 mrad/K, equivalent to
1.35.degree./K, due to the linear temperature coefficient .gamma.
of the specific rotation .alpha. with .gamma.=2.36 mrad/(mm*K).
These data correspond to a wavelength of 193 nm. In such an
embodiment, which is schematically shown in FIG. 9, the optical
axis OA of the parallel plate 901 is directed parallel or
approximately parallel to the propagation of the light (indicated
by reference numeral 950) in the optical system. Approximately
parallel means that the angle between the optical axis OA of the
parallel plate 901 and the direction of the light propagating
through the optical system is smaller than 200 mrad, preferably
smaller than 100 mrad or even smaller than 50 mrad. Controlling the
temperature of the plate 901 will result in a controlled change of
polarization. If for example the temperature of the plate will be
controlled in a range of about 20.degree. C. to 40.degree. C., the
polarization angles can be controllably changed in a range of about
.+-.13.5.degree. for such a plate 901 made of quartz. This high
sensitivity allows a control of the polarization distribution by
temperature control. In such a case even a plane plate with a
thickness d of about 0.1 mm up to 20 mm will become a
polarization-modulating optical element 901, able to controllably
adjust a polarization distribution by controlling the temperature
of the plate 901. Preferably for synthetic (crystalline) quartz the
thickness of the plate 901 is n*278.5 .mu.m (n is any integer)
which results in a rotation of a polarization plane of at least
90.degree. for n=1 and 180.degree. for n=2 and in general
n*90.degree., for a wavelength of 193 nm at about 21.6.degree. C.
For a 90.degree. rotation of the polarization plane the synthetic
quartz should be at least 278.5 .mu.m thick and for 180.degree. at
least 557.1 .mu.m, for 270.degree. the thickness should be 835.5
.mu.m and for a 360.degree. rotation of the polarization the
thickness is 1.114 mm. The manufacturing tolerances regarding
thickness are about .+-.2 .mu.m. Thus the manufacturing tolerance
results in an inaccuracy of the angle of the polarization plane of
the light which passes the plate of about .+-.0.64.degree. at about
21.6.degree. C. and 193 nm. To this inaccuracy an additional
inaccuracy caused by temperature fluctuation of the plate (or
polarization-modulating optical element) have to be considered,
which is given by the linear temperature coefficient .gamma. of the
specific rotation .alpha. with is .gamma.=2.36
mrad/(mm*K)=0.15.degree./(mm*K).
[0158] The temperature control of the plate 901 can be done by
closed-loop or open-loop control, using a temperature sensing
device with at least one temperature sensor 902, 903 for
determining the temperature of the plate 901 (or providing a
temperature sensor value which is representative or equal to the
temperature and/or the temperature distribution of the
polarization-modulating optical element), at least a heater 904,
905, preferably comprising an infrared heater, for heating the
plate by infrared radiation 906, and a control circuit 910 for
controlling the at least one heater 904, 905. As an example of a
temperature sensing device a infrared sensitive CCD-element with a
projection optics may be used, wherein the projection optics images
at least a part of the plate 901 onto the CCD-element such that a
temperature profile of the viewed part of the plate 901 can be
determined by the analysis of the CCD-element signals. The control
circuit 910 may comprise a computer system 915 or may be connected
to the computer or control system 915 of the microlithography
projection system 833 (see FIG. 8). In a preferred embodiment of
the temperature controlled plate 901 the thickness is chosen such
that a rotation of the polarization of n*90.degree., n is any
integer number, is achieved at a temperature
T=(T.sub.max-T.sub.min)/2+T.sub.min, whereas T.sub.max and
T.sub.min, are the maximum and minimum temperatures of the plate
901 (or in general the polarization-manipulating optical element).
Preferably the heater or heating system (and also any cooling
device like a Peltier element) is arranged such that it is not in
the optical path of the microlithography projection system 833, or
that it is not in the optical path of the light beam which is
propagating through the optical system according to an embodiment
of the present invention. Preferably the optical system with the
polarization control system according to the present invention is
used in a system with at least one additional optical element
arranged between the polarization-modulating optical element and
the predefined location in the optical system such that the light
beam contacts the at least one additional optical element when
propagating from the polarization-modulating optical element to the
predefined location. The additional optical element preferably
comprises a lens, a prism, a mirror, a refractive or a diffractive
optical element or an optical element comprising linear
birefringent material. Thus the optical system according to the
present invention may form a part of a microlithography projection
system 833.
[0159] In a further preferred embodiment the temperature of the
polarization-manipulating optical element 901 (the plate as shown
in FIG. 9) corresponds to a predefined temperature profile. As an
example, such a temperature profile is achieved by using a
plurality of infrared heaters 904, 905 to produce a radiation
distribution across the optical element 901 which heats the optical
element 901 in a controlled way with a control circuit as already
described. In such an embodiment also a plurality of temperature
sensors 902, 903 can be used for the control circuit 910. With this
embodiment the polarization state in a field plane or pupil plane
of the microlithography projection system 833 can be adjusted
locally.
[0160] Alternatively or in addition the heater or heating elements
904, 905 may be replaced or supplemented by one or more
Peltier-elements 907, 908. The Peltier-element or elements are
preferably connected to the control circuit 910 such that a control
by open and/or closed loop control is possible. The advantage of
the Peltier-elements is that also a controlled cooling of the
polarization-manipulating optical element 901 can be achieved.
Heating and cooling the optical element 901 at the same time result
in complex temperature distributions in the polarization-modulating
optical element 901, which result in complex polarization
distributions of the light 950 propagating e.g. through the
microlithography projection system 833, after passing the element
901. Of course, other heating and cooling means than the ones
mentioned above can be used to achieve a required temperature
profile or a required temperature of the polarization-modulating
optical element 901.
[0161] The application of the plane plate 901 as
polarization-modulating optical element 801 in the illumination
system of a microlithography projection apparatus 833 (see FIG. 8)
is preferably in the pupil plane 845 and/or at positions between
the light source unit 835 and the mentioned pupil plane 845.
Applying the plane plate 901 at these locations has the advantage
that the angle of incidence of the light which passes through the
plate 901 and also passing through the microlithography projection
apparatus is smaller than about 6.degree. (100 mrad). At these
small angles the influence of linear birefringence, caused by the
plate 901, is very small such that the polarization of the light
after passing the plate 901 is almost linear with negligible
elliptical parts, if the light was linearly polarized before
entering the plate 901.
[0162] In a further preferred embodiment of the invention the state
of the polarization of the light passed through the
polarization-modulating element 901 or the optical system according
to the present invention is measured. For this the polarization
control system comprises a polarization measuring device providing
a polarization value representative for or equal to the
polarization or the polarization distribution of the light beam at
the predetermined location in the optical system. Further, the
control circuit controls the at least one heating or cooling device
dependent on the temperature sensor value and/or the polarization
value by open or closed loop control. The measured state of
polarization is compared with a required state and in the case that
the measured state deviates more than a tolerable value, the
temperature and/or the temperature distribution of the
polarizing-modulating element like the plane plate 901 is changed
such that the difference between the measured and the required
state of polarization becomes smaller, and if possible such small
that the difference is within a tolerable value. In FIG. 9 the
measurement of the state of polarization is measured in-situ or
with a separate special measurement, depending on the polarization
measuring device 960. The polarization measuring device may be
connected with the control circuit 910, such that depending on the
measured polarization state values the heating means 904, 905
and/or 907, 908 are controlled heated and/or cooled such that the
measured and the required state of polarization becomes smaller.
The control can be done in open or closed loop modus.
[0163] The plane plate 901 used as polarization-modulating optical
element or being a part of such element is especially appropriate
to correct orientations of polarization states of the passed light
bundles.
[0164] In a further embodiment of the present invention the plane
plate 901 (comprising or consisting of optically active material),
used as a polarization-modulating optical element, is combined with
a plate 971 (see FIG. 10), comprising or consisting of linear
birefringent material. With this embodiment of the invention the
orientation and the phase of the passing light bundle 950 can be
subjected such that e.g. a plane polarized light bundle becomes
elliptically polarized after passing both plane plates 901 and 971,
or vice versa. In this embodiment at least one plate 901 or 971 is
controlled regarding its temperature and/or temperature
distribution as described in connection with FIG. 9. Further, the
sequence of the plates 901 and 971 may be changed such that the
passing light bundles are first passing through the plate 971,
comprising or consisting of linear birefringent material, and than
through the plate 901, comprising or consisting of optical active
material, or vice versa. Preferably both plates are consecutively
arranged along the optical axis OA of the system. Also, more than
one plate comprising or consisting of linear birefringent material,
and/or more than one plate comprising or consisting of optical
active material may be used to manipulate the state of polarization
of the passing light bundles. Further, a plane plate 971, or 901
may be exchanged by a liquid cell or cuvette containing optically
active material. Also the plane plates 971, comprising or
consisting of linear birefringent material, and plate 901,
comprising or consisting of optical active material, can be
arranged such that at least one other optical element 981 is placed
between these plane plates. This element 981 can be for example a
lens, a diffractive or refractive optical element, a mirror or an
additional plane plate.
[0165] In an additional embodiment of the present invention a
polarization-modulating element or in general a polarizing optical
element is temperature compensated to reduce any inaccuracy of the
polarization distribution generated by the polarization-modulating
element due to temperature fluctuations of said element, which for
synthetic quartz material is given by the linear temperature
coefficient .gamma. of the specific rotation .alpha. for quartz
(which is as already mentioned above .gamma.=2.36
mrad/(mm*K)=0.15.degree./(mm*K)). The temperature compensation
makes use of the realization that for synthetic quartz there exist
one quartz material with a clockwise and one quartz material with a
counterclockwise optical activity (R-quartz and L-quartz). Both,
the clockwise and the counterclockwise optical activities are
almost equal in magnitude regarding the respective specific
rotations .alpha.. The difference of the specific rotations is less
than 0.3%. Whether the synthetic quartz has clockwise (R-quartz) or
counterclockwise (L-quartz) optical activity dependents on the
seed-crystal which is used in the manufacturing process of the
synthetic quartz.
[0166] R- and L-quartz can be combined for producing a thermal or
temperature compensated polarization-modulating optical element 911
as shown in FIG. 11. Regarding the change of the state of
polarization such a temperature compensated polarization-modulating
optical element 911 is equivalent to a plane plate of synthetic
quartz of thickness d. For example, two plane plates 921 and 931
are arranged behind each other in the direction 950 of the light
which is propagating through the optical system which comprises the
temperature compensated polarization-modulating optical element
911. The arrangement of the plates is such that one plate 931 is
made of R-quartz with thickness d.sub.R, and the other 921 is made
of L-quartz with thickness d.sub.L, and |d.sub.R-d.sub.L|=d. If the
smaller thickness of d.sub.R and d.sub.L (min(d.sub.R, d.sub.L)) is
larger than d or min(d.sub.R, d.sub.L)>d, which in most cases is
a requirement due to mechanical stability of the optical element,
then the temperature dependence of the polarization state becomes
partly compensated, meaning that the temperature dependence of the
system of R-quartz and L-quartz plates is smaller than .gamma.=2.36
mrad/(mm*K)*d=0.15.degree./(mm*K)*d, wherein d is the absolute
value of the difference of the thicknesses of the two plates
d=|d.sub.R-d.sub.L|. The following example demonstrates this
effect. A R-quartz plate 931 with a thickness of e.g. d.sub.R=557.1
.mu.m (resulting in a 180.degree. clockwise change of the exiting
polarization plane compared to the incident polarization plane) is
combined with a L-quartz plate 921 with a thickness of
d.sub.L=557.1 .mu.m+287.5 .mu.m (resulting in a 270.degree.
counterclockwise change of the exiting polarization plane compared
to the incident polarization). This result in a 90.degree.
counterclockwise change of the polarization plane after the light
pass both plane plates 921, 931, corresponding to a 270.degree.
clockwise change of the polarization plane if just a R-quartz plate
would be used. In this case the temperature compensation is not
fully achieved, but it is reduced to value of about 0.04.degree./K
if both plates are used, compared to 0.13.degree./K if just a
R-quartz plate of d.sub.R=557.1 .mu.m+287.5 .mu.m would be used.
This is a significant reduction of temperature dependency, since
even if the temperature will change by 10.degree. C. the change of
the polarization plane is still smaller than 1.degree..
[0167] In general any structured polarization-modulating optical
element made of R- or L-quartz, like e.g. the elements as described
in connection with FIGS. 3 and 4a can be combined with a plane
plate of the respective other quartz type (L- or R-quartz) such
that the combined system 911 will have a reduced temperature
dependence regarding the change of the polarization. Instead of the
plane plate also a structured optical element made of the
respective other quartz type may be used such that in FIG. 11 the
shown plates 921 and 931 can be structured polarization-modulating
optical elements as mentioned in this specification, having
specific rotations of opposite signs, changing the state of
polarization clockwise and counterclockwise.
[0168] To generalize the above example of a temperature compensated
polarization-modulating optical element 911, the present invention
also relates to an optical system comprising an optical axis OA or
a preferred direction 950 given by the direction of a light beam
propagating through the optical system. The optical system
comprising a temperature compensated polarization-modulating
optical element 911 described by coordinates of a coordinate
system, wherein one preferred coordinate of the coordinate system
is parallel to the optical axis OA or parallel to said preferred
direction 950. The temperature compensated polarization-modulating
optical element 911 comprises a first 921 and a second 931
polarization-modulating optical element. The first and/or the
second polarization-modulating optical element comprising solid
and/or liquid optically active material and a profile of effective
optical thickness, wherein the effective optical thickness varies
at least as a function of one coordinate different from the
preferred coordinate of the coordinate system. In addition or
alternative the first 921 and/or the second 931
polarization-modulating optical element comprises solid and/or
liquid optically active material, wherein the effective optical
thickness is constant as a function of at least one coordinate
different from the preferred coordinate of the coordinate system.
As an additional feature, the first and the second
polarization-modulating optical elements 921, 931 comprise
optically active materials with specific rotations of opposite
signs, or the first polarization-modulating optical element
comprises optically active material with a specific rotation of
opposite sign compared to the optically active material of the
second polarization-modulating optical element. In the case of
plane plates, preferably the absolute value of the difference of
the first and the second thickness of the first and second plate is
smaller than the thickness of the smaller plate.
[0169] In an additional embodiment of the present invention a
polarization-modulating element comprises an optically active
and/or optically inactive material component subjected to a
magnetic field such that there is a field component of the magnetic
field along the direction of the propagation of the light beam
through the polarization-modulating element. The optical active
material component may be constructed as described above. However,
also optical inactive materials can be used, having the same or
similar structures as described in connection with the optical
active materials. The application of a magnetic field will also
change the polarization state of the light passing through the
optical active and/or optical inactive material due to the
Faraday-effect, and the polarization state can be controlled by the
magnetic field.
[0170] In the following, further embodiments of the present
invention related to the above-described aspect of
temperature-compensation are described with reference to FIGS. 12
to 16.
[0171] FIG. 12 also shows an arrangement 10 of two plane plates 11
and 12 being arranged behind each other along the optical axis oa
of an optical system and made of optically active material
(crystalline quartz). More specifically, plate 11 is made from
optically active quartz with a specific rotation of opposite sign
compared to the optically active quartz of the second plate 12. In
the illustrated example, the first plate 11 is made of right-handed
quartz, whereas the second plate 12 is made of left-handed quartz
(which can of course be vice-versa, too). In contrast to FIG. 11,
the thicknesses of plates 11 and 12 are identical and may e.g. be
(in a non-limiting example) 0.5 mm. In order to realize the
principle of the embodiment shown in FIG. 12, the thicknesses d1,
d2 of the plates 11 and 12 just have to be substantially identical,
e.g. by meeting the criterion |d1-d2|.ltoreq.0.01*(d1+d2). As a
consequence, if the first, right-handed plate 11 rotates the
orientation of the polarization of linear polarized light by an
excess of e.g. 5.9 mrad (i.e. by 5.9 mrad too much) as a result of
a temperature shift of .DELTA.5K, this effect is compensated since
the second left-handed plate 12 rotates the orientation of the
polarization of linear polarized light by a too-little amount of
5.9 mrad.
[0172] As a consequence, the temperature effects in both plates 11,
12 compensate each other, so that--due to the substantially
identical thicknesses of the plates 11, 12--the polarization state
of light passing both plates 11, 12 remains unchanged. The
arrangement shown in FIG. 12 may in particularly be used to provide
a diffractive optical element, as it is just schematically
illustrated in FIG. 13. Hereto, a diffractive structure 13 can be
applied e.g. on the first plate 11. Since such a structure 13
typically has a depth of the etched structures in the range of
200-400 nm, which is typically more than three orders of magnitude
lower than the typical thicknesses of the first and second plate,
respectively, the contribution of the structure 13 to a change of
the circular birefringence can be neglected. With the arrangements
shown in FIGS. 12 and 13, a detrimental effect of temperature
variations on the polarization state of light passing therethrough
can be avoided even with relatively large thicknesses (e.g. of
several mm) of the plates 11, 12, which qualifies the arrangement
of the plates for use as a support e.g. of a diffractive optical
element as shown in FIG. 13. Furthermore, due to the use of
crystalline material instead of e.g. amorphous glass or fused
silica, the undesired effect of thermal compaction leading to local
variations of the density and non-deterministic birefringence
properties, which would inadvertently modify or destroy the
polarization distribution after the optical arrangement, is avoided
or significantly reduced even in the presence of electromagnetic
radiation of relatively high energies.
[0173] With reference to FIGS. 14a and 14b, further arrangements
are described which enable, in addition to the above described
temperature compensation, also the use of the respective embodiment
in a region of relatively large aperture angles without occurrence
of a significant undesired modification of the polarization
distribution after the respective arrangement.
[0174] FIG. 14a shows a single plane plate 25 being made of
right-handed (or alternatively left-handed) optically active quartz
such that the optical crystal axis is aligned with the direction of
optical system axis oa (z-axis). Furthermore, the thickness of
plate 25 is selected such that the orientation of the direction of
linear polarized light which perpendicularly enters the plate 25 is
rotated by an angle of 180.degree. or an integer multiple thereof.
If synthetic, optically active quartz is used which has at a
wavelength of 193 nm a specific rotation of
.alpha.=323.1.degree./mm at a temperature of 21.6.degree. C., this
condition corresponds for a single rotation of 180.degree. to a
thickness of .apprxeq.557 .mu.m.
[0175] As to the light beam "1" which passes plate 305 along the
optical crystal axis, only circular birefringence and no linear
birefringence occurs. As to light beam "2" which passes plate 25
not parallel to the optical crystal axis, the additional effect of
linear birefringence occurs, with said linear birefringence
reaching its maximum value if the light beam is perpendicular to
the optical crystal axis, whereas the effect of circular
birefringence decreases for increasing angular between the light
beam and the optical crystal axis. Since the orientation of
polarization is rotated between the light entrance surface and the
light exit surface of plate 25 by .apprxeq.180.degree. (which is
approximately true also for beam "2" in spite of the decreasing
circular birefringence if also considering the increased travelling
path), said orientation of polarization is rotated by
.apprxeq.90.degree. after beam "2" has passed half of the thickness
of plate 25. As a consequence, a polarity inversion (i.e. a
reversal of the signs) occurs for the linear birefringence after
beam "2" has passed half of the thickness of plate 25, so that the
phase shifts collected due to linear birefringence while passing
the first half of plate 25 are corrected back by the phase shifts
collected due to linear birefringence while passing the second half
of plate 25, which means that the effect of linear birefringence is
almost nearly compensated for beam "2" after having passed the
whole plate 25.
[0176] FIG. 14b shows an arrangement similar to FIG. 12 in so far
as an arrangement 30 comprises two plane plates 31 and 32 being
arranged behind each other along the optical axis oa of an optical
system and made of optically active material (crystalline quartz).
Plate 31 is made from left-handed optically active quartz, i.e.
with a specific rotation of opposite sign compared to the
right-handed optically active quartz of the second plate 32. The
thicknesses d1 and d2 of plates 31 and 32 are at least
substantially identical, e.g. by meeting the criterion
|d1-d2|.ltoreq.0.01*(d1+d2). Furthermore, the thicknesses d1 and d2
of plates 31 and 32 are selected such that the orientation of the
direction of linear polarized light which perpendicularly enters
plate 32, or plate 31 respectively, is rotated, in each of the
plates 31 and 32, by an angle of 180.degree. or an integer multiple
thereof. If synthetic, optically active quartz is used which has at
a wavelength of 193 nm a specific rotation of
.alpha.=323.1.degree./mm at a temperature of 21.6.degree. C., this
condition corresponds for a single rotation of 180.degree. in each
plate 31, 32 to a thickness of d1=d2.apprxeq.557 .mu.m. More
generally, the thicknesses d1 and d2 of plates 31 and 32 are
selected such that the orientation of the direction of linear
polarized light which perpendicularly enters plate 32, or plate 31
respectively, is rotated, in each of the plates 31 and 32, for the
operating wavelength .lamda. (of e.g. 193 nm) by an angular in the
region of 160.degree.+N*180.degree. to 200.degree.+N*180.degree.,
more preferably in the region of 170.degree.+N*180.degree. to
190.degree.+N*180.degree., still more preferably by an angular of
N*180.degree. (with N being an integer greater or equal zero). This
arrangement also results in a relatively weak sensitivity of the
polarization state on the angle of incidence of the beam as
explained in the following.
[0177] As to the light beam "1" which passes plates 32 and 31 along
the optical crystal axis, only circular birefringence and no linear
birefringence occurs. The orientation of polarization of beam "1"
is rotated clockwise in plate 32 by 180.degree. and is then rotated
counterclockwise in plate 31 by 180.degree., so that the
orientation of polarization beam 1 is effectively not rotated when
passing the whole arrangement of plates 32 and 31. Light beam "2"
enters plate 32 under an angle of incidence larger than zero and
therefore experiences also the effect of linear birefringence,
whereas the effect of circular birefringence decreases with
increasing angle of incidence. As a consequence, the orientation of
polarization for light beam 2 is rotated clockwise in plate 32 by
less than 180.degree. (see diagram 2b on the right side of FIG.
14b), and the light beam "2" will be weakly elliptically polarized
after exit of plate 32. However, due to the above selection of
thickness of plate 32, the effect of linear birefringence is almost
compensated so that said elliptical portion is relatively weak.
Since the first plate 31 is passed with opposite rotational
direction and the same travelling distance as the second plate 32,
the orientation of polarization of light beam "2" is rotated back
by substantially the same angle when passing the second plate 32
(see diagram 2c on the right side of FIG. 14b). Accordingly, the
orientation of polarization of light beam "2" upon exit of plate 31
is substantially identical to the orientation of polarization of
light beam "2" upon entrance in plate 32 (see diagrams 2a and 2c on
the right side of FIG. 14b). Furthermore, since the decrease of the
optical activity with increasing angle of incidence is
substantially equal in both plates 31 and 32, said effect is not
disturbing the maintenance of the polarization state.
[0178] As described above with reference to FIG. 14a, the
relatively weak sensitivity of the polarization state on the angle
of incidence of the beam is also achieved for only one plane plate
25 whose thickness is selected such that the orientation of the
direction of linear polarized light which perpendicularly enters
the plate 25 is rotated by an angle of 180.degree. or an integer
multiple thereof. However, due to the combination of two plates 31
and 32 according to FIG. 14b, i.e. with specific rotations of
opposite sign compared to each other, a detrimental effect of
temperature variations on the polarization state of light passing
through the arrangement can be avoided even with relatively large
thicknesses (e.g. of several mm) of the plates 31, 32, as already
described above. As to this effect of temperature compensation
which is also achieved for the embodiment of FIG. 14b, reference
can be made to the embodiments described above with respect to
FIGS. 12 and 13.
[0179] In the embodiment of FIG. 15, two plates as described above
with respect to FIG. 12 (i.e. of right-handed or left-handed
quartz, respectively, are combined (e.g. by optical wringing) to
form a support 41 of a grey filter 40, said grey filter 40 also
comprising an absorbing structure 42 of material having a reduced
transmittance at the operating wavelength of e.g. 193 nm. This
structure can e.g. be formed of vapour-deposited chrome of variable
thickness (e.g. in the region of 200-400 nm) and density.
[0180] In the embodiment of FIG. 16, a diffractive optical element
50 comprises a support 51, which may be formed identical as the
support 40 of FIG. 15 but comprises a deepened structure 52. The
support 51 can be made according to anyone of the embodiments
described with respect to FIG. 12-14, i.e. by combining (preferably
by wringing) two plane plates of identical thickness, wherein said
thicknesses may be arbitrary but particularly may be selected such
that a rotation of the orientation of polarization of linear
polarized light that perpendicularly enters the plates is rotated
by an angle of substantially 180.degree. in each of the plates.
Preferably, the maximum depth of the structure 52 is not more than
0.1% of the thickness of the support 51 (e.g. the maximum depth of
the structure 52 is not more 1 .mu.m if the thickness of the
support 51 is 1 mm), so that the compensation effect achieved by
said 180.degree.-rotation is achieved to a large extend. According
to a further embodiment, the optical element illustrated in FIG. 16
can also be used as a diffusion panel.
[0181] As a consequence of the weak sensitivity of the grey filter
40 or the diffractive optical element 50, said micro-optical
elements are suitable to be used at a position in an illumination
system where relatively large energy densities occur, since at such
positions the avoidance of the above-discussed compaction effects
and the compensation of the effects of temperature variations are
particularly relevant. As an example, an optical arrangement or an
optical element according to anyone of the embodiments described
with reference to FIGS. 12, 13, 14b and 15 can be arranged at a
position in an illumination system where the energy density of the
illumination light is more than 130%, more particularly at least
200%, and still more particularly at least 300% of the energy
density in the reticle plane of the illumination system. Further
preferred positions of such an optical arrangement or element are
in the region of relatively large numerical aperture, e.g. at or
near the position of a filed defining element in the pupil plane
(see reference number 845 in FIG. 8). Preferred positions are
further characterized in that the maximum aperture angle of a light
beam relative to the optical axis at the respective position is not
more than 350 mrad or the numerical aperture is not more than 0.4.
A further embodiment is a diffusion panel arranged downstream of
the pupil plane (see reference number 845 in FIG. 8). As a
consequence of the relatively weak sensitivity of the polarization
state on the angle of incidence of the beam for the embodiment of
FIG. 14b, the maximum aperture angle of a light beam relative to
the optical axis at the respective position of such an optical
arrangement or element can be at least 200 mrad, more particularly
more than 300 mrad. Such an optical arrangement or element is also
advantageously used in an illumination system in combination with
certain illumination settings providing relatively large aperture
angles (such as annular illumination, dipole or quadrupole
illumination).
[0182] Going back to the embodiments of the polarization-modulating
optical element discussed before and having a variable thickness
profile measured in the direction of the optical crystal axis,
further advantageous embodiments are described in the following
with reference to FIG. 17a-d and 18 a-c.
[0183] As already mentioned above, the refraction occurring in
particular at sloped surfaces of the polarization-modulating
element can cause a deviation in the direction of an originally
axis-parallel light ray after it has passed through the
polarization-modulating element. In order to compensate for this
type of deviation, it is advantageous to arrange a compensation
plate in the light path of an optical system, with a thickness
profile of the compensation plate designed so that it substantially
compensates an angular deviation of the transmitted radiation that
is caused by the polarization-modulating optical element. In an
advantageous embodiment of the present invention which is explained
in more detail in the following, said compensation plate is also
made of an optically active material.
[0184] FIG. 17a-d shows different views on a combination of a
polarization-modulating optical element with a compensation plate
according to preferred embodiments of the present invention, while
FIG. 18a-c show thickness profiles as a function of the azimuth
angle for various embodiments with different combinations of a
polarization-modulating optical element with a compensation plate.
The view shown in FIG. 17b is a cross-section along the dashed line
in direction of the arrows "b", whereas the views shown in FIGS.
17c and 17d are side views on the arrangement in FIG. 17a from the
left (FIG. 17c) or the right (FIG. 17d), respectively.
[0185] The optical arrangement according to FIG. 17a-d comprises a
polarization-modulating optical element 110 composed of parts 110a
and 110b, and a compensation plate 120 composed of parts 120a and
120b. Of course, the composition of the polarization-modulating
optical element 110 and the compensation plate 120 is just for
technological reasons and may principally also be omitted or
replaced by a composition of more than 2 parts. The optical element
110 further has an optional central bore 130 coaxial with the
element axis.
[0186] The shape of the polarization-modulating optical element 110
shown in FIG. 12a-d corresponds to that of the
polarization-modulating optical element 301 shown in FIG. 3, but is
illustrated in FIG. 17a-d to schematically explain the relative
arrangement of a compensation plate 120 in relation to the
polarization-modulating optical element 110. Accordingly, the
polarization-modulating optical element 110 shown in FIG. 17a-d has
a planar base surface and an opposite inclined surface designed to
achieve a thickness profile as already explained above with
reference to FIG. 4d. In the special configuration illustrated in
FIG. 17, the thickness of the polarization-modulating optical
element 110 is constant along a radius R that is perpendicular to
the element axis, which again is parallel to the z-axis in the
coordinate system also illustrated in FIG. 17a-d. Thus, like in
FIG. 3, the thickness profile in the illustrated embodiment of FIG.
17, which is shown in FIG. 18b, only depends on the azimuth angle
.theta. and is given by d=d (.theta.). In another embodiment of the
polarization-optical element the thickness of the
polarization-modulating optical element 110' may vary along the
radius R such that the thickness profile is d=d(R,.theta.).
[0187] In the exemplarily embodiment, the polarization-modulating
optical element 110 may be made of R-quartz, with the optical axis
of the optically active crystal running parallel to the element
axis. "R-quartz" means that the optically active quartz is turning
the direction of polarization clockwise if seen through the
optically active quartz towards the light source.
[0188] Furthermore, although the compensation plate 120 is shown,
in FIG. 17, in front of the polarization-modulating optical element
with respect to the direction of light propagation (which is
running into the z-direction), it can of course also be arranged
behind the polarization-modulating optical element.
[0189] As can also be seen in FIG. 17, the compensation plate 120
being arranged in the light path of the optical system has a
thickness profile being a complement to the thickness profile of
the polarization-modulating optical element 110 in such a sense
that the compensation plate 120 and the polarization-modulating
optical element 110 effectively add up to a plan-parallel
structure. FIG. 18b shows, for the optical arrangement of FIGS.
17a-d, the thickness profile of both the polarization-optical
element 110 and the compensation plate 120. In FIG. 18b, the
thickness profiles of the parts 110a and 110b of the
polarization-optical element 110 being illustrated with solid lines
are designated as C1 and C2, while the thickness profiles of the
parts 120a and 120b of the compensation plate 120 being illustrated
with dashed lines are designated as D1 and D2.
[0190] In the exemplarily embodiment with the
polarization-modulating optical element 110 being made of R-quartz,
the compensation plate 120 is preferably made of L-quartz.
"L-quartz" means that the optically active quartz is turning the
direction of polarization counter-clockwise if seen through the
optically active quartz towards the light source. Of course the
polarization-modulating optical element 110 can also be, vice
versa, made of L-quartz, with the compensation plate 120 being made
of R-quartz. More generally, the compensation plate 120 comprises
an optically active material with a specific rotation of opposite
sign compared to said first optically active material.
[0191] Furthermore, as already discussed before, the invention is
not limited to the use of quartz or generally to the use of
crystalline materials, so that both the polarization-modulating
optical element and the compensation plate may also be replaced by
one or more cuvettes of appropriate shape which are comprising an
optically active liquid. In further more generalized embodiments,
as has been already described above with reference to FIGS. 3 and
4, the thickness profiles discussed with reference to FIGS. 17 and
18 are not representing the geometrical thicknesses of the
polarization-optical element or the compensation plate,
respectively, but the profile represents an optical effective
thickness D as defined above.
[0192] To evaluate the effect of this thickness profile, it has to
be considered that since the polarization-optical element 110 and
the compensation plate 120 are turning the direction of
polarization of linear polarized light into opposite directions,
the relevant factor for the net effect on each light ray traversing
the arrangement the polarization-optical element 110 and the
compensation plate 120 parallel to the optical axis of each of
these elements is the difference of the thicknesses d or optically
effective thicknesses D being passed in the L-quartz or the
R-quartz, respectively. Since this difference is just zero at the
two crossing points of the solid lines C1, C2 with the dashed lines
D1, D2, which occur for an azimuth angle of .theta.=90.degree. as
well as for an azimuth angle of .theta.=270.degree., a linearly
polarized light ray passing the arrangement under an azimuth angle
of .theta.=90.degree. or .theta.=270.degree. will leave the
arrangement with the same orientation of polarization. This means
that for a generation of a tangential polarization distribution as
it has been explained above with reference to FIG. 5, the azimuth
angles of .theta.=90.degree. or .theta.=270.degree. represent the
"new" reference angles where the orientations of polarization are
left unchanged with respect to the polarization distribution of the
light entering the arrangement. As follows from the above, the
arrangement of FIG. 17 of the polarization-optical element 110 and
the compensation plate 120 being made of optically active materials
with a specific rotation of opposite sign has to be placed in a
position being rotated by 90.degree. if compared to the position
taken by the arrangement of FIG. 3.
[0193] For thicknesses 90.degree.<.theta.<180.degree., the
traveled distance in the R-quartz of the polarization-optical
element is larger than the traveled distance in the L-quartz of the
compensation plate, leading to a clockwise net-rotation of the
direction of polarization. For thicknesses
0.degree.<.theta.<90.degree., the traveled distance in the
L-quartz of the compensation plate is larger than the traveled
distance in the R-quartz of the polarization-optical element,
leading to a counter-clockwise net-rotation of the direction of
polarization.
[0194] Since both the polarization-modulating optical element 110
and the compensation plate 120 are rotating the direction of
polarization into opposite directions, the slopes in the respective
thickness profiles of the compensation plate and the
polarization-modulating element may be reduced for each of these
elements, if compared to a situation where only the
polarization-modulating optical element is made of optically active
material. More specifically and with reference to FIG. 18b, a
tangential polarization distribution can be achieved with half the
slope of the lines C1 and C2 describing the inclined surface of the
polarization-modulating element (or D1 and D2, respectively,
describing the inclined surface of the compensation plate).
Accordingly, the thickness of the polarization-optical element 110
in this embodiment is, like in the embodiment explained with
reference to FIGS. 3 and 4d, a linear function of the azimuth angle
.theta., but with half the slope, the absolute value of which being
|m|=180.degree./(2.alpha..pi.) over each of two ranges of
0<.theta.<180.degree. and
180.degree.<.theta.<360.degree. (of course this slope is also
valid for the compensation plate 120).
[0195] A modification of the arrangement of FIG. 17 which is
comparable to the embodiment explained above with reference to FIG.
4c, but also comprises a compensation plate, is shown in FIG. 18a,
giving an example of a continuously varying thickness profile. The
thickness d or optical effective thickness D of the azimuthal
section of the polarization-optical element (whose thickness
profile is shown with solid line A) in this embodiment shows a
linear decrease over the whole azimuth-angle range of
0.ltoreq..theta..ltoreq.360.degree.. Again, the shape of the
compensation plate (whose thickness profile is shown with dashed
line B) is a complement in the sense that it shows a linear
increase over the whole azimuth-angle range of
0.ltoreq..theta..ltoreq.360.degree.. Further, as it is also the
case for the embodiment explained with reference to FIG. 18b, a
tangential polarization distribution can be achieved with half the
slope of the line A describing the inclined surface of the
polarization-modulating element (or B describing the inclined
surface of the compensation plate) if compared to FIG. 4c.
Accordingly, the absolute value of the slope of line A or B,
respectively, is |m|=180.degree./(2.alpha..pi.) over an
azimuth-angle range of 0.ltoreq..theta..ltoreq.360.degree..
Alternatively the slope can also be |m|=180.degree./(2.alpha..pi.r)
where r is the radius of a circle being centred at the element axis
EA. In this case the slope depends on the distance of the element
axis, e.g. if the polarization-modulating optical element has a
given constant screw-slope (lead of a screw).
[0196] A further modification of the arrangement of FIG. 17 which
is comparable to the embodiment explained above with reference to
FIG. 4e, but also comprises a compensation plate is shown in FIG.
18c. The thickness d or optical effective thickness D of the
azimuthal section of the polarization-optical element (whose
thickness profile is shown with solid lines E1 and E2) is in this
case a linear function of the azimuth angle .theta. with a first
slope m for 0<.theta.<180.degree. and with a second slope n
for 180.degree.<.theta.<360.degree.. The slopes m and n are
of equal absolute magnitude but have opposite signs. As explained
above with reference to FIG. 4e, the concept of using opposite
signs for the slope in the two azimuth angle ranges avoids the
occurrence of discontinuities in the thickness profile. Again, the
shape of the compensation plate (whose thickness profile is shown
with dashed lines F1 and F2) is a complement in the sense that it
also shows a linear function of the azimuth angle .theta. with a
first slope for 0<.theta.<180.degree. and with a second slope
for 180.degree.<.theta.<360.degree., but with the first and
second slope being opposite to the first slope m or the second
slope n, respectively, for the azimuthal section of the
polarization-optical element. Again, a tangential polarization
distribution can be achieved with half the slope of the lines E1,
E2 describing the inclined surface of the polarization-modulating
element (or F1, F2 describing the inclined surface of the
compensation plate) if compared to FIG. 4e. Accordingly, the
absolute value of the slopes of lines E1 or E2, respectively, are
at a distance r from the element axis
|m|=180.degree./(2.alpha..pi.r) and
|n|=180.degree./(2.alpha..pi.r).
[0197] Various embodiments for a polarization-modulating optical
element or for the optical systems according to the present
invention are described in this application. Further, also
additional embodiments of polarization-modulating optical elements
or optical systems according to the present invention may be
obtained by exchanging and/or combining individual features and/or
characteristics of the individual embodiments described in the
present application.
* * * * *