U.S. patent number 3,684,350 [Application Number 05/064,382] was granted by the patent office on 1972-08-15 for light beam polarization modulator.
This patent grant is currently assigned to Westinghouse Electric Corporation. Invention is credited to John L. Wentz.
United States Patent |
3,684,350 |
Wentz |
August 15, 1972 |
LIGHT BEAM POLARIZATION MODULATOR
Abstract
A parallel cell electro-optical phase modulator is used in
combination with two birefringent crystals and a half wave plate to
produce polarization modulation of an incident light beam. A first
birefringent crystal provides a lateral relative displacement
between the two orthogonal components of the incident light beam to
form two spaced light paths, one through each of the respective
electro-optical crystals. The half wave plate rotates the linear
polarization of the orthogonal components to allow a second
birefringent crystal to recombine the orthogonal components into a
single light beam.
Inventors: |
Wentz; John L. (Ellicott City,
MD) |
Assignee: |
Westinghouse Electric
Corporation (Pittsburgh, PA)
|
Family
ID: |
22055563 |
Appl.
No.: |
05/064,382 |
Filed: |
August 17, 1970 |
Current U.S.
Class: |
359/256;
359/259 |
Current CPC
Class: |
G02F
1/0311 (20130101); H01S 3/115 (20130101) |
Current International
Class: |
G02F
1/01 (20060101); G02F 1/03 (20060101); H01S
3/11 (20060101); H01S 3/115 (20060101); G02f
001/26 () |
Field of
Search: |
;350/147,150,157,160,DIG.2 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
Ammann, "Modification of Devices...to Allow their Use with
Arbitrarily Polarized Light" J.O.S.A. Vol. 55, No. 4 (April 1965)
pp. 412-417. .
Rowe, "Light Intensity Modulator" IBM Technical Disclosure Bulletin
Vol. 12, No. 7 (Dec. 1969) p. 910,.
|
Primary Examiner: Schonberg; David
Assistant Examiner: Miller; Paul R.
Claims
What is claimed is:
1. Light modulation apparatus for a source of polarized light
comprising a birefringent element oriented for receiving an
incident light beam parallel to an optic axis to resolve said beam
into two orthogonal components in spaced parallel lights paths,
first and second birefringent electro-optical crystals having
substantially the same index of refraction arranged, respectively,
in said parallel light paths, half-wave plate arranged across said
light paths a second birefringent element having the same
characteristics as said first birefringent element and having its
principal axis orthogonal to the principal axis of said first
birefringent element for receiving light from said parallel paths
and recombining them into a single light beam substantially
colinear with said incident light beam, said birefringent elements
being so disposed about the axis of the incident light that their
respective optic axes are 45.degree. with respect to the electric
vector of said incident light beam and means for applying a D.C.
potential across said electro-optical elements to vary the index of
refraction of said crystal.
2. A combination as set forth in claim 1, in which said
electro-optical crystals has substantial the same index of
refraction and have the respective principal optic axes effectively
optically optically perpendicular to each other, said crystals
having substantially the same length and being subjected to the
same environmental conditions, and means for supplying a modulation
voltage to said crystals with the electric fields parallel to the
respective z axes of said crystals.
3. The combination as set forth in claim 2 and means for converting
polarization modulation of said orthogonal light components into
intensity modulation of the light from said combined orthogonal
components.
4. The combination as set forth in claim 2 in which the x axis of
one of said electro-optical crystals is parallel to the y axis of
the other of said crystals and the z axis of both crystals are
perpendicular to each other.
5. The combination set forth in claim 4 with means for converting
polarization modulation of said orthogonal light components into
intensity modulation of the light from said combined orthogonal
components.
Description
CROSS REFERENCE TO RELATED APPLICATION AND PATENT
In applicant's U.S. Pat. No. 3,429,636 issued Feb. 25, 1969 there
is disclosed and claimed a light modulation apparatus for
electronically controlling the passage of polarized light. The
modulation apparatus is there disclosed as applied to the resonant
optical cavity of a stimulated emission of radiation device as well
as to a simple light valve or shutter.
That system has gone into very wide usage because of its capability
of very high frequency operation and its capability of operating at
what is considered in the art as relatively low modulation
voltages. In both that system and in the present application the
light modulation is effected by direct polarization modulation. In
the patented system the type and/or degree of polarization must be
known in order to make the proper adjustments to make the system
effective. In applicant's copending application Ser. No. 067,930,
filed Aug. 28, 1970 for Polarization Independent Light Modulation
Means Using Birefringent Crystals, there is described and claimed a
light modulation system for modulating light which system is
independent of the polarization of the incident light. In other
words, the system of the copending application is capable of
modulating light energy having random polarization. The
electro-optical modulator component of that system may be identical
with that of the patented device as the improvement there resides
in combining with the electro-optical crystals of the modulator a
birefringent crystal, similar to the birefringement crystal of this
invention between the incident light and the first electro-optical
crystal. The birefringent crystal resolves any incident light into
two orthogonal components and simultaneously produces a lateral
displacement between the orthogonal components to produce two
parallel light beams which pass through the electro-optical
components. In the copending patent application the incident beam
may be randomly polarized but in the patented system and as in the
present system the incident light beam must be polarized either
linearly, circularly, or elliptically.
The single light path of the patented system and the two light
paths of the copending application each have two electro-optical
crystals in series for the purpose of cancelling any natural
birefringence, however, each crystal operates, respectively, on
only one of the orthogonal polarization components; passage of an
orthogonal polarization component through a crystal which does not
operate on that particular component represents an unnecessary
attenuation of the light beam.
SUMMARY OF THE INVENTION
This invention relates to an improvement over the modulation system
of the single path patented construction which is intended to be
used with polarized light, that is, light in which the degree and
type of polarization is known. The object of the invention is to
provide an optical modulation system which has the advantages of
the patented construction without the light energy attenuation of
the patented system. The present invention provides a means for
reducing the optical transmission losses in a polarized light
modulation system of the type disclosed in applicant's
aforementioned patent. It provides two parallel paths for the
orthogonal components of known polarized light so that the
transmission losses are decreased by a factor of two or allows a
reduction in modulation voltage required by a factor of two for no
reduction in transmission losses. Alternatively, with the same
modulation voltage, it reduces the required length of the
electro-optical modulator by a factor of two.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic illustration for the purpose of explaining
the invention;
FIG. 2 is a diagrammatic illustration showing the components of
FIG. 1 but in addition illustrating the manner in which the
electro-optical crystals are energized;
FIGS. 3 and 4 are cross-sectional elevational views of FIG. 2 at
the respective sections indicated and looking in the direction
indicated by the arrows for two respective conditions and positions
of the light vectors as they progress through the modulator from
left to right in FIGS. 1 and 2;
FIG. 5 is a diagrammatic illustration of an embodiment of the
invention applied as a light intensity modulator; and
FIG. 6 is a diagrammatic illustration of an embodiment of the
invention applied as a Q-switch for a Fabry-Perot cavity of a
stimulated emission of radiation amplifier or oscillator.
Briefly, the present invention provides an improved electro-optical
light modulation system which may be used as a light valve, in
general, and specifically as a light modulating device and is
particularly adapted for use in modulating the Q of a Fabry-Perot
cavity of a stimulated emission of radiation amplifier or
oscillator. The system is capable of effecting continuous variation
in the transmission of light or of effecting pulse modulation
thereof. The system is capable of operating at very high speeds in
the manner of an "on-off" switch to abruptly cut-off, or on, light
energy reflected back and forth in the resonant optical cavity of a
stimulated emission of radiation amplifier or oscillator.
An illustrative embodiment of the present invention utilizes the
components of a modulation system described and claimed in
applicant's aforesaid patent in combination with double refracting
birefringent crystals and suitable means such as a half-wave plate,
to provide two optical transmission paths of equal optical path
length for selected portions of the light energy and to thereby
reduce the transmission losses for light energy having a selected
polarization. Whereas the system of applicant's copending patent
application is adapted to control light energy of any polarization,
the present invention contemplates an improved electro-optical
system in which the optical transmission losses, or the modulation
voltage, are reduced by a factor of two when the polarization of
the light energy is known.
Referring to FIG. 1, there is shown an embodiment of the present
invention wherein the system is to be used where it is merely
desired to modulate the polarization of a light beam passing in a
single direction. A later embodiment is described in which the
system is designed to control the light energy in a multi-reflected
path. The similarities and the differences between the present
invention and that described and claimed in applicant's copending
patent application for controlling randomly polarized light will be
immediately pointed up by comparing FIGS. 1 of the respective
patent applications.
The essence of the present invention resides in the association of
birefringent crystals, such as crystals 2 and 3, having
characteristics well known but not heretofore used in the
combination disclosed herein and in the use of a half wave
polarization rotator in conjunction with the birefringent crystals
to obtain equal optical path lengths through the modulator (zero
retardation) for both orthogonal polarization components of the
incident light.
In optical modulation systems of the type under consideration here,
uniaxial electro-optical crystals are commonly used to polarization
modulate light beams. Specific preferred examples are the
dihydrogen phosphate type, such as potassium dihydrogen phosphate
(KDP). These crystals which are normally uniaxial become biaxial
when an electric field is applied along one of the principal optic
axes. Such crystals have one axis, namely, the Z axis, along which
the index of refraction is not altered by an applied voltage. The
electro-optic effect is the result of changes in the index of
refraction which occur along the other axes when a modulating
electric field is applied along the Z axis.
Still referring to FIG. 1, an incident light beam indicated at 1,
linearly polarized as indicated by the vector 6, will be doubly
refracted by the crystal 2 to give two orthogonal components in the
light paths 7 and 8. The axis of component 7 will be displaced in a
direction normal to the axis of the incident light beam 1 by an
amount which is a function of the birefringence and length of the
crystal 2. Thus, the crystal 2 resolves the linearly polarized beam
1 into two laterally spaced orthogonal components in two respective
parallel optical paths. The light energy of the light paths 7 and 8
may be passed through an optical phase modulating device 4 which
includes electro-optical crystals 10 and 11 arranged to impart a
phase retardation in the paths 7 and 8, respectively. The light
energy emerging from the phase modulator 4 along paths 7 and 8 can
be combined into a single emergent light beam having the same
polarization as the incident beam by means of a half wave plate 9
and a crystal 3 which has the same characteristics as that of
crystal 2 and performs the inverse of the operation performed by
crystal 2. Since the crystals 2 and 3 pass orthogonal components of
an incoming light beam their respective optical axes are arranged
orthogonal to each other. The half wave plate 9 is used to equalize
the optical path lengths for the paths 7 and 8 in order to obtain
zero retardation at zero modulation voltage.
By applying a modulation voltage to crystals 10 and 11, sufficient
to produce a 180.degree. phase shift between the polarization
vectors of the light along paths 7 and 8, the emergent vector 6'
can be rotated 90.degree. with respect to incident vector 6.
When the present invention is being used as a light modulator or
light shutter, as illustrated in FIG. 1 of the drawings, the
emergent beam 1' is directed through an appropriate analyzer 12 to
effect intensity modulation of the light beam. The intensity
modulation is effected by polarization modulation of the resultant
emergent light vector 6' relative to the plane of polarization of
the analyzer. However, if as shown in another embodiment, the
invention is used as a Q-switch for a stimulated emission of
radiation device, the electro-optic modulator is operably
associated with the optical cavity of a laser wherein the laser
medium is polarized. Since the laser amplifies and oscillates for
only a particular plane of polarization the electro-optic modulator
of the present invention is able to control the amount of light
which is regeneratively coupled back into the laser medium. The
crystals 10 and 11 correspond, respectively, to the electro-optical
crystals 10 and 11 of applicant's patent and also corresponds to
crystals 17 and 18 of said copending patent application as regards
to their characteristics. However, it should be carefully noted
here that the patented construction is adapted to modulate or
control all the light having a known degree of polarization; the
system of said patent application is capable of operating on all of
the energy of a light beam having random polarization; and the
present invention is capable of reducing the optical transmission
losses only when the incident light energy is polarized. These
differences must be kept clearly in mind in order to understand the
distinctions between the three systems and to appreciate the
novelty of the present invention.
In the polarized light system of the patent and the randomly
polarized light system of said copending application, both
orthogonal components of the light energy must pass through both of
the electro-optical crystals in series. In the present invention
only one-half of the light energy, that is, the light energy in the
component to be operated upon, passes through one electro-optical
crystal and the other half passes through the other crystal
resulting in a reduction of the optical transmission losses for the
system by a factor of two as compared to the system of applicant's
patent and that of the copending patent application.
Referring again to detailed description of the invention, the
crystals 2 and 3 serve as means for generating, separating and
recombining, respectively, the orthogonal components of the energy
in the light beam 1, the plane of polarization of which is
indicated by the vector 6. In order to obtain sufficient spatial
separation to carry out the objectives of the invention and have
one of the components pass through one of the electro-optical
crystals 10 while the other one passes through the electro-optical
crystal 11 it is necessary to choose the proper material for the
crystals 2 and 3. Furthermore, the crystal geometry must be
optimized by carefully orienting the incident light beam with
respect to the optic axis of the said crystals. This requirement
for the present invention is substantially the same in this respect
as for the system in said copending application and it has been
found that a biaxial crystal which gives an angle separation of
approximately 9.5.degree. for a light beam having a wavelength in
the neighborhood of from 4,000 to 15,000 Angstroms can provide
sufficient separation within the practical limits of the crystal to
carry out the objectives of the invention. The separation of the
orthogonal components of the light beam, illustrated in FIG. 2 and
FIG. 3, indicates that the light beam 1 which is shown polarized at
45.degree. with respect to the horizontal and vertical axes is
resolved into two orthogonal components, one of which is the
ordinary ray (O ray). The polarization vector 13 is vertical. The
other is the extraordinary ray (E ray) which is horizontal and
indicated by the vector 14.
From FIGS. 2 and 3 it will be seen that with the physical axis of
the crystal 2 properly oriented with respect to the incident light
beam 1 the extraordinary ray E will not be deviated as it passes
through the crystal 2 but it will contain the horizontal component
indicated by the vector 14. The extraordinary ray E will coincide
with the optical axis of path 8 through the electro-optical crystal
11. The extraordinary ray E will emerge parallel to the ordinary
ray O (path 8) and will follow the path 7. The deviation of the
extraordinary ray E to make it parallel to the ordinary ray O is
caused by the bi-axial crystal 2 by virtue of its double refraction
properties. The extraordinary ray E and the ordinary ray O will
emerge from the right-hand side of the electro-optical crystals 10
and 11, respectively, parallel to each other and pass through the
half wave plate 9. The half wave plate 9 rotates the plane of
polarization of the E and O rays to produce the polarization of the
emergent rays O' and E', respectively, with respect to crystal 3 as
illustrated in FIG. 4. The emergent rays O' and E' are then
recombined in crystal 3, inverse to the manner in which separation
of the rays was obtained in crystal 2 and emerge as an output light
beam indicated at 1'.
Assuming that there is no energization of the electro-optical phase
modulator 4, the electric vectors 13 of the ordinary ray O and the
vector 14 of the extraordinary ray E will remain in the same
orthogonal relative positions in which they are shown in FIG. 3.
Both of the rays O and E will pass straight through the crystals 10
and 11, respectively, without any additional lateral axis
deviation. As the extraordinary ray E' enters the crystal 3 it will
be deviated back to the optical axis of the ordinary ray O' and the
output beam represented at 1' will have the same polarization as
the incident beam represented by the vector 6 which is at
45.degree. with respect to the horizontal and vertical axes. Now
assume that the electro-optical phase modulator 4 is energized,
that is, it is in what may be called the closed position as far as
the light valve action is concerned. As in the copending patent
application, the incident light beam will be split into the two
spaced rays E and O with paths spaced as indicated in FIGS. 1 and
2. The linear polarization of the incident beam 1 will be resolved
into two orthogonal components, one of which will be the ordinary
ray O along path 7 with vertical polarization, and the other will
be the extraordinary ray E along path 8 and this component will be
horizontal. As the two rays pass through the electro-optical phase
modulator 4 the phase difference between the E and O rays will be
modified to an extent dependent upon the magnitude of the applied
modulating voltage. Upon recombing the O' and E' rays in crystal 3,
the resultant 6' will be polarization modulated. For an induced
phase difference of 180.degree. between the E and O rays, the
polarization of the resultant 6' will be orthogonal to the
polarization of the incident beam 6. Therefore, light valve action
can be obtained by placing an analyzer 12 in the emergent light
beam 1' with the analyzer having its polarization vector orthogonal
to that of the incident light beam 1, or in other words, parallel
to the polarization modulated vector 6'.
Now if a mirror 15 were placed with its reflecting surface at the
left end surface 15 and if the electro-optical crystals 10 and 11
of the phase modulator 4 were not energized the O ray and the E ray
on paths 7 and 8, respectively, will be reflected back without
change of phase through the electro-optical crystals and to the
birefringent crystal 2 where the orthogonal components will be
recombined with the incident light beam 1 and with the same
polarization as the incident beam. This would adapt the invention
to use in the Fabry-Perot cavity of an optical stimulated emission
radiation device, schematically illustrated in FIGS. 5 and 6 show
the optical paths for such a reflected light system for creating
regenerative action in an optical maser.
With the invention applied to the Fabry-Perot cavity of a
stimulated emission of radiation amplifier as indicated in FIG. 6,
the reflected light from the mirror 15 proceeding to the
birefringent crystal 2 from the right to the left would pass
through the laser rod 16 and strike the mirror 17 and would be
reflected back through the rod 16 to the point corresponding to the
incident ray which has been described in connection with FIG. 1. As
long as the electro-optic crystals 10 and 11 are unenergized the
light can repeat the cycle of reflecting back and forth between the
two mirrors 15 and 17. When the electro-optic crystals 10 and 11
are energized with a half-wave voltage pulse, the resultant vector
of the two components through the electro-optic crystals 10 and 11
will be rotated 90.degree. so that light reflected from the mirror
15 cannot pass through the crystal 3 from right to left by virtue
of the linear polarizer 21 and thus the oscillation of the laser
will be stopped.
When the present invention is utilized in of radiation system using
the present invention includes the two mirrors 15 and 17, the laser
rod 16, a linear polarizer 21, and the optical phase modulator 4
which is identical to the one previously disclosed. One of the
mirrors such, for example, mirror 17 may be partially reflective so
that the coherent light output would be from the mirror 17 from
right to left as indicated by the arrow 18. The system also
includes a suitable source of light, such as the flash tube 22,
energized from a suitable power supply source 23 in a manner well
known in the art. The control of the modulation of the output light
beam 18 may be controlled by the voltage applied to the
electro-optical crystals from the driver 24.
The operation of the phase modulator 4 is best illustrated by
reference to FIG. 2 which illustrates the manner in which the
voltage is applied between terminal 26 and ground 27. The control
voltage is supplied by the output of the driver 24. The voltages
are applied in parallel to the electro-optical crystals 10 and 11
along their Z axes which are orthogonal with respect to each
other.
The electro-optical effect is the result of induced birefringence
which occurs when an electric field is applied to the crystal along
a particular axis. As an example a particular type of crystal which
may be used is the dihydrogen phosphate type of crystals which have
been found to be very satisfactory for operation in this device.
The electro-optic effect in these crystals occurs as a result of
field induced anisotropy of the index of refraction along their
principal crystal axes. The characteristics of electro-optical
crystals can best be described in terms of the Fresnel index
ellipsoid which has axes proportional to the principal indexes of
refraction in the crystal. Plane polarized light upon such a
crystal will produce double refraction and phase retardation
between the orthogonal components of the incident light vibrating
along the principal optical axis in the crystal.
In uniaxial crystals, two of the indices of refraction in the
ellipsoid are equal. Therefore, no phase retardation occurs for
light propagating perpendicular to the plane of equal indices. This
propagation direction determines the optical axis of the crystal.
Crystals in which the principal indices are unequal are termed
biaxial, that is, they have two optic axes. Electro-optic crystals,
which are normally uniaxial become become biaxial when the electric
field is applied parallel to the Z axis. As is clear from the
drawing in the present instance, the indices of refraction for a
light vibrating parallel to the X and Y axis is altered by applied
voltages along the Z axis and under this condition the X and Y
indices are no longer equal.
It has been pointed out previously that the optical transmission
losses are reduced by this invention for light of a known
polarization since the light energy is divided into two separate
paths so that it is not necessary that the component which is not
being operated upon in a given crystal need pass through that
crystal. The operation of the invention when it is used as a simple
light valve has already been described. In the operation of the
devices applied to the optical cavity of the stimulated emission of
radiation device it can be assumed that the laser rod 16 is made of
a material which produces a polarized output. If a rod is used
which does not produce a polarized output it would be necessary to
insert the polarizer 21 between the right hand end of the rod 16
and the birefringent crystal 2.
Then we can assume that the incident light beam 1 is polarized as
it enters the birefringent crystal 2. The extraordinary ray E and
the ordinary ray O will be generated as a result of crystal 2 and
if the phase modulator 4 is adjusted for zero phase retardation,
the two orthogonal components will proceed through the
electro-optic crystals 10 and 11 without any change of phase and
then be reflected back through the electro-optical crystals 10 and
11 and will be returned to the right hand side of the
electro-optical crystal 2. Then as the reflected light beams
proceed to the left the E and O rays will be refracted in a manner
illustrated in detail in FIG. 6, which of course is the reverse of
the operation when the incident light beam 1 propagates from left
to right to the system and will emerge from 2 with the same
polarization as the incident beam.
Considering the incident light beam 1 proceeding from an external
source having a polarization vector indicated at 6, the two
orthogonal components will be generated with the orthogonal
polarization as indicated in FIG. 3 in separate paths indicated in
FIG. 1 at 7 and 8, respectively. Assuming that the phase modulator
4 is unenergized the ordinary ray along path 7 and the
extraordinary ray along path 8 will proceed to the right,
unaffected by the phase modulator, where they will be incident upon
the half wave plate 9 and birefringent crystal 3 which by combined
action will recombine the orthogonal components to produce an
output light beam indicated at one time with the same polarization
as that indicated by the arrow 6 on the incident beam. Assuming
that the polarization of the polarizer 21 is parallel to the
polarization vector 6 the light will pass through the
polarizer.
Now assume that the phase modulator 4 is energized. The same light
beam 1 with the polarization indicated by the vector 6, regardless
of whether the light is coming from the source of unpolarized light
passing through a filter or from the output of a laser rod which is
polarized and having polarization indicated by the vector 6, will
be incident on 2 and again the two orthogonal components will be
generated as previously described with the extraordinary ray E
taking the path 7 and the ordinary ray taking the path 8. These two
rays will then pass through the electro-optical crystals 10 and 11,
respectively, but as they pass through these latter crystals their
phase difference will be modified, the degree of which is dependent
upon the magnitude of the modulating voltage. At the same time, the
half wave plate 9 and birefringent crystal 3 will recombine the
component in the path 8 with the component in the path 7 to give
the emergent beam 1' with the polarization indicated by the vector
6'. This polarization is at 90.degree. with respect to the
previously assumed polarization of the polarizer 21 blocking the
light for a 180.degree. phase retardation between components which
would result when half-wave voltage is applicating the modulator 4
and, effectively, producing a light shutter which is closed.
In the case of the invention being applied to the Fabry-Perot
cavity of a stimulated emission of radiation device and assuming
the above same conditions for the incident light beam 1 with the
polarization indicated by the vector 6 the crystal 3 and half wave
plate 9 would not be present and in its place would be a mirror
such as indicated at 15 in FIG. 6. The two orthogonal components in
the two paths 7 and 8 would be reflected by the mirror and if the
phase modulator 4 was at the zero phase retardation bias the two
components would return to the electro-optical crystals 10 and 11
and be recombined in crystal 2. When the phase modulator 4 is set
to the 180.degree. phase retardation bias the resultant
polarization would be orthogonal to the polarization of the
original incident beam represented by the arrow 6. Therefore, the
regenerative coupling between the output energy of the laser rod 16
and the excited particles of the laser medium would be cut off by
action of the polarizer 21.
Preferably, although not necessarily, the elongated electro-optical
crystals 10 and 11 may have a square cross section. They may have a
rectangular cross section, so long as the dimensions along the
respective Z axes are the same. The physical axis of each rod
should lie in or be perpendicular to the 110 plane of the crystal
and also be parallel to the X-Y plane.
Since there are two separated linearly polarized orthogonal beams
which are acted upon separately by the phase modulator 4, it is
important that the geometry of the electro-optical crystals 10 and
11 be such that the extraordinary ray E and the ordinary ray O be
absolutely parallel to one of the principal optic axes of the
respective crystals. When this is true the following phase
relationships are characteristic of the polarization of the
orthogonal components of the plane polarized light in both rays
propagating parallel to the axis of the present system.
Let N.sub.x, N.sub.y and N.sub.z be the principal indices of
refraction for the X, Y and Z crystal axes and let L be the length
of the crystals along the light path. Also let d represent the
dimension of the crystals traverse to the longitudinal axis. Since
the crystals have a square cross section, the dimension d will
always be parallel to the Z axes of the respective crystals. Let
.lambda. be the wavelength of the incident radiation represented by
the light beam 1.
In passing through the crystal 10, along the X axis of that
crystal, the Y component of the polarization undergoes a phase
change of
.PHI..sub.y = (2 .pi. L)/(.lambda.) (N.sub.y) 1.
radians and the component parallel to the Z axis undergoes a phase
change of
.PHI..sub.z = (2 .pi. L)/(.lambda.)(N.sub.z) 2.
radians. The phase change resulting from the air gap between the
two crystals 2 and 3 is the same for each component and will be
expressed as a constant, .alpha. . In passing through crystal 11
along the Y axis of the latter, the X component of the polarization
undergoes a phase change of
.PHI..sub.x = (2 .pi. L)/(.lambda.)(N.sub.x) 3.
radians and the component parallel to the Z axis undergoes a phase
change of
.PHI..sub.z = (2 .pi. L)/(.lambda.)(N.sub.z) 4.
radians. The total phase change for the X and Y components in
passing through both crystals is
.theta..sub.x = .PHI..sub.x + .PHI..sub.z + .alpha. = (2 .pi.
L)/(.lambda.)(N.sub.x + N.sub.z) + .alpha. 5.
and
.theta..sub.y = .PHI..sub.y + .PHI..sub.z + .alpha. = (2 .pi.
L)/(.lambda.)(N.sub.y + N.sub.z) + .alpha. 6.
respectively. The phase difference between the two components
is
.DELTA..theta. = .theta..sub.x - .theta..sub.y = (2 .pi.
L/(.lambda.)[[N.sub.x + N.sub.z ] - (N.sub.y + N.sub.z)] 7.
This then becomes:
.DELTA..theta. = (2 .pi. L)/(.lambda.) [N.sub.x - N.sub.y ] 8.
If no electric field is applied to the Z-axes of the respective
crystals 10 and 11, the indices of refraction N.sub.x and N.sub.y
are equal, that is N.sub.x, that is N.sub.x = N.sub.y = N.sub.o.
The phase difference between the emerging perpendicular components
of each linearly polarized input ray, is then zero, that is,
(.DELTA..theta. = O) 9.
The original polarization of each incident light ray O and E is
preserved.
When an electric field is applied along the Z-axis of the two
respective crystals, that is, when electric potential is applied to
the electrodes 10a and 10b of crystal 10 and 27a and 27b of crystal
11, the index of refraction N.sub.x and the index of refraction
N.sub.y of the two crystals are no longer equal. But significantly,
the index of refraction N.sub.z along the Z axis of the crystal
remains unchanged. When the electric field is applied to these
crystals, one of the indices increases while the other decreases.
This may be represented as
N.sub.x = N.sub.o .+-. .DELTA.N 10.
and
N.sub.y = N.sub.o .-+. .DELTA.N 11.
where .DELTA.N is the change in index of refraction brought about
about by application of the electric field. It has been determined
by others that
.DELTA.N = (r.sub.63 V.sub.z N.sub.o 3)/(2d) 12.
Substituting the value of N.sub.x and N.sub.y in Equation 8
gives
.DELTA..theta. = (2 .pi. Lr.sub.63 V.sub.z N.sub.o)/(.lambda.d)
13.
where r.sub.63 is an electro-optic constant and where V.sub.z is a
voltage applied along the Z axis.
By the application of the proper voltage to the Z axes of the two
respective crystals 10 and 11 and the voltage being properly
related to the longitudinal and transverse dimensions of the
crystals, it is possible to cause the linear components of the
input light ray emerging from the right-hand end of the crystal 11
to have a .pi. radians phase difference, that is,
.DELTA..theta. =.pi.
In this latter condition, the incident ray 1 will have its plane of
polarization, indicated by vector 6, rotated 90.degree. when it
emerges from the right-hand end of crystal 11.
The required voltage to cause a 90.degree. rotation of the input
polarization ray may be determined by substituting the values
N.sub.x = N.sub.o + N and N.sub.y = N.sub.o - .DELTA.N in Equations
10 and 11, respectively, and the value of .DELTA..theta. =.pi. in
Equation 14 into Equation 8. Solving this, gives
V.sub.2 = (.lambda.d)/(2r.sub.63 N.sub.0 3L) 15.
The factor
(.lambda.)/(2r.sub.63 N.sub.o 3)
is called the half wave voltage, that is, the voltage necessary to
produce a .pi. radians phase displacement between the emergent
components of the incident ray, resulting in a 90.degree. change
between the polarization of the incident and emergent ray when an
electric field is applied parallel to the Z axis and when the light
is also parallel to the Z axis. It will be noted that the half-wave
voltage is a function of L/d and therefore the modulation voltage
can be adjusted within practical limits by selecting the desired
value for this ratio. Since it is possible to produce a
polarization rotation between the incident and emergent rays of
90.degree. by appropriate voltages, a complete light shutter effect
can be produced. It is obvious that modulation of light in a
continuous manner from a maximum to a minimum is possible.
Since the incident light energy is resolved into two orthogonal
components, each of which is restricted to a single light path that
includes only a single electro-optical crystal for operating on
that particular component the optical transmission losses are
reduced by a factor of two over those systems in which both
components must pass through both electro-optical crystals in
series.
* * * * *