U.S. patent application number 11/146319 was filed with the patent office on 2005-10-06 for optical switch.
This patent application is currently assigned to THOMAS SWAN AND CO. LTD.. Invention is credited to Crossland, William, Holmes, Melanie, Manolis, Ilias, Redmond, Maura, Robertson, Brian, Wilkinson, Timothy.
Application Number | 20050219457 11/146319 |
Document ID | / |
Family ID | 10862084 |
Filed Date | 2005-10-06 |
United States Patent
Application |
20050219457 |
Kind Code |
A1 |
Crossland, William ; et
al. |
October 6, 2005 |
Optical switch
Abstract
An optical switch uses a polarisation insensitive spatial light
modulator operation by a double pass through a liquid crystal cell.
The switch includes two such modulators in a cross bar arrangement.
Different embodiments employing techniques for reducing cross talk
are described.
Inventors: |
Crossland, William; (Harlow,
GB) ; Holmes, Melanie; (Woodbridge, GB) ;
Manolis, Ilias; (Olympia Hleias, GR) ; Wilkinson,
Timothy; (Cambridge, GB) ; Redmond, Maura;
(Cambridge, GB) ; Robertson, Brian; (Hove,
GB) |
Correspondence
Address: |
ALLSTON L. JONES
PETERS, VERNY, JONES, SCHMITT & ASTON L.L.P.
Suite 230
425 Sherman Avenue
Palo Alto
CA
94306
US
|
Assignee: |
THOMAS SWAN AND CO. LTD.
|
Family ID: |
10862084 |
Appl. No.: |
11/146319 |
Filed: |
June 2, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11146319 |
Jun 2, 2005 |
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10089929 |
Apr 3, 2002 |
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10089929 |
Apr 3, 2002 |
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PCT/GB00/03796 |
Oct 4, 2000 |
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Current U.S.
Class: |
349/196 |
Current CPC
Class: |
G02F 1/1393 20130101;
G03H 1/02 20130101; G02F 1/141 20130101; G03H 2223/20 20130101;
G03H 2001/306 20130101; G03H 2223/19 20130101; G03H 2222/31
20130101; G03H 2222/32 20130101; G02F 2203/02 20130101; G03H
2001/0224 20130101; G03H 2001/0825 20130101; H04Q 2213/1319
20130101; H04Q 2213/1301 20130101; G03H 2225/22 20130101; G02F 1/31
20130101; G03H 2222/34 20130101; G03H 2225/32 20130101; G02B 6/264
20130101; G03H 1/08 20130101; G02F 1/136277 20130101; G02F 2203/50
20130101; G02B 6/32 20130101; G03H 2210/20 20130101; G03H 2001/261
20130101; G03H 1/2294 20130101; G03H 1/0005 20130101; G03H 2225/52
20130101; G02B 5/32 20130101; G03H 2240/41 20130101; G02F 2203/12
20130101; G03H 2001/085 20130101; G03H 2227/03 20130101; G02F
1/133638 20210101; G02F 1/1395 20130101; G03H 2001/221
20130101 |
Class at
Publication: |
349/196 |
International
Class: |
G02F 001/13 |
Foreign Application Data
Date |
Code |
Application Number |
Oct 4, 1999 |
GB |
9923428.8 |
Claims
1-30. (canceled)
31. A reflective liquid crystal spatial light modulator comprising
a transparent conductive layer, and a two dimensional array of
pixels comprising a plurality of pixels; each pixel having a
respective single reflective electrode, the reflective liquid
crystal spatial light modulator further comprising a quarter wave
plate disposed on the reflective electrodes, a liquid crystal layer
disposed over the quarter wave-plate, and a transparent conductive
layer over the liquid crystal layer, wherein the transparent
conductive layer forms a common electrode to said array.
32. The reflective liquid crystal spatial light modulator of claim
31, wherein said liquid crystal layer is a nematic liquid crystal
layer.
33. The reflective liquid crystal spatial light modulator of claim
31, wherein said liquid crystal layer is a n-cell.
34. An integrated spatial light modulator for light of a
predetermined wavelength, the integrated spatial light modulator
comprising: a transparent common electrode, a plurality of
reflective electrodes, a retardance layer having an optical
retardance of an odd integer number of quarter-waves of said
predetermined wavelength, the retardance layer being disposed on
the plurality of reflective electrodes; and a liquid crystal layer,
wherein the liquid crystal layer is disposed between the retardance
layer and the transparent common electrode, wherein the liquid
crystal layer is disposed and configured to provide out-of-plane
tilt in response to voltage applied across the liquid crystal layer
between the reflective electrodes and the transparent common
electrode; wherein the reflective electrodes are reflective pixel
electrodes disposed in a regular two-dimensional array.
35. The integrated spatial light modulator of claim 34, wherein
said liquid crystal layer is a nematic liquid crystal layer.
36. The integrated spatial light modulator of claim 34, wherein
said liquid crystal layer is a n-cell.
37. The integrated spatial light modulator of claim 34 further
comprising voltage application circuitry for applying desired
voltages across the liquid crystal layer whereby the liquid crystal
layer has desired values of out of plane tilt; the arrangement
being such that application of voltage to each electrode causes a
respective portion of the liquid crystal layer associated with a
respective reflective pixel electrode to have a specific value of
said out-of-plane tilt; and wherein the voltage application
circuitry is adapted to apply voltages to said two dimensional
pixel array for two-dimensionally steering light incident upon said
modulator.
38. A method of routing a light beam incident on an array of phase
modulating elements, the light beam having a first component
polarized in a first direction and a second component polarized in
a second direction orthogonal to the first, the method comprising:
a) providing an integrated spatial light modulator comprising a
liquid crystal layer, a wave plate layer having an optical
retardance of (2n+1) .lambda./4, a transparent conductive layer,
and a reflector layer, the liquid crystal being responsive to a
variation in a drive voltage to provide a variation in out-of-plane
director angle tilt, the spatial light modulator having: a two
dimensional array of pixels; and an array of electrodes wherein
each electrode is associated with a respective pixel of the
integrated spatial light modulator and a respective portion of the
liquid crystal layer to define a said phase modulating element
whereby the spatial light modulator comprises a said array of phase
modulating elements; b) applying respective drive voltages to each
said electrode whereby the portion of liquid crystal associated
with the electrode has a respective specific value of director
angle tilt; c) applying said beam to the integrated spatial light
modulator whereby the first and second components each pass through
the liquid crystal layer and the wave plate layer, and are
reflected at the reflector layer to again pass through the wave
plate layer and liquid crystal layer to emerge with both components
phase modulated by the same amount; and d) controlling the drive
voltages to vary a deflection direction of said light beam due to
said array of phase modulating elements.
39. An optical switch comprising an integrated spatial light
modulator for light of a predetermined wavelength, the integrated
spatial light modulator comprising: a transparent conductive layer,
a plurality of reflective pixel electrodes, said reflective pixel
electrodes being disposed in a regular two-dimensional array; a
retardance layer having an optical retardance of an odd integer
number of quarter-waves of said predetermined wavelength, the
retardance layer being disposed on the regular two-dimensional
pixel array; and a liquid crystal layer being disposed between the
retardance layer and the transparent conductive layer.
40. The switch of claim 39, wherein said liquid crystal layer is a
nematic crystal layer.
41. The switch of claim 40, wherein said liquid crystal layer is a
n-cell.
Description
FIELD OF THE INVENTION
[0001] The invention relates to the general field of optical
switching and more particularly to optical switching using
multiphase or continuous phase hologram devices.
BACKGROUND OF THE INVENTION
[0002] Optical fibre switching components are fundamental to modern
global information systems. Single-stage matrix switches operating
independently of the optical bit-rate and modulation formats,
capable of reconfigurably interconnecting N optical inputs to M
optical outputs (where N and M are generally, but not necessarily
the same number), are particularly attractive. Many switches for
achieving the required switching are limited in functional size to
less than 64.times.64, and/or suffer from relatively poor noise
performance. One method which provides good noise performance and
is potentially more scalable than other optical switch technologies
is to use reconfigurable holograms as elements for deflecting
optical beams between arrays of optical inputs and optical
outputs.
[0003] A known holographic optical switch, otherwise known as an
optical shuffle, is shown in FIG. 1.
[0004] In FIG. 1, an array of optical sources 1 and an array of
optical receivers 7 are arranged as the inputs and outputs of a
holographic switch. For many applications, the sources and
receivers may comprise cleaved or end-polished fibres. In other
applications, the inputs may be light emitting sources such as
lasers or LEDs, and the outputs may be photo-detectors. Each input
1 may transmit a different digital or analog optical signal through
the switch to one (or possibly several) of the outputs 7. Thus up
to N different inputs may be simultaneously passing through the
switch at any instant. Each input may consist of a
single-wavelength modulated by data; a number of different data
sources operating at different wavelengths (e.g. a
wavelength-multiplexed system); or a continuum of wavelengths.
Although the switch is shown in cross-section in FIG. 1, the input
& output arrays 1, 7 are typically 2-dimensional arrays, and
the holographic switch occupies a 3-dimensional volume.
[0005] To achieve switching, the input array 1 is arranged behind a
first lens array 2. Each optical signal emitted by the input array
enters free-space, where it is collimated by one of the lenses in
first lens array 2. Each collimated beam then passes through a
first hologram display device 3. The first hologram display device
3 displays a holographic pattern of phase and/or intensity and/or
birefringence which has been designed to produce a specific
deflection of the optical propagation directions of the beams
incident upon the device. The hologram pattern may also be designed
such that each optical beam experiences a different angle of
deflection. The first hologram display device 3 may also have the
effect of splitting an individual beam into several different
angles or diffraction orders. One application for utilising this
power splitting effect is to route an input port to more than one
output port.
[0006] The deflected optical signals propagate in free-space across
an interconnect region 4 until they reach a second hologram device
5. The hologram pattern at second hologram device 5 is designed in
such a way to reverse the deflections introduced at the first
hologram display device 3 so that the emerging signal beams are
parallel with the system optic axis again.
[0007] The optical signals then pass through a second lens array 6
where each lens focuses its associated optical signal into the
output ports of a receiver array 7. Thus the hologram pattern
displayed on first hologram display device 3 and the associated
"inverse" hologram pattern displayed on second hologram display
device 5 determine which output fibre or fibres 7 receive optical
data from which input fibre or fibres 1. The interconnect region 4
allows the signal beams to spatially reorder in a manner determined
by the specific hologram patterns displayed on the first 3 and
second 5 hologram display devices. The switch also operates
reversibly such that outputs 7 may transmit optical signals back to
the inputs 1.
[0008] The system shown in FIG. 1 (and functionally equivalent
configurations utilising planes of symmetry within the switch
optics) is well known as a method for static optical shuffle, using
fixed hologram recordings as first 3 and second 5 hologram display
devices whereby the input signals are "hard-wired" to specific
outputs.
[0009] It has been proposed to extend the optical shuffle of FIG. 1
to provide a reconfigurable switch by displaying hologram patterns
on a spatial light modulator (SLM). There are however a number of
practical design problems associated with the migration from a
static optical shuffle to a reconfigurable switch. Among these are
the following:
[0010] 1) Known SLMs, using a ferroelectric liquid crystal provide
binary phase modulation and such phase modulation can be
[0011] 2) polarisation-insensitive. However, the maximum
theoretical diffraction efficiency for a binary phase device is
only 40.5%. For example, the architecture shown in FIG. 1 uses two
SLM devices, and hence the maximum net diffraction efficiency of
this system is 16.4%. The diffraction efficiency of holographic
system would be improved significantly by using multiple phase
modulation. For many applications this multiple phase modulation
must be polarisation-insensitive. It is desirable that the phase
may be varied continuously between 0 and (at least) 2.pi..
[0012] 3) In order to implement a holographic switch using two
SLMs, an appropriate set of hologram patterns must be chosen. This
hologram set must be capable of routing any input channel to any
input channel whilst keeping the crosstalk figures within specified
values. In particular, the hologram set must be optimised to
prevent beams associated with unwanted diffraction orders from
being launched down the wrong channel. Increasing the number of
phase levels tends to result in a decrease in the strength of the
unwanted diffraction orders.
[0013] 4) A convenient method of constructing reconfigurable
holograms for use within an N.times.N switch would be to integrate
a layer of liquid crystal material above a silicon circuit. This
type of SLM typically operates in reflection rather than
transmission, and the switch layout shown in FIG. 1 is therefore no
longer appropriate.
[0014] Accordingly the present invention aims to address at least
some of these issues.
SUMMERY OF THE INVENTION
[0015] According to a first aspect of the invention there is
provided a switch comprising an integrated spatial light modulator
for receiving light of a predetermined wavelength, the modulator
comprising a liquid crystal layer spaced from a second layer by a
layer having an optical retardance of an odd integer number of
quarter-waves of said wavelength, wherein the second layer is
reflective of said light of said wavelength.
[0016] In one embodiment said liquid crystal layer is a nematic
crystal layer.
[0017] In another said liquid crystal layer is a .pi.-cell.
[0018] Preferably the second layer is a metallic layer.
[0019] Advantageously the metallic layer is of Aluminium.
[0020] Conveniently said wavelength is 1.57 .mu.m
[0021] According to a second aspect of the invention there is
provided a switch comprising an integrated spatial light modulator
for receiving light of a predetermined wavelength, the modulator
comprising a liquid crystal cell having a pair of opposed and
mutually substantially parallel end plates disposed substantially
parallel to an axial plane, and spaced apart by a liquid crystal
layer providing a director angle tilt in a tilt plane substantially
orthogonal to said axial plane, said liquid crystal being spaced
from a second layer by an optical layer having a retardance of an
odd integer number of quarter-waves of said wavelength, wherein the
second layer is reflective of said light of said wavelength, and
the optical layer being disposed with respect to said tilt plane
such that light polarised in said tilt plane returns through said
liquid crystal layer polarised substantially orthogonal to said
tilt plane.
[0022] Preferably said liquid crystal layer is a nematic crystal
layer.
[0023] Alternatively said liquid crystal layer is a .pi.-cell.
[0024] Preferably the second layer is a metallic layer.
[0025] Conveniently the metallic layer is of Aluminium.
[0026] Advantageously the modulator has a glass cover disposed over
said liquid crystal layer, and the metallic layer has a connection
to driving circuitry for switching the modulator.
[0027] According to another aspect of the invention there is
provided a method of switching a light beam having a first
component polarised in a first direction and a second component
polarised in a second direction orthogonal to the first, the method
comprising providing a device having a liquid crystal layer and an
optical retardance, the liquid crystal being responsive to a
variable drive voltage to provide a corresponding variation in
director angle tilt; and further comprising: applying a variable
drive voltage to said liquid crystal device; applying said beam to
said liquid crystal device to provide an intermediate beam having a
variable phase delay applied to said first component and an at
least substantially fixed phase delay to said second component; by
said retardance, rotating the polarisation of said intermediate
beam; applying the resultant light to said liquid crystal device
whereby a component of said resultant light polarised in said first
direction receives said variable phase delay and a component of
said resultant light polarised in said second direction receives
said at least substantially fixed phase delay.
[0028] Preferably the rotating step comprises rotating said
polarisation through 90 degrees whereby at least substantially
equal amounts of variable phase delay are applied to each of said
first and second components.
[0029] Advantageously the rotating step comprises a step of
reflecting said intermediate beam back along its incoming path.
[0030] According to yet another aspect of the invention there is
provided an optical switch comprising a plurality of input optical
fibres for providing plural input light beams, a plurality of
optical receivers for receiving output light beams, a first and a
second reflective spatial light modulator, and drive circuitry for
forming a respective plurality of switching holograms on each
spatial light modulator, said holograms being selected to couple
each said input optical source to a respective desired optical
receiver, wherein each spatial light modulator incorporates a
liquid crystal device for modulating the phase of light travelling
through said liquid crystal device, a reflector device for
returning light back through said liquid crystal device and a
device, disposed between said liquid crystal device and said
reflector device, for rotating the polarisation of light by 90
degrees, wherein the optical switch has an axis of symmetry and the
spatial light modulators are disposed on opposite sides of said
axis, each said switching hologram on said first spatial light
modulator being operative to deflect said input light beams to said
switching holograms on said second spatial light modulator and each
said switching hologram on said second spatial light modulator
being operative to deflect said light beams to a respective optical
receiver.
[0031] Preferably each said input optical fibre is directed towards
a respective switching hologram on said first spatial light
modulator, and each said optical receiver comprises an output
optical fibre, wherein each output optical fibre is directed
towards a respective switching hologram on said second spatial
light modulator.
[0032] In one embodiment the first and second spatial light
modulators are disposed such that a respective zero-order beam
reflected from each switching hologram on said first spatial light
modulator is incident on a respective switching hologram on said
second spatial light modulator.
[0033] Preferably a half wave plate is disposed between said first
and second spatial light modulators.
[0034] Alternatively the switching holograms are spaced apart on
said first and second spatial light modulators and the first and
second spatial light modulators are disposed such that a respective
zero-order beam reflected from each switching hologram on said
first spatial light modulator is incident on a spacing between two
adjacent switching holograms on said second spatial light
modulator.
[0035] Advantageously a half wave plate is disposed between said
first and second spatial light modulators.
[0036] Conveniently the switch further comprises respective optical
systems disposed between said input fibres and said first spatial
light modulator and between said output fibres and said second
spatial light modulator, wherein each said optical system comprises
two confocal lenses, the input and output fibres being disposed in
respective planes and a focal plane of a first lens of each optical
system coinciding with the plane of the associated fibres.
[0037] Preferably the input and output fibres are disposed in
respective planes and the optical switch further comprises
respective arrays of microlenses, said microlenses being disposed
in front of each fibre plane such that each microlens corresponds
to a respective fibre, and respective optical systems disposed
between said input fibres and said first spatial light modulator
and between said output fibres and said second spatial light
modulator, wherein each said optical system comprises two confocal
lenses, and a focal plane of a first lens of each optical system
coinciding with the output focal plane of the associated microlens
array.
[0038] Advantageously said optical fibres are thermally expanded
core (TEC) fibres.
[0039] In another embodiment the first and second spatial light
modulators are mutually offset so that no zero order beams from the
first spatial light modulator is incident on the second spatial
light modulator.
[0040] Conveniently at least one optical receiving element is
disposed in a region receiving said zero-order beams from said
first spatial light modulator, whereby input signal may be
monitored.
[0041] Advantageously, the or each element is a fibre.
Alternatively other elements such as receiver diodes could be
used.
[0042] Preferably each switching hologram provides a repeating
pattern on its spatial light modulator, whereby the repeating
patterns on the two SLMs satisfy the relation:
.theta..sub.2(u)=.theta..sub.1(-u)
[0043] where .theta..sub.2(u) is the repeating pattern on the
second SLM and .theta..sub.1(-u) is the repeating pattern on the
first SLM, and the angle of incidence is such that the Poynting
vector of the input light beam incident on the first SLM, and of
the light beams leaving the second SLM, is in the plane of tilt of
the director.
[0044] In a preferred embodiment, the output fibres are secured
together in an array by a glue containing black pigment to
attenuate misaligned light.
[0045] In another preferred embodiment, the output fibres are
secured together to form an array and the spacing between the
fibres of the array is occupied by interstitial fibres which serve
to accept and guide away cross talk from the switching zone.
BRIEF DESCRIPTION OF THE DRAWINGS
[0046] Non-limiting embodiments of the invention will now be
described with reference to the accompanying drawings, in
which:
[0047] FIG. 1 shows a prior art optical switch useful in
understanding the present invention;
[0048] FIG. 2 is a schematic diagram showing the propagation of a
planar wave front through a uniaxial liquid crystal device;
[0049] FIG. 3 shows the use of a quarter-wave plate, and
illustrates the polarisation states of an input field in a
double-pass reflective system;
[0050] FIG. 4 shows a schematic cross-sectional view of a first
embodiment of a SLM with integral quarter-wave plate;
[0051] FIG. 5 shows a schematic cross-sectional view of a second
embodiment of a SLM with integral quarter-wave plate;
[0052] FIG. 6 shows an overview of an exemplary silicon back plate
layout for the device of FIG. 5;
[0053] FIG. 7 shows a schematic diagram of a pi cell for use in the
invention;
[0054] FIG. 8 shows a partial layout diagram of a first embodiment
of an optical switch using two reflective SLMs, in accordance with
the invention;
[0055] FIG. 9 shows a schematic diagram of a part of a first
optical system useable in the switch of FIG. 8;
[0056] FIG. 10 shows a schematic diagram of a part of a second
optical system including a microlens array, useable in the switch
of FIG. 8;
[0057] FIG. 11 shows the effects of zero-order cross talk in the
device of FIG. 8;
[0058] FIG. 12 shows a partial layout diagram of a second
embodiment of an optical switch in accordance with the invention,
being a modification of FIG. 8 to include a half wave plate in the
optical path between the two SLMs;
[0059] FIG. 13 shows a partial layout diagram of a third embodiment
of an optical switch in accordance with the invention, being a
modification of FIG. 8 having the output SLM offset laterally to
reduce cross talk.
[0060] FIG. 14 shows a fourth embodiment in which the output SLM is
offset transversally to avoid cross talk;
[0061] FIG. 15 shows propagation conditions inside the liquid
crystal; and
[0062] FIG. 16 shows the differing propagation conditions inside
the input and output SLMs.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0063] In the various figures, like reference signs indicate like
parts.
[0064] FIG. 2 shows the propagation of a planar wave front 100,
travelling along the z-direction through a layer of uniaxial liquid
crystal cell 101 of uniform alignment. The cell comprises a front
plate 102 and a rear plate 103 sandwiching the liquid crystal 104.
The optical axis 105, later also referred to herein as a director
axis of the uniaxial medium has been taken in the general case to
tilt away from the x-direction by an angle .theta. on to the plane
xOz. The tilt angle .theta. is electrically controllable by a
voltage applied across the liquid crystal cell 101. The two
propagation modes travel along the z-direction with different
velocities: these may be calculated using a geometric construction
in which an ellipsoid is drawn with a long axis of length
n.sub..theta.parallel to the director. For a uniaxial medium the
other two axes of the ellipsoid have equal lengths (n.sub.0). A
plane is constructed perpendicular to the Poynting vector (in this
case the plane is parallel to the xOy plane). The intersection of
this plane with the ellipsoid defines an ellipse 110. The
directions of the major and minor axes 111, 112 of this ellipse
define the two orthogonal polarisation modes, while the lengths of
these two axes define the refractive index experienced by the
corresponding mode. For a tilt in the xOz plane, the minor axis of
this ellipse is parallel to the y direction, and the major axis is
therefore parallel to the x direction, for all values of .theta..
Hence, for any .theta., the x and y directions are parallel to the
polarisation modes, so that the components of incident light
polarised in these directions will remain in these directions on
propagation through the liquid crystal. This remains true even if
the tilt angle .theta. is changing inside the medium.
[0065] The length of the minor axis 112 is n.sub.0, for all values
of .theta.. Hence the component of the field that is parallel to
the y-axis experiences refractive index n.sub.o whatever the tilt
angle .theta. is, and therefore the phase delay caused to it by the
cell is independent of the voltage across it (ordinary wave). On
the contrary, the length of the major axis does depend on the tilt
angle .theta., and so the x-component of the field (extraordinary
wave) experiences different refractive index n for different values
of the tilt angle.
[0066] The length of the major axis 111 is n(.theta.), and is given
by equation (1): 1 1 n 2 ( ) = cos 2 ( ) n o 2 + sin 2 ( ) n e 2 (
1 )
[0067] It follows that n.sub.0.ltoreq.n(.theta.).ltoreq.n.sub.e.
The relative phase delay between the two components is then given
by the equation (2):
.DELTA..phi.=k.sub.0d.DELTA.n (2)
[0068] In equation (2), d is the thickness of the liquid crystal
cell, k.sub.0 the wavenumber of the field in free space and
.DELTA.n is given by .DELTA.n=n(.theta.)-n.sub.o. Since .DELTA.n is
a function of the voltage across the cell, equation (2) shows that
the applied voltage can continuously control the phase difference
between the two components across the cell.
[0069] It will be understood by those skilled in the art that it is
desirable to provide phase modulation that is not sensitive to
polarisation, and devices and methods for achieving this will now
be described for the situation of normally incident light:
[0070] Expression (3) shows a mathematical representation of an
arbitrary polarisation state as the superposition of two
orthogonal, linearly polarised waves: 2 E IN ( x , y , z , t ) = (
E 0 X ( t ) exp j x ( t ) E 0 Y ( t ) exp j Y ( t ) ) exp j ( kz -
t ) ( 3 )
[0071] where the amplitudes, E.sub.0Y(t) and E.sub.0X(t), and
phases .epsilon..sub.X(t) and .epsilon..sub.Y(t) vary slowly,
remaining essentially constant over a large number of oscillations.
For unpolarised light the relative amplitude,
E.sub.0Y(t)/E.sub.0X(t) and relative phase,
.epsilon..sub.Y(t)-.epsilon..sub.X(t), vary rapidly compared to the
coherence time of each linearly polarised component, i.e. the two
waves are mutually incoherent. For randomly polarised light the
relative amplitude and phases vary slowly with respect to the
coherence time, i.e. the two waves are mutually coherent. Hence the
above representation is valid for any light wave.
[0072] Such light could be modulated by applying the same phase
delay to both of these components. However, the configuration in
FIG. 2, allows just one of the two components (x-component) to be
properly phase-modulated since the y-component always gains the
same phase delay.
[0073] FIG. 3 shows a schematic diagram of a configuration that
would allow for both components to be modulated. Referring to FIG.
3, light is reflected from a mirror 30 after passing through a
liquid crystal cell 32 to enable a double-pass configuration. In
between the two passes a suitable rotator 31 is introduced, which
rotates both components through 90.degree.. As is known to those
skilled in the art, a quarter-wave plate acts to retard one
polarisation component of light relative to the orthogonally
polarised component; thus the combination of a quarter-wave plate
(with an optical axis tilted out of the plane Oxz by 45.degree.)
and a mirror acts as a 90.degree. rotator. It would of course be
possible to use a 3/4, {fraction (5/4)} etc-wave plate, the
criterion being an odd-integer number of quarter waves, so that a
double pass produces the overall 90.degree. rotation. Consider
light with an arbitrary polarisation state (as in expression 3) at
normal incidence passing through the configuration shown in FIG. 3.
Differences for off-normal incidence will be considered later.
[0074] For the first pass, on the way towards the quarter wave
plate and mirror, the polarisation component polarised in the
xdirection (E.sub.0X(t) exp j .epsilon..sub.X(t)) experiences a
refractive index n(.theta.), where .theta. depends on the applied
voltage, while the component in the y direction (E.sub.0Y(t) exp j
.epsilon..sub.Y(t)) does not, and instead experiences a refractive
index, n.sub.0, that is independent of the applied voltage. The
orientation of the quarter wave plate is such that these two
polarisation components are exchanged. For the 2.sup.nd pass, on
returning back through the liquid crystal, the component
E.sub.0X(t) exp j .epsilon..sub.X(t)) is now polarised in the y
direction, and therefore experiences a refractive index n.sub.0,
while the component E.sub.0Y(t) exp j .epsilon..sub.Y(t) is now
polarised in the x direction, and experiences a refractive index
n(.theta.). In this way both components gain overall the same
amount of phase delay through the system since they both experience
one pass under a refractive index n(.theta.) and one pass under a
refractive index n.sub.O.
[0075] In particular (equations 4 and 5):
E.sub.OX component:
.DELTA..phi..sub.OX=.DELTA..phi..sub.1ST-PASS+.DELTA..-
phi..sub.2ND-PASS=kn(.theta.)d+kn.sub.0d (4)
E.sub.OY component:
.DELTA..phi..sub.OY=.DELTA..phi..sub.1ST-PASS+.DELTA..-
phi..sub.2ND-PASS=kn.sub.0d+kn(.theta.)d (5)
[0076] The system may be described mathematically (equation 6) in
terms of Jones matrices, with the result that (as expected): 3 E
OUT ( x , y , z , t ) = ( 0 exp jkd ( n 0 + n ( ) ) exp jkd ( n 0 +
n ( ) ) 0 ) ( E 0 X ( t ) exp j x ( t ) E 0 Y ( t ) exp j Y ( t ) )
exp j ( kz - t ) = ( E 0 Y ( t ) exp j { Y ( t ) + kd ( n 0 + n ( )
) } E 0 X ( t ) exp j { x ( t ) + kd ( n 0 + n ( ) ) } ) exp j ( kz
- t ) ( 6 )
[0077] It should however be noted that the light exits the system
in the opposite orthogonal state. This Jones matrix result uses the
convention that the y-axis is inverted on reflection from the
mirror. The mathematical result confirms that both components of
the output light have the same phase change (in agreement with
equation 4 and 5) and therefore polarisation insensitive phase
modulation is feasible.
[0078] In general .theta. may vary with z, in which case the index
n(.theta.) in (6) should be replaced by (expression 7): 4 n ( )
-> 1 d z = 0 d n ( ( z ) ) z ( 7 )
[0079] The foregoing principle can be applied to an array of
modulating elements. A plane wave front of arbitrarily polarised
light, which normally impinges on to such an array of pixels, each
of which is characterised by a specific value of tilt angle (by the
application of different voltages across it), or a specific
distribution of tilt angles, can be spatially phase modulated.
[0080] Referring now to FIG. 4, a first embodiment of an integrated
spatial light modulator in accordance with the invention will now
be described:
[0081] AS seen in FIG. 4, the SLM consists of an aluminium pad 120,
which forms a pixel array, and is connected to pixel driving
circuitry by a connection figuratively shown at 126. On the pixel
array 120 there is disposed a quarter-wave plate 121. On the
quarter-wave plate, and over an intervening alignment layer, (not
shown) there is disposed a liquid crystal layer 122--here a nematic
liquid crystal is used, but the invention is not so limited. The
actual requirement is the ability to provide an out of plane tilt.
On the liquid crystal layer there is an alignment layer 123, as
known to those skilled in the art, and over the alignment layer
there is disposed a transparent conductive layer 124 such as an ITO
(Indium Tin Oxide) layer forming a common electrode plane, and an
upper glass layer 125.
[0082] The quarter-wave plate can be deposited on the pixel array
by spin-coating a proper reactive monomer, which can be polymerised
by exposure to ultraviolet light. In the cell of FIG. 4, the
aluminium pad acts as a mirror and also provides the necessary
power voltage across the cell for the liquid crystal 122 to
switch.
[0083] A second embodiment is shown in FIG. 5.
[0084] Referring to FIG. 5, a pixel array 130 is integrated on a
silicon-1.5 .mu.m-transparent backplane structure 131, and is
sandwiched between the backplane structure and one face of a liquid
crystal layer 132. The other side of the liquid crystal layer 132
is in contact with an alignment layer 133, which in turn is covered
by an ITO layer 134. A quarter wave-plate 135 is disposed between a
front aluminium mirror 136 and the ITO electrode 134. The thickness
of the quarter wave plate may be adjusted by spin-coating
techniques so that in reflection it functions as a half-wave plate
at .lambda.=1.57 .mu.m.
[0085] An embodiment of a spatial light modulator in accordance
with FIG. 5 was constructed. The pixels were constructed using the
polysilicon layer of a conventional 2 .mu.m CMOS process. FIG. 6
shows an overview of the silicon backplane layout.
[0086] Referring to FIG. 7 a further embodiment of the invention
uses a twisted nematic liquid crystal mixture in a .pi.-cell
configuration, again using a quarter-wave plate. Such a device
enables reduced liquid crystal response time. In such cells the
director of the nematic liquid crystal twists along the thickness
of the cell through an angle. FIG. 7A shows the director angle as a
series of illustrative lines 50-56 across the cell thickness, with
the cell in the unbiased state. FIGS. &B shows the other
extreme condition with maximum bias, with the directors forming a
straight line between the front and rear plates. In a pi cell flow
of material within the cell during the switching process is
minimised and the response time decreases. Given that the thickness
of the cell is large enough so that the field can be actually
wave-guided through it, the same principle of FIG. 2 applies and
the cell can give fast, polarisation insensitive switching.
[0087] Although the above discussions are in the context of an
integral retarder, it is also possible to use a non-integral
retarder, such as a non-integral quarter wave plate. The following
description is not therefore limited to an integral quarter wave
plate.
[0088] Referring now to FIG. 8, a first partial diagram of an
embodiment of a reflective switch uses a first, or input SLM 140
and a second, or output SLM 141, each divided into a set of blocks
(or holograms), and disposed spaced apart and generally parallel to
and on opposite sides of an axis of symmetry 142. The two SLMs face
the axis 142, and are spaced along it. An input fibre array 143
having an input fibre FC is directed towards the first SLM 140, and
is disposed such that light from the fibres in the array are
incident upon the input SLM at an angle .theta..sub.in to a plane
normal to the plane of the SLM. An output fibre array 144 having an
output fibre fB is similarly directed with respect to the output
SLM 141. Thus light describes a generally zigzag path from the
input fibres of the input array, to the first SLM 140, then to the
second opposing output SLM 141 and finally to a fibre of the output
array 144. As discussed above, each SLM displays plural holograms,
and the disposition of the system is such that for the input SLM
140, each hologram is associated with a particular input fibre,
while for the output SLM 141, each hologram is associated with a
particular output fibre.
[0089] Routing from input fibre fC to output fibre fB is achieved
by configuring input hologram hC to deflect the input beam to
output hologram hB, so that the angle of reflection typically
differs from the incident angle .theta..sub.in. Output hologram hB
deflects the beam incident on it to output fibre fB. In between
each hologram and its corresponding fibre there is an optical
system, embodiments of which are described later herein, that has
the function of presenting beams of appropriate diameter to the
hologram.
[0090] In order to minimise the system losses, it is desirable to
have as few lenses as possible in the optical system. A first
optical system, for use with the switch of FIG. 9, is shown in FIG.
9. Referring to FIG. 9, the optical system has a first 150 and a
second 151 confocal lens in a telescopic arrangement. The system
has the fibre array 143 to the left, as shown, of the first lens
150, and the SLM 140 on the right of the second lens 151. The focal
length f.sub.1 of the first lens 150 is shorter than the focal
length f.sub.2 of the second lens 151. The fibre array 143 is
positioned at the input focal plane of the first lens 150, while
the output focal plane of the second lens 151 is approximately
midway between the hologram devices 140, 141 (see FIG. 8). The same
system would be used at both input and output to the switch. Under
certain circumstances, as will be clear to those skilled in art, a
field flattening lens may be required.
[0091] In a co pending patent application an embodiment using
reflective SLMs has the beam passing twice through a lens
(off-axis) positioned immediately in front of the SLM.
[0092] The system of FIG. 9 has a relatively low wavelength range.
However, a number of measures can be used to improve the wavelength
range. These include:
[0093] use of fibres with a larger spot-size, such as TEC
(Thermally Expanded Core) fibres:
[0094] use of fibres with a narrower diameter thus allowing closer
packing; and
[0095] use of a microlens array after the fibre array, so that the
focused spots leaving the microlens array are in the input focal
plane of the lens of lower focal length (see FIG. 10 in which a
microlens array 153 having focal length f.sub.m is between the lens
150 and the input fibre array 143. The input microlens array 153 is
disposed with respect to the input fibres so as to focus light from
those fibres to the focal plane of the lens 150).
[0096] An advantageous option is to use both a microlens array and
larger spot-size fibres in the fibre array.
[0097] As will be clear to those skilled in the art, the required
number of pixels in each row of the hologram, M, may be calculated
using the beam spot size of the hologram and the maximum beam
steering angle, and the cross talk requirement.
[0098] The requirements of optimum performance suggest the use of
either standard fibres with a microlens array or fibres with larger
than standard spot size.
[0099] As known to those skilled in the art, a quarter-wave plate
will only work perfectly for one particular wavelength, giving rise
to errors at other wavelengths. Deviations from the theoretical
also result from fabrication tolerances in the quarter-wave plate
thickness and birefringence, and from misalignments between the
plate orientation and the plane of tilt of the liquid crystal.
[0100] It can be shown that these effects produce zero-order (i.e.
undiffracted) polarisation-dependent crosstalk in a switch
configuration due to the component of incident light in the y
polarisation direction.
[0101] For incident light polarised in the x direction, it can be
shown that the result of the errors is to produce a diffraction
order at twice the angle of the intended main diffraction order.
The amplitude of this doubled-order crosstalk varies with the
polarisation state of the input light, and hence the effect is to
generate polarisation-dependent crosstalk.
[0102] Reference to FIG. 8 shows that the input and output
holograms deflect the beam in opposite directions. As known,
maximal wavelength range is achieved when angular deflection is
equal and opposite. The consequence is that, with the SLMs parallel
as shown, the beams travelling from the input fibres to the input
holograms are parallel to the beams travelling from the output
holograms to the output fibres.
[0103] As the hologram array is regular, such that the set of tilt
angles is quantised into units of Mp/L, where M is the number of
pixels in each row of the hologram, p is the pixel pitch, and L is
the distance between the holograms, therefore to route to a fibre
n.sub.X along in the x direction, and n.sub.y along in the y
direction, the beam deflection at the input hologram is given by
equation 8: 5 ( sin X ) = n X Mp L and ( sin Y ) = n Y Mp L ( 8
)
[0104] Also the beam deflection at the output hologram is (equation
9): 6 ( sin X ) = - n X Mp L and ( sin Y ) = - n Y Mp L ( 9 )
[0105] Referring now to FIG. 11, the output SLM 141 is arranged
such that the zero-order beam reflected from the centre of any
hologram on the input SLM 140 is incident on the centre of an
output hologram of the output SLM 141. This is the configuration
that maximises the wavelength range. For example, the zero-order
reflection from hologram hA is incident on the centre of hologram
hB.
[0106] The effect of the quarter-wave plate tolerances is to route
a beam 145 of amplitude a.sub.yy from hologram hA on input SLM 140
to hologram hB on output SLM 141, where a.sub.YY is the fraction of
incident light polarised in the y direction which remains in that
state after transition through the first SLM 140. Analogous effects
at the second SLM 141 cause a beam 146 of net amplitude of up to
(a.sub.YY).sup.2 to pass into the zero-order output from hologram
hB. As a result of the system geometry, the zero-order beam 146
reaches output fibre fC. Hence the effect of the y polarised light
that remains in this polarisation state is to cause crosstalk in
fibre fC of maximum amplitude (a.sub.YY).sup.2 from the signal
entering the switch at fibre fA. The remainder of the light from
hologram hA directed to hologram hB has amplitude
a.sub.YY(1-a.sub.YY). This light will be subject to the intended
deflection angle introduced by hologram hB, and will form a light
beam 147. Let the distance in hologram units between holograms hA
and hC on first, input SLM 140 be (d.sub.X,d.sub.Y). What happens
next depends on the design of the system. For the basic system
(microlens-free system), the beam will enter output fibre fC at a
tilt angle. The system may be designed such that this light (of
maximum amplitude a.sub.YY(1.times.a.sub.YY)) is partially
attenuated by the limited angular acceptance of the output fibre
(or offset acceptance, depending on the optical architecture). It
may be shown that the attenuation, .alpha..sub.TILT, due to this
tilt is given by equation 10: 7 TILT = ( d X 2 + d Y 2 ) T where T
= - 5 C 2 log 10 e 1 - ( C / s ) 2 ( 10 )
[0107] where C is the clipping parameter at the hologram, such that
Mp=C..omega..sub.HOL, where .omega..sub.HOL is the beam spot-size
at the hologram. With a switch configured for maximum wavelength
range, the worst-case value of d.sub.X.sup.2+d.sub.Y.sup.2 is
unity. To improve crosstalk suppression, .alpha..sub.TILT should be
as high as possible: thus performance is improved by increasing the
value of the ratio of the spot-size to the fibre separation.
[0108] Referring to FIG. 12, a second embodiment of an optical
switch differs from that shown in FIG. 8 by disposing a half-wave
plate 150 between the two spatial light modulators 140, 141. The
half=wave plate exchanges for a second time the x and y
polarisation components so that the residual zero order beam 151(of
maximum amplitude a.sub.YY) from the first SLM 140 is x polarised
on reaching the second SLM 141. of this light a first output beam
152 results from a fraction a.sub.XX being deflected by twice the
intended deflection angle, and there is thus no longer crosstalk
directed precisely at output fibre fC. In fact this beam is
deflected so it comes in at twice the tilt (or twice the offset,
depending on the architecture), and the attenuation is scaled up by
a factor of 4. The rest of this polarisation-dependent zero-order
light is again deflected by the intended deflection angle, and is
subject to the same attenuation as for the system without a central
half-wave plate.
[0109] Referring to FIG. 13, a third embodiment of an optical
switch according to the invention has the second SLM 141 offset by
half a hologram's width in one plane (e.g. the x direction) . Thus
zero-order crosstalk 145, including the polarisation-dependent zero
order, is directed at a point midway 149 between output fibres. In
this case the zero-order crosstalk is subject to an offset of s/2,
with a corresponding additional attenuation dependent on the
offset.
[0110] The third embodiment is most appropriate in the presence of
good surface flatness on the SLM. For the case of offset loss, it
reduces as the ratio of the spot-size to the fibre separation is
increased. In any final design there will be an optimum value of
this ratio to obtain the overall required system performance.
[0111] Referring now to FIG. 14, in a further embodiment a further
reduction of the zero order is achieved by offsetting the output
SLM 141 with respect to the input SLM 140 by a whole SLM's height
(or more) in the direction normal to the plane of incidence. The
figure shows two light beams 70a, 70b, each incident on a first SLM
140, and having a zero-order reflection from that SLM to define a
respective plane of incidence. It can be seen that each plane of
incidence is horizontal--the x-z plane. The output SLM 141 is
offset downwardly so that zero orders do not impinge on it.
Alternatively, an upward shift could be employed. This embodiment
offers resilience to the effects of bowing or long-range surface
distortion of the reflective surface inside the SLM. In this case
the zero orders fall outside of the output fibre array, and can be
conveniently used for monitoring purposes, for example.
[0112] Now consider the polarisation-dependent doubled orders, in a
2-D system. Let these be approaching the output hologram at
deflection angles (equation 11): 8 ( sin X ) = c X Mp L and ( sin Y
) = c Y Mp L ( 11 )
[0113] In the zero-order aligned system (FIG. 8) the possible
values of c.sub.X and c.sub.Y are always even, while n.sub.X and
n.sub.Y can take any integer values. Hence it is possible for
doubled orders from the input SLM 140 to arrive at the centres of
output holograms, and afterwards be focused directly, or at a tilt,
into an output fibre. In the zero-order interleaved system (FIG.
10), however, the possible values of c.sub.X are always odd
integers, while n.sub.X can only take half-integer values. Hence
the doubled orders from the input SLM 140 will arrive between the
output holograms, and will be focused directly, or at a tilt, into
points midway between output fibres. Hence zero-order interleaving
also creates doubled-order interleaving.
[0114] In a preferred embodiment, the attenuation of beams arriving
between the output fibres is increased by adding black paint to the
glue holding the fibres together inside the fibre array. It will be
understood that other absorbers could also be used. In another
embodiment, the spacing between the fibres of the array is occupied
by interstitial fibres which serve to accept and guide away cross
talk from the switching zone. The amplitude of the doubled-order
beam is at most a.sub.XX. In the absence of a central half-wave
plate, there will be a beam of maximum amplitude a.sub.XX.sup.2
coming out at deflection angles (with reference to beams focused
directly into an output fibre) given by equation 12: 9 ( sin X ) =
( c X - 2 n X ) Mp L and ( sin Y ) = ( c Y - 2 n Y ) Mp L ( 12
)
[0115] The worst-case scenario is that c.sub.X=2n.sub.X, and
c.sub.Y=2n.sub.Y. In this case for the zero-order aligned system
(FIG. 11), the beam of maximum amplitude a.sub.XX.sup.2 will be
focused directly down the output fibre. While for the zero-order
interleaved system (FIG. 13), this beam will be focused in between
the output fibres, and will therefore be subject to an offset
loss.
[0116] In the presence of a central half-wave plate, a weak beam,
of maximum amplitude a.sub.XXa.sub.YY, will be reflected as a
zero-order reflection, and will therefore come out at deflection
angles given by equation 13: 10 ( sin X ) = c X Mp L and ( sin Y )
= c Y Mp L ( 13 )
[0117] Firstly consider what happens in the zero-order aligned
system (FIG. 11): this beam is attenuated at the output fibre due
to the limited angular acceptance. Either c.sub.X or c.sub.y could
be zero, in which case the minimum value of the tilt loss at the
output fibre is 4.alpha..sub.T.
[0118] Now consider what happens in the zero-order interleaved
system (FIG. 13). The worst-case is c.sub.Y=0 and c.sub.X=1: the
beam will be attenuated by a tilt loss of .alpha..sub.T and also
the above described offset loss. In addition, if the output SLM is
offset vertically, then the minimum value of n.sub.Y is 1, in which
case the beam will additionally be attenuated by a tilt loss of 4
.alpha..sub.T.
[0119] Now consider the remaining light in the incident doubled
order. Without a central half-wave plate, this beam will have a
maximum amplitude of a.sub.XX(1-a.sub.XX), while in the presence of
a central half-wave plate, this beam will have a maximum amplitude
of a.sub.XX(1-a.sub.YY). With or without the central half-wave
plate, this beam is deflected by the intended deflection angle, and
so leaves the output hologram at a deflection angle given by
equation 14: 11 ( sin X ) = ( c X - n X ) Mp L and ( sin Y ) = ( c
Y - n Y ) Mp L ( 14 )
[0120] For the zero-order aligned system, the worst-case is for
either c.sub.X=n.sub.X or c.sub.Y=n.sub.Y, but not both. Assume
that one of these is true. The minimum attenuation is when
.vertline.c.sub.X-n.sub.X.- vertline.=1 or when
.vertline.c.sub.Y-n.sub.Y=1 and so the beam will be attenuated by a
tilt loss of .alpha..sub.T. For the zero-order interleaved system,
the minimum attenuation is when .vertline.c.sub.X-n.sub.X=1/2 and
.vertline.c.sub.Y-n.sub.Y.vertline.=0. The minimum, attenuation is
then 0.25.alpha..sub.T, added to the offset loss. If additionally,
the output SLM 141 is offset by an odd integer number of hologram
heights, then the offset loss is doubled from that previously
defined, and the minimum value of .vertline.c.sub.Y-n.sub.Y.ve-
rtline. becomes 1/2, so the tilt attenuation is increased to 0.5
.alpha..sub.T.
[0121] To maintain desired back reflection conditions off-normal
incidence is preferable: it is likely to occur in any event due to
the geometrical constraints of the system. However the closer to
normal incidence, the better is the performance.
[0122] Where the beam has off-normal incidence, the phase of the
reflection coefficient from the mirror of the SLM becomes
polarisation-dependent, due to plasmon resonances in the metal
mirror. The effect is to increase the fraction of light in each
polarisation state that remains in that state after passing back
through the quarter-wave plate. Another effect of off-normal
incidence through the quarter-wave plate is to change, for the
worse, both the effective thickness and also the birefringence.
Hence a consequence of off-normal incidence is to increase the
strength of the polarisation-dependent crosstalk into the zero and
doubled orders.
[0123] Given off-normal incidence, it now becomes necessary to
choose the plane of incidence. In this section the effects of
off-normal incidence, but still in the x-z plane, are
investigated.
[0124] Assume the Poynting vector of the incident light to be in
the xOz plane, with a polarisation component E.sub.OY(t) exp j
.epsilon..sub.Y(t) in the y direction, and E.sub.0XZ(t) exp j
.epsilon..sub.xZ(t) in the xOz plane (in a direction mutually
orthogonal to y and the Poynting vector).
[0125] Let the light be incident at an angle .theta..sub.INC to the
mirror, as shown in FIG. 15, and let the long axis of the index
ellipsoid be in the xOz plane, at an angle .theta..sub.D to the
x-axis. A geometric method as discussed previously may be used to
analyse the propagation. As before, the index ellipse is defined by
the intersection of the plane perpendicular to the Poynting vector
with the index ellipsoid. As long as the Poynting vector remains in
the xOz plane, the light component polarised in the y direction and
travelling towards the mirror (E.sub.0Y(t) exp j
.epsilon..sub.Y(t)) experiences a refractive index n.sub.0, that is
independent of the tilt angle. This means that even if the tilt
angle is changing in the z direction, the y polarised component
still perceives a constant refractive index. This index is also
independent of the angle of incidence. The index experienced by the
orthogonal component (E.sub.0XZ(t) exp j .epsilon..sub.xZ(t)) is
the length of the major axis of this ellipse. On propagation
towards the mirror the major axis is at an angle
.theta..sub.D-.theta..sub.INC to the director in the xOz plane: the
length and direction of this axis is shown by the line AB on the
figure. Mathematically the index experienced by the orthogonal
component (E.sub.0XZ(t) exp j .epsilon..sub.xZ(t)) is given by
substituting .theta.=.theta..sub.D-.theta..sub.INC into equation
(1). After reflection from the mirror and passing back through the
quarter wave plate it is the component E.sub.0Y(t) exp j
.epsilon..sub.Y(t) that is polarised in the xOz plane. For this
second pass, the major axis of the index ellipse is now at an angle
.theta..sub.D+.theta..sub.INC to the director in the xOz plane: the
length and direction of this axis is shown by the line AC on the
figure. Mathematically the index experienced by the orthogonal
component (E.sub.0XZ(t) exp j .epsilon..sub.xZ(t)) is given by
substituting .theta.=.theta..sub.D+.theta..sub.INC into equation
(1). Hence the phase delays for the two components are now given by
equations 15 and 16:
[0126] E.sub.0XZ component:
.DELTA..phi..sub.OXZ=.DELTA..phi..sub.1ST-PASS+.DELTA..phi..sub.2ND-PASS=k-
n(.theta..sub.D-.theta..sub.INC)d+kn.sub.0d (15)
[0127] E.sub.OY component:
.DELTA..phi..sub.OY=.DELTA..phi..sub.1ST-PASS+.DELTA..phi..sub.2ND-PASS=kn-
.sub.0d+kn(.theta..sub.D+.theta..sub.INC)d (16)
[0128] Therefore the phase-modulation now has a weak polarisation
dependence, which increases with the angle of incidence, and is
given approximately (to second order) by equation 17: 12 0 Y - 0 XZ
= 2 k INC n D ( 17 )
[0129] In a cell in which the tilt angle is varying (as in 7), the
polarisation dependence of the phase modulation is given by
equation 18: 13 0 Y - 0 XZ = 2 k INC d z = 0 d n ( ( z ) ) z ( 18
)
[0130] The rate of change of n with respect to director angle is
easily shown to be (equation 19): 14 n = n 3 ( ) 2 sin 2 ( 1 n 0 2
- 1 n e 2 ) ( 19 )
[0131] Note that for tilt angles in the range 0 to .pi./2, this
derivative is always negative, while for tilt angles in the range
.pi./2 to .pi., the derivative is always positive. For a pi cell,
the tilt angle .theta. varies between 0 and .pi.. Hence the
polarisation-dependent phase modulations may partially cancel.
[0132] An important property of this plane of incidence, is that of
the directions of the two polarisation modes. Bearing in mind that
these are given by the directions of the minor and major axes of
the ellipse formed by the intersection of the plane perpendicular
to the Poynting vector, with the index ellipsoid, if the Poynting
vector is in the xOz plane, then the minor axis is always in the y
direction and the major axis is always in the xOz plane (and
parallel of course to the xOz component of the incident light).
Therefore the polarisation states of the y polarised and orthogonal
components of the incident light are not changed inside the liquid
crystal, and therefore proper polarisation component exchange
should still take place at the quarter-wave plate and mirror.
Returning now to the polarisation-dependence, the effect on a
beam-steering device, is to introduce a polarisation-dependence
into the amplitude (but not the output angle) of each diffraction
order, where this polarisation-dependence is a function of the
angle of incidence. Now consider an NxN switch using two such
devices, and let the SLM shown in FIG. 15 be the input SLM. In
order to keep the mathematics simple, an analysis is now presented
for 1-D SLMs, and hence 1-dimensional beam-steering. The results of
this analysis hold good for two dimensional SLMs. Define Fourier
coefficients a.sub.L1 and b.sub.L1 such that (equations 20 &
21): 15 a L1 = u = - .infin. .infin. exp { kn o d + ( u ) - kd INC
n D D ( u ) } exp - ( 2 Lu ) u ( 20 ) b L1 = u = - .infin. .infin.
exp { kn o d + ( u ) + kd INC n D D ( u ) } exp - ( 2 Lu ) u ( 21
)
[0133] where u is the position co-ordinate of each pixel, and
.phi.(u) is the intended phase modulation, as defined immediately
before equation (13). Hence for the input SLM, the y polarised
component of the incident field is diffracted into orders of
amplitude b.sub.L1, while the orthogonal component is diffracted
into orders of amplitude a.sub.L1. For a well-designed hologram,
almost all of the power will go into a single diffraction
order.
[0134] It is assumed that the input and output SLMs are made in the
same way. Now consider pixels in the two SLMs applying the same
nominal phase modulation (for a normally incident beam), and hence
having the same tilt angle, .theta..sub.D. Due to the geometry of
the arrangement of SLMs etc, the beam entering the 1st SLM is
parallel to the beam leaving the second SLM, as shown in FIG. 16.
Let there again be a half-wave plate between the two SLMs.
[0135] The y polarised component of the field incident on the 1st
SLM, is polarised in the xOz plane on leaving the 1st SLM, and due
to the half-wave plate is again y polarised on entering the second
SLM. This component perceives the ordinary index n.sub.0 on
propagation towards the mirror. On propagation away from the
mirror, the index perceived is given by an effective tilt angle of
.theta.=.theta..sub.D-.theta..sub.INC. Hence the total phase delay
for this component is given by (equation 22):
[0136] E.sub.OY component:
.DELTA..phi..sub.OY=.DELTA..phi..sub.1ST-PASS+.DELTA..phi..sub.2ND-PASS=kn-
(.theta..sub.D-.theta..sub.INC)d+kn.sub.0d (22)
[0137] Similarly, it can be shown that for the orthogonal polarised
component (in the xOz) plane of the beam incident on the 1st SLM,
the phase modulation at the second SLM is given by (equation
23):
[0138] E.sub.OXZ component:
.DELTA..phi..sub.OXZ=.DELTA..phi..sub.1ST-PASS+.DELTA..phi..sub.2ND-PASS=k-
n.sub.0d+kn(.theta..sub.D+.theta..sub.INC)d (23)
[0139] At the second SLM, and assuming substantially flat SLMs, the
hologram is substantially complementary to that at the first SLM.
Let the intended phase modulation at the second SLM be
.phi..sub.c(u), and let the director angle be .theta..sub.c(u). If
at the input SLM, the hologram is designed to maximise the output
into the L'th diffraction order, then at the output SLM, the
hologram should maximise the output into the -L'th diffraction
order. For this output SLM therefore, the Fourier coefficient
b.sub.-L2 that defines the amplitude of the main diffraction order
for the y polarised component of the field incident on the 1st SLM
is given by (equation 24): 16 b - L2 = u = - .infin. .infin. exp {
kn o d + C ( u ) - kd INC n C C ( u ) } exp + ( 2 Lu ) u ( 24 )
[0140] while the Fourier coefficient for the main diffraction order
from the output SLM for the orthogonal component of the field
incident on the 1st SLM is given by (equation 25): 17 a - L2 = u =
- .infin. .infin. exp { kn o d + C ( u ) + kd INC n C C ( u ) } exp
+ ( 2 Lu ) u ( 25 )
[0141] The overall holographic switching efficiency for the y
polarised component of the field incident on the 1st SLM is given
by (equation 26):
.eta..sub.0Y=.vertline.b.sub.L1.vertline..sup.2.vertline.b.sub.-L2.vertlin-
e..sup.2 (26)
[0142] while the overall holographic switching efficiency for the
orthogonal component of the field incident on the 1st SLM is given
by (equation 27):
.eta..sub.OXZ=.vertline.a.sub.L1.vertline..sup.2.vertline.a.sub.-L2.vertli-
ne..sup.2 (27)
[0143] Now consider the hologram patterns, and let the local
director angle, .theta..sub.D(u) be expressed in terms of some
fundamental repeating pattern, .theta..sub.1(u) (equation 28): 18 D
( u ) = 1 ( u ) * J = - .infin. .infin. ( J - u 0 ) ( 28 )
[0144] Given that the intended or mean phase modulation on the 1st
SLM, .phi.(u), depends on the local director angle (equations 1 and
7), then it must also show periodicity with the same period
.OMEGA., as must any derivatives with respect to .theta..sub.D(u)
(equation 19). Therefore, taking into account the effects of
off-normal incidence as in equations 20,21 etc, the net phase
modulation will still be periodic with the same period. Hence we
may define H.sup.-(u) such that (equation 29) 19 exp { kn o d + ( u
) - kd INC n D D ( u ) } = H - ( u ) * J = - .infin. .infin. ( J -
u 0 ) ( 29 )
[0145] where u.sub.0 is some (arbitrary) origin. This origin
affects the phase, but not the magnitude, of the diffraction
orders. The magnitude of a.sub.L1 may be obtained in terms of H(u)
using Fourier series analysis (equation 30): 20 a L1 = 2 - / 2 / 2
H - ( u ) exp - 2 Lu u ( 30 )
[0146] Similarly, let .theta..sub.c(u) be the director angle on the
2nd hologram, and express it in terms of another fundamental
repeating pattern, .theta..sub.2(u) (equation 31): 21 C ( u ) = 2 (
u ) * J = - .infin. .infin. ( J - u 1 ) ( 31 )
[0147] Therefore, using the same arguments as above, the phase
modulation on the second SLM must also be periodic with period
.OMEGA., and so we may define G.sup.-(u) such that (equation 32):
22 exp i { kn o d + C ( u ) - kd INC n C c ( u ) } = G - ( u ) * J
= - .infin. .infin. ( J - u 1 ) ( 32 )
[0148] where u.sub.1 is another arbitrary origin. Hence we may
calculate the magnitude of b.sub.-L2 (equation 33): 23 b - L2 = 2 -
/ 2 / 2 G - ( u ) exp + 2 Lu u ( 33 )
[0149] If we let G.sup.-(u)=H.sup.-(-u), and make the substitution
u'=-u, it is clear that (equation 34):
.vertline.a.sub.L1.vertline.=.vertline.b.sub.-L2.vertline. (34)
[0150] Physically this may be achieved by making the repeating
pattern .theta..sub.2(u) on the second SLM equal to
.theta..sub.1(-u) on the first SLM. In which case (from
equation(1)), .phi..sub.c(u)=.phi.(-u) as required. Now consider
the other two amplitude coefficients. At the first SLM, define a
periodic phase modulation H.sup.+(u), and use the same origin
(equation 35): 24 exp i { kn o d + ( u ) + kd INC D D ( u ) } = H +
( u ) * J = - .infin. .infin. ( J - u 0 ) ( 35 )
[0151] hence we obtain b.sub.L1 (equation 36): 25 b L1 = 2 - / 2 /
2 H + ( u ) exp - 2 Lu u ( 36 )
[0152] Now, at the second SLM define a periodic phase modulation
G.sup.+(u), to obtain a.sub.-L2 (equation 37, 38): 26 exp i { kn o
d + C ( u ) + kd INC n C C ( u ) } = G + ( u ) * J = - .infin.
.infin. ( J - u l ) ( 37 ) a - L2 = 2 - / 2 / 2 G + ( u ) exp + 2
Lu u ( 38 )
[0153] Again, as we have already chosen that (equation 39)
.theta..sub.2(u)=.theta..sub.1(-u) (39)
[0154] then, automatically, .phi..sub.c(u)=.phi.(-u), in which case
G.sup.+(u)=H.sup.+(-u), and therefore (equation 40)
.vertline.b.sub.L1.vertline.=.vertline.a.sub.-L2.vertline. (40)
[0155] Combining (36) and (40) we may obtain (equation 41):
.vertline.a.sub.L1.parallel.a.sub.-L2.vertline.=.vertline.b.sub.L1.paralle-
l.b.sub.-L2.vertline. (41)
[0156] Hence, if the basic periodic patterns on the two SLMs are
chosen to satisfy (39), and the angle of incidence is such that the
Poynting vector of the light incident on the first SLM, and leaving
the second SLM, is in the plane of tilt of the director (in this
case the x0z plane), the overall switch efficiencies can become
polarisation-independent (equation 42):
.eta..sub.OY=.eta..sub.OXZ (42)
[0157] Note that this analysis neglects the change in beam
direction between holograms due to diffraction-induced
beam-steering. This may create some polarisation-dependent loss,
but it is expected that the configuration described is still the
optimum, as it cancels the polarisation-dependence of the system as
a whole due to the angle of incidence.
[0158] Given that the two orthogonal components perceive different
phase modulation at each plane, the holograms must be designed that
the worst-case unwanted diffraction orders do not cause
unacceptable crosstalk.
[0159] There have thus been described devices and systems for
optical switching which are polarisation insensitive. Embodiments
of the invention as described are capable of high performance in
respect of cross talk.
* * * * *