The invention relates to spatial light modulators (SLM ^' s) and in particular to an apparatus for, and method of, performing binary, phase or intensity, spatial light modulation.

In its simplest form an SLM consists of a two dimensional array of pixels. In a ferro-electric liquid crystal SLM each pixel, as shown in Figure 1, comprises a slab 4 of ferro-electric liquid crystal (FLC) sandwiched between two optically transparent electrodes 5 and 6. Optically each pixel behaves as a uniaxial crystal with an optic axis whose angular orientation may change. The optic axis is aligned with what is termed the molecular director 3.

Dependent on whether the FLC is in smectic A* or smectic C* phase, two distinctive behaviours of the FLC occur. For the smectic A* phase, the change of orientation of the optic axis increases with an applied voltage and it is necessary to maintain the voltage if the change in orientation is to be maintained. For the smectic C* phase, the optic axis is switched by means of the applied voltage between two stable states; because of its intrinsic bistability an applied voltage is not necessarily required to maintain the optic axis in its switched state.

The terms smectic A and smectic C refer to different phases that a liquid crystal may have. A smectic liquid crystal is one in which the individual molecules form layers within which all the molecular directors point in roughly the same direction. In a smectic A liquid crystal the molecular director points normal to the layer, but in a smectic C liquid crystal the molecular director points at an angle to the normal known as the tilt angle (θ. ) . In general,

but not exclusively, a liquid crystal may be cooled from the smectic A phase into the smectic C phase. When an aligned cell is constructed with either of these liquid crystals, the layers will form with their normals lying parallel to the cell walls and pointing in the alignment direction. Further to this the molecular director in the smectic C phase will also lie parallel to the cell walls and thus at angles of +θ. or -θ. to the alignment direction when viewed through the cell (i.e. giving 2 stable states) .

When the liquid crystal molecules are chiral (i.e. they lack inversion symmetry symbolized by a *) then there will be a permanent electric dipole moment associated with each molecule. In the smectic A* phase the orientation of these dipoles is random but in the smectic C* phase they align ferroelectrically to give a bulk dipole moment at right angles to the molecular director. Thus in a cell the dipole points towards either the top electrode in the +θ. state or towards the bottom electrode in the -θ. state.

A simple view of the operation of the smectic C* device is that voltage pulses applied to the cell electrodes may be used to switch the direction of the dipole and thus the orientation of the molecular director. After switching, the liquid crystal remains in its new state with no applied voltage. Figure 7 shows a slightly less simplified version of the operation of FLC in the smectic C* phase. Figure 7 essentially shows different states of the smectic C* phase FLC which can be maintained. The six arrows shown in Figure 7 represent different orientations of the molecular director 3 three of which 31,32,33 can be described as negative orientations, the remaining three 41,42,43 being positive. When the smectic C* device has no voltage applied to it, it will adopt one of two orientations

31,41 indicated as 0 or 0 .

If the molecular director 3 of the device is initially in the 0 orientation 31 and a pulse of positive voltage is applied to the device then, subsequent to the pulse, the molecular director 3 will adopt the 0 orientation 41. If, however, a constant positive d.c. voltage is used to switch the device instead of a pulse voltage, then the director 3 will adopt the DC orientation 43. Another varient is to switch from 0 to 0 with a positive voltage pulse but to maintain the switched state by means of a small ac voltage (ac stabilisation) in which case the director 3 will adopt the ac orientation 42. Note that when an a.c. voltage is used it is to be understood that it will generally have a frequency of about 2 or 3 orders of magnitude greater than the normal switching speed of the FLC which may be about 50 Hz. Also note that it is the type of maintaining voltage used (i.e. a maintaining voltage, a.c. voltage or d.c. voltage) which determines which orientation the director 3 adopts. It does not depend on which of the negative, orientations 31,32,33 the director 3 is switched from.

.The switch from one of the positive orientations 41,42,43 to one of the negative orientations 31,32,33 is analagous to that described above with a pulse of negative voltage causing the director 3 to adopt one of the negative orientations 31,32,33 depending on the type of maintaining voltage used, with an a.c. voltage causing the director 3 to adopt the AC orientation 32 and a negative d.c. voltage causing the director 3 to adopt the DC orientation 33.

The important aspect about the switching behaviour of a smectic C* phase FLC device, however, is that, although using different types of maintaining voltage will give rise to different orientations of

the director 3, the different orientations are substantially discrete and they will not be affected by small fluctuations in the applied voltage either during switching of the device or afterwards. That is to say that the behaviour of FLC in the smectic C* phase is consistent within relatively large parameters for variations in the switching and maintaining voltage, applied to the FLC.

This, of course, is particularly useful where it is desired to construct a binary device requiring two well defined states such that the output from the device consistently varies between only two substantially precise outputs corresponding to the two different states of the device. Switching in a smectic A* device however, is very different and relies on the electroclinic effect which occurs when the temperature of the liquid crystal is held at just above the smectic A* to smectic C* phase transition. If an electric field is applied to the cell at this temperature it will tend to align the molecular dipole moments. This induces a smectic C* character to the liquid crystal and the average molecular director tilts with respect to the alignment direction. The higher the field that is applied then the larger the tilt, that is the larger the effective θ.. Conversely, if the field is removed then the liquid crystal relaxes back to the smectic A* phase with the molecular directors pointing along the alignment direction. If the direction of the applied field is reversed, a negative tilt is induced, again increasing with the magnitude of the field.

Thus a smectic C* device operates as a retardation-plate that may be switched between two bistable orientations with an applied voltage. In its simplest form removal of that voltage leaves the

retardation-plates in their switched positions. The smectic A* device operates as a retardation plate whose axis rotates as an applied voltage varies. The amount of rotation increases as the voltage increases, reduces again to zero when the voltage is removed, and is held constant only if the voltage is held constant as a maintaining voltage. The direction of rotation may be reversed by reversal of the applied voltage. The following discussion is based on the SLM of Figure 1 being constructed with ferro-electric liquid crystal in the smectic C* phase and thus it is operable to switch each pixel between two stable states which are characterised by the angular orientation of the director 3. Any one pixel is switched from one state to the other by the application of a suitable switching voltage across the electrodes 5 and 6. Figure 1 shows the director 3 as being able to adopt either one of two orientations according to whether the pixel is in state (1) or state (2). Linearly polarised input light 12

(including visible and invisible electromagnetic radiation) from a source (not shown) is incident upon the electrode 5.

The angle ø between these two orientations is termed the switching angle of the SLM and it will be understood that it is equal to twice the tile angle θ.. The switching angle is dependent on the ferro¬ electric properties of the smectic C* phase material of the slab 4 and as is apparent from the above description, on the manner in which the maintaining voltage is applied to the electrodes 5 and 6 in the case of FLC in the smectic C* phase.

An SLM might switch its director 3 between orientations 31 and 42 in which case the switching angle ø of the SLM would be the angular separation between the angular orientations 31 and 42 (thus for a

typical FLC the SLM would have a switching angle ø of about 20° ) .

Silicon backed SLM ^' s are well adapted to utilise the optimum type of maintaining voltage for any particular application. Thus it is anticipated that silicon-backed SLM ^' s are manufacturable with switching angles of up to and above 45° by switching between the DC and DC orientations 33 and 43.

When a smectic C* phase FLC SLM is used in an apparatus for performing binary, phase only spatial light modulation it is conventionally placed between a pair of crossed polarisers 7 and 8 which are termed the polariser and analyser respectively. Figure 2 shows the polariser 7 orientated such that the direction of polarisation of light incident on the SLM 10, having passed through the polariser 7, bisects the two orientations which the directors 3 of the pixels may adopt (this direction is now taken to be vertical for ease of description) . An account is now given of one beam of light, associated with one pixel, passing through the apparatus. On passing through the SLM 10 the light emerges with generally elliptical polarisation whose principal axis is rotated from the vertical by up to ø, either anti-clockwise or clockwise, depending on whether the pixel is in state (1) or state (2) respectively of Figure 1. The analyser 8 then removes the vertical component of the resulting light, leaving the output light 9 with a phase difference of π relative to the phase which it would have had, had the pixel been in its other state. In order for the arrangement to produce phase-only modulation, which has a constant output intensity both as a function of time and regardless of which state each pixel is in, it is necessary that the polarization of the input light bisects the two orientations which the director 3 of the pixel may

take and that the magnitude of the switching angle ø does not vary. These two conditions require that the positions which the director 3 may take are constant, at least for the duration of an operation of the arrangement. When a smectic C* phase FLC SLM is used this condition is satisfied automatically since the smectic C* phase is essentially bistable and thus, for a given type of maintaining voltage, the director 3 will always adopt only one of the bistable positions which are constant. If a smectic A* phase FLC SLM is used it is necessary to ensure that good control of the voltage is maintained at all times and that the necessary maintaining voltages accurately return to the same two values time and again. The optical efficiency of such a system is the ratio of the magnitude of the intensity of the output light 13 to the intensity of the input light 12 incident on the SLM 10. For the conventional arrangement described above the optical efficiency Λ c is given by: 1c = sin ² (4/2) sin ² (ø) . In this equation ^ is the retardation of the slab 4 of FLC and ø is the switching angle of the SLM. Figure 9 is a contour graph of efficiency which illustrates the equation given above. The contours range from below 10% efficiency (black) to above 90% efficiency (white) in 10% intervals.

For a slab 4 of a given type of FLC and for light of a given wavelength the retardation Zl is dependent only on the thickness of the slab 4. If this is adjusted such that A = 180 ^' the crystal will behave as a half-wave plate, the sin ² (Δ/2 ) term will be unity, and the light emerging from the SLM will be linearly polarised (which is a special case of elliptical polarisation) .

As mentioned above the switching angle ø is

dependent upon the type of smectic C* phase FLC used and the type of maintaining voltage applied. For maximum optical efficiency in the conventional arrangement it is required that the SLM has a

5 switching angle of 90 ^° . Commercially available oε

SLM ^' s, however, have much lower switching angles, e.g. model 2DX128 available from Thorn Smectic Technology has a switching angle of about 30°.

The present invention seeks to provide

10 apparatus for and a method of performing binary, phase

52 or intensity, spatial light modulation with improved optical efficiency over conventional apparatus for, and methods of performing binary, phase or intensity spatial light modulation. ic In accordance with a first aspect of the

02 present invention there is provided apparatus for performing binary spatial light modulation comprising a source of linearly polarised electromagnetic radiation; a controllable two state spatial light _Q modulator (SLM) through which radiation from the

51 source is caused to pass, the SLM being operable to vary the polarisation of the radiation to one of two possible output polarisations in dependance on the state of the SLM; a retardation plate through which c the radiation from the SLM passes; and reflection

0L means arranged to reflect radiation passing from the

SLM through the retardation plate back through the retardation plate and the SLM whereby the polarisation of the reflected radiation emerging from the SLM is

30 representative of the state of the SLM.

5 Conveniently the apparatus will also include a controlling means wherein said SLM is controlled by and connected to the controlling means which is operable to switch the SLM from one of its two states

35 to the other by the application of a suitable voltage.

Preferably there is also provided means for

separating the reflected radiation emerging from the SLM from the source radiation entering the SLM.

The SLM may be any electro optic device which can be characterised as having uniaxial crystal-like behaviour with an optic axis which can have its orientation changed.

Preferably the SLM comprises an electro-optic device which has the characteristics of a uniaxial crystal whose optic axis may take on one of two different angular positions which correspond to the two different states of the SLM, the angular separation between said two different angular positions being termed the switching angle of the SLM.

In one embodiment the reflected radiation emerging from the SLM is passed through a polariser. The thus-polarised radiation has a phase which varies by π radians in accordance with the state of the SLM.

According to a second aspect of the present invention there is provided a method of performing binary spatial light modulation said method comprising the steps of passing linearly polarised electromagnetic radiation through a controllable two state spatial light modulator (SLM) which is operable to vary the polarisation of the radiation to one of two possible output polarisations in dependence on the state of the SLM, thence through a retardation plate and thence reflecting the radiation emerging from the retardation plate back through said retardation plate and said SLM.

Commonly, the electromagnetic radiation will be in the form of visible light. The detailed description of the invention, given below, will incorporate this feature.

In a preferred embodiment of the present invention a polarising beam splitter is placed before the SLM; this has two effects. The first effect is

that it ensures that the input radiation is linearly polarised in a known direction. The second is that it separates the reflected radiation from the input radiation in such a manner that the separated radiation forms beams which differ in phase by either 0 or 180° only.

The retardation plate is preferably a quarter-wave plate.

In order to better understand the invention and several applications thereof, a detailed description of the invention will be given below with reference to the attached drawings, wherein:

Figure 1 is a diagrammatic view of a single pixel of an FLC SLM; Figure 2 is a diagrammatic view of the conventional arrangement for performing binary, phase or intensity, spatial light modulation with an FLC

SLM;

Figure 3 is a diagrammatic view of a preferred embodiment of the present invention;

■Figure 4 is a diagrammatic view of a compact embodiment of the present invention;

-Figure 5 is a diagrammatic view of a silicon backed embodiment of the present invention; Figure 6 is a diagrammatic view of an embodiment of the present invention for use in an optically addressed SLM.

Figure 7 is a diagrammatic representation of the effect of applying different maintaining voltages to a slab of smectic C* phase FLC.

Figure 8 is a diagrammatic representation of the states of polarisation of a beam of light passing through apparatus for phase only modulation in accordance with the present invention; in this Figure the retardation plate is a quarter-wave plate whose optic axis is parallel to, or orthogonal to, the

direction of polarisation of the input light.

Figure 9 is a contour graph showing how the efficiency of the conventional transmission system varies with the switching angle ø and the retardation of the SLM, for phase only modulation.

Figure 10 is a contour graph showing how the efficiency of the present invention varies with the switching angle ø and the retardation^ of the SLM, for phase only modulation; in this graph the retardation plate is a quarter-wave plate whose optic axis is parallel to, or orthogonal to, the direction of polarisation of the input light.

Figure 11 is a contour graph similar to that of Figure 10; in this graph, though, the retardation plate is not a quarter-wave plate but has a retardation of one eighth of a wavelength.

Figure 12 is a contour graph similar to that of Figure 10; in this graph, however, the retardation plate has a retardation of three eights of a wavelength.

Figure 13 is a contour graph similar to that of Figure 10; in this graph, however, the quarter-wave plate is, orientated with its optic axis at 45° to the direction of polarisation of the input light. Figure 14 is a contour graph similar to that of

Figure 9; showing how the efficiency of a conventional transmission system varies with switching angle ø and retardation of the SLM, for intensity modulation.

Figure 15 is a contour graph similar to that of Figure 10; showing how the efficiency of the present invention varies with switching angle ø and retardation^ of the SLM, for intensity modulation.

Figure 16 is a contour graph similar to that of Figure 15 showing how the efficiency of the present invention varies with switching angle ø and retardation of the SLM, for an alternate mode of

intensity modulation.

Figure 3 shows an arrangement for performing binary, phase or intensity, spatial light modulation using a preferred embodiment of the present invention. Light 11, for example from a laser source, passes through a polarising beam splitter 9 which allows only linearly polarised light to pass through, undeviated (for ease of description phase only modulation will be considered and the direction of polarisation of the light shall be taken to be vertical) . The polarised light then passes on to a SLM 10 as input radiation 12. As mentioned above, the SLM 10 generally consists of a two-dimensional array of pixels in which each pixel is in either one of the two states which each pixel may adopt; the arrangement is configured such that these two states correspond to the director making an angle of either +<z/ or - ø/„ with the vertical where ø is the switching angle of the SLM. On entering the slab 4 of FLC the light is effectively split into two components, one of which travels with its electric vector oscillating in the direction of the director 3 of the liquid crystal, the other component travelling with its electric vector oscillating orthogonally to the director 3. This latter component is retarded, relative to the former component, by an amount determined by the , of the slab of FLC. The retardation can be positive or negative. The thickness of the slab and the wavelength of the light used can be chosen such that = 180 , in which case the latter component is retarded by half a wavelength of the light used relative to the former component, this results in a

beam of light with a new linear polarisation whose direction of polarisation is either +ø or -ø from the vertical depending on whether the director is +ø/2 or -ø/2 from the vertical, respectively. This is the situation represented at stage (i) of Figure 8. If is not 180° but anything other than 0° the light will leave the pixel with elliptical polarisation whose principal axis lies between 0 and ø or 0 and -ø depending on the direction of the director again; in the case of elliptical polarisation the invention works in the same manner but the efficiency is reduced as is apparent by examining the equation of efficiency given below.

When the light has passed through the SLM it will consist of a number of small beams each one corresponding to a pixel . As shown in Figure 3 the light beams each then have to pass through a retardation plate in the form of a quarter-wave plate 15 whose optical axis may be vertical (case discussed now) or at 45° to the vertical (case discussed below) . The light then passes through two lenses 16 and 17 and then back, after reflection at a plane mirror 18, through .lenses 17 and 16 and then back through the quarter-wave plate 15 again. The purpose of the lenses is merely to image the reflected image of the SLM onto the back of the SLM. The effect of the quarter-wave plate is, after the light has passed through it twice, that of a half-wave plate, i.e. the direction of polarisation is rotated by twice the angle between the direction of polarisation and the optic axis of the quarter-wave plate, through that optic axis. This leaves the direction of polarisation of the light beam + or - ø from the vertical and + or - 3ø/ ₂ from the director, if the optical axis of the quarter-wave plate is vertical; this is the situation represented at stage (ii) of

Figure 8. Thus when the beam goes back through its associated pixel, along the same optical path, the direction of polarisation is again rotated to finally finish + or - 2ø from the vertical depending on whether the pixel was in state (2) (director ^→ -ø/→. from vertical) or in state (1) (director -ø/„ from vertical) . This is the situation represented at stage (iii) of Figure 8. The light beams from the SLM 10 then go on to the polarising beam splitter 9 where only the horizontally polarised components are reflected through 90 to form the output light 13 which consists of as many beams as there are pixels whose phases will differ by either 0 or π radians. The optical efficiency of this arrangement is given ^fa y- 4 . f|n1 = sin (Δ/2 ) sin ² (2ø) - ignoring other losses .

Figure 10 is a graphical representation of this equation. It clearly shows that the present invention gives better efficiencies for low switching angles .

Thus if the SLM had retardation^ = 180° and a switching angle ø at 45' (which, as mentioned above, is more readily obtainable than larger switching angles) the only losses would be those due to absorption and to reflection at optical boundaries.

Since any deviation from the desired position of the director 3 will be magnified because of the effect of the radiation passing through the SLM twice, it is advantageous to utilise a smectic C* phase FLC SLM as it is bistable. Thus the requirement of constancy of the positions which the director 3 may adopt is satisfied automatically without the need for complex and precise electronic control over the switching and maintaining voltage applied.

A further advantage of using smectic C* phase

FLC is that it is possible to use just a pulse voltage in which case, for the majority of the time there will be no voltage across the electrodes. This reduces the chance of the migration of the material from the FLC onto one of the electrodes which might reduce the life of the SLM.

If the retardation plate 15 is not exactly a quarter-wave plate the optical efficiency is given by: Jln1 = 2 sin ² (Δ/2 ) (cos (^/2)cos (4 ₁ ) -cos (ø) sin( /2)sin

the retardation of the retardation plate 15.

Figures 11 and 12 illustrate this equation graphically for the cases where → . = 45° and Λ = 135° respectively. From these graphs it can be seen that .good efficiencies are still obtainable with low switching angle even when the retardation plate is quite a long way off being a quarter-wave plate.

As mentioned above the quarter wave plate 15 ^a Y be orientated with its optical axis either bisecting the two directions which the directors 3 may adopt (or at 90' thereto) or rotated by ± 45° therefrom. In the latter case the efficiency will be given by: )n ₂ = sin ⁴ (4/2)sin ² (2ø) +sin ² (4) sin ² (ø)

This is illustrated graphically in Figure 13. It is clear that Λn2^Λn1 for all values of ø and ^ .

However, this method has the disadvantage that the output light 13 is vertically polarised and thus cannot be separated f om the incoming light 11 by means of a polarising beam splitter 9; use of a half- silvered mirror in place of the polarising beam splitter 9 would reduce the efficiency as a whole well below that attainable by the arrangement with the quarter wave plate 15 having its optical axis vertical. This disadvantage does not exist for

applications in which it is not necessary to separate input and output beams.

When operated with 100% efficiency, the π phase shift is introduced irrespective of the state of polarisation of the incident light.

Under different conditions, intensity modulation can be achieved. In a conventional transmission system the input polarization is parallel to the director in one state, its state of polar- ization is unchanged by the modulator and transmission through an analyser (orientated at 90° to the input polarization) is zero. For the same input polar¬ ization, if the director is switched to its other state (through ø) , then, assuming the modulator acts as a half wave plate, the output polarization is rotated through 2ø and the intensity transmitted by the analyser is sin ² (2ø) .

Using the arrangement described earlier and with the input light beam linearly polarised at an angle to the bisector of the directors of the SLM equal to the switching angle of the SLM, the intensity of the output radiation through the polarizing beam splitter. is modulated by the SLM so that in one state of the SLM no intensity is output and in the second state of the SLM there is an intensity output reduced by a factor of sin ² (4ø) .

Thus, the input light beam is linearly polarised at an angle ø to the vertical, wherein the vertical is also the bisector of the switching angle of the SLM. The two states of the SLM therefore output linearly polarised light at 0 and -2ø to the vertical, when the retardation is set at 180 ^" . The reflected output from the quarter wave plate, which has an optical axis aligned to the vertical, is therefore 0° and +2ø respectively, which results in a reflected output from the SLM of +ø and -3ø

respectively. Since the input light beam was linearly polarised using the polarising beam splitter the output of the SLM is not reflected in the first state (+ø) whereas the output of the SLM in the second state (~3ø) is reflected by the beam splitter with the reduction factor mentioned above.

With this arrangement 100% modulation can be achieved for a switching angle of only ø = 22.5°. A more complete analysis is shown in Figures 14 and 15 where the retardation of the switchable wave plates is also considered. Figure 14 shows the intensity modulation achievable with a conventional transmission system and Figure 15 the intensity modulation achievable with the present invention. The high intensity modulation possible, even with ø<45°, is clearly seen. As the retardation of the SLM varies from 180° a second fixed wave plate is required between the polarising beam splitter and the SLM. Other modes of operation are also possible, for instance, where the reflected light of the same polarisation as the incident light has high contrast for example in a display application using sheet polarisers. In this case the polarisation of the incident light is orientated at an angle of ø+45° to the bisector. The reflected light for one state of the SLM is output rotated by 90° and so no output intensity results but in the other state of the SLM the light is rotated by 4ø+90° and so the intensity of the light passing out through the input polariser is reduced by a factor sin ^: (4o) . This is shown graphically in Figure 16. As with the phase only modulation, improved performance is available even when the fixed wave plate does not have an ideal retardation. Thus, it may be seen that with the present invention suitable selection of the polarisation of

the input radiation, of the relationship between the optical axis of the retarder means and the bisector of the switching angle of the SLM, and of an appropriately aligned polariser on the output enables phase and/or intensity modulation to be achieved. Figure 4 shows a compact embodiment of the invention. It works in exactly the same way as described above except that the lenses are dispensed with as being unnecessary because the thickness of the layers 4 and 15 can be made very small thus reducing the effect of divergence of the light beams.

FLC SLM ^' s are under development in which the FLC is deposited on silicon. These SLM's are termed silicon backed SLM ^' s and are designed to operate in reflection mode.

Figure 5 shows how the invention may be applied to a silicon backed SLM to improve its efficiency for a switching angle below 90°; the silicon layer 19 is additionally operable as a substrate on which to form circuits which control the switching and maintaining voltages to be applied to the electrodes 5 and 6.

-SLM's have been designed which are optically addressed. These are formed by placing a layer of photo-conducting material 20 between the FLC layer 4 and the electrode 5. In the case of optically addressed SLM ^' s there are just two electrodes between which are sandwiched the whole of the FLC layer 4 and the photo-conducting material 20. A voltage is applied to the electrodes but only when light illuminates the photo-conductor 20 is the electric field across the FLC layer 4 great enough to cause the pixel to change its state.

Figure 6 shows how the invention can be applied to an optically addressed SLM.

The above apparatus and methods have been

described by reference to a smectic C* phase FLC. However, an SLM using the smectic A* phase material may alternatively be used. By way of example, consider a smectic A* pixel to be subjected to a controlled voltage of magnitude V the polarity of which is switchable between the positive and negative states. For a particular material in a particular cell this will give rise to two states which are characterised by orientation of the director 3 (in Figure 1 ) . The angle between the two orientations ø(V) is the equivalent of the previously referred to switching angle. With this mode of switching and this definition of switching angle the previously described apparatus applicable to the smectic C* phase can be extended to the smectic A* phase.