EP0222797A1

EP0222797A1 - Photoelastic modulators

Info

Publication number: EP0222797A1
Application number: EP86902777A
Authority: EP
Inventors: William Pui Ling
Original assignee: Australian National University
Current assignee: Australian National University
Priority date: 1985-04-30
Filing date: 1986-04-30
Publication date: 1987-05-27
Also published as: WO1986006505A1; EP0222797A4

Abstract

Plateau optique pour modulateur photo-élastique comprenant une tige ou une barre (32) allongée d'un agent optiquement transparent, un premier transducteur piézo-électrique (35) étant monté sur l'une des faces de ladite barre, de manière à appliquer à cette dernière une contrainte longitudinale alternative. Un deuxième transducteur piézo-électrique (35), destiné à détecter les oscillations transversales de la barre, est également monté sur celle-ci. Un signal provenant du deuxième transducteur piézo-électrique est utilisé dans une boucle de réaction positive pour commander la fréquence du signal conducteur du premier transducteur piézo-électrique. Les deux transducteurs sont montés à une distance éloignée d'environ un quart de la longueur de la tige ou de la barre (32) de l'une des extrémités de ladite tige ou barre. Les deux transducteurs sont de préférence combinés en un unique transducteur piézo-électrique muni d'une électrode (40) pour détecter les oscillations transversales se trouvant dans une ouverture de l'électrode de commande (38) du premier transducteur. Quant au réglage de la longueur d'onde du modulateur photo-élastique, un senseur (52) contrôle le mouvement de l'une des extrémités de la tige ou barre (32). Le signal (50) provenant de ce senseur (52) est comparé avec un signal de référence (51) qui sert à indiquer la longueur d'onde du rayon de lumière (14) traversant la barre (32), de manière à produire un signal d'erreur qui commande l'amplitude du signal produit par le conducteur (42) du premier transducteur piézo-électrique (34).Optical plate for a photoelastic modulator comprising a rod or a bar (32) elongated with an optically transparent agent, a first piezoelectric transducer (35) being mounted on one of the faces of said bar, so as to apply to the latter an alternative longitudinal constraint. A second piezoelectric transducer (35), intended to detect the transverse oscillations of the bar, is also mounted thereon. A signal from the second piezoelectric transducer is used in a positive feedback loop to control the frequency of the conductive signal from the first piezoelectric transducer. The two transducers are mounted at a distance of about a quarter of the length of the rod or bar (32) from one of the ends of said rod or bar. The two transducers are preferably combined into a single piezoelectric transducer provided with an electrode (40) for detecting transverse oscillations located in an opening of the control electrode (38) of the first transducer. As for the adjustment of the wavelength of the photo-elastic modulator, a sensor (52) controls the movement of one of the ends of the rod or bar (32). The signal (50) from this sensor (52) is compared with a reference signal (51) which is used to indicate the wavelength of the ray of light (14) passing through the bar (32), so as to produce a error signal which controls the amplitude of the signal produced by the conductor (42) of the first piezoelectric transducer (34).

Description

TITLE: "PHOTOELASTIC MODULATORS"

TECHNICAL FIELD

This invention concerns photoelastic modulators, and in particular it concerns photoelastic modulators in which an optical medium is rendered birefringent during the periodic application of stress thereto.

BACKGROUND TO THE INVENTION

Photoelastic modulators, which are also called piezo-optical birefringence modulators, have been available commercially for some time. They are commonly used in some techniques for measuring stress in materials, for birefringence measurements, for circular and linear dichroism measurements and for polarimetry and ellipsometry.

The principle of such devices has been described by James C. Kemp in an article entitled "Piezo-optical Birefringence Modulators: New Use for a Long Known Effect", which was published in the Journal of the Optical Society of America, Volume 59, No. 8, August 1969, and by K.W. Hipps and G.A. Gosby in their paper in the Journal of Physical Chemistry, Volume 83, No. 5, 8 March 1979, entitled "Applications of the Photoelastic Modulator to Polarisation Spectroscope". In essence, the modulator comprises a transparent bar of fused silica or other optically transparent medium in which an extensional vibration is set up by an acoustic transducer. A light beam, linearly polarised at 45 degrees to the axis of the bar, is directed transversely through the bar. The alternating birefringence caused by the alternating stress generated within the bar renders the light beam alternately right and left circularly polarised. The birefringence is due to a retardation of one of the two components of the light within the optical medium, and peak birefringence corresponds to a retardation of one quarter of the wavelength of the light beam. When this peak birefringence occurs, the modulated light beam can be used in circular-dichroism measurements and in the other techniques noted above. " Photoelastic modulator systems of this type, often called "Kemp modulators", or "Kemp resonators", are sold by Hinds International Incorporated of Portland, Oregon, U.S.A.

When making circular dichroism measurements, it is necessary for the degree of birefringence to remain constant while a light of a selected wavelength is used for the measurements.

It is also desirable to be able to alter the wavelength of the light beam and then establish the same condition of peak birefringence at the newly selected optical wavelength. Thus it is desirable to be able to "track" the retardation produced by the modulator as the wavelength of the beam that is transmitted through the optical medium is altered. The following simplified explanation illustrates this point. The retardation (birefringence) that is due to the optical path difference between the ordinary and the extraordinary components of the light beam depends upon the amplitude of the alternating stress within the optical medium of the modulator. If the wavelength of the light beam changes, then to establish the same degree of birefringence, the amplitude of the alternating stress must be varied. The amplitude of the alternating stress is controlled by the amplitude of the driving signal that is used to establish the alternating stress in the optical medium.

Unfortunately, maintaining a constant applired acoustic frequency and tracking the amplitude of the applied driving signal as the wavelength of the light beam varies have proved difficult in practice. In one common form of optical modulator, the acoustic transducer is a bar of crystalline quartz glued end to end with a fused silica optical medium. In order to make this complex acoustic resonator vibrate at the desired modulation frequency, both components must be carefully ground and matched, together with the joining adhesive, on a trial and error basis. Moreover, once the combination is set vibrating at the desired frequency, the assembly must be kept at constant temperature in order to avoid the thermal drifts caused by differential variations in the acoustical properties of the crystalline quartz and the optical medium (the fused silica in this example). Thermal drift degrades the efficiency of the optical modulation or retardation and, therefore, effectively limits the constancy of calibration and the linearity of wavelength tracking. Thus this type of modulator is not suited for operation in any environment where there is a significant temperature variation (such as near to a cryostat or in the vicinity of a furnace) .

A different modulator configuration is described by J.C. Canit and J. Badoz in an article entitled "New

Design for a Photoelastic Modulator", which was published in Applied Optics, Volume 22, page 592,

1983. The photoelastic modulator of Canit and Badoz uses the shear coupling mode of a thin piezo-electric transducer glued directly on to one side of the fused silica bar which serves as the optical medium. A second and similar shear-mode piezoelectric transducer is attached to the bar on the opposite side to and facing the first transducer. The second transducer is a pick-up transducer which furnishes a positive feedback signal to the driving circuit connected to the first transducer. This largely avoids the constancy of calibration problem associated with the differential thermal drift mentioned above. However, difficulties are experienced with this arrangement because (a) the acoustic frequency spectrum present in the bar is complicated (because of complex waves and multiple reflections), (b) the acoustic waves picked up by the second transducer are not only phase-shifted from the waves at the driving transducer but also vary with the driving levels, and (c) the feedback circuit must include an elaborate phase trackable filter, which introduces a significant further phase shift into the feed-back loop. This means that automatic tracking of the optical modulation (retardation) as the optical wavelength changes becomes impractical. To use this type of modulator with light beams of various wavelengths requires an independent manual setting of the modulator at each selected wavelength of the light beam, which is a laborious procedure.

Canit and Badoz have more recently proposed an optical feedback arrangement in which a sensor light beam is directed through the bar at a position opposite the driving transducer and .a suitable optical detector is employed to generate the positive feedback signal. This proposal was outlined in their paper entitled "Photoelastic modulator for polarimetry and ellipsometry", which was published in Applied Optics, Volume 23, No. 17, 1 September 1984. This arrangement, although comparatively elaborate and expensive, does reduce the phase shift problem. Nevertheless, it still does not allow ready adjustment of the retardation, let alone automatic tracking of the retardation over the operational wavelength of the transducer. Spurious signal components are still picked up and reinforced in the feedback loop and the phase shift still changes with driving level, leading to essentially the same problems experienced with the acousto-electric feedback technique.

*)

DISCLOSURE OF THE PRESENT INVENTION 5 It is an object of the present invention to provide a new modulator construction which avoids the problem of temperature stability noted above, and which also permits the modulator to be used in a mode which tracks the wavelength of the light beam being 10 modulated.

This objective is achieved by applying the alternating stress to an elongate bar of the optical medium that is to be used to provide the alternating birefringence in the modulator with a piezo-electric

15 transducer that operates in the shear coupling mode and which is mounted on the optical medium, and having, also on a piezo-electric transducer that is mounted on the optical medium, a sensor electrode which acts as a source of signals for positive

20 feedback to the driving circuit of the transducer. The piezo-electric transducer used to provide the alternating stress is mounted at a point which is substantially one quarter the length of the bar from one end thereof. The sensor electrode is mounted at

25 the same location to minimise the possibility that the electrode will pick up signals from spurious reflections within the optical medium. The basis for this approach is the realisation

(a) that the shear-mode driven optical medium is inherently more simple than the Kemp resonator;

(b) that, in such an arrangement, the best location for the sensor which furnishes the positive feedback signal is the same location as that of the driving transducer; and (c) that it is possible to mount a driving transducer and a sensing transducer at the same point, and even to combine the two associated transducers, without an adverse interaction between the respective transducers, provided the sensor electrode transducer senses transverse signals in the bar of optical material.

Thus, ^* according to a basic form of the present invention, there is provided an optical plate for use in a photoelastic modulator, said optical plate comprising

(a) an elongate rod or bar of an optical medium which exhibits birefringence when a mechanical stress is applied thereto;

(b) a first piezo-electric transducer for periodically applying a longitudinal mechanical stress to the optical medium by shear-mode coupling thereto, said piezo-electric transducer being mounted on a face of the optical medium at a location that is substantially one quarter the length of the rod or bar from one end thereof;

(c) a sensor electrode mounted on a second piezo-electric transducer and adapted to sense transverse acoustical vibrations within the optical medium and to generate signals in synchronisation with the sensed acoustical vibrations, said second piezo-electric transducer being mounted on said face of the optical medium at the same location as said first piezo-electric transducer; and

(d) a driving circuit for said first piezo-electric transducer to which said signals from the sensor electrode are connected as positive feedback signals.

Preferably, the first piezo-electric transducer and the second piezo-electric transducer are formed from a single slice of piezo-electric material, with the driving electrode for the first piezo-electric transducer positioned adjacent to the periphery -of one face of the slice and the sensor electrode positioned within a central aperture in the driving electrode.

It is also preferable, though not essential, for the sensor electrode to be an elongate electrode, extending transversely across the bar of the optical medium, so that it will be much more sensitive to the transverse perturbations induced by the standing wave in the bar than to the longitudinal perturbations which contain many spurious components.

According to a preferred form of the present invention, which is particularly suitable for use in a photoelastic modulator which is to be used with varying wavelengths of the light beam that is to be passed through the optical medium of the modulator, or when high stability of operation of the modulator is required, the optical plate also includes a sensor of the longitudinal expansion and contraction of the rod or bar, which produces a signal that is indicative of the amplitude of the alternating longitudinal stress in the bar or rod, said stress amplitude indicating signal being compared with a reference signal to generate an error signal, said error signal being supplied to a programmable power supply which controls the amplitude of the driving signal that is applied to the first piezo-electric transducer.

For wavelength tracking purposes, the reference signal is directly related to the wavelength of the light beam that is being passed transversely through the rod or bar.

For a better appreciation of the present invention, a preferred embodiment thereof will now be described. In this description, reference will be made to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a block diagram of a polarimeter incorporating a photoelastic transducer.

Figure 2 illustrates, partly schematically, an optical plate for a photoelastic modulator, constructed in accordance with the present invention. Figure 3 illustrates an alternative, and preferred, construction of the driving and sensing photo-electric transducers for the plate of Figure 2.

Figure 4 is a block diagram of one form of electrical driving circuit for the piezoelectric transducer arrangement of the optical plate.

Figure 5 is a block diagram illustrating the high stability and/or wavelength tracking feature that may be incorporated into the present invention.

Figure 6 is a combination of Figures 4 and 5, and depicts the preferred embodiment of the optical plate for a high stability, wavelength _* tracking, photoelastic modulator.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENT The polarimeter illustrated in Figure 1 comprises a broadband light source 10 (for example a Xenon lamp), the output of which is fed to a spectrometer 12 which generates a monochromatic light beam 14. The beam 14 is directed through a plain polariser 16, the optical medium 17 of a photoelastic modulator, and a sample 20 for measurement, and is monitored by a photo- multiplier detector 22. The optical plate 18 of the modulator is driven by a signal from a controller or driver 24 that is applied to the optical medium 17 through a piezo-electric transducer 13 that is connected to the signal line 26. The frequency of the output of the controller 24 is regulated by the positive feedback signal that is derived by a second piezo-electric transducer 15 that is connected to the optical medium 17 and is fed to controller 24 by line 28. The degree of modulation that is to be provided by optical medium 17 (to effect the desired retardation) is controlled by a signal 30 that is derived from the spectrometer 12. The signal 30 is proportional to the wavelength setting of the spectrometer 12 and controls the amplitude of the signal that is supplied to line 26.

Those skilled in this art will appreciate that in a polarimeter of the type illustrated in Figure 1, provided the gain of the feedback signal is kept close to unity, the retardation - in the optical medium 17 can be held as a constant proportion of jthe wavelength of the light beam 14, provided the basic signal used to drive the controller 24 is directly and accurately related to the wavelength of the light beam 14.

Previously, the feedback or servo control signal has been derived by a monitor of the modulation state of the light which has passed through the modulator. Alternatively, the servo signal has been derived from transducers which are attached directly to the body of the optical medium of the modulator, or which are mounted out of contact with the optical medium of the modulator. The present invention relies upon an improved application of this second technique for deriving the feedback signal, namely monitoring the transverse signal that is- generated in the optical medium as a result of the longitudinal mechanical oscillation of the optical medium, at substantially the point of application of the longitudinal oscillation by a piezo-electric transducer. This monitoring is effected by a pair of electrodes mounted on a piezo-electric transducer, which is preferably the same piezo-electric transducer. An embodiment which utilises this technique is illustrated in Figure 2.

The optical plate 18 illustrated in Figure 2 consists of a bar 32 of a suitable optical medium and a first piezo-electric transducer 34 which is attached (in this embodiment by glueing) to one longitudinal face of bar 32. The bar 32 may comprise a plurality..of smaller bars, assembled to form the elongate bar 32 of length 3.. The optical medium of bar 32 is typically a glass or fused silica, but any suitable optical medium material may be used for bar 32.

The transducer 34 operates in the shear coupling mode. It comprises a small slab of. piezoelectric material (for example, lead zirconate titanate or lithium niobiate) having an upper electrode 38 plated on to its upper surface and a lower electrode 36 formed on its lower surface. The lower electrode 36 forms the interface with the optical medium 32. The upper electrode 38 is the driver electrode for the piezo-electric transducer. The first piezo-electric transducer 34 has an aperture 33 formed in its central portion, and a second piezo-electric transducer 35 is located in this aperture and attached to the upper face of bar 32. The second transducer 35 comprises a small slab of piezo-electric material between an upper electrode 40 and a lower electrode 37. As shown in Figure 2 (and also in Figure 3), the upper elecrode 40 is an elongated electrode and is mounted with its elongate direction parallel to the transverse direction of the bar 32. However, various shapes of electrode 40 may be used, provided they sense the transverse mechanical oscillations of the bar 32.

The electrodes 34 and 35 are each_mounted a distance 1/4 from one end of the bar 32. This is the ideal location for electrodes 34 and 35, but a small variation from this location is acceptable in practice. This location of transducer 34 ensures that at the resonance frequency of rod 32, there is good coupling of the excitation energy into the rod

4 32. The rod 32 has a high Q (usually about 10 ) compared with a typical Q for the piezo-electric transducer of about 40 to 50. This location of the transducers also ensures that when rod 32 is in resonance, the signal detected by electrode 40 using transducer 35 represents the transverse oscillation of the rod 32 at this point; it has very little noise associated with it and is almost a pure sinusoidal shape, thus avoiding the need for a complex filtering system to derive the feedback signal for the driver of the modulator. It has been found that very little of the driving signal of the transducer 34 is picked up by the sensor electrode 40 (a maximum of about 0.1 per cent of the driving circuit signal has been detected in modulators constructed by the present inventor) .

The present inventor has also established that if the piezo-electric transducers are combined into a single transducer with separate driving and sensor electrodes, as shown in Figure 3, the same benefits as those described above for the embodiment of Figure 2 are ' obtained. Thus, in the transducer arrangement illustrated in Figure 3, the electrode 38 is the driving electrode for the "first transducer 34" of Figure 2, the electrode 40 is the sensor electrode of the "second transducer 35" of Figure 2, and the electrode 38 is a common electrode, glued to the upper face of the rod 32.

The circuit of the block diagram of Figure 4 shows how the controller 24 operates. The optical plate 18 with its transducers combined (as in Figure 3) is shown schematically. The driving signal from a driver stage 42 is connected by line 26 to the driving electrode 38 of the driving transducer. The signal generated at the sensor electrode 40 is passed through a basic filter 44 (to remove any noise that may have been detected by electrode 40), where it is amplified before being fed to one input of the driver 42, as a positive feedback signal, controlling the frequency of the output signal of driver 42. A DC signal 30, derived from the output of the spectrometer 12 and having an amplitude which is directly related to the wavelength of the light beam 12 is also supplied to the driver 42, to control the amplitude of the output signal of driver 42. The signal 30 is also input to a bias control circuit 46, which generates a bias control output signal 28. The function of the bias control circuit 46 is to maintain the gain of the positive feedback loop close to unity while allowing the depth of modulation (that

_^is, the retardation of the polarised light beam) to be set to a predetermined value, which will be changed if the wavelength of the light beam 14 is altered. ^*

For high stability of the operation of the modulator, and/or when wavelength tracking is required, the arrangement illustrated in Figure 5 is preferably adopted. In this arrangement, a sensor 52, mounted out of contact with the end of rod 32, produces a signal 50 which is indicative of the amplitude of the oscillation of the end of rod 32. Signal 50 is an analogue indication of the degree of retardation within the optical medium 17 (rod 32) that will be experienced by the beam of light 14 (which will be passed transversely through the rod 32 at a location approximately 1/4 from the end of rod 32 which is remote from the transducer assemblies). The signal 50 is input to an amplification and filtering stage 55 and thence to an analogue divider 54 which compares the amplified signal 50 with a reference signal 51. Signal 51 is a signal that is representative of the wavelength of the light that is being transmitted through the modulator and may be the signal 30 shown in Figure 4. The output of divider 54 is input to a programmable power supply 53.

The output of the analogue divider 54, being proportional to the ratio of the two applied signals, constitutes an error signal, which is used to control the amplitude of the output signal of the programmable power supply 53. A variation in the amplitude of the output of power supply 53 causes a change to occur in the amplitude of the signal applied to electrode 38, and thus causes a variation in the retardation that is generated by bar 32.

A stable reference signal 51 which is directly related to the wavelength of the light that is transmitted may be generated by known means.

Those skilled in electronics will appreciate that other servo-control arrangements may be used for controller 24.

Figure 6 illustrates a modulator which incorporates the circuits of Figures 4 and 5. Its operation should be apparent from the above description. A modulator of this type has been found to have a reliable performance and a number of important advantages over the prior art systems, including: 1. Any practical pre-defined retardation (e.g. quarter wavelength) can be maintained with change of optical wavelength from 180 nm to more than 10000 nm with suitable optical materials. This is a much wider wavelength range than the Kemp type modulator. 2. The system is highly stable and reproducibility is excellent. Under normal laboratory conditions a retardation stability of better than 0.2 per cent has been achieved in the wavelength tracking mode. 3. The system is insensitive to ambient temperature changes and therefore readily adapted to field use.

4. The linearity of the wavelength tracking is good.

5. The electronic circuitry can be very simple and reliable. Optical machining and glueing of the piezoelectric transducer is straight-forward and non-critical.

INDUSTRIAL APPLICABILITY

Photoelastic modulators which incorporate the present invention may be used in any system in which conventional photoelastic modulators may be used. These systems include a) systems to measure stress in materials (for example, to detect strain in optical materials); b) birefringence measuring systems, including systems for measuring the thickness of thin films; c) circular dichroism and linear dichroism measuring systems; d) systems for performing ellipsometry measurements; e) systems to measure polarized fluorescence; f) systems to measure the concentration of sugars in solution; g) systems to detect the orientation of polymers in plastics; and h) polarimeter systems for measuring the polarization of stars, galaxies and nebulae.

This list -is not exhaustive.

Claims

1. An optical plate (18) for a photoelastic modulator, said optical plate comprising: a) an elongate rod or bar (32) of an optical medium which exhibits birefringence when a mechanical stress is applied thereto; b) a first piezo-electric transducer (34) for periodically applying a longitudinal mechanical stress to the optical medium by shear-mode coupling thereto, said first piezo-electric transducer (34) being mounted on a face of the optical medium at a location that is substantially one quarter the length of the rod or bar (32) from one end thereof; c) a sensor electrode (40) forming part of a second piezo-electric transducer (35), said sensor electrode (40) being adapted to sense acoustical vibrations within the optical medium and to generate signals in synchronisation with the sensed acoustical vibrations, said second piezo-electric transducer (35) being mounted on said face of the optical medium at the same location as said first piezo-electric transducer (34); and d) a control circuit (24) for said first piezo-electric transducer, to which said signals from the sensor electrode (40) are connected as positive feedback signals.

2. An optical plate as defined in claim 1, in which said first piezo-electric transducer (34) comprises a thin slice of piezo-electric material mounted between a driving electrode (38) and a second electrode (36) which is affixed to said face, and said first piezo-electric transducer (34) has an aperture (33) in the centre thereof, said second piezo-electric transducer (35) being located within said aperture (33).

3. An optical plate as defined in claim 1, in which said- first and second piezo-electric transducers are formed from a single slice of piezo-electric material, the upper surface of said slice containing a driving electrode (38) for said first piezo-electric transducer and a sensor electrode (40) for said second piezo-electric transducer, said sensor electrode being located within a central aperture in said driving electrode.

4. An optical plate as defined in claim 2 or claim 3, in which said sensor electrode (40) is an elongate electrode, mounted so that the elongate direction thereof is parallel to the transverse direction of said rod or bar (32).

5. An optical plate as defined in any preceding claim, including: a) an amplitude sensor (52) positioned to monitor the amplitude of movement of an end of the rod or bar (32), said amplitude sensor producing an analogue signal (50) indicative of said amplitude of movement; and b) means responsive to said analogue signal (50) to vary the amplitude of the signal which drives said first piezo-electric transducer (34).

6. An optical plate as defined in any preceding claim, in which said control circuit (24)

. comprises a) a filter (44) to which said sensor electrode (40) is connected; and b) an amplification and driving stage (42), one input thereto being the output of said filter (44) and a second input thereto being a reference signal (30) having an amplitude which is related to the wavelength of the light beam (14) being passed transversely through said rod or bar (32), the output of said amplification and driving stage being the driving signal for said first piezo-electric transducer (34).

7. An optical plate as defined in claim 6, further including a bias control circuit (46) connected to said amplification and driving stage (42) to maintain the gain of the positive feedback signal from said filter (44) at substantially unity and to permit the amplitude of the output of said amplification and driving stage to be varied in response to variations in the wavelength of said light beam.

An optical plate as defined in claim 5, in which said means responsive to said analogue signal comprises a) an amplification and filtering stage (55), to which said analogue signal (50) is input; b) an analogue divider (54) having a first input which is the output signal from said amplification and filtering stage (55) and a second input which is a reference signal (51) that is directly related to the wavelength of the light beam (14) being passed transversely through said rod or bar (32); said analogue divider (54) producing an output signal which is proportional to the ratio of its two input signals; and c) a programmable power supply (53), controlled by the output signal of said analogue divider (54), the output of said programmable power supply controlling the operation of an amplification and driving stage (42), the output of said amplification and driving stage (42) being the driving signal for said first piezo-electric transducer (34).

9. An optical plate as defined in claim 8, including a filter (44) to which said sensor electrode (40) is connected, . the output of said filter (44) being input to said amplification and driving stage to control the frequency of the driving signal for said first piezo-electric transducer (34).

10. An optical plate for a photoelastic modulator, substantially as hereinbefore described with reference to Figures 2 to 6 of the accompanying drawings.

11. A photoelastic modulator incorporating -an optical plate -as defined in any preceding claim.