GB2184252A - Optical state-of-polarisation modulator - Google Patents

Abstract

An optical measurement system includes a polarisation modulator formed of two elements in tandem that are each cyclically driven to vary their birefringence to produce an output polarisation state that is swept over ranges such that the time integral of the system photodetector output becomes independent of polarisation. It is shown that, on the Poincare sphere, the birefringent elements must have orthogonal eigenstate axes and be driven at different but uniform rates in order for the time-weighted distribution of output polarisation states to be symmetrical about the sphere centre. The birefringence of the elements can thus be linear for one and circular (Faraday effect) for the other; or as shown can be linear for both if there is a relative physical orientation of 45 DEG , as between squeezer elements 40,41 applying stress to fibre 15. The drive waveforms are each triangular with amplitudes providing full-wave changes in birefringence. The system is a reflectometer using heterodyning of backscattered light (Fig. 1). <IMAGE>

Description

SPECIFICATION Optical state of polarisation modulation This invention relates to optical signal processing in which light is passed through an optical state of polarisation (SOP) modulatorthat is operated in such a waythatthe SOP ofitsoutput describes a path on ihe Poi ncaré sphere that exhibits time-weighted symmetry about its centre. Such signal processing finds application in certain polarisation sensitive systems forthe derivation of a detected output signal that is independent of SOP.

For example, in an optical heterodyne or homodyne system coherent light from two paths is mixed, and the amplitude of the resulting signal depends in part upon the relative SOP's ofthetwo interfering light beams.

This dependence can be inconvenient, particularly if the SOP of one of the interfering beams is unknown.A particular example is to befound for instance in a coherent light optical fibre reflectometer. In such a reflectometerthe backscatter signal from the fibre undertest is mixed with a local oscillator signal.The SOP of the light fro the local oscillator can relatively easily be set to predetermined state, typically a linearly polarised state of a preferred orientation. However the backscattered light is generally of quite indeterminate SOP.For optimum sensitivity of the reflectometer itwould be necessary to ensure that at the mixing pointthe two signals have the same SOP, but if the SOP ofthe backscattered light is indeterminate there is no obvious way of arranging to modify the SOP of the local oscillator output to match it. The optical signal processing of the present invention does not attempt two achieve this match, but it enables the local oscillator output SOPto be manipulated in such a waythatthe mixed signal, when arranged to fall upon a detector, will provide an electrical output signal which is readily convertible to a signal whosetime-averaged value is independent of the mismatch of polarisation states at the optical mixing point.

According to the present invention there is provided an optical state of polarisation (SOP) modulatorwhich modulator includes two variable birefringence elements optically in tandem which are arranged such that on a Poincaré sphere the birefringence (eigen state) axis of one is at right angles to that of the other, andwherein associated with each element is drive means for driving that element cyclically at a different frequency from that with which the other is driven.

The invention also resides in a method of optical signal processing in which light is transmitted through an optical state of polarisation (SOP) modulatorwhich modulator includes two variable birefringence elements optically in tandem that are arranged such that on a Poincaré sphere the birefringence (eigen state) axis of one is at right angles to that of the other, wherein elements are driven, one at a different frequency from that ofthe other, so asto provideforany input SOP an output SOPthatevolves on the surface ofthatsphere in a manner providing time-weighted symmetry at its centre.

There follows a description of a coherent light optical fibre reflectometerwhich incorporates an optical SOP modulatorforoperation in a manner embodying the invention in a preferred form. The description refersto the accompanying drawings in which Figure lisa schematic representation of the reflectometer, and Figure2 is a Poincare sphere diagram illustrating the mode of operation of a single variable linear birefringence elements; Figure3 is a Poincaresphere diagram illustrating the mode of operation ofthe modulator of Figure 2; and Figure 4 is a schematic representation of the SOP modulator of the reflectometer of Figure 1.

Referring to Figure 1 ,the light source for a coherent light reflectometer is provided by a laser diode 10. Light from this laser, which may incorporate a length offibre (not shown) for line narrowing purposes, is fed bya single mode fibre 11 to afibre directional coupler 12. The construction ofthe coupler is such as to transmitthe majority, typically 80%, ofthe laser light to afurthersingle mode fibre 13 terminating in an expanded beam collimating lens 14,whilethe remainder is transmitted via a single mode fibre 1 5to a fibre directional coupler 16. In the optical path between coupler 12 and 16 are located an optical SOP adjustor 17. (The nature ofthis last-mentioned optical element will be described later).Light emerging from the collimating lens passes through a Bragg acousto-optic optical frequency modulator 18 before being collected by a furthercollimating lens 19 and launched into a single mode fibre 20. Single mode fibre 20 terminates in a 3 dBfibredirectional coupler 21 one output part of which is connected to the fibre under test 22, while the other is connected to a total absorber 23. The 3dB coupler 21 directs halfthe backscattered light returning from the test fibre 22 into a length of single mode fibre 24 connecting the 3dB coupler 21 with the fibre directional coupler 16.Directional coupler 16 is constructed so that the majority, typically 80%, ofthe backscattered light in fibre 24 is directed to its output port that terminates in a photodetector 25. The other output port terminates in a total absorber26.

Directional coupler 16 thus acts as an optical heterodyne mixerthat mixes backscattered light propagating in fibre 24with 'local oscillator' light propagating in fibre 15 from the output of the SOP modulator 17bathe photodetector output current is fed via a filter 27 turned to the modulating frequency of the Bragg cell 18, typically 40 MHz, to an arithmetical processing unit 28, which integrates the square of the output current.

The output current ofthe photodetector 25 is proportional to the scalar product ELO . Ebbs, where ELO is the optical field of the optical field ofthe light propagating in fibre 15 (local oscillator), and Ess is the optical field of the light propagating in fibre 24 (backscatter).

In thecasethatELO andE85 are both linearly polarised, and thatthe angle between their planes ofpolarisation is 'A', it is seen that the output current I, ofthe photodetector 25 is given by Ii = k.lELolwiEBse cos A. Now ifthe plane of polarisation of either one of these fields (but not both) is rotated by 90 , a new value of photodetector output current 12 will resultwhich is given by 12 = k .IFLoI.iEBs. sin A. Itfollowsthereforethat by squaring and summing theoutputcurrents Ii and 12 there is formed an output signal which is independentofthe angle'A'.

All possible states of polarisation can be uniquely represented by points on a Poincaré sphere, and on the PoincarB sphere this rotation by 900 ofthe plane of polarisation is represented by a rotation of 1800 around the equatorial great circle (H PVQ = Figure 3) of linearly polarised states. These two linearly polarised states 1800 apart on the Poincaré sphere sum to the centre ofthe sphere.

So far it has been shown that if one ofthe two interferring beams is switched between two linearly polarised states that sum to the centre ofthe Poincaré sphere, then by summing the squares ofthe resulting photodetector currents it is possible to derive a signal that is independent ofthe relative SOP's of thetwo interferring beams. It will be evidentthatthis is also true if the switched SOP beam is not linearly polarised in either of its two states that sum to the centre of the Poincaré sphere, and it can be shown that the relationship still holdsforthe more general case of switching between a set of morethan two SOP statesthatsatisfythe condition that the numbers of the set sum to the centre of the sphere.Generalising further from this, it is seen that if a modulator is operated to sweep the SOP of one ofthe interfering beams along a path on the Poincaré sphere that exhibits time-weighted symmetry about its centre, for instance a path that sweeps at uniform rate cyclically around a great circle of that sphere, then it is possible by integrating the square of the photodetector outputto derive a signal that is independent ofthe relative SOP's ofthe two interfering beams.

Referring to Figure 2, linear birefringence is represented on the Poincarésphere as a rotation about a particular (eigen state) axis lying in the plane ofthe equatorial great circle HPVQ of linearly polarised states.

(On this sphere the points H and V represent horizontally and vertically polarised states, the points Land R represent left-handed and right-handed circularly polarised states, and the points P and Q representthetwo linearly polarised states with polarisation planes inclined at 45" to the horizontal and vertical planes. Forthe purpose of this specification quarter wave linear birefringence is defined to mean the birefringence afforded by an element in which the optical path length difference for its two principal directions differs by nk/4whereA is the wavelength of the light and n is an odd integer.Similarly half-wave linear birefringence is defined to mean the birefringence afforded by an elementforwhich this difference is no/2.) Arbitrarily assigning the birefringence (eigen state) axis as the axis PQ, if the strength ofthe birefringence is given by a rotation of A", then, if light enters the birefringent element with an SOP defined by some arbitrary point B, itwill leavethe elementwith the SOP defined bythe point D, where the points B and D subtend an angleAOatthe centre ofthe (small) circle that passes through B and has its centre C lying on the birefringence axis PQ.If the birefringence is stress induced, and is increased from zero up through the value of A"to 360", then the output SOP willfirst evolve along the small circlefrom Bto D, and then all the way round the small circle backto B again. Uniform procession around this small circlewill produce time-weighted symmetry about its centre C, but, if the pointB does not lie on the great circle through HLVR, in no way is it possibleto vary the rate of procession so asto producetime-weighted symmetry about the centre ofthe sphere.

One solution to this problem isto provide some form of SOP adjustor immediately upstream ofthe stress-induced birefringence element. This adjustorisfirstsetto bring the SOP and the inputtothe stress-induced birefringence element to some point on the great circle through HLVR, and then the stress-induced birefringence element, which may for instance be constituted by a length of optical fibre laterally stressed to a PZTsqueezer, can be acted upon to vary cyclically the stress applied with an amplitude providing a full-wave difference in birefringence between the points of maximum and minimum applied stress. The application of the stress has to be in a mannerto provide the required time-weighted symmetry, and could conveniently be achieved by the application of a triangularwaveform to the PZT squeezerto provide uniform exploration.

An alternative solution to this problem is provided by the method of the present invention. A particular feature ofthis solution is that it avoids the requirementforan SOP adjustorto preceded the SOP modulator.

This solution involves arranging for there to be two cyclically driven variable birefringent elements driven with differentfrequencies and configured so that the eigen state axis of one is at right angles to that of the other. It is not immediately particularly evident that in the general casethese conditions are sufficientto providethe required time-weighted symmetry, but it is more readily apparent in the particular case where the two drive frequencies are widely different.

Referring to Figure 3, and assuming forthe sake of example that the two eigen state axes are respectivelythe PZ axis and the LR axis, then, if the input SOP to the first element is defined by some arbitrary point 'B', the modulation ofthis element will cause its outputSOPto evolve aroundthesmall circle 30 on the Poincar6 sphere that intersects the point E and has its centre lying on the PZ axis. If it is further assumed thatthis evolution is very slow compared with evolution of SOP produced by the modulation ofthe second element, then, during the first full wave modulation of this second element, the evolution ofthe input to this second element around small circle 30 is substantially zero. Hence during this period the output SOP from the second element will evolve substantially around the small circle 31 that intersects the point E and has its centre lying on the LR axis. Ata later point in time by which the modulation ofthe first element has caused its outputto evolve to the point F, one full-wave modulation ofthe second element will cause its output SOP to evolve substantially around the small circle 32 that intersects the point F and has its centre lying on the LR axis.It can be seen therefore that, in the course of a period corresponding to thefull-wave modulation of the first element, the output SOP from the second element will have evolved in such a way as to cover substantially the whole of that portion ofthe surface ofthespherethat lies between the small circles 33 and 34thataretangenttosmall circle 31 and havetheircentres lying on the LR axis. Clearly this provides the requisite time-weighted symmetryaboutthe centre ofthe sphere underthe condition thatthe modulation avoids introducing any bias causing eitherelementto dwell longeratany one angle of evolution about its eigen state axis than any other.In other words the modulation of each element must be such that it exhibits aflat probability densityfunction such as is conveniently provided for instance by a sawtooth, our a triangular, waveform of appropriate amplitude to induce a peak-to-peak difference in birefringence in that element equal to one oran integral number of full-waves.

Correspondingly, if the modulation applied to the first element is of a very much higherfrequencythan that applied to the second, it will be seen that the evolution of SOP provided bythe modulation ofthesecond elementwill produce a path in which there is formed a sequence of small circles generated from a precession of small circle 31 overthe surface ofthe sphere buy a rotation about the LR axis. Thus, after about a one-fifth full-wave modulation ofthe second element, afull-wave modulation ofthefirst element will produce an SOP evolution at the output ofthe second element around the small circle 35.The nett result is that, as in theformer instance, in the course of a period corresponding tothefull-wave modulation ofthe more slowly modulated element, the output SOP from the second element will have evolved in a way covering substantially the whole ofthat portion ofthesurface ofthe sphere that lies between small circles 33 and 34.

Ifthetwofrequenciesthatare applied tothetwo elements are in simple ratio, then the outputSOPwill execute a closed loop path, analogous to a Lissajous figure, which can be shown to possess the requisite symmetry about the centre of the sphere except for the case where the two frequencies are identical.

A linearly birefringent material, such as a uniaxial crystal, has its birefringence (eigen state) axis lying in the plane containing the equatorial great circle of linearly polarised states of the Poincare' sphere, whereas a circular birefringent material has its eigen state axis aligned with the LR axis ofthe Poincaré sphere. Therefore, in order to provide the PO and LR eigen state axes configuration discussed previously with particular reference to Figure 3,the modulator 17 of Figure 1 will consist ofthe tandem arrangement of a variable linearly birefringent element and a full-wave variable circularly birefringent one.Alternatively, the requirementfora variable circularly birefringent element can be avoided by choosing, as the requisite orthogonally related eigen state axes, the PQ and HV axes in which case both elements are constituted by variable linearly birefringentelements. Variable linear birefringence may be induced by the application of modulated amplitude stress to an optical element, and a convenient form forthe modulator 17 of Figure 1 is provided by a length of single mode optical fibre 15 passing through two PZT squeezer elements 40 and 41 (Figure4) oriented with their squeeze axis physically at 45' to each other so as to define directions inclined at 90" to each other in the equatorial plane ofthe Poincare sphere. Thetwo squeezer elements are driven with sawtooth or triangularwaveforms of different periodicity each having the requisite amplitude to induce a peak-to-peak full-wave change in birefringence.

If for some reason it was desired notto usetwo variable linear birefringence elements in the modulator 17, eitherthefirstofthe second squeezer element of Figure4 could be replaced bya variable circularbirefringence element. Such an element can be constituted for instance by a Faraday effect element in which circular birefringence is induced by the presence of a magnetic field aligned with the direction of light propagation.

Such a Faraday effect element can in principle be constituted buy a length of single mode optical fibre with an appropriate winding, but at least in part because ofthe much largerVerdetconstants currently obtainable in integrated optics structures, it would generally be preferred to employ an integrated optics version ofthe element. Thevariablecircular birefringence element is like the linear birefringence elements in that it requires to be driven with a waveform having a flat probability density function, conveniently a sawtooth or a triangular waveform having the requisite amplitudeto induce a peak-to-peakfull-wave change in birefringence.

Claims (9)

1. An optical state of polarisation (SOP) modulatorwhich modulatorincludestwo variable birefringence elements optically in tandem are arranged such that on a Poincaré sphere the birefringence (eigen state) axis of one is at right angles to that ofthe other, and wherein associated with each element is driven meansfor driving that element cyclically at a different frequency from that with which the other is driven.

2. An SOP modulatoras claimed in claim 1, wherein the drive means associated with each variable birefringence element is adapted to produce a modulation of birefringence exhibiting a sawtooth, ora triangular,waveform whose peak-to-peak amplitude induces a birefringence change equal to one oran integral numberoffull-waves.

3. An SOP modulator as claimed in claim 1 or 2, wherein at least one of the variable birefringence elements is a variable linear birefringence element.

4. An SOP modulator as claimed in claim 3, wherein the or each variable linear birefringence element is provided by a length of single-mode optical fibre and associated nechanical means adapted to act upon the fibreto provide cyclically varying strain to induce linear birefringence of cyclically varying amplitude.

5. An SOP modulator as claimed in claim 3 or4, wherein both variable birefringence elements arevariable linear birefringence elements.

6. An SOP modulatorsubstantially as hereinbefore described with reference to the accompanying drawings.

7. An optical homodyne or heterodyne system in which there is included in the light path of one ofthe light beamsthat are coherently mixed bythe system an SOP modulator as claimed in any preceding claim.

8. An optical fibre time domain reflectometerincorporating an optical system as claimed in claim 7.

9. A method of optical signal processing in which light is transmitted through an optical state of polarisation (SOP) modulatorwhich modulator includes two variable birefringence elements optically in tandem that are arranged such that on a Poincaré spherethe birefringence (eigen state) axis of one is at right angles to that ofthe other, wherein elements are driven, one ata differentfrequencyfrom thatofthe other, so asto provide,for any input SOP, an output SOPthatevolves on the surface ofthatsphere in a manner providing time-weighted symmetry at its centre.