HETERODYNE MICHELSON INTERFEROMETER FOR POLARIZATION MEASUREMENTS

Abstract: The interferometer makes use of an acousto-optic device (11, 21) to perform a frequency shift of the beam sent along one of the interferometer branches, so as to allow the deter­ mination of the state of polarization by heterodyne radio­ frequency detection. The acousto-optic deuce can be inser­ ted downstream the means (8) splitting the beam emitted by the source (1) into the two beams sent along the two interferometer branches, or it can also act as the beam split­ ter.

Description: The present invention relates to polarization measurements, and more particularly to a heterodyne interferometer for determining the state of polarization of a radiation emerging from a transparent or reflecting body. It is known that a body transmitting or reflecting a light radiation can introduce variations in the state of polarization of the radiation. Knowledge of the state of polarization of the radiation emerging from the body is of importance to completely characterize the body in respect of its optical properties, and is essential when exploiting interference or beat between radiations, since these phenomena occur only when the radiations are equally polarized. Possible applications include well known applications of classical optics, optical coherent or heterodyne telecommunications (based on a beat) and optical fibre sensors or gyroscopes, requiring the use of fibres maintaining a determined state of polarization. In some applications, a fast recognition of rapidly changing states of polarization is demanded. A polarized radiation can be characterized by electromagnetic field components in a reference system with orthogonal axes x, y. Considering the electrical field alone, the two components are given by: Ex = a1 cos ω t Ey = a2 cos (ω t + Φ) where a1, a2 are the amplitudes of the two components and Φ is the relative phase. To determine the state of polarization it is necessary to measure the ratio a2/a1 between the two amplitudes and phase Φ, whose sign defines the rotation direction on the polarization image, described on plane Ex, Ey as t varies. From these two values further information can be derived necessary to characterize the body under test, e.g. polarization beat length, in case of single-mode optical fibres. As stated, the state of polarization can vary in time. In case of optical waveguides, this usually occurs owing to variable mechanical and thermal stresses which modify their optical properties. In order to determine a time-varying polarization state, some interferometric techniques have proved useful. Examples based on a Mach-Zehnder interferometer have been described by the inventors in the article "A heterodyne Mach-Zehnder polarimeter for real-time polarization measurement", Optics Communications, Vol. 54, No. 2, 15 May 1985, in the paper "A fast heterodyne interferometer for real-time fibre polarimetry" presented at IOOC-ECOC ′85, Venice, October 1985, and in EP-A-0172568. Yet these solutions require all the light beams inside the device to be coplanar, to avoid systematic errors which depend also on the polarization state to be determined and which hence cannot be eliminated by a simple instrument calibration. Further, upon use of a particular radio frequency source for heterodyning, the resulting beat frequency and consequently the response time are limited. A Michelson interferometer is intrinsically free from the disadvantages of the demand for coplaner light since the light beam emitted from the source is split into two beams which are back-reflected; such beams are obviously coplanar, and the distance between the beam-splitter and the mirrors can be maintained very short. An example of apparatus for measuring the state of polarization, based on a Michelson interferometer, is described in "Ellipsometry and polarized light", by R.M.A. Azzam and N.M. Bashara, North-Holland Publishing Company, 1977, pages 262265, and in the paper "Automated laser interferometric ellipsometry and precision reflectometry", by H.F. Hazebroek and W.M. Visser, Journal of Physics, Section E, Vol. 16, 1983, pages 654-661. These documents disclose an ellipsometer, i. e. a device for measuring the polarization state of a radiation reflected by the surface of a body. In that ellipsometer, a polarized radiation is split by a beam splitter into two fractions. One fraction is sent towards the body unter test and reflected onto a mirror by which it is reflected back onto the body and hence to the splitter; the other, acting as a reference beam, is sent to a corner reflector and therefrom to the splitter. The corner reflector is oscillated so as to change by Doppler effect the frequency of the beam sent back towards the splitter in the reference branch. The two beams are recombined by the splitter into a single beam containing both frequencies. The components parallel and perpendicular to the incidence plane on the body under test are separated and sent to different detectors. A microprocessor obtains the required information from the intensities of the beat signals supplied by the detectors. A system of this kind presents a number of disadvantages. More particularly the corner reflector position is critical, since it has to be chosen so as to make the reference beam coincide with one of the two reflector self-polarizations, in order to maintain the reference beam polarization; there are moving parts, which always entail reliability problems; the system operates at low frequency (200 Hz) so that it does not allow detection of polarization fluctuations very fast in time. These disadvantages are overcome by the device according to the invention, which does not present moving parts and operates at high frequencies (from some tens to some hundreds of MHz), so that it can follow even very short fluctuations of the state of polarization. The present invention, starting out from an interferometer as known from EP-A-0172568, i. e. comprising: a monochromatic light beam source; a light-beam splitting-recombining device, which receives a light beam coming from the source, splits it into a pair of partial beams and sends such partial beams along two branches of the interferometer; means inserted in one of such branches to give the partial beam sent along it a predetermined linear state of polarization, so as to form a reference beam; means to impart a frequency-shift to the other partial beam and including an acousto-optic device driven by a radiofrequency signal, which device receives a beam presenting the state of polarization to be determined, emits a first output beam having the same frequency as the received beam and a second output beam whose frequency differs from that of the received beam by a value equal to the frequency of the driving signal; and means to analyze in polarization the recombined beam, to generate electrical signals representing the beat between the equally polarized components of the recombined beam and to obtain the state of polarization from the intensities and the relative phase of such electrical signals; is characterized in that the interferometer is a Michelson interferometer the two branches of which end at respective mirrors arranged perpendicularly to the direction of propagation of the partial beams, that the light-beam splitting-recombining device receives and recombines into a single beam the partial beams reflected by such mirrors, and the acoustooptic device is positioned so as to send at least the second beam towards one of the mirrors and to be traversed again by the second output beam as reflected by said one mirror, whereby it emits a third and fourth output beam one of which has undergone an overall frequency shift, with respect to the reference beam, equal to twice the frequency of said radiofrequency signal and is recombined with the reference beam. A first effect is that the beat signal on which the measurements are made has a frequency twice that of the oscillator generating the radiofrequency driving the cell, and not the same frequency as the oscillator, because a frequency shifting occurs at each passage of the beam through the cell. Thus, the frequency separation between the two beams that are made to interfere is doubled. This is very important when states of polarisation which may vary very quickly are to be investigated, as it allows doubling the variation rate that can be detected. For instance, assuming that the cell is driven at 40 MHz, by the present invention states of polarisation can be appreciated which differ in time by 1/(80·10) =12.5 ns. Secondly, the beam that is passed twice through the acousto-optic cell propagates along the same direction as the beam arriving from the source at the cell whatever the driving frequency may be, as the second passage through the cell causes an angular displacement by the same extent as that caused by the first passage, but in opposite direction. Thus, even if the driving frequency of the cell is changed because a particular application of the invention requires so, there is no need to change the arrangement of the components in order that the frequency shifted beam is collected and recombination of the partial beams takes place. At most, it will be necessary to vary the inclination of the mirrors so that they are still perpendicular to the beams outgoing from the cell, but the check of the perpendicularity is an operation which is made before starting any measurement by using a Michelson interferometer. The change of the arrangement of the components would on the contrary be necessary when a beam having passed only once through the cell is used, as the angular displacement changes whenever the driving frequency changes. Further technical advantages are also obtained by the arrangement of claims 3 to 6. To make the invention clearer, reference is made to the annexed drawings, Fig. 1 and Fig. 2, which diagrammatically show two embodiments of the invention given by way of non-limiting examples. Such drawings show the application of the invention to the measurement of the state of polarization at the output of a single-mode optical fibre which is located between the source of the radiation used for the measurement and the interferometer. This arrangement is the one that better takes into account the fact that the fibre length may exceed source coherence length, so that, was the fibre inserted in an interferometer branch, precise phase relations between the two radiations to be recombined might no longer exist. With reference to Fig. 1, a light-beam source 14, e.g. a semiconductor laser without particular spectral requirements, emits a ligth beam which is collimated and focussed at the entrance of a single-mode optical fibre 4 through a suitable optical system schematized by lenses 2, 3. Beam 5, outgoing from fibre 4 and containing the information on the state of polarization to be determined, is collimated by a further optical system 6 and sent to a Michelson interferometer, denoted as a whole by 7. The interferometer comprises a beam splitting-recombining device 8, splitting beam 5 into a transmitted partial beam 5a and a reflected partial beam 5b, and two branches, ending respectively at mirrors 9, 10. Beam fraction 5a sent along the first branch enters an acousto-optic 11, mounted with its optical axis oriented at the optimal angle (Bragg angle) with respect to beam incidence direction and driven by a suitable radiofrequency electrical signal (e.g. a 40 MHz signal). Device 11, as known, lets through input beam 5a unchanged in frequency and direction, and emits a second beam 5c, with frequency equal to the sum or difference between the frequency of the optical input radiation and that of the electrical driving signal. The direction of beam 5c is determined by the Bragg diffraction law, i.e. it is such that deflection 5a-5c undergone by the beam owing to acousto-optic interaction is equal to twice the Bragg angle. By the arrangement shown in the Figure, the second beam 5c has a frequency equal to the sum of said two frequencies. Beam 5a is intercepted by a suitable absorbing screen 12, while beam 5c reaches mirror 9, perpendicular to its propagation direction, and is hence back-reflected towards acousto-optic device 11. Device 11 shifts in frequency and deviates again the received beam, operating now on beam 5c. The beam deviated and shifted twice in frequency, outgoing from device 11, is exactly superimposed on incoming beam 5a and arrives at beam splitting-recombining device 8. The outgoing beam which propagates unchanged can be intercepted by a device analogous to screen 12 or, by a suitable component arrangement, it can be let out from the interferometer without affecting the measurement. Beam fraction 5b launched into the second branch of interferometer 7 is made to pass through a device 13 giving the beam a well-defined state of polarization; device 13 can be e.g. a Glan-Taylor prism arranged to transmit the linear polarization component at 45° alone. The polarized beam outgoing from prism 13 impinges orthogonally onto mirror 10, is back-reflected, traverses prism 13 again, emerging still linearly polarized at 45°, and arrives again at splitting-recombining device 8. This beam constitutes a reference beam. Splitting-recombining device 8 forms a beam 14, comprising the transmited fraction of the reference beam and the reflected fraction of the frequency-shifted beam. Beam 14 is sent to a polarization analyzing device 15, e. g. a second Glan-Taylor prism with axes coinciding with those of splitting-recombining device 8. Beats among equally polarized components of the two radiations of recombined beam 14 are present at the two outputs of prism 15. These beats are detected by detectors 16, 17, whose output signals are suitably amplified in amplifiers 18, 19, and are fed to measurement and/or display devices 20 (e.g. a vector voltmeter and/or an oscillosccope operating in x-y mode) allowing measurement and/or display of ratio Ex/Ey and of phase difference . Suitable processing means, not shown, will obtain the desired fibre characteristics from measurements of two or more polarization states obtained under different conditions. Detector output signals have amplitude proportional to a1 and a2 and relative phase . In fact, supposing for simplicity sake that the reflected and transmitted beams outgoing from device 8 have equal intensities, the beam arriving at device 8 after reflection onto mirror 9 will be characterized by an electric field Emx = k.Eox.exp [i(ω + 2Ω)t] Emy = k.Eoy.exp {i[(ω + 2Ω)t + } where: Eox=h.a1 and Eoy=h.a2 are the intensities before the double passage through device 11; k, h, are constants taking into account losses due to the efficiency of said device and to the beam splitting in device 8, respectively, and Q is the frequency of the signal driving device 11. The reference beam, linearly polarized at 45°, is characterized by an electric field Erx = Ery = (Eo/ 2 ).exp [i(ωt +  R )] where Eo,  R are given by Eo = Eox² + Eoy² + 2EoxEoy cos  R = arctg [Eoy sin/ (Eox + Eoy cos)] The two fields are superimposed at the output of device 8 giving rise to a sum of the homonymous components (2), (3) along axes x, y. Prism 15 will send the component polarized along axis x towards detector 16 and the component polarized along axis y towards detector 17. The signals outgoing from the detectors are proportional to the intensities (i.e. the squares) of the detected field components. Consequently, once eliminated the d.c. components of the currents outgoing from detectors 16, 17 by filtering in amplifiers 18, 19, the corresponding electrical signals Sx, Sy sent to measurement and/or display devices 20 are proportional to the beats between field homonymous components (2), (3). Sx, Sy are hence oscillating electrical signals at a frequency equal to the difference between the frequencies of the two beams, and will have respectively intensity Sx = K.Eo.Eox cos(2Ω -  R ) Sy = K.Eo.Eoy cos(2Ωt -  R + ) From these relations one can see immediately that the phase difference between the two signals is actually  and that, taking into account the values of Eox, Eoy, their amplitudes are proportional to a1 and a2 respectively. In the embodiment of Fig. 2, where the interferometer is denoted by 70, beam 5 collimated by optical system 6 is directly sent to acousto-optic device 21, having the tasks of both device 11 and splitting-recombining device 8 of Fig. 1. Beam 5 enters device 21 at the Bragg angle to the optical axis of the device. Non-deviated outgoing beam 5d is collected by a total-reflection prism 22 and sent onto a mirror 23, orthogonal to the propagation direction of the beam reflected by the prism. This reflected beam is hence sent back towards prism 22 and device 21. Deviated and frequency-shifted outgoing beam 5e is on the contrary sent to Glan-Taylor prism 24 and to mirror 25, which are identical to prism 13 and mirror 10 of Fig. 1, respectively, and is reflected towards device 21. Prism 22 allows a fair spatial separation between beam 5d, 5e and an easy location of prism 24 and mirror 25, notwithstanding the small angle between the two beams: this contributes to maintaining the longitudinal interferometer dimensions limited. Device 21, owing to its arrangement, causes on beams reflected by mirrors 23, 25 a frequency shift analogous to that performed on incident beam 5. Hence, beam 5d will give rise to a beam with frequency ω - Ω (deviated) and a beam with frequency ω + Ω (non deviated); beam 5 e (with frequency ω + Ω) will give rise to a beam with frequency ω + Ω (non-deviated) and a beam with frequency ω + 2Ω (deviated). The non-deviated beam deriving from beam 5e and the deviated beam deriving from beam 5d are superimposed into a recombined beam 27 and are sent, through a second total-reflection prism 26 acting like prism 22, to Glan-Taylor prism 15 for polarization analysis and subsequent heterodyne detection through detectors 16, 17. The non-deviated beam deriving from beam 5d and the deviated beam deriving from beam 5e are superimposed upon beam 5 and can be exploited for an alignment check, using e.g. an iris 28 inserted between optical system 6 and device 21. The same iris can be used to prevent the beam from reentering the cavity of a semi-conductor laser, thereby changing the coherence length thereof. What stated above for the embodiment of Fig. 1 applies also to the embodiment of Fig. 2, apart from the fact that the beat takes place between optical frequencies ω - Ω and ω + Ω, and not between frequencies ω and ω + 2Ω. The description above clearly shows that the present invention eliminated the drawbacks of the known device. In fact there are no moving parts, and hence mechanical devices designed to generate motion are no longer necessary; the mirrors in both branches are simple plane errors and not composite members like the corner reflector of the prior art, so that no problem arises of critical orientation of the reflecting means with respect to the interferometer plane; finally, with the usual frequencies used to drive device 11 or 21, the electrical signal containing polarization information has a frequency of at least some tens MHz, and hence even very short variations in the state of polarization can be observed. It is evident that variations are possible without going out of the scope of the invention. E.g., If the state of polarization to be determined is imposed by a transparent body whose thickness is much smaller than source coherence length or by a reflecting sample (as in ellipsometric measurements), the body can be inserted inside the interferometer, in the branch which does not contain prism 13 or 24. In the case described of the measurements on a transmitted beam, the processings necessary to obtain the optical characteristics of the body from the state of polarization ought to be modified so as to take into account, in the formulations, the doubel crossing of the body by the light beam. This presents no difficulty for those skilled in the art.

Claims: 1. A heterodyne interferometer for measuring the state of polarization of a radiation outgoing from a transparent or reflecting body, comprising: a monochromatic light beam source (1); a light-beam splitting-recombining device (8; 21), which receives a light beam (5) coming from the source (1), splits it into a pair of partial beams (5a, 5b; 5d, 5e) and sends such partial beams (5a; 5b; 5d, 5e) along two branches of the interferometer; means (13; 24) inserted in one of such branches to give the partial beam sent along it a predetermined linear state of polarization, so as to form a reference beam; means (11; 21) to impart a frequency-shift to the other partial beam and including an acousto-optic device (11, 21) driven by a radiofrequency signal, which device receives a beam (5; 5a) presenting the state of polarization to be determined, emits a first output beam (5a; 5d) having the same frequency as the received beam and a second output beam (5c; 5e) whose frequency differs from that of the received beam by a value equal to the frequency of the driving signal; and means (15, 16, 17, 18, 19, 20) to analyze in polarization the recombined beam (14; 27), to generate electrical signals representing the beat between the equally polarized components of the recombined beam and to obtain the state of polarization from the intensities and the relative phase of such electrical signals; characterized in that the interferometer is a Michelson interferometer the two branches of which end at respective mirrors (9, 10; 23, 25) arranged perpendicularly to the direction of propagation of the partial beams, that the light-beam splitting-recombining device (8; 21) receives and recombines into a single beam the partial beams reflected by such mirrors (9, 10; 23, 25), and the acousto-optic device (11; 21) is positioned so as to send at least the second beam (5c; 5e) towards one of the mirrors (9; 25) and to be traversed again by the second output beam as reflected by said one mirror (9; 25), whereby it emits a third and fourth output beam one of which has undergone an overall frequency shift, with respect to the reference beam, equal to twice the frequency of said radiofrequency signal and is recombined with the reference beam. 2. An interferometer according to claim 1, characterized in that said acousto-optic device (11) is inserted along the path of said other partial beam (5a) outgoing from the beam splitting device (8), and is arranged so as to be traversed again by the second output beam only, whereby it emits said third and fourth output beam which have undergone a frequency shift equal to said radiofrequency and to twice the radiofrequency, respectively, the acousto-optic device sending to the beam splitting-recombining device (8) said fourth output beam. 3. An interferometer according to claim 1, characterized in that said acousto-optic device (21) is inserted along the path of the beam (5) emitted by the source (1) and forms the beam splitting-recombining device, the first and second output beams (5d, 5e) emitted by the acousto-optic device (21) forming said partial beams both of which traverse again the acousto-optic device (21). 4. An interferometer according to claim 3, characterized in that said acousto-optic device (21) is arranged so as to recombine beams whose frequency is the sum and respectively the difference of the frequency of the beam emitted by the source and that of the signal driving the acousto-optic device (21). 5. An interferometer according to claims 3 or 4, characterized in that along the path of one of the partial beams, between the acousto-optic device (21) and the mirror (23), and along the path of the recombined beam, between the acousto-optic device (21) and the means (15) for polarization analysis, total-reflection prisms (22, 26) are located which send such beams towards the mirror (23) and the means (15) for polarization analysis, respectively, and improve the spatial separation between said beams (5d, 27) and the closest ones (5e, 5). 6. An interferometer according to any one of claims from 3 to 5, characterized in that the acousto-optic device (21) is arranged so as to generate, when traversed again by the partial beams (5d, 5e) after reflection thereof by the mirrors (23, 25), beams having the same frequency as the beam incident thereon and to reflect back such beams along the same path as the incident beam, and in that an iris (28) is provided to intercept such beams for a check of the alignment of the interferometer components and/or to prevent such beams from reentering the source (1).

Inventors: CALVANI, RICCARDO, CAPONI, RENATO, CISTERNINO, FRANCESCO
Applicants: CSELT CENTRO STUDI E LABORATORI TELECOMUNICAZIONI S.P.A.
Application year: 1987
Main classification: G01J9
IPC codes: G01J9, G01N21, G01J4, H04B10