MULTIMODE FIBER INTERFEROMETRY AND SEVERAL-MODE FIBER POLARIMETRY VIA PHASE CONJUGATION

While the simplest fiber optics are realized by transmission intensity modulations impressed on multimode fibers, great enhancements in sensitivity are achieved by interferometric or polarimetric methods with light propagated through single-mode fibers. In this paper we report preliminary experiments on retaining the sensitivity of interferometric and/or polarimetric measurements while using only multimode fiber components. The utility of success in this endeavor can be measured by greater experimental simplicity (light injection and alignment tolerances), by cost factors (cheaper fiber optics components), or by larger intensity transmission limits (which can be translated to higher time resolution for a given signal-to-noise ratio). 14 refs., 3 figs.


INTRODUCTION
While the simpfest fiber optics sensors are realized by transmission intensity modulations impressed on multimode fibers, great enhancements in sensitivity are achieved by interferometric or polarimetric methods with light propagated through singkmode fibers. In this paper we report preliminary experiments on retaining the sensitivity of interferometric and/or polarimetric measurements while using only multimode fiber components. The utility of success in this endeavor can be measured by greater experimental simplicity (light injection and alignment tolerances), by cost factors (cheaper fiber optics components), or by !arger intensity transmission limits (which can be translated to higher time resolution for a given signal-to-noise ratio).
It Is not an intrinsic requirement for interferometrfc/polarimetric measurements that a fiber be single mode, since all modes of a multimode fiber are affected by an externally appflad stimulus. Single mode operation is, however, generally a practical necessity because of the averaging over the exit phase or Pofarizatkm, significantly dtfferent for each mode, that occurs even in the quiescent state of a multlmode fiber before the application of the stimufus.
We use phase conjugation for unscrambling of the spatially superposed mod~s at the exit of a multlmcde fiber, prior to deriving the commofl Information carried by all the modes. The phase conjugation is achieved with self-aligning, seff-pumped phase conjugation in BaTi03 [1], requiring no auxiliary beams. While the original phase :onjugate, faithful to the transverse spatial distribution extting the fiber in one pdarfzation, fomw onfy slowly (seconds) In the photorefracttve crystal, the response to subsequent spatially untforrn phase shifts along the direction of light propagation does not have a sign reversal [2]. It follows from the same argument that the response to both this kind of phase The ambient noise was reduced to about 0.2 fringes over a three-minute interval by routing two multimode fibers closeiy together along their entke length. The fibers had a length difference of 10 cm within the oven, but were made approximately equal total length by increasing the path length of the other fiber outside the oven. Both fiber outputs are phase conjugated on the same crystal, vertically dlspfaced to avoid beam overlap wtthin the c~stal, and the return beam of each is recombined with the reference beam, The two approximately 40MHz bea! patterns are then electronically processed and computer aoalyzed for their relative differences. The results during changing oven temperature were consistent wtth the one fiber measurement and are displayed in Fig, 1.
The drtft noise decreases nearfy an order of magnitude further If the total time duratlcn examined Is reduced to only several secmds. Fig, 2 shows the ambient noise (when the oven temperature Is held constant) for three different time intewals, This residual value Is not much more than the 0,02 fringes obtained Independent of time duration when two identical fibers are Intertwined along their entire length, The latter is not a~!seful configuration for an Interferometrlc measurement, but gives an approximation of our efectrorlic noise Ilmlt.
An extension of this phase of ouI' .. ;rk, deferred for that reported below, would also Incorporate a fiber In the reference arm with the acousto-optic cell and use self.allgnkrg phase conjugation on the same or a second self-pumped crystal, A by-product of this approoch would be a doubled hetarodyne frequency due to the forth~nd back transit of the Bragg cell.
When the very high frequency response of the Bragg cell hetet odyne arrangement Is not needed (e,g, temperature measllrements) It Is slmplor and mor~economical to ellmlnate the seperate reference path altogether and to put a plezo-electrlc stretcher modulalon on one of the two multlmode fiber phase conjugator Inputs This reverts to a conventional Michelson NJOarm interferometer except that both arms terminate in the same phase conjugator crystal. The piezo-electric modulation in one arm achieves the same non-integer fringe count capability and unambiguous determination of sign reversal in time of the signal as described in the beginning of this section.
This type of signal processing has been described before, e.g.  Not@that perfect cross-coupllng, le. eve~hlng from the signal arm of A returns on the signal arm of B and vice versa, would work for us with half the signal level (one transit through the phase disturbance instead of two) for a time period until the changing signal appreciably re-writes the infernal gratings.
Even so this is not of value for us because comdete crOss-couplin9~nnot be extended beyond two channels.
We summarize the above by stating that at the present time the prospects for 6 simultaneous independent interferometer pairs on a 5 mm height cvstal and 18 pairs on a 15 mm height crystal appear reasonable. We use an argon-ion laser input furnishing light through a multimode lxN star ccmpfer, each output arm spliced to one arm of a 2x2 multimode coupfer that is the input to each of N interferometers. It requires about 2 mw of light incident on the phase conjugator through each interferometer arm to get good conjugation.
There are two directions for future research whkh might increase the number of inputs in a horizontal plane possibfe on a single phase conjugator crystal. The first is using different incommensurate piezostretcher frequencies for each ver!ioal column of interferometer pairs and electrically filterfng out the cross-talk. The second is using different wavelength light inputs (multiple laser diodes repfacing the argon-ion laser source). No cross-talk between incohemt beams differing by more than 1 nm has been reported. However seff-pumped phase conjugation in BaTi03 becomes more difficult and lees efficient at the longer wavelengths charscterist!c of laser diodes [9].

SEVERAL-MODE FIBER POIARIMETRY
The circu!ar birefringence imposed on the two degenerate orthogonal polarization modes d a "single mode" fiber by a longitudinal magnetic field io the basis of Faraday rotation. Vla Ampere's law the polarization rotation through single mode fiber loops measures the total current enclosed by the loops.
The preemt status of this type of measurement is reviewed in these proceedings [10]. We report below our initial results on making Faraday rotation measurements with the BaTi03 selfpumped phmso cor~jugator at the 514 mm argon-ion laser wavelength using a Corning fiber that is single mcxb at 1,3 pm. Based on the V-number there are 10 (doubly degenerate) modes at 514pm [13]. Linearly polarized light entering the approximately 5 meter long fiber section emerges almost completely unpolarized. The fiber is loosely wound in X turns of 4 cm diameter around a damped, osciliato~capacitor discharge current. As expected, a two-polarization analyzer measurement (450 extinction separation) at the fiber exit yieldad nothing.
By using the two-orthogonal polarization input method on the BaTi03 phase conjugator of [5], (subsidia~optics put both polarizations into the @ane required by the crystal), we made the twoanalyzer-at45°measurements following a non-polarizing beam splitting at the entrance end of the fiber. The conventional processing gave the result presented in Fig. 3a A definitive result of this experiment based on the known Verdet constant of glass is that the magnitude of the rotation is that tG be expected for a one-way and not a two-way transit. We refate this to the time lag factor in forming a phase conjugate in photorefractive crystals as follows. The initial phase conjugate gratings are written prior to the applioetion of the magnetic field midway along the fiber path.
For subsequent polarization rotations the individual gratings do not change fast enough to keep up, but instead respond to a changing intensity level as the rotation decreases the intensity Ievefs in the original pdarlzation direction. The return light at the Cqsid therefore tws the same spatial structure as before rotation set in (reduced intensity), ancf In tt~e absence of rotation would 'unscramble" to the original spatial pattern and polarization direction at the fiber entrance. Polarization rotation on the return path is superposed on this patter, I and gives the one-way transit information.
The reasons for the distortions in the cument waveform are not clear at present. Either or both of two distinct problems may be invofved. The first Is that we have no knwfedge of the amount of resfdusl linear bkefringence in our ten mode fiber. As stated above I!near birefringence is known to cause distortions. If this Is the dominant probfem any of the methods used with s;ngle mode (twisting, annealing, or spun HiBi fiber) should improv6 tho results and open the way for truly multimode (farge core) fiber to be used.
The other open question is more fundamental and troubling. We do not know how well the exquisitely precise unscrambling of modes in a fiber by phase conjugatim works when the polarization of the return wave, due to polarization rotation away from the conjugdor, creates different polarization directions everywhere along the fiber palh for the forward and return beams. There is, for instance, the Goos-Hanchen Effect [14], si dif!ercntial shift along the propagation direction for ordinary and extraordinary rays undergoing total internal reflectkm. ('lhis will be suitable for experimental test when we bring together a non-blrefrlngent single mode fiber at a wavelength amenable to phase conjugation and of more than 2 mm intensity exiting the fiber,) If the distortion problem Is Indeed Inherent to phase conjugation we also do not know If Increasing the number of modes to true multlmode will increase the distortions or decrease them by fuflher averaging, In any case k seems likely that smaller rotation angles than the Z degrees maximum involved In Fig. 3a, either due !O smaller currents or fewer fiber loops, wIII improve the fidelity of the measurement.