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656 OPTICS LETTERS / Vol. 8, No. 12 / December 1983

Birefringent-fiber polarization couplerR. C. Youngquist, 1.L. Brooks, and H. J.Shaw

Edward L. Ginzton Laboratory, Stanford University, California 94305Received August 10, 1983

Periodically stressing a birefringent fiber once per beat length can cause coherent coupling to occur between polar-ization modes. Such a birefringent-fiber polarization coupler is described here. More than 30 dB of power trans-fer between polarizations has been achieved. The device has been used as the output coupler of an in-line Mach-Zehnder interferometer, and better than 25-dB on/off extinction has been measured. The device is wavelengthselective and can be used as a multiplexer or as a notch filter. A notch of 9-nm full width at half-maximum hasbeen achieved with a 60-period comb structure.

Birefringent fiber maintains two linear orthogonal po-larizations along its length.1'2 This property makes itattractive for use in fiber-optic systems, in which po-larization-dependent errors or offsets can occur. 3' 4Polarization-dependent errors in fiber gyroscopes canbe removed by using birefringent fiber, as was demon-strated by Burns et al. 5 In systems such as this, onlyone of the polarization axes is used, but there are bire-fringent fiber systems in which both axes can be used,such as in an in-line Mach-Zehnder interferometer.For double-axis systems a device that couples the lightin the two polarizations in a phase-preserving mannerwould be required. In this Letter such a birefringent-fiber polarization coupler is described. The device isbased on the principle of achieving phase matchingbetween states of different propagation velocitiesthrough periodic coupling.6 This principle has beendemonstrated in both bulk7 and integrated optics.8Birefringent fiber has two orthogonal polarizationaxes, labeled x and y in Fig. 1. Typically, for highlybirefringent fiber, light propagating down one of theaxes will not couple appreciably to the other axis. It hasbeen demonstrated that an additional birefringence,Anp, can be induced by applying pressure to the fiber.9This birefringence is given by

Anp = an3CfI2d,where a is a constant equal to 1.58 for round fiber, n isthe mean refractive index of the fiber, C is a photoelasticcoefficient, f is the force per unit length applied to thefiber, and d is the fiber diameter. In calculations, thevalues n = 1.46, C = 5 X 10-12 (mks), and d = 65 Amwere used. For small forces the additional birefringencecan be treated as a perturbation to the fiber's normalpolarization-preserving birefringence. For the purposeof analysis it is assumed that the applied force is at 450to the fiber axes. However, the angle is not critical, anddeviations from 450 can be adjusted for by increasingthe applied force. The first-order result of the per-turbation birefringence is rotation of the fiber's originalaxes through a small angle 0, as shown in Fig. 1. Thissmall birefringence does not significantly change the

magnitude of the total fiber birefringence An. Theangle 0 is given by

0 -sin(0) =Anp 2 1/22+An2 + if nAn)The total birefringence An is assumed to be constantwith wavelength and can be measured by directly ob-serving the beat length L = X/(An) of the fiber at aknown vacuum wavelength X. The fiber used in theexperiments had a measured An = 7.4 X 10-4.Light originally polarized along the x axis will de-compose into components polarized along the primedaxes when entering a squeezed region, as shown in Fig.1. The relative phase of the light in the two polariza-tions will change by 7r ad in half a beat length. If atthis distance the force on the fiber is removed, the lightwill decompose back into components along the originalaxes with an amount cos2(20) in the x polarization andsin2(20) in the y polarization. After the light hastraveled another L/2 distance, the proper phase rela-tionship in the two axes will be established such that asecond pressure region will cause further power transfer.

Fig. 1. On application of a small force to a birefringent fiber,the principal polarization axes x and y rotate by an angle 0 tobecome new principal polarizations x' and y'.

0146-9592/83/120656-03$1.00/0 1983, Optical Society of America

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December 1983 / Vol. 8, No. 12 / OPTICS LETTERS 657

Fig. 2. Birefringent fiber polarization coupler. Plastic ridgesare used to produce periodic pressure regions in the fiber.

For a single L/2-length stressed region and L/2 un-stressed region, a Jones matrix T can be written to de-scribe the amplitude polarization transformation of thisstructure:

T -cos 20 sin 26-sin 20 -cos 20]Repeating such a structure N times yields a total po-larization-transformation matrix

TN - [(...i1)N cos 2NO (_ l) N+ I sin 2NO](_.1)N sin 2NO ( 1 )N cos 2NO ]Therefore complete coupling from one polarization tothe other can be achieved by applying a force F to theN ridges such that 2NO = Ir/2. For large N (>5) this

optimal force is given byF - \/sfAnLdir/4an C.For example, if the beat length L is 0.813 mm and theparameters given above are used, a force of 1.77 N (180g) would be needed for complete coupling.A device in the form of a comb structure, as shown inFig. 2, was constructed to produce periodic pressureregions in the fiber. The fiber is squeezed between twoplates. The bottom plate consists of polished metal andthe top plate of N square ridges cut in Delrin (a plastic).Delrin is more pliable than silica and thus avoids dam-aging the fiber. Each ridge is 0.41 mm wide, and thereare 0.41-mm gaps between adjacent ridges. Threedowel pins serve to guide the plastic plate and to mini-mize rocking of the ridges on the fiber. A rotatablenotched cylinder at each end of the device allows thefiber to be positioned such that the polarization axes areat about 450 to the applied force. The fiber jacket wasremoved in order to expose the fiber directly to theridges. The total device length is 10.16 cm.The experimental configuration used to evaluate thedevice is shown in Fig. 3. Light polarized along aprincipal axis was launched into a 49-cm length of el-liptical-core birefringent fiber. With a polarizer at theoutput an extinction ratio between the fiber polarizationsof 19 dB was achieved regardless of wavelength. Thislimit may be set by scattering loss in the fiber (an early

fiber having loss of more than 150 dB/km). At certainwavelengths the extinction ratio reached 32 dB, possiblybecause of destructive interference of the scatteredlight. A coupling ratio for the device is defined as -10log(power not coupled/power coupled). When thecomb structure was placed upon the fiber and pressureapplied, a coupling ratio greater than 32 dB wasachieved, typically with a force of about 2.2 N (220 g).This ratio was observed with 10 ridges at 633 nm andwith 30 and 60 ridges at approximately 608 nm. Theloss was measured by summing both polarization in-tensities at the fiber output while operating the device.No loss was observed to within laser noise (-2%). Thedevice suffers from stability problems resulting frommaterial fatigue or relaxation.The phase dependence of the birefringent-fiber po-larization coupler can be seen by its use in a Mach-Zehnder interferometer configuration. Refer to Fig.3: the device was set to approximately 50/50 coupling.The input polarizer was then rotated 450 so that lightwas launched equally down the two polarization axes,which have different phase shifts in response to thermalchanges. A dynamic range of greater than 25 dB wasmeasured as the fiber was thermally expanded andcontracted. This demonstrates that the device couplesamplitude and can be used in interferometric systems.A complete in-line Mach-Zehnder interferometer couldbe constructed by placing two of the devices in series ona single length of fiber.The comb coupler must be designed for a particularwavelength because the beat length of the light in thefiber is not constant as a function of wavelength. Whenthe device is used at a different wavelength, the phaseshift AO over a ridge length changes from 7r rad to 7r +26 rad. Consequently, complete power transfer can nolonger take place. Assuming proper weighting of theridges so that 2Nd = 7r/2, the transfer matrix over asingle ridge and gap period becomesT = [sin2 0 - cos 2 Oet26 sin 0 cos 0(1 + ei2 )

[-sin 0 cos 0(1 + e-i2 6 ) sin2 0 - cos 2 det12 6If the light is originally launched in only one polariza-

Fig. 3. Schematic diagram of the experimental setup.

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658 OPTICS LETTERS / Vol. 8, No. 12 / December 1983

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WAVELENGTHnm)Fig. 4. Theoretical curve and experimental data of powerthat stays in the original polarization as a function of wave-length.

tion, after N ridges the fractional power coupled intothe second polarization is given by IK12,whereK = -sin 0 cos 0(1 + e-i2b) [i(1- _ -1 |b = sin2 0 - cos 2 0 cos 26.

The amplitude coupling K iS the off-diagonal matrixelement of TN. Figure 4 shows the theoretical curve(solid line) of the light left uncoupled for a 60-ridgedevice applied with uniform optimal pressure. The fullwidth at half-maximum is theoretically approximatelyX/N.The dependence of coupling on wavelength was in-vestigated experimentally by using a dye laser tunablebetween 569 and 614 nm. The device used was a 60-ridge coupler with a center wavelength of 609 nm. Theexperimental setup is shown in Fig. 3, in which the lightleft in the original polarization (i.e., not coupled) isdetected after the analyzer. A ratiometer was used tocompensate for laser-power fluctuations as the wave-length was changed. The reference beam was alignedat a shallow angle to the signal beam so that the reflec-tion from the beam splitter would be polarization in-dependent. Results are plotted in Fig. 4 and agree quitewell with theory for the central notch. A full width athalf-maximum of 9 nm was observed. However, thesidelobes were higher than predicted because of unevenpressure of the ridges on the fiber. This unequalpressure was probably caused by variations on the orderof angstroms in the fiber diameter and ridge height andcan be dealt with by constructing individually weighted

ridges. The width of the central peak indicates thepotential of this polarization coupler for use as a mul-tiplexer or notch filter.A birefringent-fiber polarization coupler has beendescribed. The device consists of a set of ridges on apiece of plastic that are used to perturb periodically thepolarization axes of a birefringent fiber. With a totalforce of approximately 2.2 N (220 g), more than 32 dBof power transfer has been repeatedly obtained. Thedevice is an amplitude coupler and can be used in theconstruction of an in-line Mach-Zehnder interferom-eter. Extinction ratios better than 25 dB have beenmeasured between the on/off states of the interferom-eter. The device s wavelength dependent and thus haspotential use as a multiplexer or filter. A full width athalf-maximum of 9 nm has been measured with a 60-ridge device. Further research is being carried out toimprove stability and explore applications of the de-vice.

The authors wish to thank Keith Doty for fabricatingthe various ridged devicesand Andrew Corporation forsupplying the birefringent fiber. This research wassupported by Litton Systems, Inc.References1. S. C. Rashleigh, W. K. Burns, and R. P. Moeller, "Polar-ization holding in birefringent single-mode fibers," Opt.Lett. 7,40 (1982).2. K. Okamato, T. Edakiro, and N. Shibata, "Polarizationproperties of single-polarization fibers," Opt. Lett. 7, 569(1982).3. R. Ulrich and M. Johnson, "Fiber-ring interferometer:polarization analysis," Opt. Lett. 4, 153 (1979).4. T. G. Giallorenzi, J. A. Buchard, A. Dandridge, G. H. Sigel,

Jr., J. H. Cole, S. C. Rashleigh, and R. G. Priest, "Opticalfiber sensor technology," IEEE J. Quantum Electron.QE-18, 626 (1982).5. W. K. Burns, R. P. Moeller, C. A. Villarruel, and M. Abebe,"Fiber optic gyroscope with polarization holding fiber,"in Digest of Topical Meeting on Optical Fiber Commu-nication, New Orleans, La., 1983. Post-deadline PaperPD 2-1.6. S. E. Miller, "On solutions for two waves with periodiccoupling," Bell Syst. Tech. J. 47, 1801 (1968).7. S. E. Harris and R. W. Wallace, "Acousto-optic tunablefilter," J. Opt. Soc. Am. 59, 744 (1969).8. R. C. Alferness and L. L. Buhl, "Waveguide electro-opticpolarization transformer," Appl. Phys. Lett. 38, 655(1981).9. M. Johnson, "In-line fiber-optical polarization trans-former," Appl. Opt. 18,1288 (1979).