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Experimental Demonstration of the Temperature Influence on an Optical Universal Compensator for Polarization Changes Induced by Birefringence on a Retracing Beam
OPTICAL FIBER TECHNOLOGY ARTICLE NO.
3, 347]355 Ž1997.
OF970228
Experimental Demonstration of the Temperature Influence on an Optical Universal Compensator for Polarization Changes Induced by Birefringence on a Retracing Beam J. L. Arce-Diego and R. Lopez-Ruisanchez ´ ´ Grupo de Ingenierıa Departamento de Tecnologıa Ingenierıa ´ Fotonica, ´ ´ Electronica ´ ´ de Sistemas y Automatica, Uni¨ ersidad de Cantabria, A¨ enida Los Castros srn, 39005 Santander, Spain ´
M. A. Muriel Departamento de Tecnologıa Escuela Tecnica Superior de Ingenieros de ´ Fotonica, ´ ´ Telecomunicacion, de Madrid, 28040 Madrid, Spain ´ Uni¨ ersidad Politecnica ´
and J. M. Lopez-Higuera ´ Grupo de Ingenierıa Departamento de Tecnologıa Ingenierıa ´ Fotonica, ´ ´ Electronica ´ ´ de Sistemas y Automatica, Uni¨ ersidad de Cantabria, A¨ enida Los Castros srn, 39005 ´ Santander, Spain Received May 22, 1997
The effect of the imperfections of the commercial Faraday rotator mirror due to the large temperature dependence of its Faraday rotator angle, and its influence on polarization change compensation induced by birefringence in reciprocal photonic circuits, is experimentally demonstrated, and then compared and discussed with the theoretical results. Q 1997 Academic Press
1. INTRODUCTION
Nonreciprocal magneto-optic devices, such as Faraday rotator mirrors, optical isolators, and circulators, are necessary for improving the performances of optical amplifiers in optical fiber communications, optical fiber amplification, and optical 347 1068-5200r97 $25.00 Copyright Q 1997 by Academic Press All rights of reproduction in any form reserved.
348
ARCE-DIEGO ET AL.
sensing, and, in general, as a universal compensator for polarization changes induced by birefringence on retracing beams. The Faraday rotator ŽFR., which is based on the Faraday effect, is the most important component in Faraday rotator mirrors ŽFRM., isolators, and circulators. In general, commercial Faraday rotators are made with ferromagnetic materials, yttrium iron garnet ŽYIG., and bismuthsubstituted iron garnet ŽBIG.. The magneto-optical properties of these ferromagnetic materials show a great temperature dependence. Martinelli w1x has shown that if a polarized light beam is passed through a medium after a combination of reflection by a Faraday rotator adjusted to give a 458 rotation and an ideal metal mirror, the resulting polarization state is orthogonal to the initial polarization state and is independent of the details of the birefringence in that medium. It is assumed that the changes in the birefringence of the reciprocal reflective photonic circuit are slow enough that the changes during the transmission time through the mentioned optical circuit can be ignored. The implication is that such an arrangement allows one to ‘‘cancel’’ the effects of reciprocal birefringence fluctuation in the medium on the polarization state. This result can be extended to optical circuits with reciprocal birefringence and dicroism, as Bhandari showed in w2x. Recently, temperature dependence of FRM polarization angle and its influence on the behavior of reciprocal reflective optical circuits have been theoretically predicted by us in w3x. To our knowledge, the first experimental demonstration of the temperature influence on FRM, and its influence on its compensation characteristics for polarization changes induced by birefringence on reciprocal reflective photonic circuits, is presented in this paper. Experiments, results, their discussion versus theoretical predictions, and conclusions are shown in the following text. 2. THEORETICAL MODEL
Ignoring the polarization-dependent loss, the Jones matrices in the forward and ª ¤ backward directions C, C, in the single-mode optical fiber, or in a reciprocal optical circuit with the suitable reference system become unitary as ª
Cs ¤
Cs
a yb*
b , a*
Ž 1a .
a yb
b* . a*
Ž 1b .
The Jones matrix of a real FRM, including the rotation angle maladjustment, denoted by " D f , and due to the temperature dependence on the Faraday rotator made with ferromagnetic materials YIG and BIG, becomes
Freal s
sin Ž "2D f . ycos Ž "2D f .
ycos Ž "2D f . . ysin Ž "2D f .
Ž 2.
349
OPTICAL UNIVERSAL COMPENSATOR
Then the Jones matrix of the complete circuit ŽFig. 1. is ¤
ª
CFreal C s cos Ž "2D f . Fideal q sin Ž "2D f . D,
Ž 3.
where Fideal is the Jones matrix of the ideal FRM w1x, and D is the matrix of maladjustment due to the temperature dependence of the magneto-optical Faraday effect and is given by Ds
ž
p yq
q , yp*
/
Ž 4.
where p s y Ž a2 q b* 2 . ,
q s yab q a*b*,
< p < 2 q < q < 2 s 1.
and
If E 5 is the Jones vector of the input light, then the Jones vector of the output light involves two terms: the first term orthogonal to E 5 Žpolarization behavior with an ideal FRM. and the second term, due to the temperature influence on the rotation angle of the Faraday rotator, that can be expressed as a linear combination of vectors orthogonal and parallel to E 5 . The extinction ratio r, as a merit figure, to relate E H Žideal. and E 5 Žunwanted. is given by rs
cos Ž "2D f . q c H sin Ž "2D f . c 5 sen Ž "2D f .
2
2
.
Ž 5.
The complex values c 5 , c H can be calculated as the inner product of the second term in Ž3. and E 5 and E H , respectively, c 5 s Ž DE 5 , E 5 . ,
Ž 6a .
c H s Ž DE 5 , E H . .
Ž 6b .
FIG. 1. Complete reciprocal optical circuit ended with a real temperature-dependent Faraday rotator mirror.
350
ARCE-DIEGO ET AL.
In the worst case, the minimum extinction ratio rmin w3x is given by rmin s
1 tan Ž "2D f . 2
.
Ž 7.
3. EXPERIMENTS
The experimental setup is shown schematically in Fig. 2. Optical continuous radiation from a Fabry]Perot laser at 1550 nm was produced and analyzed by the HP-8509B Polarization Analyzer. The reciprocal photonic circuit is composed of 2045 m of a standard single-mode-telecommunication Corning optical fiber Ž9r125 m m., arranged in a typical spool, which is followed by a fiber coil ended with a commercial pigtailed ISOWAVE FRM made with YIG material. The 20-turn 6-cm-diameter fiber coil was placed between a fixed holder and a TIRAvib 5100 shaker, in order to induce reciprocal linear birefringence perturbations depending on the amplitude and frequency of the vibrations. The FRM was placed in a HYGROS-15 climatic chamber for temperature trials. A photograph of the setup is shown in Fig. 3. Both the laser light Ž1555 nm. and the retracing beam torfrom the optical fiber circuit under test were conducted through a 3-dB single-mode fiber coupler with
FIG. 2. Experimental setup.
OPTICAL UNIVERSAL COMPENSATOR
351
FIG. 3. Photograph of the setup.
the fourth unused port ended in a matching oil in order to avoid the undesirable optical reflections. The setup equipment was fully automatically controlled using the GPIB bus by computer, which also worked as an automatic data acquisition unit. With 50% relative humidity, several series of temperature cycles from 0 to 508C, and vice versa, steady, with FRM or with metallic mirror, with or without external reciprocal perturbations Žlinear birefringence induced by vibration., were programmed and realized. It must be noted that the reference temperature used in the setup was experimentally adjusted for the value in which the SOP of the retracing light beam was orthogonal to the SOP of the launched light. This reference temperature was 258C. 4. RESULTS AND DISCUSSION
According to Eq. Ž3. if D f s 0 Žideal FRM., and E 5 is the Jones vector of the input light, then the Jones vector of the output light is orthogonal to E 5 . If not, D f / 0 Žreal FRM., as is mentioned above, the output light of the photonic circuit in Fig. 1 can be expressed as a linear combination of two vectors, one orthogonal and the other parallel to E 5 . Then the experimental extinction ratio can be calculated by
r s 10 log
< Ax <2 < Ay<2
,
Ž 8.
352
ARCE-DIEGO ET AL.
where A x is the amplitude of the desired component of the output optical electric field ŽE H . and A y is the amplitude of the unwanted component, and they can be expressed as Ax s Ay s
( (
1 q S1
Ž 9a .
2 1 y S1 2
,
Ž 9b .
where S1 is the normalized 2nd Stokes coefficient S1 s
< Ax <2 y < Ay <2 < Ax <2 q < Ay <2
,
Ž 10 .
where < A x < 2 q < A y < 2 is the S0 Stokes coefficient. As the optical polarization analyzer measures the normalized Stokes coefficients, the final expression of the experimental extinction ratio coefficient, in dB, can be calculated by r s 10 log
ž
1 q S1 1 y S1
/
.
Ž 11 .
The experimental results compared with the predicted extinction ratio in the worst case in terms of the temperature deviation from the adjusted temperature Ž258C. are shown in Fig. 4. The solid line indicates the average extinction ratio for the
FIG. 4. Plot of experimental and theoretical Žin the worst case. extinction ratios as a function of the difference between the temperature of the climatic chamber and the temperature of reference.
OPTICAL UNIVERSAL COMPENSATOR
353
temperature range and the dashed line indicates the theoretical ratio Žin the worst case.. The theoretical ratio in the worst case in the near infrared wavelength range, for YIG FRMs, has great temperature dependence. The dependence of the Faraday rotator angle at 458 is 0.048C for YIG Faraday rotators at 1.5 m m wavelength, as Imaeda and Kozuka showed in w4x. Figure 4 shows that in order to achieve a minimum theoretical extinction ratio of 40 dB, the allowable temperature increment is "78C in commercial FRM-YIG. The maximum and minimum values for the whole set of measurements are indicated by squares and triangles, respectively, for each temperature. It can be noted that the experimental and the theoretically predicted minimum coefficient extinction ratio curve shapes show very good agreement. As was expected, all experimental values, including the minimum extinction ratio values, are above the predictions in the worst case for all temperature deviation ranges, and they are always greater than 35 dB in the range of the measurements. It should also be highlighted that an important increment of the extinction ratio appears in the first 58C temperature increments, and a variation of D rrDT s y0.80 dBr8C for the range from 5 to 258C has been obtained. In order to improve the illustration of the above-mentioned influence, the Poincare ´ sphere in Fig. 5 shows the evolution of the state polarization of the backreflected light during the complete experiment. The clear deviation from the ideal case can be noted Žonly one point on the Poincare ´ sphere in the ideal case.. With the aim of comparing the effect of the FRM in the photonic circuits under study, in Fig. 6, the experimental results are shown for the case in which the FRM has been changed for a simple mirror at the end of the reciprocal optical circuit.
FIG. 5. Poincare ´ sphere showing the evolution of the state of polarization for the backreflected light from the reciprocal photonic circuit with vibrations and ended by a real FRM made of YIG with temperature changes.
354
ARCE-DIEGO ET AL.
FIG. 6. Poincare ´ sphere showing the evolution of the state of polarization for backreflected light from the reciprocal optical circuit with vibrations and ended with metallic mirror.
From this, it is clear that the FRM mirror avoids the effect of the reciprocal perturbations introduced in the optical circuit. 5. CONCLUSIONS
The temperature influence on an FRM as a compensator for polarization state changes induced in an reciprocal reflective photonic circuit, subjected to reciprocal birefringence changes, in which the FRM is inserted at the end, is experimentally obtained. Results are presented and discussed. Very good agreement with the theoretical predictions has been observed. The experimental values have always been above the theoretical prediction of minimum extinction ratio, in the worst case, for all temperature deviations of the real Faraday rotator mirror and are always greater than 35 dB in the range of rTadjusted y Tchamberr equal to 258C for a FRM made with YIG. A variation of D rrDT s y0.80 dBr8C for the range from 5 to 258C has been obtained.
ACKNOWLEDGMENT This work has been done in the R & D Photonics Engineering Lab of Cantabria University and it was supported by the Spanish Ministry of Education and Science through the CICYT Project TIC95-0631C04. The authors thank F. Madruga and A. Cobo for their assistance.
REFERENCES w1x M. Martinelli, ‘‘A universal compensator for polarization changes induced by birefringence on retracing beam,’’ Opt. Commun., vol. 72, no. 6, 341 Ž1989..
OPTICAL UNIVERSAL COMPENSATOR
355
w2x R. Bhandari, ‘‘A useful generalization of the Martinelli effect,’’ Opt. Commun., vol. 88, no. 1, 1 Ž1992.. w3x J. L. Arce-Diego, M. A. Muriel, A. Cobo, M. Morante, and J. M. Lopez-Higuera, ‘‘Temperature ´ influence on an optical universal compensator for polarization changes induced by birefringence on a retracing beam,’’ in Conference Proceedings LEOS’96, Boston, MA, vol. 2, pp. 258]259, Nov. 1996. w4x M. Imaeda, and Y. Kozuka, ‘‘Optical magnetic field sensors using iron garnet crystals,’’ in Proceedings of the Eighth Optical Fiber Sensors Conference ŽF. Leonberger, Ed.., p. 386, Institute of Electrical and Electronics Engineers, New York, 1992.
3, 347]355 Ž1997.
OF970228
Experimental Demonstration of the Temperature Influence on an Optical Universal Compensator for Polarization Changes Induced by Birefringence on a Retracing Beam J. L. Arce-Diego and R. Lopez-Ruisanchez ´ ´ Grupo de Ingenierıa Departamento de Tecnologıa Ingenierıa ´ Fotonica, ´ ´ Electronica ´ ´ de Sistemas y Automatica, Uni¨ ersidad de Cantabria, A¨ enida Los Castros srn, 39005 Santander, Spain ´
M. A. Muriel Departamento de Tecnologıa Escuela Tecnica Superior de Ingenieros de ´ Fotonica, ´ ´ Telecomunicacion, de Madrid, 28040 Madrid, Spain ´ Uni¨ ersidad Politecnica ´
and J. M. Lopez-Higuera ´ Grupo de Ingenierıa Departamento de Tecnologıa Ingenierıa ´ Fotonica, ´ ´ Electronica ´ ´ de Sistemas y Automatica, Uni¨ ersidad de Cantabria, A¨ enida Los Castros srn, 39005 ´ Santander, Spain Received May 22, 1997
The effect of the imperfections of the commercial Faraday rotator mirror due to the large temperature dependence of its Faraday rotator angle, and its influence on polarization change compensation induced by birefringence in reciprocal photonic circuits, is experimentally demonstrated, and then compared and discussed with the theoretical results. Q 1997 Academic Press
1. INTRODUCTION
Nonreciprocal magneto-optic devices, such as Faraday rotator mirrors, optical isolators, and circulators, are necessary for improving the performances of optical amplifiers in optical fiber communications, optical fiber amplification, and optical 347 1068-5200r97 $25.00 Copyright Q 1997 by Academic Press All rights of reproduction in any form reserved.
348
ARCE-DIEGO ET AL.
sensing, and, in general, as a universal compensator for polarization changes induced by birefringence on retracing beams. The Faraday rotator ŽFR., which is based on the Faraday effect, is the most important component in Faraday rotator mirrors ŽFRM., isolators, and circulators. In general, commercial Faraday rotators are made with ferromagnetic materials, yttrium iron garnet ŽYIG., and bismuthsubstituted iron garnet ŽBIG.. The magneto-optical properties of these ferromagnetic materials show a great temperature dependence. Martinelli w1x has shown that if a polarized light beam is passed through a medium after a combination of reflection by a Faraday rotator adjusted to give a 458 rotation and an ideal metal mirror, the resulting polarization state is orthogonal to the initial polarization state and is independent of the details of the birefringence in that medium. It is assumed that the changes in the birefringence of the reciprocal reflective photonic circuit are slow enough that the changes during the transmission time through the mentioned optical circuit can be ignored. The implication is that such an arrangement allows one to ‘‘cancel’’ the effects of reciprocal birefringence fluctuation in the medium on the polarization state. This result can be extended to optical circuits with reciprocal birefringence and dicroism, as Bhandari showed in w2x. Recently, temperature dependence of FRM polarization angle and its influence on the behavior of reciprocal reflective optical circuits have been theoretically predicted by us in w3x. To our knowledge, the first experimental demonstration of the temperature influence on FRM, and its influence on its compensation characteristics for polarization changes induced by birefringence on reciprocal reflective photonic circuits, is presented in this paper. Experiments, results, their discussion versus theoretical predictions, and conclusions are shown in the following text. 2. THEORETICAL MODEL
Ignoring the polarization-dependent loss, the Jones matrices in the forward and ª ¤ backward directions C, C, in the single-mode optical fiber, or in a reciprocal optical circuit with the suitable reference system become unitary as ª
Cs ¤
Cs
a yb*
b , a*
Ž 1a .
a yb
b* . a*
Ž 1b .
The Jones matrix of a real FRM, including the rotation angle maladjustment, denoted by " D f , and due to the temperature dependence on the Faraday rotator made with ferromagnetic materials YIG and BIG, becomes
Freal s
sin Ž "2D f . ycos Ž "2D f .
ycos Ž "2D f . . ysin Ž "2D f .
Ž 2.
349
OPTICAL UNIVERSAL COMPENSATOR
Then the Jones matrix of the complete circuit ŽFig. 1. is ¤
ª
CFreal C s cos Ž "2D f . Fideal q sin Ž "2D f . D,
Ž 3.
where Fideal is the Jones matrix of the ideal FRM w1x, and D is the matrix of maladjustment due to the temperature dependence of the magneto-optical Faraday effect and is given by Ds
ž
p yq
q , yp*
/
Ž 4.
where p s y Ž a2 q b* 2 . ,
q s yab q a*b*,
< p < 2 q < q < 2 s 1.
and
If E 5 is the Jones vector of the input light, then the Jones vector of the output light involves two terms: the first term orthogonal to E 5 Žpolarization behavior with an ideal FRM. and the second term, due to the temperature influence on the rotation angle of the Faraday rotator, that can be expressed as a linear combination of vectors orthogonal and parallel to E 5 . The extinction ratio r, as a merit figure, to relate E H Žideal. and E 5 Žunwanted. is given by rs
cos Ž "2D f . q c H sin Ž "2D f . c 5 sen Ž "2D f .
2
2
.
Ž 5.
The complex values c 5 , c H can be calculated as the inner product of the second term in Ž3. and E 5 and E H , respectively, c 5 s Ž DE 5 , E 5 . ,
Ž 6a .
c H s Ž DE 5 , E H . .
Ž 6b .
FIG. 1. Complete reciprocal optical circuit ended with a real temperature-dependent Faraday rotator mirror.
350
ARCE-DIEGO ET AL.
In the worst case, the minimum extinction ratio rmin w3x is given by rmin s
1 tan Ž "2D f . 2
.
Ž 7.
3. EXPERIMENTS
The experimental setup is shown schematically in Fig. 2. Optical continuous radiation from a Fabry]Perot laser at 1550 nm was produced and analyzed by the HP-8509B Polarization Analyzer. The reciprocal photonic circuit is composed of 2045 m of a standard single-mode-telecommunication Corning optical fiber Ž9r125 m m., arranged in a typical spool, which is followed by a fiber coil ended with a commercial pigtailed ISOWAVE FRM made with YIG material. The 20-turn 6-cm-diameter fiber coil was placed between a fixed holder and a TIRAvib 5100 shaker, in order to induce reciprocal linear birefringence perturbations depending on the amplitude and frequency of the vibrations. The FRM was placed in a HYGROS-15 climatic chamber for temperature trials. A photograph of the setup is shown in Fig. 3. Both the laser light Ž1555 nm. and the retracing beam torfrom the optical fiber circuit under test were conducted through a 3-dB single-mode fiber coupler with
FIG. 2. Experimental setup.
OPTICAL UNIVERSAL COMPENSATOR
351
FIG. 3. Photograph of the setup.
the fourth unused port ended in a matching oil in order to avoid the undesirable optical reflections. The setup equipment was fully automatically controlled using the GPIB bus by computer, which also worked as an automatic data acquisition unit. With 50% relative humidity, several series of temperature cycles from 0 to 508C, and vice versa, steady, with FRM or with metallic mirror, with or without external reciprocal perturbations Žlinear birefringence induced by vibration., were programmed and realized. It must be noted that the reference temperature used in the setup was experimentally adjusted for the value in which the SOP of the retracing light beam was orthogonal to the SOP of the launched light. This reference temperature was 258C. 4. RESULTS AND DISCUSSION
According to Eq. Ž3. if D f s 0 Žideal FRM., and E 5 is the Jones vector of the input light, then the Jones vector of the output light is orthogonal to E 5 . If not, D f / 0 Žreal FRM., as is mentioned above, the output light of the photonic circuit in Fig. 1 can be expressed as a linear combination of two vectors, one orthogonal and the other parallel to E 5 . Then the experimental extinction ratio can be calculated by
r s 10 log
< Ax <2 < Ay<2
,
Ž 8.
352
ARCE-DIEGO ET AL.
where A x is the amplitude of the desired component of the output optical electric field ŽE H . and A y is the amplitude of the unwanted component, and they can be expressed as Ax s Ay s
( (
1 q S1
Ž 9a .
2 1 y S1 2
,
Ž 9b .
where S1 is the normalized 2nd Stokes coefficient S1 s
< Ax <2 y < Ay <2 < Ax <2 q < Ay <2
,
Ž 10 .
where < A x < 2 q < A y < 2 is the S0 Stokes coefficient. As the optical polarization analyzer measures the normalized Stokes coefficients, the final expression of the experimental extinction ratio coefficient, in dB, can be calculated by r s 10 log
ž
1 q S1 1 y S1
/
.
Ž 11 .
The experimental results compared with the predicted extinction ratio in the worst case in terms of the temperature deviation from the adjusted temperature Ž258C. are shown in Fig. 4. The solid line indicates the average extinction ratio for the
FIG. 4. Plot of experimental and theoretical Žin the worst case. extinction ratios as a function of the difference between the temperature of the climatic chamber and the temperature of reference.
OPTICAL UNIVERSAL COMPENSATOR
353
temperature range and the dashed line indicates the theoretical ratio Žin the worst case.. The theoretical ratio in the worst case in the near infrared wavelength range, for YIG FRMs, has great temperature dependence. The dependence of the Faraday rotator angle at 458 is 0.048C for YIG Faraday rotators at 1.5 m m wavelength, as Imaeda and Kozuka showed in w4x. Figure 4 shows that in order to achieve a minimum theoretical extinction ratio of 40 dB, the allowable temperature increment is "78C in commercial FRM-YIG. The maximum and minimum values for the whole set of measurements are indicated by squares and triangles, respectively, for each temperature. It can be noted that the experimental and the theoretically predicted minimum coefficient extinction ratio curve shapes show very good agreement. As was expected, all experimental values, including the minimum extinction ratio values, are above the predictions in the worst case for all temperature deviation ranges, and they are always greater than 35 dB in the range of the measurements. It should also be highlighted that an important increment of the extinction ratio appears in the first 58C temperature increments, and a variation of D rrDT s y0.80 dBr8C for the range from 5 to 258C has been obtained. In order to improve the illustration of the above-mentioned influence, the Poincare ´ sphere in Fig. 5 shows the evolution of the state polarization of the backreflected light during the complete experiment. The clear deviation from the ideal case can be noted Žonly one point on the Poincare ´ sphere in the ideal case.. With the aim of comparing the effect of the FRM in the photonic circuits under study, in Fig. 6, the experimental results are shown for the case in which the FRM has been changed for a simple mirror at the end of the reciprocal optical circuit.
FIG. 5. Poincare ´ sphere showing the evolution of the state of polarization for the backreflected light from the reciprocal photonic circuit with vibrations and ended by a real FRM made of YIG with temperature changes.
354
ARCE-DIEGO ET AL.
FIG. 6. Poincare ´ sphere showing the evolution of the state of polarization for backreflected light from the reciprocal optical circuit with vibrations and ended with metallic mirror.
From this, it is clear that the FRM mirror avoids the effect of the reciprocal perturbations introduced in the optical circuit. 5. CONCLUSIONS
The temperature influence on an FRM as a compensator for polarization state changes induced in an reciprocal reflective photonic circuit, subjected to reciprocal birefringence changes, in which the FRM is inserted at the end, is experimentally obtained. Results are presented and discussed. Very good agreement with the theoretical predictions has been observed. The experimental values have always been above the theoretical prediction of minimum extinction ratio, in the worst case, for all temperature deviations of the real Faraday rotator mirror and are always greater than 35 dB in the range of rTadjusted y Tchamberr equal to 258C for a FRM made with YIG. A variation of D rrDT s y0.80 dBr8C for the range from 5 to 258C has been obtained.
ACKNOWLEDGMENT This work has been done in the R & D Photonics Engineering Lab of Cantabria University and it was supported by the Spanish Ministry of Education and Science through the CICYT Project TIC95-0631C04. The authors thank F. Madruga and A. Cobo for their assistance.
REFERENCES w1x M. Martinelli, ‘‘A universal compensator for polarization changes induced by birefringence on retracing beam,’’ Opt. Commun., vol. 72, no. 6, 341 Ž1989..
OPTICAL UNIVERSAL COMPENSATOR
355
w2x R. Bhandari, ‘‘A useful generalization of the Martinelli effect,’’ Opt. Commun., vol. 88, no. 1, 1 Ž1992.. w3x J. L. Arce-Diego, M. A. Muriel, A. Cobo, M. Morante, and J. M. Lopez-Higuera, ‘‘Temperature ´ influence on an optical universal compensator for polarization changes induced by birefringence on a retracing beam,’’ in Conference Proceedings LEOS’96, Boston, MA, vol. 2, pp. 258]259, Nov. 1996. w4x M. Imaeda, and Y. Kozuka, ‘‘Optical magnetic field sensors using iron garnet crystals,’’ in Proceedings of the Eighth Optical Fiber Sensors Conference ŽF. Leonberger, Ed.., p. 386, Institute of Electrical and Electronics Engineers, New York, 1992.