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Nonlinear birefringence of optical fibers
15 June 1994 OPTICS COMMUNICATIONS Optics Communications 109 ( 1994) 151-154
ELSEVIER
Nonlinear birefringence of optical fibers X.D. Cao, D.D. Meyerhofer Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, NY 14623-1299, USA
Received 29 October 1993; revised manuscript received 14 February 1994
Abstract
The nonlinear birefringence of low birefringent optical fibers has been studied experimentally. It is found that the experimental results are consistent with theoretical predictions. Earlier discrepancies between experimental results and theory could be due to the failure to compensate for the linear birefringence adequately.
When the intensity of a light wave propagating in a birefringent optical fiber is large enough, the refractive indices of the fast and slow axes are changed by different amounts depending on the polarization direction of incident light wave. This phenomenon, referred to as nonlinear birefringence or self-induced birefringence, has many applications. The optical Kerr effect in fibers can be used as an optical shutter with picosecond response time [ 1 ]. Nonlinear birefringence induced by a pulse can be used to modify its own shape, in other words, pulse shaping [2-4]. Recently Tapir and Mourou used this effect to remove the pedestal associated with the pulses compressed by a fiber-pulse compressor, and a contrast ratio as high as 107 was obtained [ 5 ]. Nonlinear birefringence can also be used to make fiber-optic logic gates [6,7], and has important effects on soliton propagation in single-mode optical fibers [8,9 ]. Recently, the polarization changes induced by a strong wave on a copropagating weaker wave in a singlemode low birefringent fiber was investigated [ 10 ]. Large phase changes of as much as 12n were reported at peak input powers of 12 W in a nitrobenzene-cored weakly birefringent single-mode optical fiber [ll]. I f the angle between the polarization of incident Elsevier ScienceB.V. SSDI 0030-4018 ( 94 ) 00147-M
laser light and fast axis of optical fiber is not zero, the electric fields along both fast and slow axes will not be zero; therefore both components induce refractive index changes not only along its own axis but also along the other axis, that is, the refractive index change along one axis is due to both self-phase modulation and cross-phase modulation. As a consequence of this nonlinear birefringence, the polarization of the total electric field rotates, and the electric field polarization will be elliptical in general. If the linear birefringence is compensated for and a polarizer is used to block low intensity light that does not have a polarization rotation, then the transmitted light will depend on the incident power and polarization direction. Previous experiments [3,6] only confirmed the power dependence of the transmission; discrepancies were found in the relation between transmission and input polarization. For example, when incident polarization is along one of the optical axes, there is no electric field along the other axis, thus there should be no nonlinear birefringence, hence, zero transmission. Experimental results showed that the nonlinear birefringence was not zero, and no experimental results confirmed the overall behavior of transmission with respect to the polarization direction. In fact, the dependence of polariza-
X.D. Coo, D.D. Meyerhofer / Optics Communications 109 (1994) 151-154
152
tion changes on input polarizations have been investigated in both cw regime [10] and pulsed regime [11 ]. However, the linear birefringence was not compensated in these experiments [ 10,11 ] which strongly affected the switching contrast. This discrepancy was believed to be due to the random fluctuations of the birefringent axis and the misalignment of the incident polarization angle in the experiments. An elliptical rotation of polarization due to the four-wave mixing was also considered important for low birefringent fibers [ 12 ]. However, it is shown in this paper that this discrepancy is not physical, and good agreement between theory and experiment is verified. The experimental setup is shown in Fig. 1. A 50 ps Nd: YLF laser pulse (2 = 1.053 ~tm) was coupled into a 800 m single-mode optical fiber. A chirped pulse with spectrum broaden to 2.4 nm is formed due to self-phase modulation. A double-pass grating was then used to compress the chirped pulse to 1 ps before being coupled into a 3 m single-mode fiber of type FS-LB-4211 (product of 3M company) by a microscope objective. The core diameter of the fiber is 4 ~tm. Another microscope objective was used to collimate the output laser light. A quarter wave plate was used to compensate for the linear birefringence of the optical fiber. A polarizer was positioned to block the low intensity light. For high intensity light, the polarization direction of the light pulse will rotate a finite angle depending on light intensity and fiber length. Therefore, part of high intensity pulse is expected to pass through the polarizer. The transmission induced by nonlinear birefringence is given by [ 2 ]
T=sin2[yPoL c o s ( 2 0 ) / 6 ] sin2(20) ,
section, tt 2 is the Kerr parameter of optical fiber. For used silica, n 2= 3.2 × 10- l 6 c m 2 / W . In our experiment, as much as 50% of incident light was coupled into the low birefringent fiber, which gave a peak power of 150-300 W depending on the pulse width. It was not difficult to find the two optical axes. The extinction ratio was measured to be about 400. It was found that the linear birefringence fluctuates randomly for different values of 0. It is important to compensate the linear birefringence as much as possible, otherwise the transmission will suffer a large deviation. Fig. 2 shows the experimental result. The fiber was wound on a drum of a diameter of 20.5 cm with some axial twisting introduced. The vertical axis is the transmission, and the horizontal axis is the incident polarization angle 0. The smooth cure is fit using Eq. ( 1 ) with Po = 150 W and L = 3 m. The pulsed response of the system is obtained by assuming an instantaneous nonlinearity and integrating the cw response over the pulse envelope. the pulse shape is assumed to be Gaussian with fwhm = 1 ps. It should be pointed out that the transmission T strongly depends on the optical power or (gm ~-" ~PoL, a 50% change in ~n~will cause Tto be three times smaller in the weak nonlinear regime studied here. Although the transmission is nonzero throughout, the overall behavior is consistent with the theory. The data points in Fig. 2 are 50 ° apart. Fig. 3 shows the transition with more data points (every 2 ° apart) and different winding. The overall behavior is the same to that of Fig. 2. Fig. 3 was ob0.4
..................
(1)
where Po is the input power and 0 is the incident polarization angle with respect to the fast axis of the fiber. y= 2~znE/).Acffand Ae~ is the effective fiber cross
i1 f
E t.£ u~
r:
/
0.2
/
¢:
X
I'-
;V2
MO
Fiber
MO
;V4
P
0.0 0.0 P1139
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Fig. 1. Experimental setup. 2/2: half wave plate; MO: × 10 micro-objective; 2/4: quarter wave plate; P: polarizer.
0.5
1.0
1.5
2.0 (×10 2)
e (°) Fig. 2. Experimental results of nonlinear transmission for a twisted fiber. The data points are 5 ° apart.
X.D. Coo, D.D. Meyerhofer /Optics Communications 109 (1994) 151-154 0.4
.
.
.
.
,
.
.
.
.
i
.
.
.
.
r
~
"
E "~ 0.2
g
0.0 0.0
0.5
1.0
1.5
2.0 (x 10 2)
o(o) Fig. 3. Experimental results of nonlinear transmission for a loosely placed fiber. The data points are 2 ° apart. The transmission shows periodic modulations. rained with the fiber loosely placed on an optical table with the bending and twisting reduced as much as possible. The main difference between Fig. 2 and Fig. 3 was the absolute values of the transmission. From the theory, the higher the nonlinearity, the larger the transmission. It was confirmed that the nonlinearity of fiber can be increased by introducing axial twisting of the fiber. The fine scale fluctuations in Fig. 2 and Fig. 3 are believed to be due to the error in adjusting the polarization angle and the incident laser power. In order to compensate the linear birefringence, we need to reduce the incident laser power to make sure that the nonlinear effect is negligible. Since both the 2 / 2 waveplate for the control o f incident power and the 2 / 4 waveplate used to compensate the linear birefringence are adjusted manually, an error o f a significant fraction of 1 ° is expected. From Eq. ( 1 ), an error o f 5% in transmission is possible if an error o f 0.5 ° is introduced in adjusting the polarization angle. It is found that the transmission is very sensitive to the polarization angle. It is also very difficult to compensate the linear birefringence completely due to the finite extinction o f ratio of the polarizer and the error in adjusting the polarization angle. A more precise control of the waveplate and polarizer is needed to obtain a better result with less fluctuations. On the other hand, the peak power is also fluctuating because o f the thermal fluctuations o f the laser bandwidth. Since the l ps pulses are obtained by compressing the frequency broadened os-
153
cillator pulses, the fluctuations in the laser bandwidth will result in fluctuations o f the peak power of the compressed pulses. Both Fig. 2 and Fig. 3 show that the transmission is always nonzero. However, this is not considered as a large discrepancy between theory and experiment, since the overall behavior o f experimental result is so close to that o f theory. It is believed that the error in the compensation o f the linear birefringence, the finite extinction ratio of the polarizer, and the angular misalignment o f incident polarization angle could be the important reasons for the nonzero transmission at 0 = 0 °, 45 °, 90 °, 135 °, and 180 °. It seems that nonlinear elliptical rotation is not as important as the factors mentioned above. In fact, any failure compensate the linear birefringence could destroy the observed results completely. In summary, the nonlinear birefringence of low birefringent fiber has been studied experimentally. It is found that the earlier discrepancies between experimental results and theory could be due to the failure to compensate the linear birefringence, and the experimental results obtained in this paper are consistent with theory. Finally, it should be mentioned that the dependence o f nonlinear transmission on the polarization angle could be used in pulse shaping, optical switching, and other applications as well. The authors thank G.P. Agrawal for many useful comments. This work was supported by the U.S. Department of Energy Office o f Inertial Confinement Fusion under Cooperative Agreement No. DE-FC0392SF19460 and the University of Rochester. The support o f D O E does not constitute an endorsement by D O E of the views expressed in this article.
References
[ 1] M.A. Duguay, in: Progress in optics, Vol. 14, ed. E. Wolf (North-Holland, Amsterdam, 1976) p. 163. [2] R.H. Stolen, J. Botineau and A. Ashkin, Optics Lett. 7 (1982) 512. [3] B. Nikolaus, D. Grischkowskyand A.C. Balant, Optics Lett. 8 (1983) 189. [4] N.J. Halas and D. Grischkowsky, Appl. Phys. Lett. 48 (1986) 823. [ 51 J.-L. Tapi6 and G. Mourou, Optics Lett. 17 ( 1992) 136. [6] K. Kitayama, Y. Kimura and S. Seikai, Appl. Phys. Len. 46 (1985) 317.
154
X.D. Coo, D.D. Meyerhofer / Optics Communications 109 (1994) 151-154
[7] Y. Kimura, K.-I. Kitayama, N. Shibata and S. Seikai, Electron. Lett. 22 (1986) 277. [8] C.R. Menuyk, Optics Lett. 12 (1987) 614; J. Opt. Soc. Am. B 5 (1988) 392. [9] Y.S. Kivshar, J. Opt. Soc. Am. B 7 ( 1991 ) 2204.
[ 10] E. Lichtman, R.G. Waarts, A.A. Friesem and S. Tang, Appl. Optics 28 (1989) 4056. [ 11 ] R. Kashyyap and N. Finlayson, Optics Lett. 17 ( 1992 ) 405. [ 12 ] H.G. Winful, Appl. Phys. Lett. 47 ( 1985 ) 213.
ELSEVIER
Nonlinear birefringence of optical fibers X.D. Cao, D.D. Meyerhofer Laboratory for Laser Energetics, University of Rochester, 250 East River Road, Rochester, NY 14623-1299, USA
Received 29 October 1993; revised manuscript received 14 February 1994
Abstract
The nonlinear birefringence of low birefringent optical fibers has been studied experimentally. It is found that the experimental results are consistent with theoretical predictions. Earlier discrepancies between experimental results and theory could be due to the failure to compensate for the linear birefringence adequately.
When the intensity of a light wave propagating in a birefringent optical fiber is large enough, the refractive indices of the fast and slow axes are changed by different amounts depending on the polarization direction of incident light wave. This phenomenon, referred to as nonlinear birefringence or self-induced birefringence, has many applications. The optical Kerr effect in fibers can be used as an optical shutter with picosecond response time [ 1 ]. Nonlinear birefringence induced by a pulse can be used to modify its own shape, in other words, pulse shaping [2-4]. Recently Tapir and Mourou used this effect to remove the pedestal associated with the pulses compressed by a fiber-pulse compressor, and a contrast ratio as high as 107 was obtained [ 5 ]. Nonlinear birefringence can also be used to make fiber-optic logic gates [6,7], and has important effects on soliton propagation in single-mode optical fibers [8,9 ]. Recently, the polarization changes induced by a strong wave on a copropagating weaker wave in a singlemode low birefringent fiber was investigated [ 10 ]. Large phase changes of as much as 12n were reported at peak input powers of 12 W in a nitrobenzene-cored weakly birefringent single-mode optical fiber [ll]. I f the angle between the polarization of incident Elsevier ScienceB.V. SSDI 0030-4018 ( 94 ) 00147-M
laser light and fast axis of optical fiber is not zero, the electric fields along both fast and slow axes will not be zero; therefore both components induce refractive index changes not only along its own axis but also along the other axis, that is, the refractive index change along one axis is due to both self-phase modulation and cross-phase modulation. As a consequence of this nonlinear birefringence, the polarization of the total electric field rotates, and the electric field polarization will be elliptical in general. If the linear birefringence is compensated for and a polarizer is used to block low intensity light that does not have a polarization rotation, then the transmitted light will depend on the incident power and polarization direction. Previous experiments [3,6] only confirmed the power dependence of the transmission; discrepancies were found in the relation between transmission and input polarization. For example, when incident polarization is along one of the optical axes, there is no electric field along the other axis, thus there should be no nonlinear birefringence, hence, zero transmission. Experimental results showed that the nonlinear birefringence was not zero, and no experimental results confirmed the overall behavior of transmission with respect to the polarization direction. In fact, the dependence of polariza-
X.D. Coo, D.D. Meyerhofer / Optics Communications 109 (1994) 151-154
152
tion changes on input polarizations have been investigated in both cw regime [10] and pulsed regime [11 ]. However, the linear birefringence was not compensated in these experiments [ 10,11 ] which strongly affected the switching contrast. This discrepancy was believed to be due to the random fluctuations of the birefringent axis and the misalignment of the incident polarization angle in the experiments. An elliptical rotation of polarization due to the four-wave mixing was also considered important for low birefringent fibers [ 12 ]. However, it is shown in this paper that this discrepancy is not physical, and good agreement between theory and experiment is verified. The experimental setup is shown in Fig. 1. A 50 ps Nd: YLF laser pulse (2 = 1.053 ~tm) was coupled into a 800 m single-mode optical fiber. A chirped pulse with spectrum broaden to 2.4 nm is formed due to self-phase modulation. A double-pass grating was then used to compress the chirped pulse to 1 ps before being coupled into a 3 m single-mode fiber of type FS-LB-4211 (product of 3M company) by a microscope objective. The core diameter of the fiber is 4 ~tm. Another microscope objective was used to collimate the output laser light. A quarter wave plate was used to compensate for the linear birefringence of the optical fiber. A polarizer was positioned to block the low intensity light. For high intensity light, the polarization direction of the light pulse will rotate a finite angle depending on light intensity and fiber length. Therefore, part of high intensity pulse is expected to pass through the polarizer. The transmission induced by nonlinear birefringence is given by [ 2 ]
T=sin2[yPoL c o s ( 2 0 ) / 6 ] sin2(20) ,
section, tt 2 is the Kerr parameter of optical fiber. For used silica, n 2= 3.2 × 10- l 6 c m 2 / W . In our experiment, as much as 50% of incident light was coupled into the low birefringent fiber, which gave a peak power of 150-300 W depending on the pulse width. It was not difficult to find the two optical axes. The extinction ratio was measured to be about 400. It was found that the linear birefringence fluctuates randomly for different values of 0. It is important to compensate the linear birefringence as much as possible, otherwise the transmission will suffer a large deviation. Fig. 2 shows the experimental result. The fiber was wound on a drum of a diameter of 20.5 cm with some axial twisting introduced. The vertical axis is the transmission, and the horizontal axis is the incident polarization angle 0. The smooth cure is fit using Eq. ( 1 ) with Po = 150 W and L = 3 m. The pulsed response of the system is obtained by assuming an instantaneous nonlinearity and integrating the cw response over the pulse envelope. the pulse shape is assumed to be Gaussian with fwhm = 1 ps. It should be pointed out that the transmission T strongly depends on the optical power or (gm ~-" ~PoL, a 50% change in ~n~will cause Tto be three times smaller in the weak nonlinear regime studied here. Although the transmission is nonzero throughout, the overall behavior is consistent with the theory. The data points in Fig. 2 are 50 ° apart. Fig. 3 shows the transition with more data points (every 2 ° apart) and different winding. The overall behavior is the same to that of Fig. 2. Fig. 3 was ob0.4
..................
(1)
where Po is the input power and 0 is the incident polarization angle with respect to the fast axis of the fiber. y= 2~znE/).Acffand Ae~ is the effective fiber cross
i1 f
E t.£ u~
r:
/
0.2
/
¢:
X
I'-
;V2
MO
Fiber
MO
;V4
P
0.0 0.0 P1139
Y
Fig. 1. Experimental setup. 2/2: half wave plate; MO: × 10 micro-objective; 2/4: quarter wave plate; P: polarizer.
0.5
1.0
1.5
2.0 (×10 2)
e (°) Fig. 2. Experimental results of nonlinear transmission for a twisted fiber. The data points are 5 ° apart.
X.D. Coo, D.D. Meyerhofer /Optics Communications 109 (1994) 151-154 0.4
.
.
.
.
,
.
.
.
.
i
.
.
.
.
r
~
"
E "~ 0.2
g
0.0 0.0
0.5
1.0
1.5
2.0 (x 10 2)
o(o) Fig. 3. Experimental results of nonlinear transmission for a loosely placed fiber. The data points are 2 ° apart. The transmission shows periodic modulations. rained with the fiber loosely placed on an optical table with the bending and twisting reduced as much as possible. The main difference between Fig. 2 and Fig. 3 was the absolute values of the transmission. From the theory, the higher the nonlinearity, the larger the transmission. It was confirmed that the nonlinearity of fiber can be increased by introducing axial twisting of the fiber. The fine scale fluctuations in Fig. 2 and Fig. 3 are believed to be due to the error in adjusting the polarization angle and the incident laser power. In order to compensate the linear birefringence, we need to reduce the incident laser power to make sure that the nonlinear effect is negligible. Since both the 2 / 2 waveplate for the control o f incident power and the 2 / 4 waveplate used to compensate the linear birefringence are adjusted manually, an error o f a significant fraction of 1 ° is expected. From Eq. ( 1 ), an error o f 5% in transmission is possible if an error o f 0.5 ° is introduced in adjusting the polarization angle. It is found that the transmission is very sensitive to the polarization angle. It is also very difficult to compensate the linear birefringence completely due to the finite extinction o f ratio of the polarizer and the error in adjusting the polarization angle. A more precise control of the waveplate and polarizer is needed to obtain a better result with less fluctuations. On the other hand, the peak power is also fluctuating because o f the thermal fluctuations o f the laser bandwidth. Since the l ps pulses are obtained by compressing the frequency broadened os-
153
cillator pulses, the fluctuations in the laser bandwidth will result in fluctuations o f the peak power of the compressed pulses. Both Fig. 2 and Fig. 3 show that the transmission is always nonzero. However, this is not considered as a large discrepancy between theory and experiment, since the overall behavior o f experimental result is so close to that o f theory. It is believed that the error in the compensation o f the linear birefringence, the finite extinction ratio of the polarizer, and the angular misalignment o f incident polarization angle could be the important reasons for the nonzero transmission at 0 = 0 °, 45 °, 90 °, 135 °, and 180 °. It seems that nonlinear elliptical rotation is not as important as the factors mentioned above. In fact, any failure compensate the linear birefringence could destroy the observed results completely. In summary, the nonlinear birefringence of low birefringent fiber has been studied experimentally. It is found that the earlier discrepancies between experimental results and theory could be due to the failure to compensate the linear birefringence, and the experimental results obtained in this paper are consistent with theory. Finally, it should be mentioned that the dependence o f nonlinear transmission on the polarization angle could be used in pulse shaping, optical switching, and other applications as well. The authors thank G.P. Agrawal for many useful comments. This work was supported by the U.S. Department of Energy Office o f Inertial Confinement Fusion under Cooperative Agreement No. DE-FC0392SF19460 and the University of Rochester. The support o f D O E does not constitute an endorsement by D O E of the views expressed in this article.
References
[ 1] M.A. Duguay, in: Progress in optics, Vol. 14, ed. E. Wolf (North-Holland, Amsterdam, 1976) p. 163. [2] R.H. Stolen, J. Botineau and A. Ashkin, Optics Lett. 7 (1982) 512. [3] B. Nikolaus, D. Grischkowskyand A.C. Balant, Optics Lett. 8 (1983) 189. [4] N.J. Halas and D. Grischkowsky, Appl. Phys. Lett. 48 (1986) 823. [ 51 J.-L. Tapi6 and G. Mourou, Optics Lett. 17 ( 1992) 136. [6] K. Kitayama, Y. Kimura and S. Seikai, Appl. Phys. Len. 46 (1985) 317.
154
X.D. Coo, D.D. Meyerhofer / Optics Communications 109 (1994) 151-154
[7] Y. Kimura, K.-I. Kitayama, N. Shibata and S. Seikai, Electron. Lett. 22 (1986) 277. [8] C.R. Menuyk, Optics Lett. 12 (1987) 614; J. Opt. Soc. Am. B 5 (1988) 392. [9] Y.S. Kivshar, J. Opt. Soc. Am. B 7 ( 1991 ) 2204.
[ 10] E. Lichtman, R.G. Waarts, A.A. Friesem and S. Tang, Appl. Optics 28 (1989) 4056. [ 11 ] R. Kashyyap and N. Finlayson, Optics Lett. 17 ( 1992 ) 405. [ 12 ] H.G. Winful, Appl. Phys. Lett. 47 ( 1985 ) 213.