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Phase noise insensitive measurements of the nonlinear refractive index in fiber links
15 April 1999
Optics Communications 162 Ž1999. 333–339
Full length article
Phase noise insensitive measurements of the nonlinear refractive index in fiber links Andrea Fellegara
a,)
, Andrea Melloni b, Paolo Sacchetto
a
a
b
ITALTEL, R & D Transport and Access Business Unit, 20019 Castelletto di Settimo Milanese, Milan, Italy Department of Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy Received 28 October 1998; accepted 12 February 1999
Abstract A method for measuring the nonlinear refractive index, n 2 , along optically amplified fiber transmission lines of high-bit-rate transmission systems is presented in this paper. Measurements of the Kerr-induced nonlinear phase-shift as a function of the optical power are performed through a cross-phase-modulation scheme by using a coherent delayed-self-homodyne technique that we demonstrate to be a solution particularly insensitive to the phase noise in high-frequency operation. Experiments performed at 2.5 Gbitrs are in agreement with theoretical predictions. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Refractive index; Fiber links; Nonlinear coefficient
1. Introduction Nonlinearities play a role of fundamental importance in assessing the performance of transmission systems which operate in the high optical power regime. In fact, the interplay between dispersive and nonlinear effects can give rise to severe pulse distortions, or, under certain conditions, a balance between the two effects can lead to soliton-like behaviour. Therefore, the determination of the nonlinear coefficient n 2rA eff , where n 2 is the nonlinear refractive index and A eff is the effective area, of optical fibers is a really important issue. To date, several methods for measuring n 2 have been developed by using self- and cross-phase modulation w1–4x, modulation instability w5x, four-wave mixing w6x, ortho-conjugated mirrors w7x, and very recently, Sagnac interferometers w8x. Most of the experiments reported in the literature have been performed
) Corresponding author. Present address: Wind Telecomunicazion: Spa, Rome, Italy.
in a laboratory environment, and very little data is available from the installed fiber cables. The aim of this work is to propose and demonstrate an experimental technique for measuring the nonlinear refractive index along the installed optical links of in-the-field transmission systems. Among the various techniques for measuring n 2 , we selected interferometric methods which can give accurate measurements of the peak phase shifts as a function of peak power, bit-rate and fiber length. Interferometers, however, are sensitive to acoustic and thermal disturbances of the optical path caused by the unavoidable random environmental changes of operating transmission lines. To overcome this practical difficulty, we measure the Kerr-phase signal by resorting to a particular coherent delayed-self-homodyne scheme that we will demonstrate to be a particularly suitable solution because of its intrinsic phase noise insensitivity in high frequency operation Žthe case of noncoherent delayed-self-homodyne and its applications are treated in Ref. w9x.. Finally, an experimental work is presented in this paper that verifies the theoretical predictions and shows that the coherent delayed-self-homodyne technique may work with realistic perturbations.
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 0 8 1 - 4
334
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
2. Measurement concept and experimental results The concept of our measurement method is illustrated in Fig. 1a. From the TX-pump, an intensity modulated strong optical signal is emitted, whereas, a CW relatively weak signal power is sent by the TX-probe. The signals combine at the coupler C1, and enter into the fiber link under test. The phase of the copropagating probe signal
follows the temporal shape of the pump, through the cross-phase modulation XPM w4x, according to DF Ž t . s 2 b
2p
n2
l probe A eff
L
H0 P
pump
ž
tyl
1
1 y
Õpump
Õprobe
/
=exp Ž ya l . d l Ž1. where PpumpŽ t . is the pump power, Õpump and Õprobe the group velocities, L the fiber length, A eff the effective area,
Fig. 1. Ža. Measurement concept. Žb. Kerr-phase signal reconstruction according to the coherent delayed-self-homodyne technique.
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
n 2 the nonlinear refractive index, l probe the probe wavelength and b s 2r3 the polarization parameter w7x. Hence, measurements of the nonlinear Kerr phase-shift can be performed by using a coherent delayed-self-homodyne detection technique. In this technique, the pump light is blocked by a bandpass filter and the probe signal is sent to a Mach–Zehnder interferometer in which the light in one arm is delayed by t with respect to the other. The phase signal detected by the interferometer is D f Ž t . s f Kerr Ž t . y f Kerr Ž t y t . q fnoise Ž t . y fnoise Ž t y t .
Ž2.
where f Kerr Ž t ., w f Kerr Ž t y t .x and fnoiseŽ t ., w fnoiseŽ t y t .x represent the Kerr phase signal and the phase noise suffered by the optical beam during the propagation along the optical fiber at the time t and w t y t x, respectively. By using a probe with a very narrow linewidth, such as an external cavity laser, and for t < Tc Žnoise correlation time., the noise terms fnoiseŽ t ., w fnoiseŽ t y t .x become approximately equal, significantly reducing the impact of the noise on the interferometric detection Žsee Appendix A for details.. By setting the delay t s T bit Žbit time., the interferometric phase signal becomes two times larger than the Kerr phase shift induced by the pump signal, as can be seen in Fig. 1b. To verify the validity of the theoretical predictions, we performed measurements on a 600-m long dispersionshifted ŽDS. single-mode fiber coil with an independently determined effective area of A eff s 50 mm2. To simulate the real environment of the operating systems the coil has been installed in the test plant area of the ITALTEL Business Unit Transport and Access without any protective box against the noise disturbances. Fig. 2 is the schematic of the experimental setup. A DFB laser at l s 1550 nm is externally modulated at 2.5 Gbitrs by a digital word Ž1010 . . . . and powered up to 22 dBm by an erbium-doped amplifier. By choosing the probe source at l probe s 1525
335
nm, the velocity mismatch in the dispersion shifted fiber is negligible and the phase of the copropagating probe signal follows the pump temporal shape w4x. Then, the effect of fiber attenuation a is taken into account by introducing the effective length Leff s Ž1 y expŽya L..ra . In the present experiment, the time delay between the two arms is set equal to t s 400 ps, i.e., D l f 8 cm. Fig. 3a shows a comparison between the theoretical nonlinear phase-shifts Žsolid line., calculated with the help of Eq. Ž1., and the corresponding experimental values Žcircles. as a function of the peak power. Fig. 3b shows the measured nonlinear refractive index Žcrosses. as a function of the peak power together with the average value of n 2 s 2.41 = 10y20 m2 Wy1. The good agreement between the n 2 measurements and the values of the nonlinear refractive index reported in the current literature for DS fibers is apparent. We have checked the reliability of our experimental data by repeating measurements reported in Fig. 3b several times: measurement accuracy ranges within 3–5%, with a total uncertainty, including polarization and power fluctuations, estimated within 10–15%. It should be noted that the proposed set-up can be applied for measuring the Kerr-induced nonlinear phase shift at different points of an optical link. In this way, any variations of the nonlinear coefficient n 2rA eff along the fiber can be accurately determined. For highly dispersive fibers, such as standard fibers Ži.e., zero-dispersion at l s 1300 nm., the effect of the dispersion should be considered, resulting in a velocity mismatch between probe and pump. To recover accurate values of n 2 from Eq. Ž1., one possibility is to choose a square wave modulated pump power. In this case, the temporal behaviour of the nonlinear phase-shift has some interesting features. First, the nonlinear phase-shift has a maximum value for pump modulation frequencies f F f 0 s 1rŽ2 d L., where d s Ž1rÕpump y 1rÕprobe . is the mismatch factor. Second, the nonlinear phase-shift shows a trapezoidal time-dependence
Fig. 2. The schematic of the experimental set-up.
336
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
Fig. 3. Ža. Nonlinear phase-shift versus peak power. Žb. n 2 measurements versus peak power. Data are: l probe s 1525 nm, a s 0.2 dBrkm, L s 615 m, A eff s 50 mm2 . Fiber under test: dispersion-shifted fiber.
for f - f 0 and a triangular shape at f s f 0 . For f ) f 0 , the nonlinear phase-shift starts decreasing and for f 4 f 0 the
XPM effects are negligible Ždetails concerning demonstrations are given in Ref. w4x..
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
337
Fig. 4. Nonlinear phase-shift for various probe wavelengths. Ža. l probe s 1540 nm, Žb. l probe s 1530 nm, Žc. l probe s 1520 nm. Data are: peak Pprobe s q19 dBm, a s 0.2 dBrkm, L s 1211 m, A eff s 71 mm2 . Fiber under test: standard fiber Žzero-dispersion at l s 1310 nm..
In Fig. 4, the nonlinear phase-shift of a 1200-m long standard fiber for various wavelengths is reported, showing an excellent agreement with the theoretical predictions reported in Ref. w4x. The value of n 2 , measured at a pump peak power of P s 19 dBm is n 2 s 1.7 = 10y20 m2 Wy1. Furthermore, the obtained results clearly indicate that this technique is also very effective in investigating the dynamical XPM effect between channels of WDM systems w10x. Finally, despite the fact that all measurements have been performed in a test plant environment, we believe, due to the elevated phase noise insensitivity tested in this work Žsee Appendix A., to achieve the same results, at least, with buried and submerged fiber-optic cables.
3. Conclusions A measurement method based on the cross-phase-modulation scheme which allows simple and immediate measurements of the nonlinear refractive index along the optically amplified transmission lines is presented in this paper. This technique works in coherent delayed-self-homodyne configuration that we demonstrate to be a solution
particularly suitable for the investigations on in-the-field systems because of its phase noise insensitivity in highfrequency operation. Measurements of the nonlinear refractive index, performed on both dispersion shifted and standard fibers, show a good agreement with the current literature. Acknowledgements Acknowledgements are especially made to Prof. M. Martinelli for his continuous advice and many stimulating discussions. We would like to thank the anonymous reviewers for their valuable comments. One of the authors, P. Sacchetto, acknowledges the support of ITALTEL for a stage at R & D Transmission Lab as a part of his thesis work at Politecnico di Milano. Appendix A To provide a better insight into how the interferometer performance changes with the noise disturbances it is useful to give some practical examples. To this end, let us
338
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
consider the scheme in Fig. 1a with a pump sinusoidally modulated at f pump s 1 GHz. The environmental noise is
assumed to have a band-limited frequency spectrum with a cut-off frequency of f noise s 100 kHz w11x. With the help
Fig. 5. Ža. Output interference in a Mach–Zehnder interferometer, when CW probe feeds both interferometer arms. The fiber under test is 615 m long. Žb. Same operating conditions of Fig. 4a test by using a coherent delayed-self-homodyne detection scheme.
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
of Eq. Ž2., the phase signal detected by the interferometer can be written as D f Ž t . s 2 sin Ž p f pumpt . cos 2p f pump Ž t y tr2 . qsin Ž p f noiset . cos w 2p f noise Ž t y tr2 . x 4
Ž A.1 . by choosing the time delay t s 1r2 f pump , a trivial calculation yields
339
processing Žsee Ref. w11x and references therein.. Since fiber optic cables are deployed through public areas it may be difficult to protect them from noise disturbances caused by random environmental changes, unless special cases are considered. Fig. 5b shows the measurement of the output interference performed on the same fiber under test by using a coherent delayed-self-homodyne detection scheme. As can be seen, all effects of the noise are suppressed in agreement with the calculations of Eq. ŽA.2..
References ŽA.2.
It is thus evident, from Eq. ŽA.2., that the noise level is dramatically reduced. To provide a direct evidence of the obtained result a simple experiment was performed. Two fiber coils with the same length, fiber under test and reference fiber, respectively, were used to realize the two arms of a Mach–Zehnder interferometer. Fig. 5a shows the output interference detected by a receiver when a CW probe feeds both interferometer arms. The phase noise is so strong in this case Žcross bars indicate levels that correspond to "p ., that no reliable measurements are possible. In fact, it is well known that fiber interferometers are realized by inserting their optical paths in temperaturecontrolled and acoustically insensitive boxes, by winding the two arms of the interferometer in one single coil or by means of special configurations and sophisticated signal
w1x R.H. Stolen, C. Lin, Phys. Rev. A 17 Ž1978. 1448. w2x R.H. Stolen, W.A. Reed, K.S. Kim, G.T. Harvey, J. Lightwave Technol. 16 Ž1998. 1006. w3x Y. Namihira, A. Myata, N. Tanahashi, Electron. Lett. 30 Ž1994. 1171. w4x P. Boffi, A. Fellegara, M. Martinelli, Opt. Commun. 129 Ž1996. 155. w5x M. Artiglia, E. Ciaramella, B. Sordo, Electron. Lett. 31 Ž1995. 1012. w6x L. Prigent, J.P. Hamaide, IEEE Photon. Technol. Lett. 5 Ž1993. 1092. w7x A. Fellegara, L. Amato, P. Sacchetto, P. Boffi, A. Melloni, M. Martinelli, in: Proc. OFC’96, paper ThS4, 1996, p. 288. w8x D. Monzon-Hernadez, A.N. Starodumov, Yu.O. Barmenkov, I. Torres-Gomez, F. Mendoza-Santoyo, Opt. Lett. 23 Ž1998. 1274. w9x A. Wada, T. Tsun, R. Yamauchi, in: Proc. ECOC’92, paper MoB1.2, 1992, p. 45. w10x T. Ogata, Y. Aoki, T. Koga, I. Matsuoka, in: Proc. OFC’96, 1996, p. 42. w11x R. Rønnekleiv, Appl. Opt. 36 Ž1997. 2076.
Optics Communications 162 Ž1999. 333–339
Full length article
Phase noise insensitive measurements of the nonlinear refractive index in fiber links Andrea Fellegara
a,)
, Andrea Melloni b, Paolo Sacchetto
a
a
b
ITALTEL, R & D Transport and Access Business Unit, 20019 Castelletto di Settimo Milanese, Milan, Italy Department of Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy Received 28 October 1998; accepted 12 February 1999
Abstract A method for measuring the nonlinear refractive index, n 2 , along optically amplified fiber transmission lines of high-bit-rate transmission systems is presented in this paper. Measurements of the Kerr-induced nonlinear phase-shift as a function of the optical power are performed through a cross-phase-modulation scheme by using a coherent delayed-self-homodyne technique that we demonstrate to be a solution particularly insensitive to the phase noise in high-frequency operation. Experiments performed at 2.5 Gbitrs are in agreement with theoretical predictions. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Refractive index; Fiber links; Nonlinear coefficient
1. Introduction Nonlinearities play a role of fundamental importance in assessing the performance of transmission systems which operate in the high optical power regime. In fact, the interplay between dispersive and nonlinear effects can give rise to severe pulse distortions, or, under certain conditions, a balance between the two effects can lead to soliton-like behaviour. Therefore, the determination of the nonlinear coefficient n 2rA eff , where n 2 is the nonlinear refractive index and A eff is the effective area, of optical fibers is a really important issue. To date, several methods for measuring n 2 have been developed by using self- and cross-phase modulation w1–4x, modulation instability w5x, four-wave mixing w6x, ortho-conjugated mirrors w7x, and very recently, Sagnac interferometers w8x. Most of the experiments reported in the literature have been performed
) Corresponding author. Present address: Wind Telecomunicazion: Spa, Rome, Italy.
in a laboratory environment, and very little data is available from the installed fiber cables. The aim of this work is to propose and demonstrate an experimental technique for measuring the nonlinear refractive index along the installed optical links of in-the-field transmission systems. Among the various techniques for measuring n 2 , we selected interferometric methods which can give accurate measurements of the peak phase shifts as a function of peak power, bit-rate and fiber length. Interferometers, however, are sensitive to acoustic and thermal disturbances of the optical path caused by the unavoidable random environmental changes of operating transmission lines. To overcome this practical difficulty, we measure the Kerr-phase signal by resorting to a particular coherent delayed-self-homodyne scheme that we will demonstrate to be a particularly suitable solution because of its intrinsic phase noise insensitivity in high frequency operation Žthe case of noncoherent delayed-self-homodyne and its applications are treated in Ref. w9x.. Finally, an experimental work is presented in this paper that verifies the theoretical predictions and shows that the coherent delayed-self-homodyne technique may work with realistic perturbations.
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 0 8 1 - 4
334
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
2. Measurement concept and experimental results The concept of our measurement method is illustrated in Fig. 1a. From the TX-pump, an intensity modulated strong optical signal is emitted, whereas, a CW relatively weak signal power is sent by the TX-probe. The signals combine at the coupler C1, and enter into the fiber link under test. The phase of the copropagating probe signal
follows the temporal shape of the pump, through the cross-phase modulation XPM w4x, according to DF Ž t . s 2 b
2p
n2
l probe A eff
L
H0 P
pump
ž
tyl
1
1 y
Õpump
Õprobe
/
=exp Ž ya l . d l Ž1. where PpumpŽ t . is the pump power, Õpump and Õprobe the group velocities, L the fiber length, A eff the effective area,
Fig. 1. Ža. Measurement concept. Žb. Kerr-phase signal reconstruction according to the coherent delayed-self-homodyne technique.
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
n 2 the nonlinear refractive index, l probe the probe wavelength and b s 2r3 the polarization parameter w7x. Hence, measurements of the nonlinear Kerr phase-shift can be performed by using a coherent delayed-self-homodyne detection technique. In this technique, the pump light is blocked by a bandpass filter and the probe signal is sent to a Mach–Zehnder interferometer in which the light in one arm is delayed by t with respect to the other. The phase signal detected by the interferometer is D f Ž t . s f Kerr Ž t . y f Kerr Ž t y t . q fnoise Ž t . y fnoise Ž t y t .
Ž2.
where f Kerr Ž t ., w f Kerr Ž t y t .x and fnoiseŽ t ., w fnoiseŽ t y t .x represent the Kerr phase signal and the phase noise suffered by the optical beam during the propagation along the optical fiber at the time t and w t y t x, respectively. By using a probe with a very narrow linewidth, such as an external cavity laser, and for t < Tc Žnoise correlation time., the noise terms fnoiseŽ t ., w fnoiseŽ t y t .x become approximately equal, significantly reducing the impact of the noise on the interferometric detection Žsee Appendix A for details.. By setting the delay t s T bit Žbit time., the interferometric phase signal becomes two times larger than the Kerr phase shift induced by the pump signal, as can be seen in Fig. 1b. To verify the validity of the theoretical predictions, we performed measurements on a 600-m long dispersionshifted ŽDS. single-mode fiber coil with an independently determined effective area of A eff s 50 mm2. To simulate the real environment of the operating systems the coil has been installed in the test plant area of the ITALTEL Business Unit Transport and Access without any protective box against the noise disturbances. Fig. 2 is the schematic of the experimental setup. A DFB laser at l s 1550 nm is externally modulated at 2.5 Gbitrs by a digital word Ž1010 . . . . and powered up to 22 dBm by an erbium-doped amplifier. By choosing the probe source at l probe s 1525
335
nm, the velocity mismatch in the dispersion shifted fiber is negligible and the phase of the copropagating probe signal follows the pump temporal shape w4x. Then, the effect of fiber attenuation a is taken into account by introducing the effective length Leff s Ž1 y expŽya L..ra . In the present experiment, the time delay between the two arms is set equal to t s 400 ps, i.e., D l f 8 cm. Fig. 3a shows a comparison between the theoretical nonlinear phase-shifts Žsolid line., calculated with the help of Eq. Ž1., and the corresponding experimental values Žcircles. as a function of the peak power. Fig. 3b shows the measured nonlinear refractive index Žcrosses. as a function of the peak power together with the average value of n 2 s 2.41 = 10y20 m2 Wy1. The good agreement between the n 2 measurements and the values of the nonlinear refractive index reported in the current literature for DS fibers is apparent. We have checked the reliability of our experimental data by repeating measurements reported in Fig. 3b several times: measurement accuracy ranges within 3–5%, with a total uncertainty, including polarization and power fluctuations, estimated within 10–15%. It should be noted that the proposed set-up can be applied for measuring the Kerr-induced nonlinear phase shift at different points of an optical link. In this way, any variations of the nonlinear coefficient n 2rA eff along the fiber can be accurately determined. For highly dispersive fibers, such as standard fibers Ži.e., zero-dispersion at l s 1300 nm., the effect of the dispersion should be considered, resulting in a velocity mismatch between probe and pump. To recover accurate values of n 2 from Eq. Ž1., one possibility is to choose a square wave modulated pump power. In this case, the temporal behaviour of the nonlinear phase-shift has some interesting features. First, the nonlinear phase-shift has a maximum value for pump modulation frequencies f F f 0 s 1rŽ2 d L., where d s Ž1rÕpump y 1rÕprobe . is the mismatch factor. Second, the nonlinear phase-shift shows a trapezoidal time-dependence
Fig. 2. The schematic of the experimental set-up.
336
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
Fig. 3. Ža. Nonlinear phase-shift versus peak power. Žb. n 2 measurements versus peak power. Data are: l probe s 1525 nm, a s 0.2 dBrkm, L s 615 m, A eff s 50 mm2 . Fiber under test: dispersion-shifted fiber.
for f - f 0 and a triangular shape at f s f 0 . For f ) f 0 , the nonlinear phase-shift starts decreasing and for f 4 f 0 the
XPM effects are negligible Ždetails concerning demonstrations are given in Ref. w4x..
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
337
Fig. 4. Nonlinear phase-shift for various probe wavelengths. Ža. l probe s 1540 nm, Žb. l probe s 1530 nm, Žc. l probe s 1520 nm. Data are: peak Pprobe s q19 dBm, a s 0.2 dBrkm, L s 1211 m, A eff s 71 mm2 . Fiber under test: standard fiber Žzero-dispersion at l s 1310 nm..
In Fig. 4, the nonlinear phase-shift of a 1200-m long standard fiber for various wavelengths is reported, showing an excellent agreement with the theoretical predictions reported in Ref. w4x. The value of n 2 , measured at a pump peak power of P s 19 dBm is n 2 s 1.7 = 10y20 m2 Wy1. Furthermore, the obtained results clearly indicate that this technique is also very effective in investigating the dynamical XPM effect between channels of WDM systems w10x. Finally, despite the fact that all measurements have been performed in a test plant environment, we believe, due to the elevated phase noise insensitivity tested in this work Žsee Appendix A., to achieve the same results, at least, with buried and submerged fiber-optic cables.
3. Conclusions A measurement method based on the cross-phase-modulation scheme which allows simple and immediate measurements of the nonlinear refractive index along the optically amplified transmission lines is presented in this paper. This technique works in coherent delayed-self-homodyne configuration that we demonstrate to be a solution
particularly suitable for the investigations on in-the-field systems because of its phase noise insensitivity in highfrequency operation. Measurements of the nonlinear refractive index, performed on both dispersion shifted and standard fibers, show a good agreement with the current literature. Acknowledgements Acknowledgements are especially made to Prof. M. Martinelli for his continuous advice and many stimulating discussions. We would like to thank the anonymous reviewers for their valuable comments. One of the authors, P. Sacchetto, acknowledges the support of ITALTEL for a stage at R & D Transmission Lab as a part of his thesis work at Politecnico di Milano. Appendix A To provide a better insight into how the interferometer performance changes with the noise disturbances it is useful to give some practical examples. To this end, let us
338
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
consider the scheme in Fig. 1a with a pump sinusoidally modulated at f pump s 1 GHz. The environmental noise is
assumed to have a band-limited frequency spectrum with a cut-off frequency of f noise s 100 kHz w11x. With the help
Fig. 5. Ža. Output interference in a Mach–Zehnder interferometer, when CW probe feeds both interferometer arms. The fiber under test is 615 m long. Žb. Same operating conditions of Fig. 4a test by using a coherent delayed-self-homodyne detection scheme.
A. Fellegara et al.r Optics Communications 162 (1999) 333–339
of Eq. Ž2., the phase signal detected by the interferometer can be written as D f Ž t . s 2 sin Ž p f pumpt . cos 2p f pump Ž t y tr2 . qsin Ž p f noiset . cos w 2p f noise Ž t y tr2 . x 4
Ž A.1 . by choosing the time delay t s 1r2 f pump , a trivial calculation yields
339
processing Žsee Ref. w11x and references therein.. Since fiber optic cables are deployed through public areas it may be difficult to protect them from noise disturbances caused by random environmental changes, unless special cases are considered. Fig. 5b shows the measurement of the output interference performed on the same fiber under test by using a coherent delayed-self-homodyne detection scheme. As can be seen, all effects of the noise are suppressed in agreement with the calculations of Eq. ŽA.2..
References ŽA.2.
It is thus evident, from Eq. ŽA.2., that the noise level is dramatically reduced. To provide a direct evidence of the obtained result a simple experiment was performed. Two fiber coils with the same length, fiber under test and reference fiber, respectively, were used to realize the two arms of a Mach–Zehnder interferometer. Fig. 5a shows the output interference detected by a receiver when a CW probe feeds both interferometer arms. The phase noise is so strong in this case Žcross bars indicate levels that correspond to "p ., that no reliable measurements are possible. In fact, it is well known that fiber interferometers are realized by inserting their optical paths in temperaturecontrolled and acoustically insensitive boxes, by winding the two arms of the interferometer in one single coil or by means of special configurations and sophisticated signal
w1x R.H. Stolen, C. Lin, Phys. Rev. A 17 Ž1978. 1448. w2x R.H. Stolen, W.A. Reed, K.S. Kim, G.T. Harvey, J. Lightwave Technol. 16 Ž1998. 1006. w3x Y. Namihira, A. Myata, N. Tanahashi, Electron. Lett. 30 Ž1994. 1171. w4x P. Boffi, A. Fellegara, M. Martinelli, Opt. Commun. 129 Ž1996. 155. w5x M. Artiglia, E. Ciaramella, B. Sordo, Electron. Lett. 31 Ž1995. 1012. w6x L. Prigent, J.P. Hamaide, IEEE Photon. Technol. Lett. 5 Ž1993. 1092. w7x A. Fellegara, L. Amato, P. Sacchetto, P. Boffi, A. Melloni, M. Martinelli, in: Proc. OFC’96, paper ThS4, 1996, p. 288. w8x D. Monzon-Hernadez, A.N. Starodumov, Yu.O. Barmenkov, I. Torres-Gomez, F. Mendoza-Santoyo, Opt. Lett. 23 Ž1998. 1274. w9x A. Wada, T. Tsun, R. Yamauchi, in: Proc. ECOC’92, paper MoB1.2, 1992, p. 45. w10x T. Ogata, Y. Aoki, T. Koga, I. Matsuoka, in: Proc. OFC’96, 1996, p. 42. w11x R. Rønnekleiv, Appl. Opt. 36 Ž1997. 2076.