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OPTICS LETTERS / Vol. 39, No. 12 / June 15, 2014
Gain-saturated spectral characteristics in a Ramanassisted fiber optical parametric amplifier Xiaojie Guo,* Xuelei Fu, and Chester Shu Department of Electronic Engineering and Center for Advanced Research in Photonics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China *Corresponding author: [email protected] Received March 7, 2014; revised May 14, 2014; accepted May 14, 2014; posted May 16, 2014 (Doc. ID 207851); published June 12, 2014 We investigate the gain spectral characteristics in the course of saturation in a Raman-assisted fiber optical parametric amplifier (FOPA). It is experimentally observed that the saturated gain spectrum is modified with suppressed signal wavelength dependence as compared to a conventional FOPA. The gain at signal wavelengths on both farther and closer sides of the unsaturated gain peak from the pump saturates in a similar way. The modification of the saturated gain spectrum is explained by distributed nonlinear phase mismatch caused by the Raman effect. © 2014 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2320) Fiber optics amplifiers and oscillators; (060.4370) Nonlinear optics, fibers. http://dx.doi.org/10.1364/OL.39.003658
Ultrafast gain saturation of fiber optical parametric amplifiers (FOPAs) plays an important role in the application of optical regeneration in fiber-optic communication systems. When operated in the saturation region, FOPAs are capable of performing phase-preserving amplitude regeneration to suppress the nonlinear phase noise in transmission for signals up to 640 Gbit∕s [1–3]. Simultaneous amplitude and phase regeneration has also been demonstrated in a saturated phasesensitive FOPA [4]. In most reported applications using saturated FOPAs, only the linear-gain peak was selected as the wavelength for operation. One of the limits on the operation at other wavelengths is the significant signal wavelength dependence of gain saturation in FOPAs [5]. Consequently, it is difficult to achieve comparable performance of optical regeneration at different wavelengths. The use of a backward Raman pump in a FOPA is attractive because of the flexibility in selecting the wavelength of the parametric pump provided by Raman scattering [6]. In such a Raman-assisted FOPA, the combination of the parametric amplification and the Raman scattering enables gain-window extension and gain enhancement in addition to the inherent advantages of a conventional FOPA [7–10]. Recently, it has been reported that the interaction between the two types of nonlinearities also leads to different gain saturation characteristics compared to a conventional FOPA with the same linear gain [11]. The study focused on a specific wavelength near the linear-gain peak instead of the whole gain spectrum. In a Raman-assisted FOPA, the Raman scattering process can modify the nonlinear phase mismatch by contributing distributed Raman gain on the optical fields involved in the parametric process. Accordingly, the phase matching of the parametric process in the Ramanassisted FOPA is affected by the Raman pump, resulting in new behaviors of the saturated gain spectrum. Until now, the phase matching in a Raman-assisted FOPA has not been given much consideration. In this Letter, we investigate the saturation characteristics over the gain spectrum in a Raman-assisted FOPA. 0146-9592/14/123658-04$15.00/0
It is observed that the saturated gain spectrum is modified in a way that the signal wavelength dependence of gain saturation is suppressed. Signals at wavelengths on both farther and closer sides of the linear-gain peaks from the pump have similar saturation behaviors, unlike the observation in a conventional FOPA. The original physical mechanism leading to the modified saturated gain spectrum is verified through simulations incorporating the distributed nonlinear phase mismatch caused by Raman amplification. First, the gain spectra under both linear-gain and saturation conditions are experimentally observed. The experimental setup is illustrated in Fig. 1. A continuouswave (CW) tunable laser (TL1) is used as the signal. The gain spectrum is obtained by sweeping the output wavelength of TL1. The signal power can be adjusted by a variable optical attenuator (VOA). The parametric pump at 1555 nm is generated from another CW tunable laser (TL2). A 10 Gb∕s 27 − 1 pseudorandom binary sequence (PRBS) is used to phase modulate the pump to suppress stimulated Brillouin scattering in the highly nonlinear fiber (HNLF). The pump is then amplified, followed by a 1 nm optical bandpass filter (OBPF) to suppress the amplified spontaneous emission noise generated from the EDFA. It is combined with the signal by a 75∕25 coupler at the input of a 1-km HNLF after optimization of their polarization states. The power of the parametric pump at the input of the HNLF is 21.7 dBm.
Fig. 1. Experimental setup of the Raman-assisted FOPA. TL, tunable laser; PM, phase modulator; PRBS, pseudorandom binary sequence; EDFA, erbium-doped fiber amplifier; OBPF, optical band pass filter; CIR, optical circulator; VOA, variable optical attenuator; HNLF, highly nonlinear fiber; and OSA, optical spectrum analyzer. © 2014 Optical Society of America
June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS
The HNLF has a nonlinear coefficient γ 11.7 W−1 km−1 and a Raman gain coefficient γ R 3.8 W−1 km−1 . The zero dispersion wavelength (ZDW) is 1549 nm. The dispersion, dispersion slope, and attenuation coefficient at 1550 nm are 0.02 ps • km−1 nm−1 , 0.019 ps • km−1 nm−2 , and 0.79 dB • km−1 , respectively. A 30.4-dBm, 1455-nm CW fiber laser is used as the Raman pump. It is launched into the HNLF in the opposite direction of the parametric pump. The amplified signal is extracted from the HNLF through an optical circulator (CIR2) and is then analyzed by an optical spectrum analyzer (OSA). The 30.4 dBm Raman pump can provide a peak on–off gain of 16.7 dB at 1554 nm and a 3 dB bandwidth of 24 nm, as depicted in Fig. 2(a). It should be noted that in the Raman-assisted FOPA, the Raman pump is operated in the saturation condition, which offers 8.9 dB gain for the 21.7 dBm parametric pump. Figure 2(b) shows the gain spectra for input signal powers in the linear-gain region (−25 dBm) and the saturation region (−5 and −2 dBm) of the Raman-assisted FOPA. The unsaturated gain spectrum plotted with the black triangles is symmetric with two gain peaks located
Fig. 2. (a) Raman gain spectrum of the 30.4 dBm Raman pump. (b) Gain spectra of the Raman-assisted FOPA at input signal powers of −25 dBm (black triangles), −5 dBm (red crosses), and −2 dBm (blue diamonds). (c) Gain spectra of the conventional FOPA at input signal powers of −25 dBm (black triangles), −8 dBm (red crosses), and −5 dBm (blue diamonds).
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at 1546.5 nm (anti-Stokes side) and 1563.5 nm (Stokes side). The unsaturated peak gain is 28.4 dB. Asymmetry is observed in the saturated gain spectra in that the saturated gain on the Stokes side is higher than that of the anti-Stokes side. The asymmetry is not caused by the Raman amplification since, even without the Raman pump, an asymmetric profile is still observed in the conventional FOPA as shown in Fig. 2(c). In fact, the gain asymmetry can be attributed to the interaction between the high-order four-wave mixing products excited in saturation and the dispersive waves emitted because of third-order dispersion [12]. With input signal power increasing from −25 to −2 dBm, the gain over the whole spectrum starts to saturate and the gain spectrum is flattened compared to the unsaturated one. At signal wavelengths that are farther away from the linear-gain peak, less saturation is observed. Moreover, signals with the same linear gain at wavelengths on both sides of the linear-gain peak show comparable on–off gain in the saturation condition. As indicated in Fig. 2(b), at an input signal power of −2 dBm, the variation in the gain is 2 dB over the 6 nm wavelength range from 1544 to 1550 nm around the anti-Stokes linear-gain peak. The characteristics are distinct from the observation in a conventional FOPA. We measure the output of a conventional FOPA with a similar unsaturated gain spectrum and depict the results in Fig. 2(c). With the input signal power increasing from −25 to −5 dBm, a weaker gain saturation is observed as the signal wavelength becomes close to that of the pump. On the other hand, a significant gain drop appears at wavelengths farther from the pump with respect to the linear-gain peak. As a result, the signals have much lower output powers at these wavelengths under the saturation condition. As shown in Fig. 2(c), at an input power of −5 dBm, there is a 5.2 dB variation in the saturated output power over the 6 nm wavelength range around the anti-Stokes linear-gain peak. The results in Figs. 2(b) and 2(c) indicate that the saturated gain spectra are modified in the Raman-assisted FOPA. The saturation behaviors at wavelengths on the two sides of the linear-gain peak become more symmetric. Next, the wavelength dependence of gain saturation in the Raman-assisted FOPA is characterized by considering two wavelengths on the anti-Stokes side of the gain spectrum. The signal wavelengths are chosen at 1544.5 and 1549 nm with an equal unsaturated gain of 26.1 dB. At each wavelength, the output signal power is measured as a function of the input signal power. As shown in Fig. 3(a), the signal input–output behaviors are nearly identical. The output powers at both wavelengths reach a maximum at the same input power of −1 dBm. It is in contrast to the behavior in the conventional FOPA. Figure 3(b) depicts the gain saturation behavior of a conventional FOPA at two wavelengths, 1543.5 and 1548 nm, where identical linear gains of 25.6 dB are obtained. The output signal at the shorter wavelength saturates quickly and reaches a maximum at a lower input power of −6.5 dBm, as compared to −2 dBm at the longer wavelength. In addition, the difference in the maximum output powers between the two wavelengths is ∼4 dB. Hence, from the results in Figs. 3(a) and 3(b), it is concluded that
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Fig. 3. Signal output power as a function of input signal power for (a) Raman-assisted FOPA and (b) conventional FOPA. Triangles and diamonds are experimental results for the shorter and the longer wavelength, respectively. Dashed and solid curves are the corresponding simulation results.
the signal wavelength dependence of gain saturation is suppressed in the Raman-assisted FOPA. Simulations have been carried out to analyze the experimental results based on the nonlinear Schrödinger equation with inclusion of the Raman effect [11]. The phase matching condition is given specific consideration in the analysis. In the parametric process, the signal gain in both the linear and saturation regions is affected by the total phase mismatch expressed as [10]: Δk ΔkL γ2P p − P s − P i ;
(1)
where ΔkL is the linear phase mismatch determined by the fiber dispersion. The second term on the right side of Eq. (1) is the nonlinear phase mismatch ΔkNL . Here, γ is the nonlinear coefficient of the HNLF, and P p , P s , and P i are the powers of the parametric pump, signal and idler, respectively. In the linear-gain region, the total phase mismatch in Eq. (1) can be simplified as: Δk ΔkL 2γP p ;
tion imposes a distributed nonlinear phase shift that modifies the phase matching condition of the parametric process. The supposition is confirmed by the simulation results in the linear-gain condition, illustrated by the black curves in Fig. 4 for signals at 1544.5 and 1549 nm. At both wavelengths, Δk gradually increases to a positive value near the output of the HNLF. Note that Δk 0 at the input of the HNLF for 1549 nm because ΔkL at this wavelength happens to be compensated by 2γP p with the 21.7-dBm parametric pump. One can understand the suppression of the signal wavelength dependence in the saturated Raman-assisted FOPA by considering the unique phase mismatch which includes a distributed nonlinear phase. According to Eq. (1), P s and P i become large and thus Δk becomes small when the input signal power enters the saturation region. Because P s and P i are growing and P p is being depleted with the increase of the fiber length, the reduction of Δk is more significant near the output of the HNLF. As shown in Fig. 4, Δk is clearly decreasing in the last 200 m of the HNLF when the input signal power is increasing from the unsaturated region (−25 dBm) to the saturation region. Although the exact values of Δk for signals at the shorter and the longer wavelengths are different, Δk in both cases evolves in the same direction as the input signal power increases. Note that for each wavelength in Fig. 4, Δk is positive near the end of the HNLF before the signal gain saturates. With the increasing input signal power, Δk becomes small and approaches perfect phase matching (Δk 0) near the output of the HNLF. The phase-matching condition is recovered in the last 200 m of the HNLF as compared to the unsaturated case. Consequently, the parametric efficiency is enhanced at both wavelengths, which partly compensates the gain reduction caused by the pump depletion. Figure 5(a) shows that the signal powers at 1544.5 and 1549 nm grow with an increasing slope along the HNLF at an input power of −5 dBm. Therefore, the signal at the shorter wavelength
(2)
since the powers of signal and idler are much lower than the pump power. For the unsaturated conventional FOPA, Δk is essentially unchanged along the HNLF because the depletion of the parametric pump is negligible. In addition, Δk is 0 at the linear-gain peak. It becomes negative at wavelengths farther from the pump (e.g., 1543.5 nm) and positive at wavelengths closer to the pump (e.g. 1548 nm). However, for the Raman-assisted FOPA, the parametric pump is progressively amplified along the HNLF by the backward Raman pump. According to Eq. (2), Δk in the linear-gain region is not constant but monotonically increases along the HNLF. That is, the Raman amplifica-
Fig. 4. Evolution of phase mismatch along the fiber in the Raman-assisted FOPA for signals at (a) 1544.5 and (b) 1549 nm. Curves with different colors are obtained with signals at different powers.
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Fig. 5. (a) Profiles of signal power for signals at 1544.5 and 1549 nm in the Raman-assisted FOPA. (b) Profiles of signal power for signals at 1543.5 and 1548 nm in the conventional FOPA. The input signal power is −5 dBm.
resembles the saturation behavior of that at the longer wavelength, in consistence with the experimental and simulation results in Fig. 3(a). In contrast, in the saturated conventional FOPA, the reduction of the nonlinear phase mismatch leads to the opposite behaviors of Δk [5]. From the previous analysis, the signs of Δk in the conventional FOPA are opposite for the shorter and the longer wavelengths in the linear-gain condition. At the shorter wavelength, Δk is negative before the signal gain saturates. Phase matching is further degraded in the saturation region. Hence, the signal power at 1543.5 nm stops growing in the last 200 m of the HNLF, as shown in Fig. 5(b). This explains the difference in the saturation characteristics between 1543.5 and 1548 nm in Fig. 3(b). The suppressed signal wavelength dependence of gain saturation results in the modification of the saturated gain spectra for the Raman-assisted FOPA as shown in Fig. 2(b). Because of the small difference between the saturated signal gain for wavelengths at farther and closer sides of the linear-gain peaks from the pump, the saturated gain spectrum is flattened compared to that of the conventional FOPA.
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In summary, the gain spectral characteristics in the course of saturation in a backward-pumped Raman assisted FOPA have been investigated. A modified gain spectrum has been observed experimentally and analyzed through simulations. It is found that the saturated gain spectrum is broadened and the wavelength dependence of saturation is suppressed in comparison to a conventional FOPA. Unlike the conventional FOPA, the signals at wavelengths farther and closer to the pump have similar saturation behaviors. This phenomenon is attributed to the unique distributed nonlinear phase mismatch of the parametric process. On both sides of the gain peak, the total phase mismatch is positive near the fiber end in the linear-gain condition and approaches zero when the gain saturates. The same direction of phase-mismatch evolution leads to similar saturation behaviors and thus reduces the signal wavelength dependence of saturation in the Raman-assisted FOPA. This work was supported by a GRF grant (CUHK 416213) and a CUHK direct grant. References 1. M. Matsumoto and T. Kamio, IEEE J. Sel. Top. Quantum Electron. 14, 610 (2008). 2. M. Gao, J. Kurumida, and S. Namiki, Opt. Lett. 35, 3468 (2010). 3. Z. Lali-Dastjerdi, M. Galili, H. C. H. Mulvad, H. Hu, L. K. Oxenløwe, K. Rottwitt, and C. Peucheret, Opt. Express 21, 25944 (2013). 4. F. P. R. Slavik, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, Nat. Photonics 4, 690 (2010). 5. K. Inoue and T. Mukai, Opt. Lett. 26, 10 (2001). 6. M. N. Islam, IEEE J. Sel. Top. Quantum Electron. 8, 548 (2002). 7. C. J. S. de Matos, D. A. Chestnut, P. C. Reeves-Hall, and J. R. Taylor, Opt. Lett 26, 1583 (2001). 8. J. F. L. Freitas, M. B. Costa e Silva, S. R. Lüthi, and A. S. L. Gomes, Opt. Commun. 255, 314 (2005). 9. S. H. Wang, L. Xu, P. K. A. Wai, and H. Y. Tam, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 2008), paper JThA13. 10. M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2007). 11. X. Guo, X. Fu, and C. Shu, Opt. Lett. 38, 4405 (2013). 12. Z. Lali-Dastjerdi, K. Rottwitt, M. Galili, and C. Peucheret, Opt. Express 20, 15530 (2012).
OPTICS LETTERS / Vol. 39, No. 12 / June 15, 2014
Gain-saturated spectral characteristics in a Ramanassisted fiber optical parametric amplifier Xiaojie Guo,* Xuelei Fu, and Chester Shu Department of Electronic Engineering and Center for Advanced Research in Photonics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China *Corresponding author: [email protected] Received March 7, 2014; revised May 14, 2014; accepted May 14, 2014; posted May 16, 2014 (Doc. ID 207851); published June 12, 2014 We investigate the gain spectral characteristics in the course of saturation in a Raman-assisted fiber optical parametric amplifier (FOPA). It is experimentally observed that the saturated gain spectrum is modified with suppressed signal wavelength dependence as compared to a conventional FOPA. The gain at signal wavelengths on both farther and closer sides of the unsaturated gain peak from the pump saturates in a similar way. The modification of the saturated gain spectrum is explained by distributed nonlinear phase mismatch caused by the Raman effect. © 2014 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2320) Fiber optics amplifiers and oscillators; (060.4370) Nonlinear optics, fibers. http://dx.doi.org/10.1364/OL.39.003658
Ultrafast gain saturation of fiber optical parametric amplifiers (FOPAs) plays an important role in the application of optical regeneration in fiber-optic communication systems. When operated in the saturation region, FOPAs are capable of performing phase-preserving amplitude regeneration to suppress the nonlinear phase noise in transmission for signals up to 640 Gbit∕s [1–3]. Simultaneous amplitude and phase regeneration has also been demonstrated in a saturated phasesensitive FOPA [4]. In most reported applications using saturated FOPAs, only the linear-gain peak was selected as the wavelength for operation. One of the limits on the operation at other wavelengths is the significant signal wavelength dependence of gain saturation in FOPAs [5]. Consequently, it is difficult to achieve comparable performance of optical regeneration at different wavelengths. The use of a backward Raman pump in a FOPA is attractive because of the flexibility in selecting the wavelength of the parametric pump provided by Raman scattering [6]. In such a Raman-assisted FOPA, the combination of the parametric amplification and the Raman scattering enables gain-window extension and gain enhancement in addition to the inherent advantages of a conventional FOPA [7–10]. Recently, it has been reported that the interaction between the two types of nonlinearities also leads to different gain saturation characteristics compared to a conventional FOPA with the same linear gain [11]. The study focused on a specific wavelength near the linear-gain peak instead of the whole gain spectrum. In a Raman-assisted FOPA, the Raman scattering process can modify the nonlinear phase mismatch by contributing distributed Raman gain on the optical fields involved in the parametric process. Accordingly, the phase matching of the parametric process in the Ramanassisted FOPA is affected by the Raman pump, resulting in new behaviors of the saturated gain spectrum. Until now, the phase matching in a Raman-assisted FOPA has not been given much consideration. In this Letter, we investigate the saturation characteristics over the gain spectrum in a Raman-assisted FOPA. 0146-9592/14/123658-04$15.00/0
It is observed that the saturated gain spectrum is modified in a way that the signal wavelength dependence of gain saturation is suppressed. Signals at wavelengths on both farther and closer sides of the linear-gain peaks from the pump have similar saturation behaviors, unlike the observation in a conventional FOPA. The original physical mechanism leading to the modified saturated gain spectrum is verified through simulations incorporating the distributed nonlinear phase mismatch caused by Raman amplification. First, the gain spectra under both linear-gain and saturation conditions are experimentally observed. The experimental setup is illustrated in Fig. 1. A continuouswave (CW) tunable laser (TL1) is used as the signal. The gain spectrum is obtained by sweeping the output wavelength of TL1. The signal power can be adjusted by a variable optical attenuator (VOA). The parametric pump at 1555 nm is generated from another CW tunable laser (TL2). A 10 Gb∕s 27 − 1 pseudorandom binary sequence (PRBS) is used to phase modulate the pump to suppress stimulated Brillouin scattering in the highly nonlinear fiber (HNLF). The pump is then amplified, followed by a 1 nm optical bandpass filter (OBPF) to suppress the amplified spontaneous emission noise generated from the EDFA. It is combined with the signal by a 75∕25 coupler at the input of a 1-km HNLF after optimization of their polarization states. The power of the parametric pump at the input of the HNLF is 21.7 dBm.
Fig. 1. Experimental setup of the Raman-assisted FOPA. TL, tunable laser; PM, phase modulator; PRBS, pseudorandom binary sequence; EDFA, erbium-doped fiber amplifier; OBPF, optical band pass filter; CIR, optical circulator; VOA, variable optical attenuator; HNLF, highly nonlinear fiber; and OSA, optical spectrum analyzer. © 2014 Optical Society of America
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The HNLF has a nonlinear coefficient γ 11.7 W−1 km−1 and a Raman gain coefficient γ R 3.8 W−1 km−1 . The zero dispersion wavelength (ZDW) is 1549 nm. The dispersion, dispersion slope, and attenuation coefficient at 1550 nm are 0.02 ps • km−1 nm−1 , 0.019 ps • km−1 nm−2 , and 0.79 dB • km−1 , respectively. A 30.4-dBm, 1455-nm CW fiber laser is used as the Raman pump. It is launched into the HNLF in the opposite direction of the parametric pump. The amplified signal is extracted from the HNLF through an optical circulator (CIR2) and is then analyzed by an optical spectrum analyzer (OSA). The 30.4 dBm Raman pump can provide a peak on–off gain of 16.7 dB at 1554 nm and a 3 dB bandwidth of 24 nm, as depicted in Fig. 2(a). It should be noted that in the Raman-assisted FOPA, the Raman pump is operated in the saturation condition, which offers 8.9 dB gain for the 21.7 dBm parametric pump. Figure 2(b) shows the gain spectra for input signal powers in the linear-gain region (−25 dBm) and the saturation region (−5 and −2 dBm) of the Raman-assisted FOPA. The unsaturated gain spectrum plotted with the black triangles is symmetric with two gain peaks located
Fig. 2. (a) Raman gain spectrum of the 30.4 dBm Raman pump. (b) Gain spectra of the Raman-assisted FOPA at input signal powers of −25 dBm (black triangles), −5 dBm (red crosses), and −2 dBm (blue diamonds). (c) Gain spectra of the conventional FOPA at input signal powers of −25 dBm (black triangles), −8 dBm (red crosses), and −5 dBm (blue diamonds).
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at 1546.5 nm (anti-Stokes side) and 1563.5 nm (Stokes side). The unsaturated peak gain is 28.4 dB. Asymmetry is observed in the saturated gain spectra in that the saturated gain on the Stokes side is higher than that of the anti-Stokes side. The asymmetry is not caused by the Raman amplification since, even without the Raman pump, an asymmetric profile is still observed in the conventional FOPA as shown in Fig. 2(c). In fact, the gain asymmetry can be attributed to the interaction between the high-order four-wave mixing products excited in saturation and the dispersive waves emitted because of third-order dispersion [12]. With input signal power increasing from −25 to −2 dBm, the gain over the whole spectrum starts to saturate and the gain spectrum is flattened compared to the unsaturated one. At signal wavelengths that are farther away from the linear-gain peak, less saturation is observed. Moreover, signals with the same linear gain at wavelengths on both sides of the linear-gain peak show comparable on–off gain in the saturation condition. As indicated in Fig. 2(b), at an input signal power of −2 dBm, the variation in the gain is 2 dB over the 6 nm wavelength range from 1544 to 1550 nm around the anti-Stokes linear-gain peak. The characteristics are distinct from the observation in a conventional FOPA. We measure the output of a conventional FOPA with a similar unsaturated gain spectrum and depict the results in Fig. 2(c). With the input signal power increasing from −25 to −5 dBm, a weaker gain saturation is observed as the signal wavelength becomes close to that of the pump. On the other hand, a significant gain drop appears at wavelengths farther from the pump with respect to the linear-gain peak. As a result, the signals have much lower output powers at these wavelengths under the saturation condition. As shown in Fig. 2(c), at an input power of −5 dBm, there is a 5.2 dB variation in the saturated output power over the 6 nm wavelength range around the anti-Stokes linear-gain peak. The results in Figs. 2(b) and 2(c) indicate that the saturated gain spectra are modified in the Raman-assisted FOPA. The saturation behaviors at wavelengths on the two sides of the linear-gain peak become more symmetric. Next, the wavelength dependence of gain saturation in the Raman-assisted FOPA is characterized by considering two wavelengths on the anti-Stokes side of the gain spectrum. The signal wavelengths are chosen at 1544.5 and 1549 nm with an equal unsaturated gain of 26.1 dB. At each wavelength, the output signal power is measured as a function of the input signal power. As shown in Fig. 3(a), the signal input–output behaviors are nearly identical. The output powers at both wavelengths reach a maximum at the same input power of −1 dBm. It is in contrast to the behavior in the conventional FOPA. Figure 3(b) depicts the gain saturation behavior of a conventional FOPA at two wavelengths, 1543.5 and 1548 nm, where identical linear gains of 25.6 dB are obtained. The output signal at the shorter wavelength saturates quickly and reaches a maximum at a lower input power of −6.5 dBm, as compared to −2 dBm at the longer wavelength. In addition, the difference in the maximum output powers between the two wavelengths is ∼4 dB. Hence, from the results in Figs. 3(a) and 3(b), it is concluded that
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Fig. 3. Signal output power as a function of input signal power for (a) Raman-assisted FOPA and (b) conventional FOPA. Triangles and diamonds are experimental results for the shorter and the longer wavelength, respectively. Dashed and solid curves are the corresponding simulation results.
the signal wavelength dependence of gain saturation is suppressed in the Raman-assisted FOPA. Simulations have been carried out to analyze the experimental results based on the nonlinear Schrödinger equation with inclusion of the Raman effect [11]. The phase matching condition is given specific consideration in the analysis. In the parametric process, the signal gain in both the linear and saturation regions is affected by the total phase mismatch expressed as [10]: Δk ΔkL γ2P p − P s − P i ;
(1)
where ΔkL is the linear phase mismatch determined by the fiber dispersion. The second term on the right side of Eq. (1) is the nonlinear phase mismatch ΔkNL . Here, γ is the nonlinear coefficient of the HNLF, and P p , P s , and P i are the powers of the parametric pump, signal and idler, respectively. In the linear-gain region, the total phase mismatch in Eq. (1) can be simplified as: Δk ΔkL 2γP p ;
tion imposes a distributed nonlinear phase shift that modifies the phase matching condition of the parametric process. The supposition is confirmed by the simulation results in the linear-gain condition, illustrated by the black curves in Fig. 4 for signals at 1544.5 and 1549 nm. At both wavelengths, Δk gradually increases to a positive value near the output of the HNLF. Note that Δk 0 at the input of the HNLF for 1549 nm because ΔkL at this wavelength happens to be compensated by 2γP p with the 21.7-dBm parametric pump. One can understand the suppression of the signal wavelength dependence in the saturated Raman-assisted FOPA by considering the unique phase mismatch which includes a distributed nonlinear phase. According to Eq. (1), P s and P i become large and thus Δk becomes small when the input signal power enters the saturation region. Because P s and P i are growing and P p is being depleted with the increase of the fiber length, the reduction of Δk is more significant near the output of the HNLF. As shown in Fig. 4, Δk is clearly decreasing in the last 200 m of the HNLF when the input signal power is increasing from the unsaturated region (−25 dBm) to the saturation region. Although the exact values of Δk for signals at the shorter and the longer wavelengths are different, Δk in both cases evolves in the same direction as the input signal power increases. Note that for each wavelength in Fig. 4, Δk is positive near the end of the HNLF before the signal gain saturates. With the increasing input signal power, Δk becomes small and approaches perfect phase matching (Δk 0) near the output of the HNLF. The phase-matching condition is recovered in the last 200 m of the HNLF as compared to the unsaturated case. Consequently, the parametric efficiency is enhanced at both wavelengths, which partly compensates the gain reduction caused by the pump depletion. Figure 5(a) shows that the signal powers at 1544.5 and 1549 nm grow with an increasing slope along the HNLF at an input power of −5 dBm. Therefore, the signal at the shorter wavelength
(2)
since the powers of signal and idler are much lower than the pump power. For the unsaturated conventional FOPA, Δk is essentially unchanged along the HNLF because the depletion of the parametric pump is negligible. In addition, Δk is 0 at the linear-gain peak. It becomes negative at wavelengths farther from the pump (e.g., 1543.5 nm) and positive at wavelengths closer to the pump (e.g. 1548 nm). However, for the Raman-assisted FOPA, the parametric pump is progressively amplified along the HNLF by the backward Raman pump. According to Eq. (2), Δk in the linear-gain region is not constant but monotonically increases along the HNLF. That is, the Raman amplifica-
Fig. 4. Evolution of phase mismatch along the fiber in the Raman-assisted FOPA for signals at (a) 1544.5 and (b) 1549 nm. Curves with different colors are obtained with signals at different powers.
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Fig. 5. (a) Profiles of signal power for signals at 1544.5 and 1549 nm in the Raman-assisted FOPA. (b) Profiles of signal power for signals at 1543.5 and 1548 nm in the conventional FOPA. The input signal power is −5 dBm.
resembles the saturation behavior of that at the longer wavelength, in consistence with the experimental and simulation results in Fig. 3(a). In contrast, in the saturated conventional FOPA, the reduction of the nonlinear phase mismatch leads to the opposite behaviors of Δk [5]. From the previous analysis, the signs of Δk in the conventional FOPA are opposite for the shorter and the longer wavelengths in the linear-gain condition. At the shorter wavelength, Δk is negative before the signal gain saturates. Phase matching is further degraded in the saturation region. Hence, the signal power at 1543.5 nm stops growing in the last 200 m of the HNLF, as shown in Fig. 5(b). This explains the difference in the saturation characteristics between 1543.5 and 1548 nm in Fig. 3(b). The suppressed signal wavelength dependence of gain saturation results in the modification of the saturated gain spectra for the Raman-assisted FOPA as shown in Fig. 2(b). Because of the small difference between the saturated signal gain for wavelengths at farther and closer sides of the linear-gain peaks from the pump, the saturated gain spectrum is flattened compared to that of the conventional FOPA.
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In summary, the gain spectral characteristics in the course of saturation in a backward-pumped Raman assisted FOPA have been investigated. A modified gain spectrum has been observed experimentally and analyzed through simulations. It is found that the saturated gain spectrum is broadened and the wavelength dependence of saturation is suppressed in comparison to a conventional FOPA. Unlike the conventional FOPA, the signals at wavelengths farther and closer to the pump have similar saturation behaviors. This phenomenon is attributed to the unique distributed nonlinear phase mismatch of the parametric process. On both sides of the gain peak, the total phase mismatch is positive near the fiber end in the linear-gain condition and approaches zero when the gain saturates. The same direction of phase-mismatch evolution leads to similar saturation behaviors and thus reduces the signal wavelength dependence of saturation in the Raman-assisted FOPA. This work was supported by a GRF grant (CUHK 416213) and a CUHK direct grant. References 1. M. Matsumoto and T. Kamio, IEEE J. Sel. Top. Quantum Electron. 14, 610 (2008). 2. M. Gao, J. Kurumida, and S. Namiki, Opt. Lett. 35, 3468 (2010). 3. Z. Lali-Dastjerdi, M. Galili, H. C. H. Mulvad, H. Hu, L. K. Oxenløwe, K. Rottwitt, and C. Peucheret, Opt. Express 21, 25944 (2013). 4. F. P. R. Slavik, J. Kakande, C. Lundström, M. Sjödin, P. A. Andrekson, R. Weerasuriya, S. Sygletos, A. D. Ellis, L. Grüner-Nielsen, D. Jakobsen, S. Herstrøm, R. Phelan, J. O’Gorman, A. Bogris, D. Syvridis, S. Dasgupta, P. Petropoulos, and D. J. Richardson, Nat. Photonics 4, 690 (2010). 5. K. Inoue and T. Mukai, Opt. Lett. 26, 10 (2001). 6. M. N. Islam, IEEE J. Sel. Top. Quantum Electron. 8, 548 (2002). 7. C. J. S. de Matos, D. A. Chestnut, P. C. Reeves-Hall, and J. R. Taylor, Opt. Lett 26, 1583 (2001). 8. J. F. L. Freitas, M. B. Costa e Silva, S. R. Lüthi, and A. S. L. Gomes, Opt. Commun. 255, 314 (2005). 9. S. H. Wang, L. Xu, P. K. A. Wai, and H. Y. Tam, in Optical Fiber Communication Conference, OSA Technical Digest Series (Optical Society of America, 2008), paper JThA13. 10. M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices (Cambridge University, 2007). 11. X. Guo, X. Fu, and C. Shu, Opt. Lett. 38, 4405 (2013). 12. Z. Lali-Dastjerdi, K. Rottwitt, M. Galili, and C. Peucheret, Opt. Express 20, 15530 (2012).
