1. Introduction

The distributed fiber Raman amplifiers have been used to improve the optical signal-to-noise ratio (OSNR) and reduce the impact of nonlinearity on transmission system’s performance. However, the performance of fiber Raman amplified systems could be degraded by various noise sources, such as amplified spontaneous emission (ASE) noise, multi-path interference (MPI), pump-to-signal crosstalk, signal-pump-signal crosstalk, etc [1–4]. For example, double Rayleigh scattering which is inherently generated within the transmission fiber would induce a large amount of MPI with a high Raman gain. It has been well known that this MPI imposes a fundamental limitation on Raman amplified systems’ performance [2–3]. Recently, there have also been some efforts to investigate the combined effect of MPI with ASE noise [5] or relative-intensity noise (RIN) of pump laser [6]. Especially, in fiber Raman amplifiers, pump-intensity noise could be transferred to signal, which, in turn, causes a pump-to-signal crosstalk [4]. In order to suppress the effect of this crosstalk, counter-pumped configurations have been widely used in Raman amplified systems. This is because the different direction of signal and pump propagation could average the impact of pump-to-signal crosstalk in counter-pumped configurations. However, it has been reported that the MPI would be enhanced by the pump-intensity noise in a counter-pumped Raman amplifier [6].

In this paper, we analyze the combined effect of pump-intensity noise and reflections on the performance of counter-pumped Raman amplified systems. The modified analytical solutions for the MPI with pump-intensity noise and the pump-to-signal crosstalk with discrete reflection were derived, respectively. Using these equations, the required level of pump-intensity noise was evaluated for negligible enhancement of MPI and pump-to-signal crosstalk. From the results, we show that the enhancement of MPI would be negligible as long as commercially available pump lasers are used to implement the Raman amplifiers. In addition, we find that a high reflection within effective length of fiber could increase the effect of pump-to-signal crosstalk even for the counter-pumped Raman amplifiers.

2. Multi-path interference (MPI) with pump-intensity noise

MPI occurs when the optical signal is multiply reflected within transmission fiber. Moreover, the level of MPI becomes intolerable if reflections (such as Rayleigh backscattering or discrete reflections) lie in the region of amplifier. This is because the MPI components are amplified multiply with the gain of amplifier. The effect of MPI on the fiber Raman amplified system’s performance has been investigated by using an analytical solution and experimental measurements [2–3]. Recently, it has been also reported that MPI in a counter-pumped Raman amplifier could be significantly enhanced by the presence of pump-intensity noise [6]. However, the amount of MPI enhancement was measured by using an intensity-modulated pump laser in [6]. Therefore, in this case, it is not easy to figure out the required level of pump-intensity noise for negligible enhancement of MPI.

In order to evaluate the enhanced amount of MPI with pump intensity noise, we assume that the MPI component experiences the different Raman gain when it propagates in different directions. That is to say, the co- and counter-pumping gains of fiber Raman amplifier are slightly changed by the gain fluctuations due to pump-intensity noise [4]. Then, the modified equation for the MPI with pump-intensity noise is given by

where, L_eff is the effective length of fiber, α_s is the attenuation at the signal wavelength, S is the Rayleigh backscatter capture coefficient, G _{R_co} is the co-pumping Raman gain, and G _{R_ct} is the counter-pumping Raman gain.

Figure 1 shows the amount of MPI as a function of mean gain of Raman amplifier (which doesn’t include the gain fluctuation terms). In this calculation, we assumed that the level of pump-intensity noise was ranging from -10 dB/Hz to -90 dB/Hz. For comparison, we also calculated the amount of MPI without taking into account pump-intensity noise. It can be seen from Fig. 1 that the enhancement of MPI would be negligible even when the level of pump-intensity noise was as high as -40 dB/Hz. Even though the pump laser had a -10 dB/Hz of intensity noise, the level of MPI was increased by only 3 dB at the Raman gain of 20 dB. It has been known that the intensity noise levels of commercially available Raman pump laser modules are generally lower than -90 dB/Hz. Therefore, we confirm that the effect of pump-intensity noise on the enhancement of MPI would be negligible as long as commercially available Raman pumps are used for the implementation of fiber Raman amplifiers.

 

Fig. 1. The calculated level of MPI as a function of fiber Raman gain. The level of pump-intensity noise was ranging from -10 dB/Hz to -90 dB/Hz. S is the Rayleigh backscatter capture coefficient, D is the chromatic dispersion of transmission fiber, L is the length of fiber, α_s is the attenuation at the signal wavelength, and α_p is the attenuation at the pump wavelength.

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3. Pump-to-signal crosstalk with discrete reflection

In fiber Raman amplifiers, pump-to-signal crosstalk would be generated by the transfer of pump-intensity noise to signal-intensity noise It has been reported that the level of pump-intensity noise should be less than -120 dB/Hz for negligible system penalties in co-pumped Raman amplifiers, whereas pump-intensity noise levels as high as -60 dB/Hz are suitable for counter-pumped Raman amplifiers [4]. Recently, our experimental results showed that a high reflection (larger than -20 dB) could enhance the effect of pump-to-signal crosstalk for counter-pumped Raman amplifiers [7].

 

Fig. 2. Effect of discrete reflectance on pump-to-signal crosstalk for a counter-pumped Raman amplifier. L is the length of fiber, z′ is the reflection point, and R is the discrete reflectance.

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In order to analyze the effect of discrete reflection on the generation of pump-to-signal crosstalk, we assumed that a discrete reflectance of R is located at point z′ in a counter-pumped Raman amplifier, as shown in Fig. 2. In this analysis, we ignored the effect of signal reflection at z′ on the enhancement of pump-to-signal crosstalk. The signal could be reflected by the discrete reflectance at z′ in both directions; the original signal reflected back to the start of the fiber span and the Rayleigh-backscattered signal reflected to the end of the fiber span. It has been reported that these reflected signals would increase the amount of MPI [2–3]. Therefore, in order to simplify the analysis, only pump power reflected by the discrete reflectance was taken into account. Then, the equation for the signal-intensity noise with a discrete reflection in a counter-pumped Raman amplifier is given by

where, r_s is the signal-intensity noise, r_p is the pump-intensity noise, G_R is the Raman gain, V_s is the velocity of the signal, L is the length of fiber, α_p is the attenuation at the pump wavelength, T is the transit time over the fiber length L, t′ is the transit time over the fiber length (L-z′), D is the chromatic dispersion of fiber, and Δλ is the wavelength separation between signal and pump. In Eq. (2), the first term on right side represents the signal-intensity noise generated by the counter-propagating pump and signal [4]. As shown in Fig. 2, if some portion of counter-propagating pump power was reflected at z′, then the reflected pump was propagating in the same direction as signal. Therefore, the second term on right side represents the signal-intensity noise generated by the co-propagating reflected pump and signal. The amount of noise transfer due to discrete reflection depends on the value of reflectance and reflection point, as expected. Thus, Eq. (2) becomes identical to the previous result [4], when the discrete reflectance isn’t taken into account. We also confirm that the chromatic dispersion of the fiber averages the transfer of intensity noise in the second term.

The degradation in system’s performance could be estimated by using the quality factor (Q). Therefore, we calculated the Q-penalties (the baseline Q value was 10.) of counter-pumped Raman amplifier as a function of discrete reflectance (Fig. 3(a)), reflection point (Fig. 3(b)) and Raman gain (Fig. 3(c)), respectively, as shown in Fig. 3. In this calculation, we assumed that an optical signal was transmitted through a 100-km long non-zero dispersion-shifted fiber (D = 2 ps/nm/km, α_p = 0.25 dB/km) and amplified by using a Raman pump module which had a pump-intensity noise of -90 dB/Hz. In addition, the penalty was estimated by integrating the spectra of signal-intensity noise across the receiver bandwidth (10 kHz to 20 GHz) [4]. As shown in Fig. 3(a) and (b), the Q-penalties would be negligible as long as the value of reflectance was less than -20 dB and the reflection point was located outside the effective length of fiber. It is clear that as reflection point approaches closer to the end of fiber span, a larger amount of residual pump power would be reflected and co-propagated with signal, which in turn causes a larger pump-to-signal crosstalk-induced Q-penalty. We have also investigated the effect of Raman gain on the pump-to-signal crosstalk-induced Q-penalty, as shown in Fig. 3(c). The Q-penalty was increased by 1 dB when the Raman gain was changed from 10 dB to 20 dB. From the results, we confirmed that the pump-to-signal crosstalk could be enhanced significantly, only when a high reflection (larger than -20 dB) occurred within the effective length of transmission fiber. Therefore, the enhancement of pump-to-signal crosstalk would be negligible if care is taken to eliminate all discrete reflections within the effective length of transmission fiber.

Figure 4 shows the Q-penalties as a function of level of pump-intensity noise (RIN of pump laser) in co- and counter-pumped Raman amplified systems. The levels of pump-intensity noise for negligible Q-penalty were estimated to be -120 dB/Hz for co-pumped Raman amplifiers and -60 dB/Hz for counter-pumped fiber amplifiers, respectively, without taking into account the effect of discrete reflection. These results agree well with the previous results [4]. However, if there would exist a discrete reflectance of -20 dB and -10 dB (@ z′ = 96 km) in counter-pumped Raman amplifiers, the required level of pump-intensity noise for negligible Q-penalty were decrease to be -80 dB/Hz and -100 dB/Hz, respectively. From these results, we believe that care must be taken to choose the pump laser module even for counter-pumped Raman amplifiers, if the installed fiber might have poor reflection characteristics.

 

Fig. 3. The calculated Q-penalties as a function of (a) reflectance, (b) reflection point and (c) Raman gain. G is the Raman gain, D is the chromatic dispersion of transmission fiber, L is the length of fiber, z′ is the reflection point, r_p is the level of pump-intensity noise, α_p, is the attenuation at the pump wavelength and R is the level of discrete reflectance.

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Fig. 4. The calculated Q-penalty as a function of relative-intensity noise (RIN) of pump laser.

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4. Summary

We have derived the modified analytical solutions for multi-path interference (MPI) with pump-intensity noise and pump-to-signal crosstalk with discrete reflection in counter-pumped Raman amplifiers. From the calculations, the enhancement of MPI was estimated to be 3 dB even when the level of pump-intensity noise was as high as -10 dB/Hz at the Raman gain of 20 dB. We have also estimated the level of pump-intensity noise for negligible Q-penalty due to pump-to-signal crosstalk with a discrete reflection. The significant enhancement of pump-to-signal crosstalk was observed only when a high reflection (larger than -20 dB) occurred within the effective length of transmission fiber. Therefore, careful attention must be paid to the reflectance level of the installed fiber, if excessive penalty caused by the combined effect of pump-intensity noise and reflection is to be avoided in systems.