4. Stability of Raman fiber lasers 49
4.2. Optimization of RFLs for low-noise co-pumped Raman amplifiers
We now turn to the problem of designing an RFL as a pump source for a co-pumped Raman amplifier such that the performance degradation of the transmission span due to RIN transfer in the amplifier is minimized. The results presented here form part of [KCRB06]. It will be assumed in the following that the RIN of the considered RFLs stems exclusively from pump-to-Stokes RIN transfer, see section 4.1.
4.2.1. Overview of the optimization task
Assuming that the noise on the RFA’s pump laser (the RFL to be designed) can be treated as Gaussian and neglecting the noise on “0” bits in the signal stream, the penalty dBQ in the signal-quality factorQ can be estimated as [FHM01]
dBQ= 10 log
whererS(f) is the RIN of the signal at the receiver due to RIN transfer in the amplifier, and equals the product of the RIN spectrumrRFL(f) of the pumping RFL and the RIN transfer functionHA(f) of the amplifier. The latter is modelled as a low-pass filter,
HA(f) = HA(0)
1 +f2/fc2, (4.25)
and we assume a cut-off frequency offc= 5 MHz and a DC RIN transfer ofHA(0) = 5 dB, corresponding to a Raman amplifier with an on-off gain of 7.72 dB [FHM01]. The signal quality at the receiver without Raman-induced RIN is taken as QS = 7, corresponding to a bit-error ratio (BER) of 1.3×10−12.
We now assume that the RIN spectrum rRFL(f) of the RFA’s pump laser (the RFL to be designed) is exclusively due to transfer of RIN from the RFL’s pump laser to the output of the RFL. Thus,rRFL(f) =r0HRFL(f), where r0 is the RIN of the pump laser of the RFL (assumed constant, r0 = −95 dB/Hz, compare Fig. 4.2b), and HRFL(f) is the RIN transfer function of the RFL to be designed. We aim at optimizing HRFL(f) such that dBQ is minimized.
What we do below can be summarized as follows. We pick a certain RFL configuration and, from the BVP (4.9)–(4.12), we calculate the steady-state solution at the given pump power. From the BVP (4.18)–(4.21), the RIN transfer function of the RFL is then calculated at a sufficiently large number of frequencies between f = 0 and f = fmax, wherefmax is set to a sufficiently large value so that a further increase does not change the final results (we have usedfmax= 200 MHz, which is well above the cut-off frequency of the low-pass filter of the RIN transfer function of the amplifier). The calculated RIN transfer function is then multiplied with r0 and with HA(f) and then integrated from f = 0 to f = fmax, yielding the integral in Eq. (4.24) and thus the Q-factor penalty dBQ induced by the RIN of the particular RFL under consideration.
Note that the case of a counter-pumped Raman amplifier can be modeled by a low-pass filter similar to Eq. (4.25) with a much lower cut-off frequencyfc<10 kHz [FHM01,
0
Figure 4.6.: Q-factor penalty introduced by a noisy Raman fiber laser in a Raman-amplified transmission span, as a function of the output-coupler reflectivityRr of the RFL. The pump power is adjusted such that the output power is constant for all RFLs.
MHB02, MBH03]. Consequently, resulting Q-factor penalties are much lower, and the RIN requirements on a counter-pumping RFL are much less critical.
4.2.2. Dependence of Q penalty on RFL parameters
Fig. 4.6 shows the variation of Q-factor penalty dBQ with the reflectivity Rr of the output coupler of an RFL. The remaining parameters of the RFL are a moderate Raman gain of 1.5 (Wkm)−1, pump and Stokes wavelengths ofλp = 1060 nm andλs= 1110 nm, respectively, fiber attenuation constants of αp = 0.91 dB/km and αs = 0.76 dB/km, fiber length L = 150 m, group velocities vp = vs = 2×108m/s, and a left-hand FBG reflectivity of Rl = 99%. The steady-state pump power ¯P0 is adjusted such that the output power of all compared RFLs is ¯Pout = 1.5 W.
Fig. 4.6 shows clearly that a high-reflectivity output coupler is advantageous for low-noise operation of a co-pumped Raman-amplified transmission span. For example, the BER of the system can be reduced by three orders of magnitude simply by using a 90% FBG instead of a 40% one. However, the required pump power for the RFL also depends on the reflectivity of the output coupler. The reflectivity required for maximum conversion efficiency is evidently not the same as the one required for optimal noise performance, so there is a tradeoff between pump power and noise performance.
For the results shown in Fig. 4.7, the output-coupler reflectivity is kept fixed atRr = 60%, and only the Raman-gain coefficient of the fiber used for the RFL is varied. The results show clearly that a high Raman gain leads to a lower BER of the co-pumped transmission system, and it also reduces the pump power required to obtain the desired 1.5 W of output power.
Finally, Fig. 4.8 shows the dependence of the Q-factor penalty on the length of the
0.2
Raman-gain coefficient of RFL fiber [1/Wkm]
BER = 2.1 x 10-10
BER = 1.4 x 10-11
Figure 4.7.: Q-factor penalty introduced by a noisy Raman fiber laser in a Raman-amplified transmission span, as a function of the Raman-gain coefficientgof the fiber used for the RFL.
The pump power is adjusted such that the output power is constant for all RFLs.
0.4
Figure 4.8.: Q-factor penalty introduced by a noisy Raman fiber laser in a Raman-amplified transmission span, as a function of the lengthLof the RFL. The pump power is adjusted such that the output power is constant for all RFLs.
fiber used in the RFL, while all other parameters are kept fixed. In contrast to above, we now use an output-coupler reflectivity of Rr = 25%, a high-Raman-gain fiber with a gain constant of g = 4 (Wkm)−1, and the output power of the RFL is kept fixed at P¯out = 4.5 W. The results show that there is an optimal value for the fiber length both in terms of noise performance as well as conversion efficiency. However, the optimal lengths are different, so again there is a tradeoff. For the sake of completeness, Fig. 4.9 shows the RIN spectrum of the RFL with the length chosen such that noise performance in the transmission system is optimal (marked with the thick cross in Fig. 4.8).
-106 -104 -102 -100 -98 -96 -94 -92 -90
0 0.5 1 1.5 2 2.5 3
RINofRamanfiberlaser[dB/Hz]
Frequency f [MHz]
0 2 4 6
Frequency f / FSR
1 3 5 7 109
49 49.5 50
108 110
Figure 4.9.: RIN spectrum of the optimum RFL from Fig. 4.8 (marked with the thick cross).
The lower axis shows the frequency in units of the free spectral range (FSR).