## Abstract

This report presents an investigation of composite fiber Raman amplifiers (i.e., a distributed fiber Raman amplifier followed by a discrete fiber Raman amplifier) with incoherent pumping, compared to conventional coherent pumping. It is shown that a flatter gain, noise figure and optical signal-to-noise ratio (OSNR) over 100-nm bandwidth can be achieved simultaneously by using two counter-incoherent pumps, compared to using six counter-coherent pumps. Moreover, it is found that a further improvement in gain, noise figure and OSNR flatness can be obtained in composite fiber Raman amplifiers with bi-directional incoherent pumping. The flatness of both gain and OSNR with a ripple of 1 dB is predicted by using one co- incoherent pump and one counter- incoherent pump.

© 2005 Optical Society of America

## 1. Introduction

For optical fiber transmission systems, it has been shown that Raman amplification can be obtained in optical fibers and can be employed to improve the optical transmission performances in terms of optical signal-to-noise ratio (OSNR) [1–3]. Extensive studies [4–6] have been carried out to investigate the fiber Raman amplifiers (FRAs) application in broadband dense multi-wavelength division (DWDM) transmission using multiple-wavelength pumping to achieve a flat gain. However, due to the interaction of pump-pump, pump-ASE noise (ASE- amplified spontaneous emission), and pump-signal, four-wave mixing (FWM) may occur and degrade transmission [7–14]. To reduce the FWM generation, using time-division multiplexed pumping has been reported recently with increase of double Rayleigh scattering [10–14]. Another alternative to obtain the broadband Raman gain without the FWM generation is to use incoherent pumping which possesses the random phase and polarization [15]. On the other hand, it has been well known that the noise performance of shorter-wavelength signals is worse than that of longer-wavelength signals for counter-pumped FRAs and the transmission channels will not have the uniform performance over the broadband such as OSNR and noise figure [16]. Then, the flatness of both gain and noise figure as well as OSNR at the output of FRAs is desirable and should be taken into account in the design of fiber Raman amplifiers. For FRAs with the conventional coherent pumping, a bi-directional pumping scheme has to be used to obtain both flat gain and noise figure as well as OSNR [17], but the relative intensity noise of the co-pumping sources becomes a very stringent requirement. In this study, we found that the flatness for both gain and OSNR for the composite FRAs using the counter incoherent pumping sources can be significantly improved compared to that using multiple counter coherent pumping sources, because the ASE peak using incoherent pumping can be shifted outside of the transmission window.

In order to better describe Raman amplifiers’ application in DWDM transmissions, the noise nonlinear figure (NNF), defined as the ratio of OSNR divided by accumulated nonlinear phase shift, was suggested in [16]. Because the gain flatness is always considered in our investigation and every channel shall have almost the same power, the accumulated nonlinear phase is expected to be almost the same for all the channels. Consequently the spectral shape of NNF shall almost resembles OSNR when the composite FRA gain is flattened as shown in [16]. For the sake of simplicity, we shall focus the OSNR rather than NNF to evaluate the overall performance of composite FRAs (i.e., a distributed FRA followed by a discrete FRA) for this study.

In this report, we present the investigation of Raman gain, noise figure and OSNR of composite fiber Raman amplifiers employing incoherent pumping. Our study shows that the performance in terms of gain, noise figure and OSNR flatness over 100 nm (1515 ~ 1615 nm) of the composite FRAs with incoherent pumping can be significantly improved compared to those using conventional multiple coherent pumps.

## 2. Model and numerical analysis

The simulation of fiber Raman amplification is carried out by numerically solving the steady-state coupled differential equations with the iteration method described in [18–19] and scaled Raman gain coefficients [20]. A composite fiber Raman amplifier, which consists of a distributed FRA followed by a discrete FRA, is considered in this study. For the distributed amplification, a span of TW-Reach fiber of 80 km is used, and a spool of dispersion-compensating fiber (DCF) of 8 km is used for the discrete amplification. The measured fiber parameters for TW-Reach and DCF are used in our simulations. The TW-Reach parameters are as follows: fiber loss varying from 0.4 dB/km at 1262 nm to 0.2 dB/km at 1573 nm and with water induced loss peak of 0.33 dB/km at 1382 nm, Rayleigh scattering coefficient changing from -33.7 dB/km at 1500 nm to -35.4 dB/km at 1620 nm, and fiber core effective area being 46 *μm*
^{2} at 1440 nm to 58 *μm*
^{2} at 1590 nm. The Raman gain coefficient has the peak value of 0.608 (*W* ∙ *km*)^{-1} at the frequency shift of 13.3 THz, measured by using the pump wavelength of 1460 nm. The DCF parameters are: fiber loss varying from 0.95 dB/km at 1260 nm to 0.42 dB/km at 1610 nm, Rayleigh scattering coefficient changing from -33.3 dB/km at 1500 nm to -35.9 dB/km at 1600 nm, and fiber core effective area being 13 *μm*
^{2} at 1440 nm to 26.6 *μm*
^{2} at 1600 nm. Its Raman gain coefficient has the peak value of 2.45 (*W* ∙*km*)^{-1} at the frequency shift of 13.05 THz, measured by using the pump wavelength of 1460 nm. We assume 122 input DWDM signals, from 1515 to 1615 nm with 100-GHz channel spacing, and the input power is -2 dBm per channel. The investigation is carried out in such a manner that we optimize the pumping wavelengths, full-width at half magnitude (FWHM) and powers to achieve both flat gain and noise figure as well as OSNR. Commercial incoherent pumps can have a FWHM of up to 100 nm [15]. In the simulation, the noise figure of the composite FRA is given by *NF _{t}* (

*λ*) =

*NF*

_{1}(

*λ*) + [

*NF*

_{2}[λ] - 1]/

*G*(

*λ*), where

*G*(

*λ*) is the on-off gain in the distributed FRA,

*NF*

_{1}(

*λ*) - the effective noise figure of the distributed FRA, and

*NF*

_{2}(

*λ*) - the noise figure of the discrete FRA, and OSNR is calculated with an optical bandwidth of 100 GHz. We optimize pump wavelengths and powers for coherent pumps and additional FWHM for incoherent pumps in order to have both flat gain and OSNR simultaneously. The objective of optimizing pump parameters is to achieve gain and OSNR flatness of within 1 dB. However, if the flatness in gain and OSNR is impossible to be within 1 dB and beyond 1 dB, we re-optimize the pump parameters by balancing gain and OSNR flatness so that gain and OSNR flatness is similar or close.

First we consider the composite FRA with counter- coherent pumping. Using six pumping

lasers to pump both the distributed and discrete FRAs individually, the optimal pump wavelengths and corresponding powers can be found to achieve a flat gain, noise figure and OSNR as given in Figs. 1(a) and (b). The total pump power for the distributed FRA is 602.7 mW, and 716 mW for the discrete FRA with an average gain of 16 dB. It can be noticed that most of the pump power is allocated in the shorter pump wavelength region for the distributed FRA, and in the longer wavelength region for the discrete FRA. This consequence is directly due to the fact of meeting the requirement of not only flat gain but also noise figure or OSNR as given in [16].

Then we investigate the composite FRAs with counter- incoherent pumping. Besides the pump wavelength and power, the FWHM of the incoherent pump is also optimized. For the case of one incoherent pump used for both the distributed and discrete FRAs, a pump power of 817 mW is needed for the distributed FRA and 679.5 mW for the discrete FRA as shown in Fig. 2(a). For the sake of comparison, we also study the case with two incoherent pumps for both the distributed and discrete FRAs, and optimized pump parameters are shown in Fig. 2(b) for the composite FRA with an average gain of 16 dB. It is interesting to note that the optimal FWHM of the pumps for the discrete FRA is much narrower than that for the distributed FRA. This is because the pump wavelength for the discrete FRA is longer and more close to the signals (see Fig. 2(b)) (longer pump wavelengths result in increased ASE in the signal band). Once the incoherent pump tail reaches the signal band, we assumed that there is an optical notch filter to remove the pump power before launching into the FRAs.

The performances of the composite FRAs with the above three cases are shown in Fig. 3. Figure 3(a) shows the gain comparison, and for all the three cases the composite FRA has an average gain of 16 dB. It can be seen that the composite FRA with six coherent pumps has a gain ripple of 1.6 dB over 100-nm bandwidth, while the gain ripple of 2 dB for the case with one incoherent pump and 1 dB with two incoherent pumps. Figures 3(b) and (c) show the corresponding noise figure and OSNR for the composite FRA with three different pump schemes, respectively. We can clearly see that the noise figure is reduced in shorter signal wavelengths, and noise figure and OSNR over 100 nm become flatter, even by using one incoherent pump compared to using six coherent pumps. When using two incoherent pumps, the performance of the composite FRA is further improved, i.e. not only flatter gain, but also lower noise figure in the shorter signal wavelengths and flatter OSNR compared to the case of six coherent pumps. The physical origin for the improved noise performance in the shorter signal wavelengths by using incoherent pumping can be understood as follows. Figure 4 shows the on-off gain in the distributed FRAs, output ASE power (in 1 nm) of the distributed FRAs, and total output ASE power of the composite FRAs corresponding to Fig. 3. It is observed from Fig. 4(b) that more ASE is generated by using incoherent pumping, but with a broader bandwidth compared to coherent pumping, particularly for the case of two incoherent pumps. For the case of one incoherent pump, the peak of ASE spectrum is close to that for the six coherent pumps, but with lower intensity because of broader bandwidth. For the case of two incoherent pumps, the peak of ASE spectrum is shifted to a shorter wavelength of outside transmission window, even though the ASE spectrum is similar in peak intensity and has broader bandwidth compared to that for the case of six coherent pumps. It is well known that noise spectrum generated in a FRA using coherent pumps resembles the gain spectrum. However, the noise spectrum generated in a FRA with incoherent pumps does not resemble the gain spectrum [15, 21], and has a peak shifted to a shorter wavelength than the gain peak as shown also in Fig. 4(b). For the counter-pumping, the noise level is higher in the shorter signal wavelengths than the longer ones because the shorter signal wavelengths are more close to the pump wavelengths. The noise peak for incoherent pumping can be further shifted to a shorter wavelength by using shorter wavelength pumps as shown in Fig. 4(b). Then the optimized pump wavelengths for the incoherent pumps as shown in Fig. 2 are found to be much shorter than those for the coherent pumps to achieve a flat gain and flat noise figure. For example, the noise peak is shifted to 1503 nm for the case of the two incoherent pumps. Figure 4(c) clearly shows that the total ASE power over 100 nm is about the same for the three cases; but the flatness of ASE intensity for the case of two incoherent pumps is much better than that of the other two cases. Consequently, the noise performance of the composite FRA with two incoherent pumps is better than that with six coherent pumps as shown in Fig. 3. It is worth to mention the small saws in ASE power in Fig. 4(b) and (c) are due to signal induced multi-path interference.

In order to further improve the flatness of both gain and noise figure and thus OSNR, we now consider using bi-directional pumping scheme as in [17] for the composite FRAs with incoherent pumping. We suppose that each of the distributed and discrete FRAs has a co-incoherent pump and a counter-incoherent pump, i.e. bi-directionally pumped. In order to achieve a further flatter noise figure or OSNR, while still having a flat gain, the co-pumps should have shorter pump wavelengths than the counter-pumps in both the distributed and discrete FRAs and the optimized pump parameters are shown in Fig. 5(a) and (b) for the distributed and discrete FRAs, respectively. The resulted pumping parameters are attributed from that the co-pumps with a shorter wavelength result in a ASE peak shifted outside of the transmission window in order to improve the noise performance in shorter signal wavelengths. The resulting gain, noise figure and OSNR are shown in Fig. 6(a), (b) and (c), respectively. It can be seen that both gain and OSNR are further flattened with a ripple of less than 1 dB over the 100-nm bandwidth. In comparison, the ripple of OSNR is better than 1 dB in Fig. 6(c) compared to ~3 dB for one counter- incoherent pump in Fig. 3(c). Therefore, it is feasible to achieve a flat gain, and OSNR within 1 dB of ripple in bi-directionally pumped composite FRAs with one incoherent pump (totally four incoherent pump lasers).

For further understanding the impact of the distributed and discrete FRAs on the flatness of gain and noise figure as well as OSNR, we further investigate the composite FRA by varying the pump power distribution (percentage) between the distributed and discrete FRAs. The composite FRA considered is the same as in Fig. 6, i.e. bi-directional pumping and having an average Raman gain of ~16 dB. The percentage is defined as the ratio of the pump power for the distributed FRA to the total pump power. Figure 7 shows the spectral shape change of gain, noise figure and OSNR for the percentages of 59%, 62% and 73%, respectively. For each percentage we optimize the pump power and thus the total pump power is changed for different percentages, to obtain the flat gain and OSNR. It is obvious that the flatness of OSNR becomes worse even when the flatness of both gain and noise figure is hardly changed. This is because the spectral shapes of gain and noise figure are changed even though their flatness may not be changed. When more pump power for the distributed FRAs is used and thus more gain is obtained in the distributed FRAs, OSNR in the shorter signal wavelengths is improved but the flatness of OSNR may not be improved as shown in Fig. 7(c). Because OSNR is a combined parameter of both gain and noise figure, it may be better to include OSNR flatness in design of optical amplifiers because the spectral shape change of both gain and noise figure is taken into account in OSNR.

## 3. Conclusion

We have investigated the broadband composite fiber Raman amplifiers by using incoherent pumping, with comparison to coherent pumping. It has been shown that a flatter Raman gain, and noise figure as well as OSNR over 100 nm can be achieved by using two counter-incoherent pumps than that by using six counter-coherent pumps. For the composite FRA with bi-directional pumping, a flat gain, and OSNR with a ripple of 1 dB over 100 nm bandwidth can be achieved by using one incoherent pump for one co-pump and one counter-pump in both the distributed and discrete FRA. In addition, the impact of the distribution of pump power between distributed and discrete FRAs is investigated. It is shown that even though the flatness of both gain and noise figure may not be changed, OSNR may have an obvious change in flatness. In other words, an optimal pump power distribution between distributed FRAs and discrete FRAs should exist to have a flattest OSNR for a given gain. Because of the advantages of incoherent pumped FRAs, i.e. not only flatter gain but also flatter noise figure as well as OSNR with significantly reduced number of pump wavelengths compared to conventional coherent pumping, the incoherent pumped FRAs would be a cost-effective approach for the application in broadband DWDM transmission.

## Acknowledgments

The authors would like to express their gratitude to Dr. X. Zhou of AT&T LABS-Research for his help. They also want to thank Dr. P. Gaarde of OFS Denmark for providing the fiber parameters and Dr. I. Mandelbaum for his help in the fiber Raman amplifier model.

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