# Automated optimization tools design Raman amplifiers

Fiber Raman amplifiers in WDM systems have recently received much more attention because of their greatly extended bandwidth and distributed amplification with the installed fiber as gain medium. It has been shown that the bandwidth of the amplifier can be further increased and gain spectrum can be tailored by using pumping with multiple wavelengths.

Several strategies are proposed for static gain-flattening. Wideband amplifier gain spectrums have been demonstrated using either a hybrid fiber amplifier consisting of erbium-doped fiber amplifers (EDFAs), lumped Raman amplifiers, and a gain-equalizer, or fiber Raman amplifiers pumped at multiple wavelengths. At the device level, optical amplifiers come in a variety of configurations: backward-, forward-, and bidirectionally pumped, discrete or distributed, single- or multistage ^{1, 2 }

One of the main difficulties of designing a multipumped Raman amplifier is that pump-to-pump and signal-to-signal Raman interactions make the system highly nonlinear, thereby complicating the design process and requiring a high number of iterations. Optical-communication design tools can be used to determine the proper pump configuration to get optimum gain flatness.

Most optical-communication design tools provide a simple optimization option based on parameter sweeps. Using such an option for optimization requires a manual investigation of the results, a large number of iterations, and a great deal of simulation time. A generic automated optimization tool could greatly simplify this process by eliminating user interaction and unnecessary simulations.

An automatic optimization tool would examine current simulation results, compare them to the design goals, and then adjust the parameters to reach the defined design goals. Sophisticated optimization technologies are available that can minimize the required number of simulation runs; however, there is a risk of winding up with a local optimum. Therefore, the optimization procedure should be customized to a specific application. Furthermore, the parameter range and behavior of the component or system can be utilized as constraints to the optimizer.

For example, Optiwave has developed a generic and flexible optimization tool as a part of its OptiSystem and OptiAmplifier packages based on a customized version of optimization procedures of Mathlab, a widely accepted and proven package from MathWorks. This tool provides powerful multiparameter, multitarget optimization procedures, including minimization, maximization, goal attainment, least square, and gain flattening.

The minimization and maximization procedures minimize or maximize a single result by manipulating multiple parameters. Goals are achieved by obtaining multiple results as multiple user-defined parameters are changed. The least-square procedure minimizes the sum of squares of multiple results by altering multiple parameters. The gain-flattening procedure is used to optimize the parameters of amplifiers, filters, and pumps for the best gain flatness. It can also force several user-defined constraints on selected parameters.

The optimization tool attempts to reach a target gain for each channel, and at the same time tries to keep the gain flatness under a given value (see Fig. 1). The ultimate goal is to achieve a certain gain for all channels and keep the gain flatness at a reasonable value.

This goal is achieved by using an optimization procedure, dependent on the designer's selection, that either adjusts the amplifier parameters, the pump parameters, or both. For each set of parameters, the modified version of the design is simulated, and results are evaluated. For example, the measuring device can be a dual-port WDM analyzer or an internal analyzer model of the Raman amplifier.

Optimization of Raman amplifiers by using a multipump configuration is a complicated and time-consuming procedure, given that the required pump power for a certain Raman gain is affected by several factors, including Raman gain coefficient, polarization effect, fiber length, fiber loss at pump wavelength, pump depletion, and pump-to-pump Raman interaction.

From the numerical standpoint, the large number of channels further complicates the problem in the system, and the fact that interaction between every pair of channels needs to be taken into account. Therefore, it is crucial to input accurate estimated initial values—especially for pump wavelengths—into the optimizer.

For example, a general guideline is based on the fact that the gain profile of a multiwavelength pumped Raman amplifier can be expressed as a logarithmic superposition of the gain profiles caused by respective pumping wavelengths (with the assumption that the magnitude of Raman gain is only determined by the corresponding pump power and wavelength).^{2 }Even though this is not correct, it will provide a rough estimate for the pump channel locations.

Unless it is beyond the limit, the predicted gain profile is sure to be realized by an appropriate pump power level. When an accurate estimation is provided, the optimization procedure can find the optimum pump powers and wavelengths by adjusting the pump powers and refining the pump wavelengths. In a majority of cases, optimizing only the pump powers may give sufficient gain flatness.

The predicted gain profile can also be useful to provide an extra constraint to the optimizer. For example, putting min/max constraints on the total pump power will ensure that the achieved gain is close to the required gain. Otherwise, the optimization may result in a set of optimum parameters that generates an acceptable level of flatness but a lower average gain.

As illustrations, we show two gain-flattening designs with backward multipumped Raman-amplifier configuration. The first one shows the optimization of pump powers and wavelengths, and the second one shows the optimization of pump powers for given wavelength allocations. Even though several pumping schemes are possible we have chosen these examples because they enable direct comparison with readily available theoretical and experimental results.

We included the following effects in our simulations: attenuation, Rayleigh backscattering gain, stimulated Raman-scattering (SRS) gain, spontaneous Raman-scattering gain, and pump depletion in SRS.^{3} Our first design contains 64 channels between 1512 and 1562.4 nm with 0.8-nm separations. The average power of each channel is -20 dBm. The fiber used as the gain medium is a 25-km fiber with 9.5e-14-m/W peak Raman-gain coefficient. The effective area of the fiber is 55 µm^{2}. The loss of the fiber is 0.2 dB/km. Target amplifier forward gain is 10 dB. Four CW pumps were used (see table). With this initial pump allocation, we observed a gain flatness, defined as 10log(Gmax/Gmin), of 3.8 dB (see Fig. 2).^{4 }

We then applied the gain-flattening optimization procedure to optimize the pump powers and wavelengths and compared our findings to published results.^{2} We bound the pump powers between 0 and 300 mW and we specified a gain flatness lower than 2.1 dB.^{5} As an extra constraint, we limited the total pump power to between 800 and 1000 mW. This is necessary to ensure that we can get a gain as high as required and force the optimizer to find a global optimum not a local one.

Optimum pump powers and wavelengths are obtained after 81 calculations (see table). In the resulting amplifier gain, the achieved gain flatness in the reference was approximately 2.6 dB (see Fig. 2). We achieved a better gain flatness than this value. After the optimization, the achieved forward gain flatness is 2 dB, maximum forward on/off gain is 15 dB; maximum forward gain is approximately 9 dB; and the forward effective noise-figure flatness is 1.6 dB.

As a second illustration we optimized pump powers in the design of a gain-flattened Raman amplifier by using a 12-wavelength-channel WDM laser-diode unit and compared our findings with published experimental data.4 The optimized design contained channels between 1528 and 1620 nm with 4-nm separations. The average power of each channel was 0 dBm. The fiber used as the gain medium was a 25-km single-mode fiber (SMF) with 9.9e14-m/W peak Raman-gain coefficient. A 12-wavelength-channel WDM high-power pump-laser-diode unit was used for backward pumping. The spacing in the short-wavelength section (Pump I; 1405 to 1457.5 nm) was 7.5 nm (~1 THz), while that in the long-wavelength section (Pump II; 1465 to 1510 nm) was 15 nm (~2 THz). The initial pump powers were 140 mW for the first four pumps and 80 mW for the remaining pumps.^{6} The pump powers were bound between 20 and 160 mW.

With this initial pump configuration, the observed gain flatness was 1.2 dB. The target gain provided to the optimizer was 2.0 dB. As a constraint, we specified a gain flatness of less than 1.5 dB. The optimization tool reached the optimum pump powers after 45 calculations (see Fig. 3). Note the similar trend of pump power allocation with the experimental findings of the reference work. Gain flatness achieved in the reference work was approximately 1 dB (±0.5 dB). We achieved better gain flatness in comparison (see Fig. 4). After the optimization, the achieved forward gain flatness is 0.73 dB; the maximum forward on/off gain is 8.8 dB; the maximum forward gain is 3.02 dB; and the forward effective noise-figure flatness is 2.1 dB.

To investigate the interchannel effect of multiwavelength pumps, we first removed the second group of pumps (Pump II; last three pumps) and then removed the first group of pumps (Pump I; first nine pumps), leaving Pump II active (see Fig. 4). The gain flatness in the first case is 8.6 dB, and in the second case is 2.7 dB. It shows that the pump at 1495 nm absorbs energy from the other pumps, resulting in much more gain at 1600 nm than just the sum of each gain in the respective cases of Pump I and Pump II.

Automated optimization tools can greatly reduce the design time and required work, resulting in enhanced Raman-amplifier performance. The application of these tools is not limited to backward multipump Raman amplifiers, but can also be used to optimize any type of amplifier or design configuration.

**Tamer H. Coskun** is a research scientist, **Ivan Uzunov** a research manager, and **Jackson Klein** is a product manager at Optiwave, 7 Capella Ct., Ottawa, Ontario, K2E 7X1, Canada. Tamer Coskun can be reached at tamer.coskun@optiwave.com.

- M. N. Islam, IEEE J. Select. Top. Quan. Elect. 8, 548 (2002).
- Y. Emori et al., Opt. Fib. Tech. 8, 107 (2002).
- C. Bernard et al., Opt. Net. Mag. 63 (September/October 2001).
- M. Yan et al., IEEE Photon. Tech. Lett. 13, 948 (2001).
- Note that 14xx-nm pump laser diodes have achieved more than 300 mW at a commercial level. For example see T. Fukushima et. al., Proc. SPIE 4905, 47 (2002) and references therein.
- Y. Emori et al., Elect. Lett. 35, 1355 (1999).