We develop a rigorous procedure for the optimum design of few-mode erbium (Er)-doped fiber amplifiers, which is tackled as a multiobjective optimization problem, in an approach based on the combination of the topology optimization and genetic algorithm techniques. We demonstrated that the usual ring-like doping distributions are necessarily the best choices only if the pump intensity shows no azimuthal dependence. Additionally, in general, the optimum doping distribution will be a function of the signal and pump azimuthal mode numbers. For the particular case of the LP11 pump, we also provide a triple-ring Er-doping profile that maximizes modal equalization for seven-group modes over the whole C-band, the highest modal count proposed in the literature so far.
Space-division multiplexing allows an increase of link capacity by using either multicore or single-core few-mode (FM) optical fibers. In the case of FM systems, each mode carries its own data stream and long-haul transmission can be hampered by the use of conventional erbium-doped fiber amplifiers (EDFAs), since because of distinct field profile configurations, each mode experiences a different value of optical gain. The role of the FM-EDFA designer, usually done by solving rate and propagation equations, is to define both the fiber cross-section and the pumping configuration to provide the best possible mode equalization of optical gain and noise figure. An optimization method is proposed here based on the definition of a figure of merit related to the equalization of the pump-mode signal overlap integral, significantly reducing computation time and allowing a multiobjective optimization approach. The results obtained were validated against the solution provided by the full set of rate and propagation equations and we conducted an FM-EDFA optimization case study. Our double-ring Er doping profile design requires a single 180-mW LP11 pump to provide a mean gain of 21.3 dB, within 0.6 dB of equalization for each of the four modes considered.
Long-haul optical communications links based on space-division multiplexing use space as the final degree of multiplexing freedom, possibly exploring the modal orthogonality in a few-mode fiber (FMF). However, if conventional EDFAs are used, each mode will experience a different value of optical gain, on account of distinct field profile configurations. This lack of gain equalization imposes difficulties for mode demultiplexing and may impair the system performance. The FMF-EDFA designer should define Er doping and/or refractive index profiles, as well as the pumping configuration, to provide the best possible mode equalization of optical gain and noise figure. In the case of the FMFEDFA, the problem is involved because each mode contributes with its own set of coupled differential equations. To use this approach to carry out a rigorous optimization procedure is not feasible and typical FMF-EDFAs designs proposed in the literature are empirical. A novel optimization method is proposed here. The definition of a figure of merit related to the equalization of the pump-mode signal overlap integral significantly reduces computation time, allowing the implementation of a multiobjective optimization approach. The results obtained were validated against the solution provided by the full set of rate and propagation equations and we conducted a FMF-EDFA optimization case study. Our double-ring Er doping profile design requires a single 350 mW LP<sub>11,p</sub> pump to provide a mean gain of 21.6 dB, within 0.6 dB of equalization for each of the four modes considered.