Optimization criteria and design of few-mode Erbium-doped fibers for cladding-pumped amplifiers

We propose a novel optimization method that combines two design criteria to reduce the differential modal gain (DMG) in few-mode cladding-pumped erbium-doped fiber amplifiers (FM-EDFAs). In addition to the standard criterion that considers the mode intensity and dopant profile overlap, we introduce a second criterion that ensures that all doped regions have the same saturation behavior. With these two criteria, we define a figure-of-merit (FOM) that allows the design of FM-EDFAs with low DMG without high computational cost. We illustrate this method with the design of six-mode erbium-doped fibers (EDFs) for amplification over the C-Band targeting designs that are compatible with standard fabrication processes. The fibers have either a step-index or a staircase refractive index profile (RIP), with two ring-shaped erbium-doped regions in the core. With a staircase RIP, a fiber length of 29 m and 20 W of pump power injected in the cladding, our best design leads to a minimum gain of 22.6 dB while maintaining a DMG_max under 0.18 dB. We further show that the FOM optimization achieves a robust design with low DMG over a wide range of variations in signal power, pump power and fiber length.