Data-driven gain equalization for few-mode erbium-doped waveguide amplifiers using deep neural networks.

This study addresses the formidable challenge of structural optimization in few-Mode erbium-doped waveguide amplifiers (FM-EDWAs), which arises from the intricate coupling among multiple variables and objectives. To overcome the difficulty of integrating structural parameters with key performance indicators (specifically gain equalization and crosstalk suppression) into a unified optimization framework, we propose a joint multi-objective optimization method. This approach synergistically integrates the Transformer model with an improved NSGA-II algorithm to design FM-EDWAs capable of six-mode amplification. For the first time, our method establishes a precise mapping between waveguide structural parameters and performance metrics, enabling the simultaneous optimization of average gain, differential mode gain, and effective refractive index difference within a single framework. Under single LP01 pumping, the optimized device achieves balanced amplification across six modes (LP01, LP11a, LP11b, LP21a, LP21b, and LP02). The resulting waveguide structure delivers an average gain of 21.84 dB, a differential mode gain of 0.84 dB, and crosstalk lower than -22.6 dB within the 1550 nm band, demonstrating effective suppression of mode crosstalk alongside enhanced gain performance. These findings offer new insights for on-chip multimode amplifier design and represent a significant advancement for high-capacity mode-division multiplexing systems.