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, LP_11a, LP_11b, LP_21a, LP_21b, 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.