Low-loss and compact arbitrary-order silicon mode converter based on hybrid shape optimization

Mode converters (MCs) play an essential role in mode-division multiplexing (MDM) systems. Numerous schemes have been developed on the silicon-on-insulator (SOI) platform, yet most of them focus solely on the conversion of fundamental mode to one or two specific higher-order modes. In this study, we introduce a hybrid shape optimization (HSO) method that combines particle swarm optimization (PSO) with adjoint methods to optimize the shape of the S-bend waveguide, facilitating the design of arbitrary-order MCs featuring compactness and high performance. Our approach was validated by designing a series of 13 μm-long MCs, enabling efficient conversion between various TE modes, ranging from TE₀ to TE₃. These devices can be fabricated in a single lithography step and exhibit robust fabrication tolerances. Experiment results indicate that these converters achieve low insertion losses under 1 dB and crosstalks below −15 dB across bandwidths of 80 nm (TE₀–TE₁), 62 nm (TE₀–TE₂), 70 nm (TE₀–TE₃), 80 nm (TE₁–TE₂), 55 nm (TE₁–TE₃), and 75 nm (TE₂–TE₃). This advancement paves the way for flexible mode conversion, significantly enhancing the versatility of on-chip MDM technologies.