Compact mode dimension sorter enabled by an on-chip graded-index metamaterial lens

Precise manipulation of on-chip optical modes using subwavelength structures is critical for miniaturizing devices and scaling high-speed optical interconnects, especially in Mode Division Multiplexing (MDM) systems. Leveraging advances in nanofabrication, devices engineered with subwavelength features enable versatile control over on-chip optical fields. Here, we propose a compact mode sorter based on a subwavelength waveguide grating, designed using the eigenmode expansion method. We analyze the optical field distribution at the focal plane of the on-chip lens for various incident modes. Implemented on a silicon-on-insulator (SOI) platform, the device achieves efficient separation of TE₀, TE₁, and TE₃ modes, within a footprint of only 8.3 µm. When assembled into a complete (de)multiplexer, the device yields a 0.79 dB, 0.97 dB, and 0.91 dB insertion loss for the TE₀, TE₁, and TE₃ channels, and 114 nm (1493-1607 nm) bandwidth for all channels with insertion loss is under 1.5 dB while crosstalk below 15 dB. Our simulation of fabrication tolerances demonstrates that this approach offers superior robustness compared to traditional devices. This work presents a generalizable design framework for metamaterial-based on-chip lenses using eigenmode analysis, paving the way for compact mode splitting and reconstruction applications.