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

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.