Scaling Limits of Multichannel Spectral Routers for Snapshot Imaging

Inverse‐designed spectral routers can enable compact snapshot spectral imaging by directing different wavelengths to designated detector sub‐pixels without mechanical scanning or absorptive filters. This study examines how routing performance scales as the number of spectral channels increases over a fixed visible bandwidth. The routing condition is first formulated as a channel‐count‐dependent minimum separation between output states, then evaluated against Tucker‐ and Miller‐type delay‐bandwidth capacities to estimate the finite thickness required for a prescribed worst‐channel efficiency. Adjoint‐based topology optimization and three‐dimensional finite‐difference time‐domain simulations then yield TiO 2 /SiO 2 routers with 9, 16, 25, and 36 channels under matched material, bandwidth, thickness, and optimization conditions. The average routing efficiency increases with sub‐pixel size and approaches a plateau, whereas the maximum near‐plateau efficiency decreases monotonically from 97.0% for 9 channels to 82.3% for 36 channels. At a fixed channel count, compressing the wavelength spacing to 8 nm or rearranging the wavelength‐to‐sub‐pixel assignment changes the efficiency by less than one percentage point. Therefore, the observed efficiency penalty is governed mainly by the number of wavelength‐dependent routing constraints rather than by wavelength spacing or local wavelength arrangement. This result indicates a practical trade‐off between spectral sampling and optical throughput.