Designing open channels in random scattering media for on-chip spectrometers

Abstract

On-chip spectrometers with tailored spectral range and compact footprint have been pursued widely in the last decade. Splitting different frequencies typically requires a propagation length that scales inversely with the frequency resolution, which leads to a trade-off between resolution and size. Scattering media in the diffusive regime provide a long light path and multipath interference in a compact area, resulting in strong dispersive properties that can be used for on-chip compressive spectrometry. However, the performance suffers from the low light transmission through the diffusive medium. It has been found that there exist “open channels” such that light with certain wavefronts can pass through the medium with high transmission. Here we show that a scattering structure can be designed so that open channels match target input/output channels in order to maximize transmission while keeping the dispersive properties typical of diffusive media. Specifically, we use inverse design to generate a scattering structure where the open channels match the output waveguides at desired wavelengths. For a proof of concept, we propose a 1 × 10 multiplexer covering a band of 500 nm in the mid-infrared spectrum, with a footprint of only 9.4 µ m × 14.4 µ m . We also show that filters with nearly arbitrary spectral response can be designed, enabling a new degree of freedom in on-chip spectrometer design, and we investigate the ultimate resolution limits of these structures. The structures can also be designed based on a simple geometry consisting of circular holes with diameters from 200 to 700 nm etched in a dielectric slab, making them highly suited for fabrication. With the help of compressive sensing, the proposed method represents an important tool in the quest towards integrated lab-on-a-chip spectroscopy.