Optimization strategy of ultra-compact metasurface-based filter ordering on sensors for improved spectral retrieval

CMOS technologies can provide miniature filters with few-nm passband in the visible, much suited to on-chip spectrometers and hyperspectral imaging. However, crosstalk can become challenging and degrade spectral retrieval at the smallest sizes. A filter/metasurface bank design is a first demanding step for this scope, playing with in-plane patterns/“atoms”. For a miniature device of 10–100 small pixels, each 1–3 μm wide, the filters finite extent incurs an extra penalty: cross-talk between neighbor pixels, hard to minimize through electromagnetic tools. A distinct and useful minimization suited to the CMOS context is then to select the arrangement of N filters on the array to privilege the less penalizing neighbor pairs. This amounts to a path selection problem in the N×(N−1) space of the inter-micro-filter cross-talks. We evaluate the resulting benefit in terms of the condition number of the system’s spectral function matrix, the basic ingredient for spectral retrieval. In one dimension, we find that small arrays can be tackled by brute force up to N∼15 filters, but a minimization through a simply weighted proxy, a summed cross-talk combination, is more advantageous beyond. In two-dimensions, the topology only partly changes the trend. Relevant examples of infinite and finite filters based on amorphous silicon and silica are also provided to justify the choice of a rather broad cross-talk distribution in the inter-filter space. Gains of c⁻¹∕〈c⁻¹〉=1.5–2.5 on the inverse of the condition number c (and thus the accuracy of spectral retrieval) emerge from the study.