  Recent years have seen the rapid development of miniaturized reconstructive
spectrometers (RSs), yet they still confront a range of technical challenges,
such as bandwidth/resolution ratio, sensing speed, and/or power efficiency.
Reported RS designs often suffer from insufficient decorrelation between
sampling channels, which results in limited compressive sampling efficiency, in
essence, due to inadequate engineering of sampling responses. This in turn
leads to poor spectral-pixel-to-channel ratios (SPCRs), typically restricted at
single digits. So far, there lacks a general guideline for manipulating RS
sampling responses for the effectiveness of spectral information acquisition.
In this study, we shed light on a fundamental parameter from the compressive
sensing theory - the average mutual correlation coefficient v - and provide
insight into how it serves as a critical benchmark in RS design with regards to
the SPCR and reconstruction accuracy. To this end, we propose a novel RS design
with multi-resonant cavities, consisting of a series of partial reflective
interfaces. Such multi-cavity configuration offers an expansive parameter
space, facilitating the superlative optimization of sampling matrices with
minimized v. As a proof-of-concept demonstration, a single-shot, dual-band RS
is implemented on a SiN platform, tailored for capturing signature spectral
shapes across different wavelength regions, with customized photonic crystal
nanobeam mirrors. Experimentally, the device demonstrates an overall operation
bandwidth of 270 nm and a <0.5 nm resolution with only 15 sampling channels per
band, leading to a record high SPCR of 18.0. Moreover, the proposed
multi-cavity design can be readily adapted to various photonic platforms. For
instance, we showcase that by employing multi-layer coatings, an
ultra-broadband RS can be optimized to exhibit a 700 nm bandwidth with an SPCR
of over 100.
