Breaking the resolution-bandwidth limit of chip-scale spectrometry by harnessing a dispersion-engineered photonic molecule.

The chip-scale integration of optical spectrometers may offer new opportunities for in situ bio-chemical analysis, remote sensing, and intelligent health care. The miniaturization of integrated spectrometers faces the challenge of an inherent trade-off between spectral resolutions and working bandwidths. Typically, a high resolution requires long optical paths, which in turn reduces the free-spectral range (FSR). In this paper, we propose and demonstrate a ground-breaking spectrometer design beyond the resolution-bandwidth limit. We tailor the dispersion of mode splitting in a photonic molecule to identify the spectral information at different FSRs. When tuning over a single FSR, each wavelength channel is encoded with a unique scanning trace, which enables the decorrelation over the whole bandwidth spanning multiple FSRs. Fourier analysis reveals that each left singular vector of the transmission matrix is mapped to a unique frequency component of the recorded output signal with a high sideband suppression ratio. Thus, unknown input spectra can be retrieved by solving a linear inverse problem with iterative optimizations. Experimental results demonstrate that this approach can resolve any arbitrary spectra with discrete, continuous, or hybrid features. An ultrahigh resolution of <40 pm is achieved throughout an ultrabroad bandwidth of >100 nm far exceeding the narrow FSR. An ultralarge wavelength-channel capacity of 2501 is supported by a single spatial channel within an ultrasmall footprint (≈60 × 60 μm 2 ), which represents, to the best of our knowledge, the highest channel-to-footprint ratio (≈0.69 μm -2 ) and spectral-to-spatial ratio (>2501) ever demonstrated to date.