  We present an ultra-compact single-shot spectrometer on silicon platform with
broad operation bandwidth and high resolution. It consists of 32 stratified
waveguide filters (SWFs) with diverse transmission spectra for sampling the
unknown spectrum of the input signal and a specially designed ultra-compact
structure for splitting the incident signal into 32 filters with low imbalance.
Each SWF has a footprint less than 1um x 30um, while the 1x32 splitter and 32
filters in total occupy an area of about 35um x 260um, which to the best of our
knowledge, is the smallest footprint spectrometer realized on silicon photonic
platform. Experimental characteristics of the fabricated spectrometer
demonstrate a broad operating bandwidth of 180nm centered at 1550nm and
narrowband peaks with 0.45nm Full-Width-Half-Maximum (FWHM) can be clearly
resolved. This concept can also be implemented using other material platforms
for operation in optical spectral bands of interest for various applications.
