  The on-chip broadband optical spectrometers which cover the entire tissue
transparency window ({\lambda}=650-1050 nm) with high resolution are highly
demanded for the miniaturized bio-sensing and bio-imaging applications. Here,
we propose a novel type of spatial heterodyne Fourier transform spectrometer
(SHFTS) integrated with a sub-wavelength grating coupler (SWGC) for the
dual-polarization bandpass sampling on the Si3N4 platform. Through tuning the
coupling angles with different polarization, we experimentally demonstrated the
unprecedented broadband spectrum retrieval results with the overall bandwidth
coverage of 400 nm, bridging the wavelengths from 650 nm to 1050 nm, with the
resolution of 2-5 nm. By applying the bandpass sampling theorem, we
circumvented the intrinsic trade-off limitation between the bandwidth and
resolution of SHFTS without having an outrageous number of Mach-Zehnder
interferometer (MZI) arrays or adding additional active components. The
bandpass sampling SHFTS is designed to have linearly unbalanced 32 MZIs with
the maximum optical path length difference of 93 {\mu}m within an overall
footprint size of 4.7 mm x 0.65 mm, and the coupling angles of SWGC are varied
from 0{\deg} to 32{\deg} to cover the entire tissue transparency window.
