  Recent advancements in silicon photonics are enabling the development of
chip-scale photonics devices for sensing and signal processing applications,
among which on-chip spectrometers are of particular interest for precision
wavelength monitoring and related applications. Most chip-scale spectrometers
suffer from a resolution-bandwidth trade-off, thus limiting the uses of the
device. Here we report on a novel passive, chip-scale, hybrid speckle-enhanced
Fourier transform device that exhibits a two order-of-magnitude improvement in
finesse (bandwidth/resolution) over the state-of-the art chip-scale speckle and
Fourier transform spectrometers. In our proof-of-principle device, we
demonstrate a spectral resolution of 140 MHz with 12-nm bandwidth for a finesse
of $10^4$ that can operate over a range of 1500-1600 nm. This chip-scale
spectrometer structure implements a typical spatial heterodyne discrete Fourier
transform interferometer network that is enhanced by speckle generated from the
wafer substrate. This latter effect, which is extremely simple to invoke,
superimposes the high wavelength resolution intrinsic to speckle generated from
a strongly guiding waveguide with a more broadband but lower resolution
discrete Fourier transform modality of the overarching waveguide structure.
This hybrid approach signifies a new pathway for realizing chip-scale
spectrometers capable of ultra-high resolution and broadband performance.

Applied Physics;Materials Science;Instrumentation and Detectors;Optics