On-Chip Compressed Sensing Fourier-Transform Visible Spectrometer

We demonstrate a novel compressed sensing Fourier-transform spectrometer (FTS) in a compact format. This FTS consists of 160 planar-waveguide Mach-Zehnder interferometers (MZIs) arrayed on a photonic chip, effecting a discrete Fourier-transform of the input spectrum. Incoherence between the sampling domain, and the signal domain permits compressive sensing retrieval of sparse spectra using an undersampled measurement of the interferogram. In our fabricated device, we print a fraction of the MZIs required to form the full interferogram corresponding to our selected spectral bandwidth and resolution; the resulting system is undersampled by 1/4th the critical sampling rate, simultaneously reducing chip footprint and concentrating the interferogram in fewer pixels. We develop a scheme for multi-aperture broadband coupling to 83 single-mode waveguides using an array of microlenses bonded to the surface of the chip, and aligned with a grid of vertically illuminated waveguide apertures. The microlens array accepts a collimated beam with near 100% fill-factor, and the resulting spherical wavefronts are coupled into the single-mode waveguides using 45° mirrors etched into the waveguide layer via focused ion-beam. Interferograms from the waveguide outputs are imaged using a CCD, and inverted via l1-norm minimization to correctly retrieve sparse input spectra, verifying the instrument architecture and measurement principle.