Demonstration of a compressive-sensing Fourier-transform on-chip spectrometer

We demonstrate compressive- sensing (CS) spectroscopy in a planar- waveguide Fourier- transform spectrometer ( FTS) device. The spectrometer is implemented as an array of Mach- Zehnder interferometers ( MZIs) integrated on a photonic chip. The signal from a set of MZIs is composed of an undersampled discrete Fourier interferogram, which we invert using l(1)-norm minimization to retrieve a sparse input spectrum. To implement this technique, we use a subwavelength- engineered spatial heterodyne FTS on a chip composed of 32 independent MZIs. We demonstrate the retrieval of three sparse input signals by collecting data from restricted sets ( 8 and 14) of MZIs and applying common CS reconstruction techniques to this data. We show that this retrieval maintains the full resolution and bandwidth of the original device, despite a sampling factor as low as one- fourth of a conventional ( non- compressive) design. (C) 2017 Optical Society of America