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.