Abstract
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 l1-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.
Highlights
Miniature spectrometers are an invaluable tool in many applications, including environmental and biological sensing, medical diagnostics, geology, security, and planetary science, to name a few [1,2]
An Fourier-transform spectrometer (FTS) can be implemented in planar waveguides as an array of Mach–Zehnder interferometers (MZIs) with linearly increasing optical path delays (OPDs) [7,8], called a spatial heterodyne Fouriertransform spectrometer (SHFTS)
The SHFTS is based on spatial sampling, unlike a scanning FTS [9], where the interferogram is scanned in the temporal domain and captured by a single detector operating at a high readout rate
Summary
Miniature spectrometers are an invaluable tool in many applications, including environmental and biological sensing, medical diagnostics, geology, security, and planetary science, to name a few [1,2]. An FTS can be implemented in planar waveguides as an array of Mach–Zehnder interferometers (MZIs) with linearly increasing optical path delays (OPDs) [7,8], called a spatial heterodyne Fouriertransform spectrometer (SHFTS).
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