Compressive sensing for single-shot two-dimensional coherent spectroscopy

In this work, we explore the use of compressive sensing for the rapid acquisition of two-dimensional optical spectra that encodes the electronic structure and ultrafast dynamics of condensed-phase molecular species. Specifically, we have developed a means to combine multiplexed single-element detection and single-shot and phase-resolved two-dimensional coherent spectroscopy. The method described, which we call Single Point Array Reconstruction by Spatial Encoding (SPARSE) eliminates the need for costly array detectors while speeding up acquisition by several orders of magnitude compared to scanning methods. Physical implementation of SPARSE is facilitated by combining spatiotemporal encoding of the nonlinear optical response and signal modulation by a high-speed digital micromirror device. We demonstrate the approach by investigating a well-characterized cyanine molecule and a photosynthetic pigment-protein complex. Hadamard and compressive sensing algorithms are demonstrated, with the latter achieving compression factors as high as ten. Both show good agreement with directly detected spectra. We envision a myriad of applications in nonlinear spectroscopy using SPARSE with broadband femtosecond light sources in so-far unexplored regions of the electromagnetic spectrum.