Speeding up Field-Resolved Spectroscopy by Compressed Sensing

Time domain spectroscopy, in particular, field-resolved spectroscopy has been a crucial tool for characterizing the transient electric field for decades [1]. Here, upon light-matter interaction, a detailed description of the constituent and internal dynamics of the matter is encoded on the electric field of light. When short laser pulses are used, the response of the medium is temporally separated from the main excitation pulses. This response which is enriched with the entire spectroscopic information of the sample lasts from hundreds of femtoseconds to tens of nanoseconds and is analytically shown to be sparse in the frequency domain [2]. To resolve the electric field and temporal decay of the transmitted or reflected transient, a short laser pulse probes the response at various temporal delays. By subsequent Fourier transformation, the full spectroscopic information is acquired. However, the measurement's speed is limited by i) the required number of sample points dictated by Nyquist-Shannon criteria, and ii) the speed of the delay line. In this work, we overcome these limitations and demonstrate field-resolved spectroscopy of vapor water molecules by Compressed Sensing. To the best of our knowledge, this is the first report on the reconstruction of absorption frequencies in the time domain beyond the Nyquist-Shannon limit. Our approach is enabled by developing a randomly sampling, rapidly scanned delay line, which speeds up the measurement time by three orders of magnitude allowing for sensitive, real-time sample analysis.