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Abstract

Ultrashort time-domain spectroscopy and field-resolved spectroscopy of molecular fingerprints are gold
standards for detecting samples’ constituents and internal dynamics. However, they are hindered by the
Nyquist criterion, leading to prolonged data acquisition, processing times, and sizable data volumes.
In this work, we present the first experimental demonstration of compressed sensing on field-resolved
molecular fingerprinting by employing random scanning. Our measurements enable pinpointing the primary
absorption peaks of atmospheric water vapor in response to terahertz light transients while sampling
beyond the Nyquist limit. By drastically undersampling the electric field of the molecular response at a
Nyquist frequency of 0.8 THz, we could successfully identify water absorption peaks up to 2.5 THz with a
mean squared error of 12 × 10−4. To our knowledge, this is the first experimental demonstration of timedomain
compressed sensing, paving the path toward real-time field-resolved fingerprinting and acceleration
of advanced spectroscopic techniques.