Spectral Lock-in Detection for High-Sensitivity Spectroscopy
The ability to recover weak signals without sacrificing their spectral information is central to precision spectroscopy, yet conventional lock-in detection achieves noise rejection at the expense of spectral dimensionality and ultimately imposes a trade-off between detection bandwidth and sensitivity. Here, we introduce spectral lock-in detection, a versatile framework that extends lock-in noise rejection independently to every resolved component of a broadband spectrum. By separating the fast-time coordinate encoding spectral information from the slow-time coordinate carrying temporal modulation, the measured waveform is spectrally resolved before demodulation, enabling each frequency channel to be independently detected and integrated. We show analytically that, for spectrally stable signals, the signal power in each spectral channel remains invariant, while the noise power ideally decreases by 10 dB per decade of integration time, enabling spectral features buried beneath the instantaneous noise floor to emerge without loss of frequency information. We experimentally validate this framework in both phase-incoherent heterodyne terahertz spectroscopy and phase-coherent terahertz time-domain spectroscopy, demonstrating more than six orders of magnitude of sensitivity enhancement across the spectrally resolved channels. Because spectral discrimination is performed computationally on the acquired waveform, the approach requires neither sequential spectral scanning nor additional spectral-selection, multichannel-detection, or interferometric hardware. Spectral lock-in detection therefore provides a broadly applicable route to enhancing sensitivity across diverse spectroscopic platforms and frequency regimes, opening new opportunities for high-sensitivity, information-rich measurements across the electromagnetic spectrum.