High-resolution single-photon spectrum and its applications in vibration measurements

Conventional optical spectrum measurement techniques are constrained by the performance of dispersive elements and detector devices, making it challenging to meet the demands of high-resolution and high-sensitivity optical spectrum measurements. This paper proposes a single-photon optical spectrum measurement method that combines heterodyne detection with sparse-photon frequency-domain analysis based on compressed sensing. A narrow-linewidth laser serves as a frequency reference, and the weak signal light interferes with the reference light. The resulting beat signal is detected by a single-photon detector, and the optical spectrum is reconstructed using discrete Fourier analysis of photon arrival times. Our method allows spectral recovery even under extremely low photon flux, thanks to its compatibility with compressed-sensing-inspired statistical reconstruction. In the experiment, we accomplished an optical spectrum measurement with a spectral range of 2 GHz and a resolution of 11.72 Hz at an average photon count rate of 15 kcps for the signal light. Moreover, we demonstrated the application of this method in long-distance fiber-optic vibration sensing. Our proposal provides a perspective for single-photon optical spectrum measurement and expands the application scope of optical spectrum detection.