Coherent lidar at low signal powers: Basic considerations on optical heterodyning

In a number of optical heterodyne systems it may happen that the signal power is so low that only a few, or even fractions of, photons enter the receiver in a characteristic time interval. As the heterodyne receiver basically employs the beating effect, such intricate questions as “is there still a beating between the (many) local oscillator photons and the few return photons?” or “how can a single photon produce an intermediate frequency?” arise. We show that the semiclassical theory, which provides exact results as long as optical fields with an adequate classical description are used, is capable of answering those questions. The term “photon” must thereby be assigned its (semiclassically) correct meaning, which is an abbreviation for “discrete interaction of light and matter.” We illustrate our discussion by providing a numerical example related to a space-borne CO2 Doppler wind lidar instrument.