Theory of Optical Beating in Photoconductors (Phenomenological Modification of Semiclassical Treatment)

Recent laser experiments have shown that two coherent light waves of slightly different frequency, when simultaneously incident on a photodetector, produce a photosignal modulated at the beat frequency $\Delta f$. The theory of this photomixing process is developed by means of a modification of the usual semiclassical treatment of radiation. This modification takes into account the finite lifetime $\tau$ of excited electronic states in the quantum-mechanical equations of motion. The photosignal is found to be proportional to ${[1+4\mathrm{}{\pi }^2{\tau }^2{\left(\Delta f\right)}^2]}^{-\frac{1}{2}}$. This result suggests an experimental means of determining the lifetime by measuring the frequency response of the photosignal to the beat frequency. The theory compares favorably with experiments on $p$-type extrinsic gold-doped germanium.