Signal-to-noise ratio in optical heterodyne detection for Gaussian fields.

The signal-to-noise ratio of optical heterodyne detection is discussed for Gaussian fields. The ratio of the aperture radius a of the detector to the smallest spot size w(s) of the signal has serious effects on the SNR. The conditions that maximize the SNR are obtained for a given signal or local oscillator field. The effects of field mismatching or misalignment are also discussed. Numerical analyses show that when such mismatching or misalignment exists, the spot size of the local oscillator field should be larger than that of the signal with a ratio of a/w(s) approximately 1.2. Then the heterodyne efficiency is rather insensitive to the errors and yet takes reasonable values (above 0.8).