Line shape of a delayed self-heterodyne varied with noise types and delays

The delayed self-heterodyne and self-homodyne (DSH) method is widely used for measuring the line shapes of high coherent lasers. This method results in an autocorrelation of a laser line under the condition of a delay that is much larger than its coherent time. In practice, the delay is often not so long, especially for very narrow linewidth lasers, resulting in errors in rebuilding the laser's line shape from the DSH line. Many papers were devoted to the topic, but most of them are based on the formula for white noise. Analytical formulas of phase variance for 1/f noises are presented in this paper; the DSH line shapes for different noise types and different delay lengths are simulated based on the formulas. Some experimental data of the DSH line, combined with the power spectral density of frequency noise, are processed, showing good agreement with the theoretical analysis. It is indicated that the DSH line shape shows complicated behaviors varied with the delay, with noise types, and with the measurement duration. Such effects are to be compensated for in retrieving the laser's linewidth from the DSH data.