Lineshape Analysis of the Beat Signal Between Optical Carrier and Delayed Sidebands

This paper presents the lineshape analysis of the beat signal between the optical carrier and the shifted and delayed sidebands produced by sinusoidal amplitude modulation. It is shown that the beat signal has a typical lineshape with a very narrow ¿ -peak superposed on a quasi-Lorentzian profile. Theoretical explanation for the appearance of this peak has been given based on optical spectral structure constructed by a large number of optical wave trains. It is predicted that the ¿-peak is originated from the beat between the wave trains in the carrier and those in the delayed sidebands when their average coherence length is longer than the delay line. Experiments carried out using different delay lines clearly show that the ¿ -peak is always located at the modulation frequency and decreases with the increasing delay line. Our analysis explicitly indicates that the linewidth is related to the observation time. It is also suggested that the disappearance of the ¿ -peak can be used as the criterion of coherence elimination.