The generation of picosecond pulses in passively mode-locked solid-state lasers. III. Intensity maxima and their probability distribution

Abstract

This is the third in a series of papers analysing the generation of picosecond pulses in passively mode-locked solidstate lasers. The growth of intensity fluctuations inside the cavity and the corresponding development of a train of pulses are carefully considered. This paper is particularly concerned with intensity maxima and their probability distribution.It is shown that the hitherto accepted method of uniform sampling of the intensity profile leads to errors and that it is better to obtain the required probability distribution directly from the power spectrum of the intensity fluctuations inside the cavity. It is assumed that below threshold the electromagnetic radiation inside the cavity has the character of narrow-band noise. Above threshold the amplitude of each mode ceases to be a random quantity, stochastic properties of the system being expressed by phase fluctuations alone, the envelope of the wave now acquiring the form R = R (φ1…, φJ; t), where φ1 is the phase of the jth mode, the total numbe...