FM and AM mode locking of the homogeneous laser - Part I: Theory

A new general analysis for mode-locked operation of a homogeneously broadened laser with either internal phase (FM) or amplitude (AM) modulation is presented in this paper. In this analysis, a complex Gaussian pulse is followed through one pass around the laser cavity. Approximations are made to the line shape and modulation characteristics to keep the pulse Gaussian. After one round trip, a self-consistent solution is required. This yields simple analytic expressions for the pulse length, frequency chirp, and bandwidth of the mode-locked pulses. The analysis is further extended to include effects of detuning of the modulator, in which case analytical expressions are obtained for the phase shift of the pulse within the modulation cycle, the shift of the pulse spectrum off line center, the change in pulse length, and the change in power output. Numerical results for a typical Nd:YAG laser are given. In the case of the FM mode-locked laser it is found that there is a frequency chirp on the pulse and that this causes pulse compression and stretching when the modulator is detuned. Etalon effects and dispersion effects are also considered.