Influence of detuning on the properties of laser equations

The five semiclassical laser equations are studied in the mean-field limit for the simple model of two-level atoms with homogeneous broadening in a single-mode unidirectional ring cavity, taking into account detuning between atomic and cavity frequencies. The analysis concentrates on the properties of the laser at and beyond the second threshold in the bad-cavity case. It is first shown that the position of the second threshold depends on the excitation mechanism: When the pump parameter is increased either adiabatically or abruptly, two different thresholds occur. The sequence of periodic and chaotic solutions beyond the second threshold is then discussed as a function of the detuning and the pump parameter.