In this paper the butterfly effects of single mode laser oscillation are studied. It is shown that the detuning between laser oscillation and atomic transition frequency leads to a decrease in second threshold, which makes the demonstration of chaos theory in experiment easy.
We study the five semiclassical laser equations 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. Our analysis concentrates on the properties of the laser at and beyond the second thresh-old in the bad-cavity case. We first show 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.
An exact analysis has been carried out for general analytical expressions for the second threshold of a single-mode homogeneously broadened laser and for the initial pulsation frequency at the second threshold, for arbitary physical values of the relaxation rates, and at an arbitrary detuning between the cavity frequency and the atomic resonance frequency. These expressions also give correspondingly exact forms for asymptotic cases that have been previously studied with some approximations. Earlier approximate results are partly confirmed and partly improved by these more general expressions. The physical status of various expressions and approximations is reconsidered and specified more clearly, including an analysis of what reasonably can be attained in lasers or masers. A general analytical proof is given of the fact that, for a larger detuning of the laser cavity from resonance, a higher value of the laser excitation is required to destabilize the steady-state solution (the second threshold). We also present results for the minimum value of the second threshold at fixed detuning as a function of the other parameters of the system and for the dependence of the ratio of the second threshold to the first threshold as a function of detuning. Minima of the second threshold and of the threshold ratio occur only if the population relaxation rate is equal to zero. The minima of the threshold ratio are shown to be bounded from above as well as from below (as functions of the relaxation rates, so long as the second threshold exists). The upper bound on the minima ratio is equal to 17. The variation of the second threshold in the semi-infinite parameter space of the decay rates is shown at various detunings in plots with a finite domain by normalizing the material relaxation rates to the cavity decay rate.
We have compared the impact of loss, pump, and frequency modulations on a single-mode homogeneously broadened laser under varying detunings and modulation frequencies. In the case of loss and gain modulations the impact on intensity shows a minimal behavior at the line center for gain values more than twice the lasing threshold. The system relaxation time with respect to any transient perturbation depends on the magnitude of detuning and is minimal at the line center. In the case of frequency modulation, the impact on intensity vanishes at the line center irrespective of the gain values. These results are based on linear analysis.
As the laser linewidth arises under the influence of spontaneous emission, it is of considerable interest to find effects that decrease it. In this paper it is considered the effect of cooperative atomic interactions on the linewidth of a single-mode laser. It can be shown by suitably generalizing the Scully-Lamb theory that the cooperative effects tend to decrease the natural linewidth of the laser at high intensities. Considering the interaction of two-two- level atoms with a single-mode quantized field and the effect of cooperative atomic interactions it was obtained an expression for the natural linewidth of the system. Based on the theoretical models we obtain the numerical results for the laser linewidth as a function of the cooperation parameter. We then present a set of graphs by suitably plotting these data and we discuss the results.