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Successful Applications of Mathematica in Laser Instabilities

A. Bakasov
Journal / Anthology

International Centre for Theoretical Physics (ICTP): Preprint
Year: 1992

At arbitrary physical values of the relaxation rates, and at arbitrary detuning between the cavity frequency and the atomic resonance frequency, the exact analytical expression for the second threshold of a single-mode homogeneously broadened laser has been derived and analyzed both in general and in some asymptotic cases. The initial pulsation frequency at the second threshold has also been found. Another possible analytical solution for the second threshold is shown to be unphysical both for the resonantly tuned and detuned laser. Earlier approximate results concerning both the second threshold and initial pulsation frequency have been partly confirmed and partly improved on the basis of more general expressions, and their physical status has been reconsidered and specified more clearly. A number of new asymptotic results have been obtained and distinctions are made of which can reasonably be attained in lasers or masers. A general analytical proof that increasing the detuning increases the second threshold is given. Results concerning the physical meaning of the complex Lorenz model in laser physics have been summarized and discussed. Finally, the variation of the second threshold in relation to the semi-infinite parameter space of the decay rates is shown in a plot with a finite domain by normalizing the material relaxation rates to the cavity decay rate.

*Science > Physics > Optics