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Acta Physica Sinica

A SEMICLASSICAL THEORY OF MODE COUPLING IN DYE LASERS

PAN SHAO-HUA, 中国科学院物理研究所

Published Jan 1, 1981• 0 citations
Publisher

Abstract

The semiclassical laser theory proposed by Lamb for two-level system is extended to the case of dye lasers. Mode coupling equations are deduced, and a discussion is given.
DOI
10.7498/aps.30.1067

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The semiclassical Lamb theory of gas lasers is extended to the case of lasers operating simultaneously on two coupled transitions. The theory is formulated in terms of the density-matrix equations for a three-level gaseous laser medium interacting with the field through electric-dipole transitions, so that there are two allowed transitions and one two-photon transition. It is assumed that there is a single resonator mode near each of the transition frequencies. Previous treatments of such three-level gas lasers either have used simple rate equations or have solved the density-matrix equations in an approximate fashion valid only for low intensities. Thus the numerical approach developed herein represents, to our knowledge, the first semiclassical theory of three-level gas lasers which is accurate for arbitrary detuning and intensity. Significant deviations from earlier, approximate treatments are found.
The semiclassical interaction of a two-level system with a multimode electromagnetic field is discussed in detail. The equations of motion for the macroscopic density matrix are transformed into a single integral equation for the population density, with a complex kernel which can take into account both running- and standing-wave configurations. The iterative solution to this integral equation, which corresponds to an expansion in terms of powers of the electromagnetic field amplitudes, turns out to be divergent when the field amplitudes are greater than some critical value. In the case in which the kernel is a periodic or quasiperiodic function of time, a general solution to the integral equation is found, and this solution turns out to be unique and convergent for every value of the electromagnetic (e.m.) field amplitude. This solution is expressed through a continued-fraction expansion, whose terms are matrices, which can be readily obtained from the kernel. This solution is a generalization of the continued-fraction expansion usually met in the strong-signal semiclassical theory of lasers. Some particular cases are then treated in detail; among them, the solution to the multimode operation in laser devices is given in which the excited level lifetime is long compared with the period of the beating term between two adjacent modes. Although the theory presented is directed towards the steady-state regime in multimode lasers, it may also treat the transient regime of laser operations, or it may be extended to include phenomena where a strong e.m. field, made up of several modes equally spaced in frequency, interacts with a two-level system.