Semiclassical Theory of Laser Transmission Loss

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Abstract
Conventional laser theory deals with discrete ‘cavity modes’ and introduces artificial mechanisms to simulate radiation field losses caused by beam extraction. A more realistic model of a laser with a transmitting window, previously investigated by Lang, Scully and Lamb, is reanalysed semiclassically. In the previous work, the continuous radiation field spectrum was treated as the limit of a discrete but very dense spectrum of modes, and the narrowness of the laser linewidth was attributed to the locking together of these modes. Working entirely within the continuous spectrum, we find that the treatment is considerably simplified, leading to an explicit solution for single-quasimode operation within the linear approximation which exhibits the role of the excitation conditions in the build-up of the laser field. As was pointed out by Lang and Scully, the transmission loss plays the role of an effective noise source, satisfying the fluctuation-dissipation theorem. However, the continuum treatment does not support the mode-locking mechanism, but rather the usual explanation of the laser linewidth in terms of gain narrowing. The nonlinear analysis agrees with the main conclusion of Lang, Scully and Lamb that the ‘mode amplitude’ of the conventional theory should be interpreted as a collective variable that satisfies the well-known rotating-wave Van der Pol oscillator equation. The domain of validity of this result and of the laser quasimode concept depends on an approximation, analogous to the Weisskopf-Wigner approximation, which is well satisfied for the usual case of very long-lived quasimodes.