Single-mode rate equations

A F J Levi

Robert J. Lang, Amnon Yariv

We present a general formalism for obtaining a coupled set of first-order rate equations for the optical field at a finite number of points in an optical resonator. We compare these local-field equations to an expansion in modes of the individual resonators and point out a shortcoming of the latter technique that has not been recognized before. We consider the special case of a set of two coupled resonators and derive the coupled rate equations for the fields in each of the two cavities with coupling coefficients. The resulting formulas are both simpler than those derived from coupled-mode theory and more accurate in the sense that they give a steady-state response which agrees with that calculated from the composite cavity modes. We show how the use of a single local-field rate equation can carry the same information as a full set of multimode rate equations in some cases, in particular, that of partial reflection back into a laser from a distant source.

J. Donald Rimstidt

Óscar G. Calderón, Víctor M. Pérez‐García, I. Martín +1 more

In this paper we analyze the transverse pattern-forming characteristics of a two-level and single-longitudinal-mode laser. The corrections to the classical empty cavity modes due to pumping and losses are specifically considered, leading to different excitation rates for the different transverse modes. The near-threshold excitation rates provide a selection mechanism that is studied and compared to the results from numerical simulations of the Maxwell-Bloch equations. \textcopyright{} 1996 The American Physical Society.

Rainer Salomaa, Stig Stenholm

This paper discusses the case of a Doppler-broadened gas laser with a saturable intracavity absorber gas. The semiclassical equations governing the field intensities and the atomic density-matrix elements are set up. The latter are written as Fourier series, the components of which are shown to obey coupled difference equations. In this paper the exact steady-state solution in single-mode operation is obtained. The lowest approximation (rate-equation approximation) is used to compute detailed characteristics of the system. In particular, the influence of the pumping rates in the two cells are investigated and displayed in the figures. The regions of bistable operation are determined and conditions for the occurrence of an inverted Lamb dip are given. The effect of a slow modulation of the pumping rates is discussed. The range of validity of the lowest approximation is investigated both analytically and numerically. Finally, there is a brief discussion of the influence of pressure on the parameters of the theory.