Theory of a One-Dimensional Laser with Output Coupling Nonlinear Theory

Abstract

In a previous paper we considered the linear problem of a one-dimensional laser having output coupling. In this paper we derive the nonlinear equation for the same model of the laser and solve it for steady state. The output coupling is exactly taken into account and the field is treated as having a continuous spectrum composed of the normal modes of the universe. Damping terms for the atomic polarization and for the population inversion are introduced phenomenologically. The fluctuating forces due to these damping terms and to the initial field are ignored. The resultant field inside the cavity consists of two oppositely travelling waves whose amplitudes are functions of the distance from the coupling surface. Outside the cavity we have a monochromatic, outgoing wave whose amplitude does not change with distance. The threshold inversion and the oscillation frequency are the same as those derived in the linear theory.