Effect of longitudinal pump inhomogeneity on the energy characteristics of steady-state raman lasers

Abstract

The energy characteristics of externally pumped Raman lasers are calculated taking inhomogeneities in the active medium into account. Equations for the power and steady-state lasing threshold in these systems as function of the parameters of the cavity, pump, and Raman active medium are obtained over the entire ranges of their possible variations. The conditions for applicability of the model of averaged (uniform) fields, which is widely used in the theory of Raman lasers, are determined and interrelations among the cavity parameters favor unidirectional lasing in ring cavity Raman lasers are identified.Keywords: Raman laser, laser power, lasing threshold, Q-factor, inhomogeneous field distributions, averaged field model. Introduction.Raman lasers, i.e., lasers which employ stimulated Raman scattering for conversion of the laser output frequency, continue to be of great interest to researchers, developers, and users of laser technology. These systems are built either by placing a Raman conversion medium in the cavity of a primary laser (intracavity pumped Raman laser) or by placing this kind of medium in its own cavity and using an external laser for pumping (externally pumped Raman laser). The important feature of the second approach is that the cavity has a high Q at the frequency of the converted (Stokes) radiation, while that for the pump radiation should be low because of the high transparency of the mirror through which the pump light passes. This feature is typically neglected in theoretical analyses of the operation of these lasers. It is usually assumed in estimating the gain for the Stokes radiation and the corresponding attenuation of the pump radiation that the variation in the intensities of these fields along the cavity axis can be neglected. Simple arguments confirm that this so-called point model (more precisely, a model of an averaged, i.e., homogeneous, field) is entirely permissible for cavities with a high Q at the frequencies of all the interacting fields. If, however, the high Q condition is not satisfied for any of the frequencies of the interacting fields, then the averaged field model is not strictly applicable and an analysis of the operation of the system as a whole requires a more accurate approach.In this paper the steady-state lasing characteristics of an externally pumped Raman laser are calculated using a rigorous solution of the equations for the powers of the Stokes radiation and pump radiation in the Raman active medium. Equations for the power and lasing threshold as functions of the cavity and pump parameters are obtained over wide ranges and the limits of applicability of the averaged field model are determined.Raman Lasers with a Ring Cavity. General equations. Steady-state Raman amplification of the first Stokes component for spectrally narrow pumping can be described by the following system of equations [1-4]: