Optical extraction from Nd:YAG lasers with ASE gain depumping losses

Abstract

Optical extraction characteristics of steady-state solid-state Nd:YAG lasers with amplified spontaneous emission (ASE) gain depumping losses are discussed. The gain model includes gain depumping losses by ASE and assumes that the medium is homogeneously-broadened. The rate equations describing the spatial growth of the intracavity intensities for a stable optical resonator are summarized, the threshold lasing condition is derived, and the coupled equations solved for the optical extraction efficiency using both first-order perturbation theory and a new numerical method in which the two-point boundary value problem is recast as an integral equation to be solved for the geometric mean of the forward and backward intensities at the optic axis. Solutions are determined for the optical extraction efficiency for medium parameters appropriate to high gain Nd:YAG lasers. Comparisons with the simple, uniform intracavity intensity model show the latter is not always a good approximation. The well-established empirical critera that the gain-length product satisfy ge < 2-4 to limit ASE power losses is shown to be a consequence of a constraint arising to ensure the validity of a perturbation solution of the stable resonator model and its upper limit is shown to be determined by the spectroscopic and lifetime parameters of the gain media.