Steady-state Ab Initio Laser Theory: Generalizations and Analytic Results

TL;DR

This paper advances steady-state ab initio laser theory by introducing a basis set that simplifies calculations for complex cavities, enabling efficient and analytic predictions of laser behavior including nonlinear effects.

Contribution

It generalizes SALT using a new basis set and develops a single-pole approximation that simplifies analysis of complex laser systems.

Findings

Single-pole approximation agrees well with exact SALT for high-Q cavities.

The method efficiently predicts thresholds and intensities including nonlinear interactions.

Analytic predictions include a gain-clamping transition and modal suppression.

Abstract

We improve the steady-state ab initio laser theory (SALT) of Tureci et al. by expressing its fundamental self-consistent equation in a basis set of threshold constant flux states that contains the exact threshold lasing mode. For cavities with non-uniform index and/or non-uniform gain, the new basis set allows the steady-state lasing properties to be computed with much greater efficiency. This formulation of the SALT can be solved in the single-pole approximation, which gives the intensities and thresholds, including the effects of nonlinear hole-burning interactions to all orders, with negligible computational effort. The approximation yields a number of analytic predictions, including a "gain-clamping" transition at which strong modal interactions suppress all higher modes. We show that the single-pole approximation agrees well with exact SALT calculations, particularly for high-Q cavities. Within this range of validity, it provides an extraordinarily efficient technique for modeling realistic and complex lasers.