Abstract

A long-standing problem in laser theory is the formulation of a model for lasing which correctly treats the openness of the lasing medium/cavity and the non-linearity of the coupled matter-field equations. The steady-state electric field within and outside of single or multi-mode lasers arises as a solution of the non-linear coupled matter-field equations, the simplest of which are the two-level Maxwell-Bloch equations. While the basic equations involved have been known for many years, and many aspects of their temporal dynamics have been studied [1], relatively little progress has been made in understanding the spatial structure of the non-linear electric field, particularly in the case of multi-mode solutions for which spatial hole-burning and other non-linear effects are critical. It is natural to attempt to understand the non-linear solutions in terms of solutions of a linear wave equation. The two standard choices are either the hermitian solutions of a perfectly reflecting (closed) passive laser cavity, or the non-hermitian non-orthogonal resonances of the open passive cavity. In fact the intuitive picture of a lasing mode is that it arises when one of the resonances of the passive cavity is “pulled” up to the real axis by adding gain to the resonator. Often comparison of the numerically generated lasing modes with calculated linear resonances do show strong similarities in spatial structure, providing useful interpretation of lasing modes, although not a predictive theory. However with the current interest in complex laser cavities based on wave-chaotic shapes, photonic bandgap media or random media, it is important to have a quantitative and predictive theory of the lasing states, as the numerical simulations required to solve the time-dependent Maxwell-Bloch equations are time-consuming and not easy to interpret.

© 2007 IEEE