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A semiclassical theory of single and multi-mode lasing is derived for opencomplex or random media using a self-consistent linear response formulation.Unlike standard approaches which use closed cavity solutions to describe thelasing modes, we introduce an appropriate discrete basis of functions whichdescribe also the intensity and angular emission pattern outside the cavity.This constant flux (CF) basis is dictated by the Green function which ariseswhen formulating the steady state Maxwell-Bloch equations as a self-consistentlinear response problem. This basis is similar to the quasi-bound state basiswhich is familiar in resonator theory and it obeys biorthogonality relationswith a set of dual functions. Within a single-pole approximation for the Greenfunction the lasing modes are proportional to these CF states and theirintensities and lasing frequencies are determined by a set of non-linearequations. When a near threshold approximation is made to these equations ageneralized version of the Haken-Sauermann equations for multi-mode lasing isobtained, appropriate for open cavities. Illustrative results from theseequations are given for single and few mode lasing states, for the case ofdielectric cavity lasers. The standard near threshold approximation is found tobe unreliable. Applications to wave-chaotic cavities and random lasers arediscussed.Comment: 18 pages, 9 figure

Self-consistent multimode lasing theory for complex or random lasing media