  We derive and test a generalization of Steady-State Ab Initio Laser Theory
(SALT) to treat complex gain media. The generalized theory (C-SALT) is able to
treat atomic and molecular gain media with diffusion and multiple lasing
transitions, and semiconductor gain media in the free carrier approximation
including fully the effect of Pauli blocking. The key assumption of the theory
is stationarity of the level populations, which leads to coupled
self-consistent equations for the populations and the lasing modes that fully
include the effects of openness and non-linear spatial hole-burning. These
equations can be solved efficiently for the steady-state lasing properties by a
similar iteration procedure as in SALT, where a static gain medium with a
single transition is assumed. The theory is tested by comparison to much less
efficient Finite Difference Time Domain (FDTD) methods and excellent agreement
is found. Using C-SALT to analyze the effects of varying gain diffusion
constant we demonstrate a cross-over between the regime of strong spatial hole
burning with multimode lasing to a regime of negligible spatial hole burning,
leading to gain-clamping, and single mode lasing. The effect of spatially
inhomogeneous pumping combined with diffusion is also studied and a relevant
length scale for spatial inhomogeneity to persist under these conditions is
determined. For the semiconductor gain model, we demonstrate the frequency
shift due to Pauli blocking as the pumping strength changes.

Optics