We review our recent work leading to steady-state solutions of the
semiclassical (Maxwell-Bloch) equations of a laser. These are coupled
non-linear partial differential equations in space and time which have
previously been solved either by fully time-dependent numerical simulations or
by using major approximations which neglect non-linear modal interactions
and/or the openness of the laser system. We have found a time-independent
technique for determining these stationary solutions which can treat lasers of
arbitrary complexity and degree of openness. Our method has been shown to agree
with time-dependent numerical solutions to high accuracy and has been applied
to find the electric field patterns (lasing modes) of random lasers, which lack
a laser cavity and are so strongly damped that the linear system has no
detectable resonances. Our work provides a link between an important non-linear
wave system and the field of quantum/wave chaos in linear systems.Comment: 22 pages, 10 figures, final version, selected for the cover
illustration of the journal Nonlinearity in 200
