  A semiclassical theory of single and multi-mode lasing is derived for open
complex or random media using a self-consistent linear response formulation.
Unlike standard approaches which use closed cavity solutions to describe the
lasing modes, we introduce an appropriate discrete basis of functions which
describe also the intensity and angular emission pattern outside the cavity.
This constant flux (CF) basis is dictated by the Green function which arises
when formulating the steady state Maxwell-Bloch equations as a self-consistent
linear response problem. This basis is similar to the quasi-bound state basis
which is familiar in resonator theory and it obeys biorthogonality relations
with a set of dual functions. Within a single-pole approximation for the Green
function the lasing modes are proportional to these CF states and their
intensities and lasing frequencies are determined by a set of non-linear
equations. When a near threshold approximation is made to these equations a
generalized version of the Haken-Sauermann equations for multi-mode lasing is
obtained, appropriate for open cavities. Illustrative results from these
equations are given for single and few mode lasing states, for the case of
dielectric cavity lasers. The standard near threshold approximation is found to
be unreliable. Applications to wave-chaotic cavities and random lasers are
discussed.
