  We present a multimode laser-linewidth theory for arbitrary cavity structures
and geometries that contains nearly all previously known effects and also finds
new nonlinear and multimode corrections, e.g. a bad-cavity correction to the
Henry $\alpha$ factor and a multimode Schawlow--Townes relation (each linewidth
is proportional to a sum of inverse powers of all lasing modes). Our theory
produces a quantitatively accurate formula for the linewidth, with no free
parameters, including the full spatial degrees of freedom of the system.
Starting with the Maxwell--Bloch equations, we handle quantum and thermal noise
by introducing random currents whose correlations are given by the
fluctuation--dissipation theorem. We derive coupled-mode equations for the
lasing-mode amplitudes and obtain a formula for the linewidths in terms of
simple integrals over the steady-state lasing modes.
