  We review and interpret a modern approach to laser theory, steady-state ab
initio laser theory (SALT), which treats lasing and amplification in a unified
manner as a non-unitary scattering problem described by a non-linear scattering
matrix. Within the semiclassical version of the theory the laser line has zero
width as the lasing mode corresponds to the existence of an eigenvector of the
S-matrix with diverging eigenvalue due to the occurrence of a pole of the
scattering matrix on the real axis. In this approach the system is infinite
from the outset and no distinction is made between cavity modes and modes of
the universe; lasing modes exist both in the cavity and in the external region
as solutions satisfying Sommerfeld radiation boundary conditions. We discuss
how such solutions can be obtained by a limiting procedure in a finite box with
damping according to the limiting absorption principle. When the
electromagnetic and matter fields are treated as operators, quantum
fluctuations enter the relevant correlation functions and a finite linewidth is
obtained, via a generalization of SALT to include noise (N-SALT). N-SALT leads
to an analytic formula for the linewidth that is more general than all previous
corrected versions of the Schawlow-Townes formula, and can be evaluated simply
from knowledge of the semiclassical SALT modes. We derive a simpler version of
this formula which emphasizes that the noise is dominated by the fluctuations
in the polarization of the gain medium and is controlled by the rate of
spontaneous emission.
