  Using a scattering matrix formalism, we derive the general scattering
properties of optical structures that are symmetric under a combination of
parity and time-reversal (PT). We demonstrate the existence of a transition
beween PT-symmetric scattering eigenstates, which are norm-preserving, and
symmetry-broken pairs of eigenstates exhibiting net amplification and loss. The
system proposed by Longhi, which can act simultaneously as a laser and coherent
perfect absorber, occurs at discrete points in the broken symmetry phase, when
a pole and zero of the S-matrix coincide.
