  Within the framework of exact quantization of the electromagnetic field in
dispersing and absorbing media the input-output problem of a high-$Q$ cavity is
studied, with special emphasis on the absorption losses in the coupling mirror.
As expected, the cavity modes are found to obey quantum Langevin equations,
which could be also obtained from quantum noise theories, by appropriately
coupling the cavity modes to dissipative systems, including the effect of the
mirror-assisted absorption losses. On the contrary, the operator input-output
relations obtained in this way would be incomplete in general, as the exact
calculation shows. On the basis of the operator input-output relations the
problem of extracting the quantum state of an initially excited cavity mode is
studied and input-output relations for the $s$-parameterized phase-space
function are derived, with special emphasis on the relation between the Wigner
functions of the quantum states of the outgoing field and the cavity field.
