  The definition of natural modes for confined structures is one of the central
problems in physics, as in nuclear physics, astrophysics, etc. The main problem
is due to the boundary conditions, when they are such to push out the problem
from the class of Sturm-Liouville. This occurs when boundary conditions imply
the presence of eigen-values, as for example when a scatterer excited from the
outside gives rise to a transmitted and reflected field. An open cavity with an
external or internal excitation represents a "non-canonical" problem, in the
sense of a Sturm-Liouville's problem, due to the fact that cavity modes couple
themselves with external modes. This problem is crucial when one intends to
study light-matter interaction effects as absorption, spontaneous emission,
stimulated emission, as they occur in micro-cavities.
