Classical and Quantum Approach of Quasi Normal Modes in Linear Optical Regime: An Application to One Dimensional Photonic Crystals

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.