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. The e.m. field inside an open cavity can be obtained by suitable methods as the transfer matrix or the ray method. The representation of the e.m. field inside an open cavity can be given also as a superposition of Quasi Normal Modes (QNMs) which describe the coupling between the cavity and the environment. The importance of the QNM’s approach lies in the fact that it is possible to recover the orthogonal representation of the e.m. field, as it is necessary to consider quantum and non linear processes.