Quasi Normal Modes description of transmission properties for Photonic Band Gap structures

In this paper, we use the 'Quasi Normal Modes' (QNM) approach for discussing the transmission properties of double-side opened optical cavities: in particular, this approach is specified for one dimensional (1D) 'Photonic Band Gap' (PBG) structures. Moreover, we conjecture that the density of the modes (DOM) is a dynamical variable which has the flexibility of varying with respect to the boundary conditions as well as the initial conditions; in fact, the e.m. field generated by two monochromatic counter-propagating pump waves leads to interference effects inside a quarter-wave (QW) symmetric 1D-PBG structure. Finally, here, for the first time, a large number of theoretical assumptions on QNM metrics for an open cavity, never discussed in literature, are proved, and a simple and direct method to calculate the QNM norm for a 1D-PBG structure is reported.