Quasi-normal-modes description of transmission properties for photonic bandgap structures

Abstract

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 bandgap” (PBG) structures. Moreover, we conjecture that the density of the modes is a dynamical variable that has the flexibility of varying with respect to the boundary conditions as well as the initial conditions; in fact, the electromagnetic (e.m.) field generated by two monochromatic counterpropagating pump waves leads to interference effects inside a quarter-wave symmetric 1D-PBG structure. Finally, here, for the first time to the best of our knowledge, 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.