The e.m. field nside the unidimensional Photonic Crystals - Study at optical frequencies applying "Quasi-Normal-Modes" theory

TL;DR

This paper investigates the electromagnetic behavior inside one-dimensional photonic crystals at optical frequencies using Quasi-Normal Modes theory, accounting for radiation losses and non-Hermitian properties of open cavities.

Contribution

It applies Quasi-Normal Modes theory to 1D photonic bandgap structures, providing a more realistic analysis of their electromagnetic properties at optical frequencies.

Findings

Modes are complex quasi-autofrequencies due to energy leakage.

The analysis uses Green's function and biorthogonal spaces.

The study accounts for non-Hermitian operators in open cavities.

Abstract

In this thesis, the behavior of the electromagnetic field is studied, at optical frequencies, in the one-dimensional photonic crystals, using the theory of "Quasi-Normal Modes (QNM). The following thesis is inspired by the QNM theory, recently developed for homogeneous cavity open just on one side. It is stressed that any 1D-PBG is an open cavity on both sides which allows the confinement of the e.m. field, but that causes radiation losses; the em field initially present within it, on the passing of time, can only propagate outwards. In general, the 1D-PBG is not a conservative system and the natural evolution of the e.m. field can not be described by a Hermitian operator: in short, a discussion in terms of normal modes of the field radiation is abandoned. The method of QNM uses, as tools of analysis, the Green's function and biorthogonal spaces. The 1D-PBG is studied in a more realistic way : a finite structure, immersed in an unlimited space. The renunciation of energy conservation for the system under consideration has important consequences, both numerical and conceptual: it goes from real autofrequencies to complex quasi-autofrequencies. Moreover, as the operator describing the evolution of space-time is not hermitian, the modes are no longer normal, but quasi-normal: in fact, only under appropriate conditions, they not only provide a basis orthogonal, but their space-time evolution is similar to that of the Hermitian normal modes.