Orthonormalization of Radiation Modes in Effective Resonator Model of Dielectric Multilayer Structure

Abstract

In this paper, the orthonormal mode set is derived from electromagnetic field distributions of a dielectric multilayer structure, which have been obtained using the effective resonator model, presented in Acta Phys. Pol. A 111, 323 (2007)

Orthonormalization of Substrate and Guided Modes in Effective Resonator Model of Dielectric Multilayer Structure

“…The value of the above expression in the upper limit is 0, and, as it has been shown in [2], the term resulting from the lower limit cancels out with the term resulting from the upper limit in the region j = N R − 1. The integral (6) for substrate modes is very similar to the one obtained for two radiation modes…”

“…The basis of the model has been presented in [1], orthonormalization of radiation modes has been performed in [2], and orthonormalization of substrate and guided modes has been the subject of this paper. The application of an orthonormalization procedure for each type of modes has been shown separately, but it is an obvious observation that two modes of different types are always orthogonal (it follows from the delta functions appearing in (14)).…”

“…Using the notation adopted in the effective resonator model [1,2], the relation between the incident, reflected and transmitted (with amplitude t) wave is…”

“…Calculations that can be found here are a continuation of [2], where they have been conducted for radiation modes, therefore, the adopted notation, as well as definitions, are the same as therein.…”

“…can be constructed in the same way as they have been obtained in the case of radiation modes in [2]. Starting with non-orthonormal modes ψ k , after calculation of a similar integral, they can be related to the orthonormal modes f k by their linear combinations, forming a set of linear equations, which can be easily solved.…”