Effective medium approximation for the effective optical constants of a bilayer and a multilayer structure based on the characteristic matrix technique

Abstract

This article presents a derivation of the effective optical constants of a bilayer using the characteristic matrix technique. The derivation is simple, and in essence, adds an extra step to an approximate treatment of near-normal incidence spectroscopy, based on the characteristic matrix technique for stratified media. By this method, the effective optical constants of a bilayer consisting of two thin layers, each with a thickness much less than the wavelength of the incident radiation, are determined. This step leads to a modified procedure for calculating the optical properties of a layered stack that consists of thin bilayer units. The method, though still an effective medium approximation, is distinct from previous approximations. It introduces a more consistent parallelism to the fundamental theory of the characteristic matrix technique, and leads to a simplified analog of a multilayer viewed as one system of definite effective optical constants. Such a task has been difficult to achieve for structures with an arbitrary number of layers.

Subwavelength multilayer dielectrics: ultrasensitive transmission and breakdown of effective-medium

“…Accordingly, surface plasmon resonances can lead to a strong and short ranged interaction of light with the structure and can be sensitive to details such as surface termination which are otherwise totally negligible in the effective medium description [4,5]. On the other hand, all-dielectric systems, which fundamentally do not support such surface waves and resonances, are believed to be insensitive to subwavelength structural features and are well described by an effective medium approach [5].Here, we examine a stratified dielectric structure, and show that its transmission can depend on nanometric structural features. We show that even when the layers are 0.02λ thin, impedance matching with the exterior medium (from which the EM waves enter the multilayer structure) is not always possible.…”

Field-matter integral overlap to estimate the sensitivity of surface plasmon resonance biosensors

“…For ambient changes considered in Subsection 2.A.1, ε d ε a . For an interaction that forms a layer described in Subsection 2.A.2, ε d may be obtained by layered evanescent wave models [30,31]. If anglescanning SPR detection is assumed and thus dispersive material properties may be disregarded, Eq.…”

Effect of coupled graphene oxide on the sensitivity of surface plasmon resonance detection

“…The refractive indices of h-IgG and a-h-IgG being identical allows the complex biomolecular chemistry that takes place in the sandwiched assay to be simplified as an optical model of Fig. 1(a), because the resonance shifts measured as a result of an immune-reaction between h-IgG and a-h-IgG can be described as a change in the layer thickness [40]. h-IgG and a-h-IgG layers were assumed to be 7 and 9 nm, respectively, in thickness in line with [41].…”

“…The field amplitude was normalized by that of an incident light field. Also, for metal-enhanced SPR detection of sandwiched immunoassays: t SiO2 = (d) 0, (e)40, and (f) 80 nm. Thickness of GO or gold: 0-10 nm.…”