Analysis of defect modes in one-dimensional photonic crystals with two defects

TL;DR

This paper derives analytical expressions for defect modes in one-dimensional photonic crystals with two defect layers, enhancing understanding and simplifying analysis of optical sensors and filters based on these structures.

Contribution

It introduces the first analytical formulas for defect mode wavelengths and conditions for their merging in 1D photonic crystals with two defect layers.

Findings

Derived analytical expressions for defect mode wavelengths.

Analyzed the behavior of defect modes and their merging conditions.

Provided insights into electromagnetic field distribution within photonic bandgaps.

Abstract

In this paper, for the first time, analytical expressions for determination of the wavelength of defect modes (DMs) in one-dimensional (1D) photonic crystals (PCs) with two defect layers (DLs) were obtained from the condition of zero reflection. Analytical formulas on the conditions for the merging of two DMs and on the DMs with zero value of the reflection coefficient were obtained. Different typical 1D PC structures with two DLs were considered and compared, including their DMs behavior. The distribution of electromagnetic field within the first photonic bandgap (PBG) was analyzed for several cases of DM merging and for the different orders of DMs. The results of this research permit the simplification of the analysis of optical sensors and filters based on 1D PCs with two DLs, as well as a more comprehensive understanding of the DM behavior within the PBGs of such PC structures. Furthermore, this paper helps to explain the results obtained by other researchers earlier in this field, too.