Fourier-Bessel Analysis of Cylindrically Symmetric Dielectric Structures, Slot Channel Refractive Index Sensors

Abstract

Maxwell's wave equations can be solved using different techniques in order to extract optical properties of a variety of dielectric structures. For structures that contain an extended axis, for instance cylindrical symmetry, it is shown that an expansion of the fields and inverse of relative permittivity using a set of basis functions of Fourier-Bessel terms, provide access to an eigenvalue formulation from which the eigen-states can be computed. For cylindrically symmetric structures the computational technique provides a significantly reduced matrix order to be populated when compared to the plane wave method applied to these structures. The steps used to convert Maxwell's equation into an eigenvalue formulation are discussed and the technique is tested on various dielectric structures. Several novel refractive index sensors based on slot channel configuration are presented and the sensitivity of each structure is discussed. Using the Fourier-Bessel technique the eigenvalues are calculated and the slot channel field profiles are plotted based on the computed eigenvectors.