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

Maxwell’s wave equations can be solved using different techniques in order to extract optical properties of a variety of dielectric structures. For structures contain an extended axis which serve for reference for 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 eigen-states can be computed. For cylindrically symmetric structures, computational technique provides a significantly reduced matrix order to be populated when compared to plane wave method applied to these structures. Steps used to convert Maxwell’s equation into an eigenvalue formulation are discussed and technique is tested on various dielectric structures. Several novel refractive index sensors based on slot channel configuration are presented and sensitivity of each structure is discussed. Using Fourier-Bessel technique eigenvalues are calculated and slot channel field profiles are plotted based on computed eigenvectors.