Application of Fourier-Bessel technique for computing Eigen-states in a Bragg cylindrical space slot channel waveguide

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 which serve for the reference for cylindrical symmetry, we have shown that an expansion of the fields and inverse of the relative dielectric profile using a simplified and complete set of basis functions of Fourier-Bessel terms provide access to an eigenvalue formulation from which the eigen-states can be computed. We review the steps used to convert Maxwell's equation into an eigenvalue formulation, and then proceed to discuss several applications of the technique. For cylindrically symmetric structures, the computational technique provides a significantly reduced matrix order to be populated. New target structure for the presentation consists of cylindrical space slot channel waveguide in which the channel extends in azimuthal (ψ) direction. The channel is provided by considering the etching of external side walls of"Bragg fiber". The configuration is similar to a structure that can support whispering-gallery modes, except that the modes highest field locations are within the ambient medium of the channel. Optical properties of this structure can be best examined through Ez- field component which is discontinuous by ratio of relative dielectric constants when passing air-Bragg interfaces. The ability to select Bragg dielectric properties and to introduce non-uniformities in Bragg plane spacing provides access to tuning slot channel waveguide properties and design several novel configurations