For spherically symmetric dielectric structures, a basis set composed of Bessel, Legendre and Fourier functions, BLF, are used to cast Maxwell's wave equations into an eigenvalue problem from which the localized modes can be determined. The steps leading to the eigenmatrix are reviewed and techniques used to reduce the order of matrix and tune the computations for particular mode types are detailed. The BLF basis functions are used to expand the electric and magnetic fields as well as the inverse relative dielectric profile. Similar to the common plane wave expansion technique, the BLF matrix returns the eigen-frequencies and eigenvectors, but in BLF only steady states, non-propagated, are obtained. The technique is first applied to a air filled spherical structure with perfectly conducting outer surface and then to a spherical microsphere located in air. Results are compared published values were possible.

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Keywords Eigen-matrix, Fourier Bessel Legendre, Maxwell's equations, Resonator states, spherical space dielectric structures, Steady states
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Conference Photonic and Phononic Properties of Engineered Nanostructures V
Alzahrani, M.A. (Mohammed A.), & Gauthier, R. (2015). Spherical space Bessel-Legendre-Fourier mode solver for Maxwell's wave equations. Presented at the Photonic and Phononic Properties of Engineered Nanostructures V. doi:10.1117/12.2076061