Cylindrical and spherical space equivalents to the plane wave expansion technique of Maxwell's wave equations

Robert C. Gauthier; Mohammed A. Alzahrani; Seyed Hamed Jafari

doi:10.1117/12.2076384

27 February 2015 Cylindrical and spherical space equivalents to the plane wave expansion technique of Maxwell's wave equations

Robert C. Gauthier, Mohammed A. Alzahrani, Seyed Hamed Jafari

Author Affiliations +

Proceedings Volume 9371, Photonic and Phononic Properties of Engineered Nanostructures V; 93711R (2015) https://doi.org/10.1117/12.2076384
Event: SPIE OPTO, 2015, San Francisco, California, United States

Abstract

The plane wave expansion (PWM) technique applied to Maxwell’s wave equations provides researchers with a supply of information regarding the optical properties of dielectric structures. The technique is well suited for structures that display a linear periodicity. When the focus is directed towards optical resonators and structures that lack linear periodicity the eigen-process can easily exceed computational resources and time constraints. In the case of dielectric structures which display cylindrical or spherical symmetry, a coordinate system specific set of basis functions have been employed to cast Maxwell’s wave equations into an eigen-matrix formulation from which the resonator states associated with the dielectric profile can be obtained. As for PWM, the inverse of the dielectric and field components are expanded in the basis functions (Fourier-Fourier-Bessel, FFB, in cylindrical and Fourier- Bessel-Legendre, BLF, in spherical) and orthogonality is employed to form the matrix expressions. The theoretical development details will be presented indicating how certain mathematical complications in the process have been overcome and how the eigen-matrix can be tuned to a specific mode type. The similarities and differences in PWM, FFB and BLF are presented. In the case of structures possessing axial cylindrical symmetry, the inclusion of the z axis component of propagation constant makes the technique applicable to photonic crystal fibers and other waveguide structures. Computational results will be presented for a number of different dielectric geometries including Bragg ring resonators, cylindrical space slot channel waveguides and bottle resonators. Steps to further enhance the computation process will be reported.

Citation Download Citation

Robert C. Gauthier, Mohammed A. Alzahrani, and Seyed Hamed Jafari "Cylindrical and spherical space equivalents to the plane wave expansion technique of Maxwell's wave equations", Proc. SPIE 9371, Photonic and Phononic Properties of Engineered Nanostructures V, 93711R (27 February 2015); https://doi.org/10.1117/12.2076384

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