Perturbation approach to resonator state solution using the Fourier-Bessel numerical solver

Gauthier, Robert C.

doi:10.1016/j.optcom.2016.10.043

Cited by 3 publications

(1 citation statement)

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“…The lower two figures show the unperturbed structure serving as the reference on the left and on the right a perturbation applied to the regions characterized by a perturbation profile. The material perturbation applied to the reference structure can be treated as the residue profile and when the matrix is populated provides the perturbation matrix   If the perturbations applied to the reference structure are small and the states are non-degenerate the eigenvalues and eigenvectors of the perturbed system can be obtained directly through the following expressions [50]:…”

Section: Offset-residue Materials Segmentationmentioning

confidence: 99%

Spherical Space Bessel-Legendre-Fourier Mode Solver for Electromagnetic Fields

Alzahrani¹

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Controlling and confining light in three dimensions is of significant interest as it represents devices in their entirety with minimal approximations. Localized modes in resonator structures are commonly modelled using the supercell plane wave expansion method, finite element method, or the finite difference time domain. However, these standard techniques are expensive in terms of computational resources when applied to three-dimensional structures. The technique presented in this thesis is a new method for solving Maxwell's vector wave equations for localized modes in three-dimensional spherically resonator structures as well as its application to sensor configurations. The technique requires minimal implementation, provides normalized results, works for finite size and is computationally efficient. The method is such that the structures under test can be arbitrary shape, isotropic, anisotropic, lossless, or lossy. For the structures examined, a modified basis set composed of spherical Bessel, Legendre and Fourier functions (BLF) are used to expand the electric, magnetic, and inverse relative permittivity. These expansions allow for Maxwell's wave equations to be cast as an eigenvalue problem from which the steady state localized modes (not propagating) can be determined from the eigen-frequencies and eigenvectors. This work applies to a number of spherically symmetric structures. Selections of structures whose resonator properties are reported in the literature are used to compare and verify the accuracy of the use of the BLF functions as an expansion basis.iii Acknowledgement I would like to begin by thanking Prof. Gauthier for the great support he has provided throughout my post-graduate studies. I appreciate everything he has done for me during my stay here as international student, I feel that I have found a good friend as well as a supervisor.

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Section: Offset-residue Materials Segmentationmentioning

confidence: 99%