Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves

Alzahrani, Mohammed; Gauthier, Robert C.

doi:10.1364/oe.23.025717

Cited by 7 publications

(7 citation statements)

References 41 publications

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“…The modified spherical basis functions greatly simplify the computer implementation. The BLF technique and its applications has been published by the author (as principle author) in a peer review journal paper (chapter 3 and 4) [28] and three conference contributions, 2 oral presentations (main theory of the technique and segmentations) [33,34] and a poster presentation (slot channel sensors) [35]. At the time of writing this thesis two papers are in preparation, one about the new formulation in chapter 5 and the other one about application of the segmentations approach.…”

Section: Contributionsmentioning

confidence: 99%

“…Recently, new approaches have been developed to analyze structures that possess rotational symmetry [27,28]. They are based on taking Maxwell's wave equation and expanding the electromagnetic fields and the inverse relative permittivity of the dielectric profile using Fourier-Bessel (FB) basis functions in polar coordinates, and Fourier-Fourier-Bessel (FFB) basis functions in the cylindrical coordinates.…”

Section: Recent Techniquesmentioning

confidence: 99%

“…They are based on taking Maxwell's wave equation and expanding the electromagnetic fields and the inverse relative permittivity of the dielectric profile using Fourier-Bessel (FB) basis functions in polar coordinates, and Fourier-Fourier-Bessel (FFB) basis functions in the cylindrical coordinates. FB and FFB were used to demonstrate a relationship between the rotational order of the structure and the rotational order of the localized modes [27,28]. A significant reduction in the eigen-matrix order is possible using symmetry, which greatly reduces the computation time.…”

Section: Recent Techniquesmentioning

confidence: 99%

“…That technique is reconfigured here such that it is applicable to spherical objects of arbitrary internal structure. When solved the eigenvalue problem yields resonator state frequencies or wavelengths (eigenvalues) and field profiles (reconstructed using the eigenvectors) [28].…”

Section: Chapter: Introductionmentioning

confidence: 99%

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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: Contributionsmentioning

confidence: 99%

Section: Recent Techniquesmentioning

confidence: 99%

Section: Recent Techniquesmentioning

confidence: 99%

Section: Chapter: Introductionmentioning

confidence: 99%

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

Alzahrani¹

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“…Spherical space localized modes solver employing the same approach was introduced by other members of professor Gauthier's group using Bessel-Legendre-Fourier technique [8].…”

Section: Chapter 1 Introductionmentioning

confidence: 99%

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

Jafari¹

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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, for instance 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 the eigen-states can be computed. For cylindrically symmetric structures the computational technique provides a significantly reduced matrix order to be populated when compared to the plane wave method applied to these structures. The steps used to convert Maxwell's equation into an eigenvalue formulation are discussed and the technique is tested on various dielectric structures. Several novel refractive index sensors based on slot channel configuration are presented and the sensitivity of each structure is discussed. Using the Fourier-Bessel technique the eigenvalues are calculated and the slot channel field profiles are plotted based on the computed eigenvectors.

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Reformulation of the Fourier–Bessel steady state mode solver

Gauthier

2016

Optics Communications

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Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves

Cited by 7 publications

References 41 publications

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

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

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

Reformulation of the Fourier–Bessel steady state mode solver

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