A modified finite-element method for dielectric waveguides using an asymptotically correct approximation on infinite elements

Svedin, Jan

doi:10.1109/22.102968

Cited by 12 publications

(11 citation statements)

References 24 publications

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“…The study of the electromagnetic field propagation inside waveguides which contain isotropic, anisotropic, or bi-isotropic materials is a common topic in the electromagnetic community. For this task, different numerical methods have been developed in both time and frequency domains [1][2][3][4][5][6][7][8][9]. Among them, we highlight the transmission line method (TLM) [1,2] and the finitedifference (FDTD) in the time domain [3,4], and the finite-element method (FEM) [5,6] and the coupled mode method (CMM) [7][8][9] in the frequency domain.…”

Section: Resultsmentioning

confidence: 99%

Efficient numerical tool for the analysis and design of reflectarrays based on cells with three parallel dipoles

Florencio

Boix

Carrasco

et al. 2013

Micro & Optical Tech Letters

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In this article, the Method of Moments in the spectral domain (MoM‐SD) is applied to the analysis of multilayered periodic structures, containing three coplanar parallel dipoles in the unit cell. It is shown that the use of basis functions with edge singularities in the modeling of the current density on the dipoles leads to important computer memory and CPU times savings in the analysis of the periodic structures. The MoM‐SD home‐made software is used in the analysis of a shaped beam reflectarray antenna made of cells with three parallel dipoles under the local periodicity assumption. The numerical results obtained for the radiation pattern of the antenna are compared with numerical results provided by the commercial software CST® and with measurements and good agreement is found. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:1212–1216, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27533

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Section: Resultsmentioning

confidence: 99%

Efficient numerical tool for the analysis and design of reflectarrays based on cells with three parallel dipoles

Florencio

Boix

Carrasco

et al. 2013

Micro & Optical Tech Letters

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“…Each infinite element is adjacent to a finite element, and has 3 nodes along the common segment N+l (6) f(r) is any interpolation function in the radial direction, Ν is the order of the interpolation function, Φ β , ( are unknown constants to be determined, η is a local coor-Brought to you by | Stockholms Universitet Authenticated Download Date | 7/14/15 9:13 AM dinate which varies linearly along the common segment, -1 < η< 1. Each infinite element is adjacent to a finite element, and has 3 nodes along the common segment N+l (6) f(r) is any interpolation function in the radial direction, Ν is the order of the interpolation function, Φ β , ( are unknown constants to be determined, η is a local coor-Brought to you by | Stockholms Universitet Authenticated Download Date | 7/14/15 9:13 AM dinate which varies linearly along the common segment, -1 < η< 1.…”

Section: Infinite Element Discretizationmentioning

confidence: 99%

“…References [5][6] have used infinite elements for the unbounded region, and the vectorial finite element formulation for the interior region. These techniques preserve the linearity and avoid the spurious solutions.…”

Section: Introductionmentioning

confidence: 99%

Computer Modeling of Optical Dielectric Waveguides by Edge Infinite Elements

Salameh¹,

Alkhawaldeh²

2000

Journal of Optical Communications

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This paper considers the solutions to optical fibers and integrated optical dielectric waveguides. The unbounded medium surrounding the waveguide is modeled by infinite elements with edge bases. The inhomogeneous part of the waveguide is discretized into a recently-developed edge finite elements. To match the infinite elements with adjacent finite elements, compatible interpolation functions are proposed for the infinite elements. In consequence, the boundary conditions between finite and infinite elements are exactly satisfied. Also, the formulation in this paper is presented such that any decay function in the radial direction may be employed. However, explicit representations for the infinite element matrices are given for the case of an inverse power decay function. Other functions will be investigated in the future work. The solutions to the final system of equations provide the dispersion characteristics of the optical waveguide. A computer program and an automatic mesh generator were written and shown to be valid by comparing the solutions with other published data.

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“…By applying the standard Galerkin procedure to (1) [8]. As only sparse matrices (Duff [21]) of density O(1/R) (R is the problem dimension) are involved, efficient sparse eigenvalue solvers may be exploited [16].…”

Section: Theorymentioning

confidence: 99%

“…In order to evaluate the accuracy of the presented method a number of numerical examples including both optical fibers and integrated optical waveguides, isotropic as well as anisotropic, have been considered [8]. Here, three examples will be given:…”

Section: Numerical Examplesmentioning

confidence: 99%

A Novel Finite-Element Method for Propagation Analysis of Open Dielectric Waveguides

Svedin

1990

20th European Microwave Conference, 1990

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A modified finite-element method for propagation analysis of open dielectric waveguides, such as optical fibers and integrated optical waveguides, is presented. The method is based on the full vectorial finite-element formulation (Svedin [6]), which has been found to be absent of spurious modes. An asymptotically correct, exponentially decaying approximation of thie radial field behaviour has been incorporated in the infinite-element expansion used for the exterior region. The exponential decay is hereby controlled by a set of transversal wavenumbers related to each medium. The linearity of the original finite-element method has been conserved, which results in a sparse generalized eigenvalue problem. Numerical examples including both optical fibers and integrated optical waveguides, isotropic as well as anisotropic, have been analyzed in order to confinm the validity of the method. The observed correspondence with analytical or elsewhere reported solutions has been found excellent. For some waveguides a high accuracy near cut-off has been obtained by adding a special near-field wavenumber. No spurious modes have been observed using the proposed method.

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A modified finite-element method for dielectric waveguides using an asymptotically correct approximation on infinite elements

Cited by 12 publications

References 24 publications

Efficient numerical tool for the analysis and design of reflectarrays based on cells with three parallel dipoles

Efficient numerical tool for the analysis and design of reflectarrays based on cells with three parallel dipoles

Computer Modeling of Optical Dielectric Waveguides by Edge Infinite Elements

A Novel Finite-Element Method for Propagation Analysis of Open Dielectric Waveguides

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