Journal ArticleDOI
High-accuracy finite-difference equations for dielectric waveguide analysis I: uniform regions and dielectric interfaces
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In this article, a methodology is presented that allows the derivation of low-truncation-error finite-difference representations or the two-dimensional Helmholtz equation, specific to waveguide analysis.Abstract:
A methodology is presented that allows the derivation of low-truncation-error finite-difference representations or the two-dimensional Helmholtz equation, specific to waveguide analysis. This methodology is derived from the formal infinite series solution involving Bessel functions and sines and cosines. The resulting finite-difference equations are valid everywhere except at dielectric corners, and are highly accurate (from fourth to sixth order, depending on the type of grid employed). None the less, they utilize only a nine-point stencil, and thus lead to only minor increases in numerical effort compared with the standard Crank-Nicolson equations.read more
Citations
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Proceedings ArticleDOI
High accuracy field differencing in the proximity of dielectric corners
TL;DR: In this paper, a semi-vectorial higher order finite-difference scheme for rectangular dielectric waveguides is presented, which incorporates new difference equations for mesh points next to a dielectrics interface and points near a die-lectric corner.
The application of Trefftz-FLAME to electromagnetic wave problems
TL;DR: In this paper, a 2D Trefftz-FLAME (flexible local approximation MEthod) method is proposed to calculate the reflection and transmission coefficients for photonic crystal devices.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Journal ArticleDOI
Finite-element solution of integrated optical waveguides
B. M. A. Rahman,J.B. Davies +1 more
TL;DR: In this paper, a vector H -field finite-element method has been used for the solution of optical waveguide problems, where the permittivity of the guiding structures can be an arbitrarily tensor, only limited to being lossless.
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