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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Journal ArticleDOI
Coordinate stretching for finite difference optical waveguide mode solvers
Suhua Wei,Ya Yan Lu +1 more
TL;DR: In this paper, a technique for optimizing the coordinate stretching function based on discrete reflection coefficients is proposed, which is applicable to waveguides with arbitrary refractive index profiles and it is easy to implement.
Book ChapterDOI
Integrated optics design: software tools and diversified applications
TL;DR: Aspects of system design and the multi-physics character of IO-microsystems are considered, and the potential complexity ofIO-design is demonstrated for a micro-optical coupling of a fibre and a photonic crystal waveguide.
Journal ArticleDOI
A conforming discontinuous Galerkin finite element method for elliptic interface problems
Yue Wang,Fuzheng Gao,Jintao Cui +2 more
TL;DR: In this article , a new conforming discontinuous Galerkin method, which is based on weak GAs, is introduced for solving second order elliptic interface problems with discontinuous coefficient, and the error estimates in H 1 and L 2 norms are established, which are the optimal order convergence.
Electromagnetic Applications of a New
TL;DR: The flexible local approximation method (FLAME) as discussed by the authors is a generalization of the Taylor expansion polynomials (TEP) for finite-difference analysis in electromagnetics.
Proceedings ArticleDOI
Yee-mesh-based finite difference eigenmode analysis algorithms for optical waveguides and photonic crystals
Hung-chun Chang,Chin-Ping Yu +1 more
TL;DR: In this paper, the effect of dielectric interface treatment on numerical accuracy was examined, and the Yee-mesh-based finite difference algorithm was used to solve the Eigenvalue equations for solving full-vector modes of optical waveguides.
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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