Journal ArticleDOI
High-accuracy finite-difference equations for dielectric waveguide analysis I: uniform regions and dielectric interfaces
Reads0
Chats0
TLDR
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
More filters
Journal ArticleDOI
Flexible approximation schemes with numerical and semi‐analytical bases
TL;DR: In this paper, the generalized finitedifference calculus of flexible local approximation methods (FLAME) is extended to problems where local analytical solutions are unavailable, and the FLAME basis is constructed by solving small local finite element problems or, alternatively, by a local multipole-multicenter expansion.
Journal ArticleDOI
Meshless local numerical procedure based on interpolating moving least squares approximation and exponential time differencing fourth-order Runge–Kutta (ETDRK4) for solving stochastic parabolic interface problems
Mostafa Abbaszadeh,Mehdi Dehghan +1 more
TL;DR: The main propose of this investigation is to develop an interpolating meshless numerical procedure for solving the stochastic parabolic interface problems by employing a fourth-order time discrete scheme that is well-known as the explicitFourth-order exponential time differencing Runge-Kutta method (ETDRK4).
Proceedings ArticleDOI
What is the future for beam propagation methods
TL;DR: The role of BPM is reviewed, its present day limitations are considered and the issues that need to be addressed are discussed if it is to move forward in the future.
Journal ArticleDOI
Accuracy of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities
TL;DR: In this article, a rigorous truncation error analysis of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities is given.
Proceedings ArticleDOI
A new computational method for plasmon resonances of nanoparticles and for wave propagation
TL;DR: The Flexible Local Approximation Method (FLAME) as mentioned in this paper provides an accurate representation of material interfaces on geometrically nonconforming simple Cartesian grids and achieves the same level of accuracy as the finite element method with two orders of magnitude fewer unknowns.
References
More filters
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.
Related Papers (5)
High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
The Explicit-Jump Immersed Interface Method: Finite Difference Methods for PDEs with Piecewise Smooth Solutions
Andreas Wiegmann,Kenneth P. Bube +1 more
the immersed interface method for elliptic equations with discontinuous coefficients and singular sources
Randall J. LeVeque,Zhilin Li +1 more