Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cutoff

Hewlett, S. J.; Ladouceur, François

doi:10.1109/50.372431

Cited by 58 publications

(21 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This type of grid growth is particularly suitable for a modal analysis of an optical waveguide, because the region with a large field amplitude, which predominates the accuracy, is densely discretized, while the region with a small field amplitude is coarsely discretized. Equation (2) has been successfully used for the eigenmode analysis of optical waveguides [32], [33].…”

Section: A Computational Space Methods (Csm)mentioning

confidence: 99%

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Shibayama

Matsubara²,

Sekiguchi³

et al. 1999

J. Lightwave Technol.

View full text Add to dashboard Cite

Abstract-Efficient nonuniform schemes, based on the generalized Douglas (GD) scheme, are developed for the finite-difference beam propagation method (FD-BPM). For a two-dimensional (2-D) problem, two methods are presented: a computational space method and a physical space method. In the former, the GD scheme is employed, after replacing a nonuniform grid in the physical space with a uniform one in the computational space. In the latter, the GD scheme is directly extended to a nonuniform grid in the physical space. We apply these two methods to paraxial and wide-angle FD-BPM's. The fourth-order accuracy is achieved in the transverse direction, provided that the grid growth factor between two adjacent grids is r = 1 + O(1x). For the paraxial BPM, the reduction in the truncation error is demonstrated through modal calculations of a graded-index waveguide using an imaginary distance procedure. For the wide-angle BPM, the propagating field in a tilted waveguide is analyzed to show the effectiveness of the present scheme. As an application of the physical space method, an adaptive grid is introduced into the multistep method.Index Terms-Finite-difference methods, optical beam propagation, optical waveguides.

show abstract

Section: A Computational Space Methods (Csm)mentioning

confidence: 99%

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Shibayama

Matsubara²,

Sekiguchi³

et al. 1999

J. Lightwave Technol.

View full text Add to dashboard Cite

show abstract

“…We have not performed an extensive search for an optimum transform in terms of accuracy or convergence performance. Rather, our choice was motivated by its easy implementation with Fourier expansion techniques and has been inspired by an earlier work 17 on the use of Fourier series for calculating bounded modes of rectangular core waveguides under the scalar-wave approximation with real nonlinear transforms. The chosen coordinate transform X = F͑xЈ͒ is given in Appendix A.…”

Section: Implementation With Fourier-modal Expansion Techniquesmentioning

confidence: 99%

Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization

2005

View full text Add to dashboard Cite

A modified formulation of Maxwell's equations is presented that includes a complex and nonlinear coordinate transform along one or two Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow one to map an infinite space to a finite space and to specify graded perfectly matched absorbing boundaries that allow the outgoing wave condition to be satisfied. The approach is validated by numerical results obtained by using Fourier-modal methods and shows enhanced convergence rate and accuracy.

show abstract

“…In addition, the present method can be directly applied to simulate this coupler without using effective index method [5]. In dealing with the boundary conditions, a tangent-type function [6], [7] is applied to map the infinite plane into a unit square. As a result, the artificial boundary conditions [8], [9] are eliminated.…”

Section: Introductionmentioning

confidence: 99%

Simulation of symmetric directional coupler with optical rib waveguide using 3D-BPM based on the Galerkin method

Xiao

Sun

Zhang

2001

Fiber Optics and Optoelectronics for Network Applications

View full text Add to dashboard Cite

The symmetric directional coupler with optical rib waveguide is simulated using a novel three-dimensional beam propagation method (3D-BPM) based on the Galerkin method. The coupling ratio is as high as 99.4%. The matrix derived from the present method is small. Consequently, the calculation is efficient. A tangent-type function is applied to map the infinite region into a closed region. As a result, the artificial boundary conditions are eliminated.

show abstract

Fourier decomposition method applied to mapped infinite domains: scalar analysis of dielectric waveguides down to modal cutoff

Cited by 58 publications

References 10 publications

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods

Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization

Simulation of symmetric directional coupler with optical rib waveguide using 3D-BPM based on the Galerkin method

Contact Info

Product

Resources

About