Fourth‐order accurate sub‐sampling for finite‐difference analysis of surface plasmon metallic waveguides

Hu, Bei; Sewell, P.; Wykes, J.; Vuković, Ana; Benson, T.M.

doi:10.1002/mop.23271

Cited by 5 publications

(2 citation statements)

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“…To numerically compute the guided fiber modes of a given refractive index profile, a transversal discretization concept has to be chosen [14]. This can be a local strategy such as a finite element [15] or a finite difference [16][17][18] approach for which a discretization i.e., mesh (either uniform or non-uniform) is used to linearize the differential operators in the corresponding wave equation(s). Afterward, a corresponding set of equations has to be solved.…”

Section: Introductionmentioning

confidence: 99%

Full-Vectorial Fiber Mode Solver Based on a Discrete Hankel Transform

Steinke

2021

Photonics

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It is crucial to be time and resource-efficient when enabling and optimizing novel applications and functionalities of optical fibers, as well as accurate computation of the vectorial field components and the corresponding propagation constants of the guided modes in optical fibers. To address these needs, a novel full-vectorial fiber mode solver based on a discrete Hankel transform is introduced and validated here for the first time for rotationally symmetric fiber designs. It is shown that the effective refractive indices of the guided modes are computed with an absolute error of less than 10−4 with respect to analytical solutions of step-index and graded-index fiber designs. Computational speeds in the order of a few seconds allow to efficiently compute the relevant parameters, e.g., propagation constants and corresponding dispersion profiles, and to optimize fiber designs.

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Section: Introductionmentioning

confidence: 99%

Full-Vectorial Fiber Mode Solver Based on a Discrete Hankel Transform

Steinke

2021

Photonics

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“…Fur− ther, the method of expanding field values at both sides of the discontinuity and matching them at the interface was used in for the derivation of the 5−point [5,10] and more recently even 7− and 9−point FD schemes [11]. The Chiou's et al ap− proach [5] was also extended to allow for the inclusion of the refractive index variation features on the scale much smaller than the grid size [12,13]. Also many 2 dimensional (2D) FD approximations used in the beam propagation method and modal solvers, to the best knowledge of the author with the exception only of [14][15][16] Even though there is a large body of the literature on the applications of FDs to the analysis of the optical wave propa− gation in discontinuous media, and the truncation errors were studied in many papers using either approximate methods or directly by comparing the calculated results with the known exact solution, there are no publications on the rigorous ana− lysis of the FD truncation error.…”

Section: Introductionmentioning

confidence: 99%

Accuracy of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities

Sujecki

2011

Opto-Electronics Review

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A rigorous truncation error analysis of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities is given. As the basis for the analysis we use the exact coefficients of the series that expresses the field value at a given finite difference node in terms of the field value and its derivatives at a neighbouring node. This series is applied to develop a rigorous formalism for the truncation error analysis of the three-point finite difference approximations used in the numerical modelling of light propagation in optical waveguides with step-wise discontinuities of the refractive index profile. The results show that the approximations reach O(h2) truncation error only asymptotically for sufficiently small values of the mesh size.

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