Semivectorial polarised finite difference method for optical waveguides with arbitrary index profiles

Stern, M.S.

doi:10.1049/ip-j.1988.0013

Cited by 181 publications

(99 citation statements)

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“…Moreover, it is observed that QSCM and FDM mode solver have the same convergence rate. However, with the same grid size, namely the same amount of computation effort, QSCM mode solver is more accurate than conventional FDM mode solver [4,5], however, it should be addressed that the current QSCM loses the advantage comparing to the improved finite difference method [7,10,11] where higher order boundary conditions are applied. The improved QSCM with higher order boundary conditions will be our future work.…”

Section: Verification Of Qsc Methodsmentioning

confidence: 99%

“…In the past decades, researchers have proposed and developed various numerical methods; among which the finite-difference method (FDM) and the finite element method (FEM) are two of the most popular approaches [2][3][4][5][6][7][8][9][10][11]. The finite difference method (FDM) gains its popularity owing to its simplicity and effectiveness [4][5][6][7][8][9][10][11]. On the other hand, the finite element method (FEM) is more adaptive for complex waveguide structures with irregular interfaces [2,3].…”

Section: Introductionmentioning

confidence: 99%

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Vector Mode Analysis of Optical Waveguides by Quadratic Spline Collocation Method

Mu¹,

Liang²,

Li³

et al. 2012

PIER M

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Abstract-We present an accurate, efficient numerical analysis for vector modes of dielectric optical waveguide structures with an arbitrary refractive index profile using a quadratic spline collocation method (QSCM). The unknown weights of the polynomials are determined by forcing the errors at the collocation points to be zero. Consequently, the original second order differential equation is converted to a set of algebraic equations which can be solved by matrix techniques. The proposed QSCM method demonstrates better performance than the standard finite-difference method of the same convergence rate in terms of grid size with the same degree of computational complexity.

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Section: Verification Of Qsc Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vector Mode Analysis of Optical Waveguides by Quadratic Spline Collocation Method

Mu¹,

Liang²,

Li³

et al. 2012

PIER M

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“…The first such approximate FD stencil was developed by Stern [1]. The 3−point FD approxi− mation proposed by Stern allowed for obtaining a good approximation for the field distributions and propagation constants if the discontinuities were placed half way be− tween the nodal points.…”

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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“…C ONSIDERABLE effort has been made to improve a finite-difference (FD) formula for the analysis of a step-index optical waveguide [1]- [4]. Pioneering work on a modified FD formula was carried out by Stern [1], who introduced the concept of a semivectorial mode.…”

Section: Introductionmentioning

confidence: 99%

“…Pioneering work on a modified FD formula was carried out by Stern [1], who introduced the concept of a semivectorial mode. This approach assumes that all the discontinuities of dielectric materials are either parallel or orthogonal to -and -axes, and that the fields are either -or -polarized.…”

Section: Introductionmentioning

confidence: 99%

Semivector Finite-Difference Formula for the Analysis of a Step-Index Waveguide With a Tilted Interface

Yamauchi

Harada

Kobori

et al. 2009

IEEE Photon. Technol. Lett.

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Abstract-A three-point finite-difference formula is derived for the analysis of a step-index waveguide with a tilted interface. The formula is suitable for the use of the alternating-direction implicit method. Through the analysis of a rib waveguide with a sloped side wall and a hollow triangular waveguide, improvement in accuracy and stability is demonstrated.Index Terms-Alternating-direction implicit method (ADIM), beam-propagation method (BPM), finite-difference (FD) formula.

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Semivectorial polarised finite difference method for optical waveguides with arbitrary index profiles

Cited by 181 publications

References 0 publications

Vector Mode Analysis of Optical Waveguides by Quadratic Spline Collocation Method

Vector Mode Analysis of Optical Waveguides by Quadratic Spline Collocation Method

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

Semivector Finite-Difference Formula for the Analysis of a Step-Index Waveguide With a Tilted Interface

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