A local boundary condition coupled to a finite element method to compute guided modes of optical fibres under the weak guidance assumptions

Abstract

An efficient method coupling a local boundary condition to a finite element technique is proposed to compute guided modes of optical fibres under the weak guidance assumptions. This method is designed to provide accurate solutions for optical fibres with no restriction on their shape as well as on their refractive index profile. Several numerical experiments are performed to demonstrate this point. Copyright © 2000 John Wiley & Sons, Ltd.

Construction of local boundary conditions for an eigenvalue problem using micro-local analysis: application to optical waveguide problems

“…We have accomplished such analysis in Section 4.2 and have showed that the corresponding solutions have the same properties as the solutions of the original problem (the eigenvalue problem set in R 2 ). From the numerical point of view, these two conditions are (a) easy to implement in any finite element code since they requires only additional mass-like matrices on the artificial boundary (see Section 5.1), and (b) more versatile than the boundary condition suggested in [11] because they are applicable to any convex geometry of the artificial boundary. Consequently, for non-circular-shaped cores, it is expected that these conditions allow smaller computational domains and then, lead to better computational efficiencies.…”

“…Given that, solving the variational problem (11) and (12) consists in solving the following quadratic eigenvalue problem…”

“…However, these higher order conditions are not of practical interest because their expressions contain the eigenvalue k R with negative powers [3]. • Second, in the case where R is a circle, the condition (8 and 9) is identical to the one proposed in [11]. However, the requirement of a circular-shaped artificial boundary R often leads to a larger than needed computational domain, which hampers computational efficiency.…”

Construction of local boundary conditions for an eigenvalue problem using micro-local analysis: application to optical waveguide problems

“…We have accomplished such analysis in Section 4.2 and have showed that the corresponding solutions have the same properties as the solutions of the original problem (the eigenvalue problem set in R 2 ). From the numerical point of view, these two conditions are (a) easy to implement in any finite element code since they requires only additional mass-like matrices on the artificial boundary (see Section 5.1), and (b) more versatile than the boundary condition suggested in [11] because they are applicable to any convex geometry of the artificial boundary. Consequently, for non-circular-shaped cores, it is expected that these conditions allow smaller computational domains and then, lead to better computational efficiencies.…”

“…Given that, solving the variational problem (11) and (12) consists in solving the following quadratic eigenvalue problem…”

“…However, these higher order conditions are not of practical interest because their expressions contain the eigenvalue k R with negative powers [3]. • Second, in the case where R is a circle, the condition (8 and 9) is identical to the one proposed in [11]. However, the requirement of a circular-shaped artificial boundary R often leads to a larger than needed computational domain, which hampers computational efficiency.…”

Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides

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Construction of local boundary conditions for an eigenvalue problem using micro-local analysis: application to optical waveguide problems

“…We have accomplished such analysis in Section 4.2 and have showed that the corresponding solutions have the same properties as the solutions of the original problem (the eigenvalue problem set in R 2 ). From the numerical point of view, these two conditions are (a) easy to implement in any finite element code since they requires only additional mass-like matrices on the artificial boundary (see Section 5.1), and (b) more versatile than the boundary condition suggested in [11] because they are applicable to any convex geometry of the artificial boundary. Consequently, for non-circular-shaped cores, it is expected that these conditions allow smaller computational domains and then, lead to better computational efficiencies.…”

“…Given that, solving the variational problem (11) and (12) consists in solving the following quadratic eigenvalue problem…”

“…However, these higher order conditions are not of practical interest because their expressions contain the eigenvalue k R with negative powers [3]. • Second, in the case where R is a circle, the condition (8 and 9) is identical to the one proposed in [11]. However, the requirement of a circular-shaped artificial boundary R often leads to a larger than needed computational domain, which hampers computational efficiency.…”

Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides

“……”

“……”

Construction of local boundary conditions for an eigenvalue problem using micro-local analysis: application to optical waveguide problems

“…We have accomplished such analysis in Section 4.2 and have showed that the corresponding solutions have the same properties as the solutions of the original problem (the eigenvalue problem set in R 2 ). From the numerical point of view, these two conditions are (a) easy to implement in any finite element code since they requires only additional mass-like matrices on the artificial boundary (see Section 5.1), and (b) more versatile than the boundary condition suggested in [11] because they are applicable to any convex geometry of the artificial boundary. Consequently, for non-circular-shaped cores, it is expected that these conditions allow smaller computational domains and then, lead to better computational efficiencies.…”

“…Given that, solving the variational problem (11) and (12) consists in solving the following quadratic eigenvalue problem…”

“…However, these higher order conditions are not of practical interest because their expressions contain the eigenvalue k R with negative powers [3]. • Second, in the case where R is a circle, the condition (8 and 9) is identical to the one proposed in [11]. However, the requirement of a circular-shaped artificial boundary R often leads to a larger than needed computational domain, which hampers computational efficiency.…”

Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides

“……”

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