The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type

Dmitriy Divakov; Mikhail Malykh; Leonid Sevastianov; Anton Sevastianov; Anastasiia Tiutiunnik

doi:10.1117/12.2267902

14 April 2017 The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type

Dmitriy Divakov, Mikhail Malykh, Leonid Sevastianov, Anton Sevastianov, Anastasiia Tiutiunnik

Author Affiliations +

Proceedings Volume 10337, Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III; 103370G (2017) https://doi.org/10.1117/12.2267902
Event: Saratov Fall Meeting 2016: Fourth International Symposium on Optics and Biophotonics, 2016, Saratov, Russian Federation

Abstract

In the paper we construct a method for approximate solution of the waveguide problem for guided modes of an open irregular waveguide transition. The method is based on straightening of the curved waveguide boundaries by introducing new variables and applying the Kantorovich method to the problem formulated in the new variables to get a system of ordinary second-order differential equations. In the method, the boundary conditions are formulated by analogy with the partial radiation conditions in the similar problem for closed waveguide transitions.

The method is implemented in the symbolic-numeric form using the Maple computer algebra system. The coefficient matrices of the system of differential equations and boundary conditions are calculated symbolically, and then the obtained boundary-value problem is solved numerically using the finite difference method. The chosen coordinate functions of Kantorovich expansions provide good conditionality of the coefficient matrices. The numerical experiment simulating the propagation of guided modes in the open waveguide transition confirms the validity of the method proposed to solve the problem.

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Dmitriy Divakov, Mikhail Malykh, Leonid Sevastianov, Anton Sevastianov, and Anastasiia Tiutiunnik "The numerical-analytical implementation of the cross-sections method to the open waveguide transition of the "horn" type", Proc. SPIE 10337, Saratov Fall Meeting 2016: Laser Physics and Photonics XVII; and Computational Biophysics and Analysis of Biomedical Data III, 103370G (14 April 2017); https://doi.org/10.1117/12.2267902

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KEYWORDS

Waveguides

Computing systems

Matrices

Differential equations

Condition numbers

Finite difference methods

Wave propagation

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