Advanced FEM analysis of optical waveguides: algorithms and applications

Schmidt, Frank; Burger, Sven; Pomplun, Jan; Zschiedrich, Lin

doi:10.1117/12.765720

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…The choice of the three field components from the six components of the vectors ⃗ 𝐸 and ⃗ 𝐻 can be done in different ways, which leads to different formulations of the problem. A. N. Bogolyubov and T. V. Edakina [5,6] and Frank Schmidt [7,8] used the components of vector ⃗ 𝐻, in the papers by E. Lezar and D. Davidson [9] vector ⃗ 𝐸 was used, A. L. Delitsyn [10][11][12][13] formulated the problem in terms of 𝐻 𝑥 , 𝐻 𝑦 , 𝐸 𝑧 . Normal modes of an axially symmetric waveguide with a dielectric core were considered by N. A. Novoselova, S. B. Raevsky and A.…”

Section: Introductionmentioning

confidence: 99%

On a dispersion curve of a waveguide filled with inhomogeneous substance

Kroytor

Malykh

2022

Discrete and Continuous Models

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The paper discusses the relationship between the modes traveling along the axis of the waveguide and the standing modes of a cylindrical resonator, and shows how this relationship can be explored using the Sage computer algebra system. In this paper, we study this connection and, on its basis, describe a new method for constructing the dispersion curve of a waveguide with an optically inhomogeneous filling. The aim of our work was to find out what computer algebra systems can give when calculating the points of the waveguide dispersion curve. Our method for constructing the dispersion curve of a waveguide with optically inhomogeneous filling differs from those proposed earlier in that it reduces this problem to calculating the eigenvalues of a self-adjoint matrix, i.e., a well-studied problem. The use of a selfadjoint matrix eliminates the occurrence of artifacts associated with the appearance of a small imaginary addition to the eigenvalues. We have composed a program in the Sage computer algebra system that implements this method for a rectangular waveguide with rectangular inserts and tested it on SLE modes. The obtained results showed that the program successfully copes with the calculation of the points of the dispersion curve corresponding to the hybrid modes of the waveguide, and the points found fit the analytical curve with graphical accuracy even when with a small number of basis elements taken into account.

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Section: Introductionmentioning

confidence: 99%

On a dispersion curve of a waveguide filled with inhomogeneous substance

Kroytor

Malykh

2022

Discrete and Continuous Models

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“…The choice of these three components from the set of six components of the vectors ⃗ and ⃗ can be different, which leads to different formulations of the problem. A. N. Bogolyubov and T. V. Edakina [6] and Frank Schmidt [12], [13] used the components of the vector ⃗ , E. Lezar and D. Davidson [14] working in the framework of the FEniCS Project used the components of the vector ⃗ , A. L. Delitsyn [15]- [17] used the components , , . Normal modes of an axially symmetric waveguide with a dielectric core were considered by N.A.…”

Section: Introductionmentioning

confidence: 99%

“…It is not clear how precisely these conditions are approximated in published papers. In papers on optical waveguides [6], [12], [13] the authors assume that the field is zero on the walls. From a physical point of view, this assumption is very reasonable, but unfortunately it leads to a conflict with Müller's theorem on a field equal to zero on an element of an analytic surface [28].…”

Section: Introductionmentioning

confidence: 99%

Calculation of the normal modes of closed waveguides

Malykh

Divakov

Egorov

et al. 2020

Discrete and Continuous Models

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The aim of the work is the development of numerical methods for solving waveguiding problems of the theory of waveguides, as well as their implementation in the form of software packages focused on a wide range of practical problems from the classical issues of microwave transmission to the design of optical waveguides and sensors. At the same time, we strive for ease of implementation of the developed methods in computer algebra systems (Maple, Sage) or in software oriented to the finite element method (FreeFem++). The work uses the representation of electromagnetic fields in a waveguide using four potentials. These potentials do not reduce the number of sought functions, but even in the case when the dielectric permittivity and magnetic permeability are described by discontinuous functions, they turn out to be quite smooth functions. A simple check of the operability of programs by calculating the normal modes of a hollow waveguide is made. It is shown that the relative error in the calculation of the first 10 normal modes does not exceed 4%. These results indicate the efficiency of the method proposed in this article.

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