Modeling Open Transitions of the “Horn” Type between Open Planar Waveguides

Divakov, D. V.; Sevastianov, Leonid A.; Nikolaev, N. E.

doi:10.1051/epjconf/201610802020

Cited by 5 publications

(4 citation statements)

References 2 publications

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“…We substitute this solution into (5) and perform the Galerkin method procedure [2]. As a result we obtain the mixed boundary value problem with respect to the desired Kantorovich coefficient functions V j (y, z) [3,5,6]:…”

Section: Introductionmentioning

confidence: 99%

Quasi-Vector Model of Propagation of Polarized Light in a Thin-Film Waveguide Lens

et al. 2018

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Abstract. Maxwell equations describe the propagation with diffraction of waveguide modes through a thin-film waveguide lens. If the radius of the thin-film lens is large, then the thickness of the lens varies slowly in the yz plane. For this case we propose the model, which is based on the assumption of a small change in the electromagnetic field in a direction y. Under this assumption the vector diffraction problem is reduced to a number of scalar diffraction problems. The solutions demonstrate the vector nature of the electromagnetic field, which allows us to call the proposed model a quasi-vector model.

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Section: Introductionmentioning

confidence: 99%

Quasi-Vector Model of Propagation of Polarized Light in a Thin-Film Waveguide Lens

et al. 2018

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“…The incomplete Galerkin method is a projection method for solving waveguide problems, which uses the Kantorovich decomposition to represent the approximate solution [8]. For description of the problem, Sveshnikov's partial radiation conditions are used [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…By applying the separation of variables method to the Helmholtz equation 8 waveguides accordingly [4][5][6]9]:…”

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confidence: 99%

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Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides

2018

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This paper describes the algorithm for the numerical solution of the diffraction problem of waveguide modes at the joint of two open planar waveguides. For planar structures under consideration, we can formulate a scalar diffraction problem, which is a boundary value problem for the Helmholtz equation with a variable coefficient in two-dimensional space. The eigenmode problem for an open three-layer waveguide is the Sturm-Liouville problem for a second-order operator with piecewise constant potential on the axis, where the potential is proportional to the refractive index. The described problem is singular and has a mixed spectrum and therefore the Galerkin method can not be used in this definition. One way to adapt the Galerkin method for the problem solution is to artificially limit the area, which is equivalent to placing the open waveguide in question in a hollow closed waveguide whose boundaries are remote from the real boundaries of the waveguide layer of the open waveguide. Thus, we obtain a diffraction problem on a finite interval and with a discrete spectrum, which can be solved by the projection method, as done in this paper.

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Numerical and Analytical Modeling of Guided Modes of a Planar Gradient Waveguide

Ayrjan

Gevorkyan

Kulyabov

et al. 2016

Communications in Computer and Information Science

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Modeling Open Transitions of the “Horn” Type between Open Planar Waveguides

Cited by 5 publications

References 2 publications

Quasi-Vector Model of Propagation of Polarized Light in a Thin-Film Waveguide Lens

Quasi-Vector Model of Propagation of Polarized Light in a Thin-Film Waveguide Lens

Algorithm for Numerical Solution of Diffraction Problem on the Joint of Two Open Three-Layer Waveguides

Numerical and Analytical Modeling of Guided Modes of a Planar Gradient Waveguide

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