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

Divakov, D. V.; Malykh, M. D.; Sevastianov, Leonid A.; Sevastianov, Anton; Ayryan, Е. A.

doi:10.1051/epjconf/201817302007

Cited by 3 publications

(8 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This algorithm was implemented in the computer algebra system Maple [4,5,9,10]. In the algorithm there is a function of the accuracy problem of calculations.…”

Section: Solution Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Symbolic-Numeric Computation of the Eigenvalues and Eigenfunctions of the Leaky Modes in a Regular Homogeneous Open Waveguide

2018

Self Cite

View full text Add to dashboard Cite

Abstract. In this paper the algorithm of finding eigenvalues and eigenfunctions for the leaky modes in a three-layer planar dielectric waveguide is considered. The problem on the eigenmodes of open three-layer waveguides is formulated as the Sturm-Liouville problem with the corresponding boundary and asymptotic conditions. In the case of guided and radiation modes of open waveguides, the Sturm-Liouville problem is formulated for self-adjoint second-order operators on the axis and the corresponding eigenvalues are real quantities for dielectric media. The search for eigenvalues and eigenfunctions corresponding to the leaky modes involves a number of difficulties: the boundary conditions for the leaky modes are not self-adjoint, so that the eigenvalues can turn out to be complex quantities. The problem of finding eigenvalues and eigenfunctions will be associated with finding the complex roots of the nonlinear dispersion equation. In the present paper, an original scheme based on the method of finding the minimum of a function of several variables is used to find the eigenvalues. The paper describes the algorithm for searching for eigenvalues, the algorithm uses both symbolic transformations and numerical calculations. On the basis of the developed algorithm, the dispersion relation for the weakly flowing mode of a three-layer open waveguide was calculated in the Maple computer algebra system.

show abstract

“…This algorithm was implemented in the computer algebra system Maple [4,5,9,10]. In the algorithm there is a function of the accuracy problem of calculations.…”

Section: Solution Algorithmmentioning

confidence: 99%

“…Applying the separation of variables method, we obtain the equation for the transverse and longitudinal parts [4][5][6][7][8][9]   2 2 2 2 0 0…”

Section: Introductionmentioning

confidence: 99%

Symbolic-Numeric Computation of the Eigenvalues and Eigenfunctions of the Leaky Modes in a Regular Homogeneous Open Waveguide

2018

Self Cite

View full text Add to dashboard Cite

show abstract

“…This waveguide has the same field representation as the given open waveguide in the area of the waveguiding layer. This fact allows the comparison of the reduced Galerkin's method of [1] with the current approach using Goos-Hanchen shifts. …”

Section: Numerical Results and Conclusionmentioning

confidence: 99%

“…Through the transformations of the Maxwell equations similar to [1], a waveguide problem is obtained for the Helmholtz equation with respect to the tangential component E y (x, z).…”

Section: Introductionmentioning

confidence: 99%

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

Divakov

Sevastianov

Nikolaev

2016

EPJ Web of Conferences

View full text Add to dashboard Cite

show abstract

“…The waveguide joint is the simplest model of waveguide transition, and therefore the description of the diffraction problem at the interface is similar to the definition of the problem for a waveguide transition [1][2][3]. The classical method for solving diffraction problems in closed waveguides is the so-called incomplete Galerkin method [4][5][6][7]. The incomplete Galerkin method is a projection method for solving waveguide problems, which uses the Kantorovich decomposition to represent the approximate solution [8].…”

Section: Introductionmentioning

confidence: 99%

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

2018

Self Cite

View full text Add to dashboard Cite

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.

show abstract

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

Cited by 3 publications

References 2 publications

Symbolic-Numeric Computation of the Eigenvalues and Eigenfunctions of the Leaky Modes in a Regular Homogeneous Open Waveguide

Symbolic-Numeric Computation of the Eigenvalues and Eigenfunctions of the Leaky Modes in a Regular Homogeneous Open Waveguide

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

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

Contact Info

Product

Resources

About