Integral Equation Approach for the Propagation of TE-Waves in a Nonlinear Dielectric Cylindrical Waveguide

Smirnov, Yury; Schürmann, H. W.; Shestopalov, Yury

doi:10.2991/jnmp.2004.11.2.10

Cited by 38 publications

(20 citation statements)

References 9 publications

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“…Constant C 1 is assumed to be known, and the constant C 2 is determined using transmission conditions (6).…”

Section: Dispersion Equationmentioning

confidence: 99%

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Propagation of TE waves in a double-layer nonlinear inhomogeneous cylindrical waveguide

Smolkin

2014

Proceedings of the International Conference Days on Diffraction 2014

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The problem of propagation of monochromatic electromagnetic TE waves in a double-layer cylindrical dielectric waveguide filled with nonlinear inhomogeneous medium is considered. The physical problem is reduced to solving a nonlinear transmission eigenvalue problem for ordinary differential equation. Eigenvalues of the problem are the propagation constants of the waveguide. The paper proposes a method to determine approximate eigenvalues of the nonlinear problem. This method is based on solving an auxiliary Cauchy problem (the shooting method). Existence of the eigenvalues, which correspond to a new propagation regime, is predicted. A comparison with the linear case is given.

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“…Constant C 1 is assumed to be known, and the constant C 2 is determined using transmission conditions (6).…”

Section: Dispersion Equationmentioning

confidence: 99%

“…Using the transmission condition on the boundary ρ = R 2 (see (6)) and the solutions ρ > R 2 (see (7)) we obtain…”

Section: Consider the Functionmentioning

confidence: 99%

Propagation of TE waves in a double-layer nonlinear inhomogeneous cylindrical waveguide

Smolkin

2014

Proceedings of the International Conference Days on Diffraction 2014

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“…To the best of our knowledge, the first rigorous study of polarized electromagnetic wave propagation in a nonlinear circle cylindrical dielectric homogeneous waveguide is in [7,8]. Then, there were several works, where some important cases for nonlinear but homogeneous permittivity have been investigated; see [9][10][11][12]. The next step was to apply earlier developed technique to the cases of multilayered waveguides and inhomogeneous nonlinear permittivity.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Double-Layer Bragg Waveguide: Analytical and Numerical Approaches to Investigate Waveguiding Problem

Smirnov

Smolkin

Валовик

2014

Advances in Numerical Analysis

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The paper is concerned with propagation of surface TE waves in a circular nonhomogeneous two-layered dielectric waveguide filled with nonlinear medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function. The existence of propagating TE waves for chosen nonlinearity (the Kerr law) is proved using the contraction mapping method. Conditions under which k waves can propagate are obtained, and intervals of localization of the corresponding propagation constants are found. For numerical solution of the problem, a method based on solving an auxiliary Cauchy problem (the shooting method) is proposed. In numerical experiment, two types of nonlinearities are considered and compared: the Kerr nonlinearity and nonlinearity with saturation. New propagation regime is found.

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“…Some numerical results are shown in [7]. The article [8] is devoted to strict mathematical results about the problem (solvability, existence of the solution, etc. ).…”

Section: Introductionmentioning

confidence: 99%

“…Propagation of TE-waves in a nonlinear dielectric waveguide was considered in [7,8] by Yu. G. Smirnov, H.-W. Shurmann and Yu.…”

Section: Introductionmentioning

confidence: 99%

Boundary Eigenvalue Problem for Maxwell Equations in a Nonlinear Dielectric Layer

Smirnov¹,

Валовик²

2010

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The propagation of TM-polarized electromagnetic waves in a dielectric layer filled with lossless, nonmagnetic, and isotropic medium is considered. The permittivity in the layer defines by Kerr law. We look for eigenvalues of the problem and reduce the issue to the analysis of the corresponding dispersion equation. The equivalence of the boundary eigenvalue problem and the dispersion equation is proved. We show that the solution of the problem exists and from dispersion equation it can be numerically obtained. Using this solution the components of electromagnetic field in the layer can be numerically obtained as well. Transition to the limit in the case of a linear medium in the layer is proved. Some numerical results are presented also.

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Integral Equation Approach for the Propagation of TE-Waves in a Nonlinear Dielectric Cylindrical Waveguide

Cited by 38 publications

References 9 publications

Propagation of TE waves in a double-layer nonlinear inhomogeneous cylindrical waveguide

Propagation of TE waves in a double-layer nonlinear inhomogeneous cylindrical waveguide

Nonlinear Double-Layer Bragg Waveguide: Analytical and Numerical Approaches to Investigate Waveguiding Problem

Boundary Eigenvalue Problem for Maxwell Equations in a Nonlinear Dielectric Layer

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