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Smirnov, Y., Smolkin, E. & Shestopalov, Y. (2019). Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line. Radio Science, 54(1), 151-157
Open this publication in new window or tab >>Diffraction of a TE-Polarized Wave by a Nonlinear Goubau Line
2019 (English)In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 54, no 1, p. 151-157Article in journal (Refereed) Published
Abstract [en]

The diffraction of a cylindrical wave by a nonlinear metal-dielectric waveguide filled with nonlinear medium is considered. Two widely used types of nonlinearities (Kerr nonlinearity and nonlinearity with saturation) are considered. The problem is to find amplitudes of the reflected and the transmitted fields when the amplitude of the incident field is known. The analytical and numerical solution techniques are developed. Numerical results are presented. ©2019. American Geophysical Union. All Rights Reserved.

Place, publisher, year, edition, pages
Blackwell Publishing Ltd, 2019
Keywords
nonlinear waveguide, numerical method, TE polarization, the diffraction problem, Dielectric waveguides, Numerical methods, Analytical and numerical solutions, Diffraction problem, Kerr nonlinearity, Nonlinear metals, Nonlinear waveguides, Numerical results, TE polarizations, Transmitted field, Diffraction
National Category
Mathematics Other Engineering and Technologies
Identifiers
urn:nbn:se:hig:diva-30478 (URN)10.1029/2018RS006629 (DOI)000458731300012 ()2-s2.0-85060646358 (Scopus ID)
Projects
Largescale
Funder
Swedish Institute
Note

Funding agencies:

- Ministry of Education and Science of the Russian Federation Grant no. 1.894.2017/4.6

- University of Gavle, Sweden  

Available from: 2019-08-09 Created: 2019-08-09 Last updated: 2019-08-09Bibliographically approved
Shestopalov, Y., Smolkin, E. & Snegur, M. (2019). New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial. In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC): . Paper presented at URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India. New Dehli: IEEE, Article ID 8738241.
Open this publication in new window or tab >>New Propagation Regimes of TE Waves in a Waveguide filled with a Nonlinear Dielectric Metamaterial
2019 (English)In: 2019 URSI Asia-Pacific Radio Science Conference (AP-RASC), New Dehli: IEEE, 2019, article id 8738241Conference paper, Published paper (Refereed)
Abstract [en]

We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) metamaterial medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Place, publisher, year, edition, pages
New Dehli: IEEE, 2019
Keywords
dielectric waveguides, differential equations, eigenvalues and eigenfunctions, electromagnetic wave propagation, optical metamaterials, optical waveguides, new propagation regimes, TE waves, nonlinear dielectric metamaterial, circular metal-dielectric waveguide, nonlinear metamaterial medium, Kerr nonlinearity, nonlinear transmission eigenvalue problem, ordinary differential equation, eigenvalues, problem correspond, propagation constants, auxiliary Cauchy problem, Electromagnetic waveguides, Dielectrics, Permittivity, Metamaterials, Electromagnetics, Electromagnetic scattering
National Category
Electrical Engineering, Electronic Engineering, Information Engineering Mathematics
Identifiers
urn:nbn:se:hig:diva-30555 (URN)10.23919/URSIAP-RASC.2019.8738241 (DOI)2-s2.0-85068617892 (Scopus ID)978-908-25987-5-9 (ISBN)978-908-25987-4-2 (ISBN)978-1-5386-8551-8 (ISBN)
Conference
URSI AP-RASC 2019, 09 - 15 March 2019, New Delhi, India
Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-08-22Bibliographically approved
Shestopalov, Y., Smolkin, E. & Smirnov, Y. (2019). On the existence of the nonlinear leaky TE-polarized waves in a metal–dielectric cylindrical waveguide. Wave motion, 91, Article ID 102378.
Open this publication in new window or tab >>On the existence of the nonlinear leaky TE-polarized waves in a metal–dielectric cylindrical waveguide
2019 (English)In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 91, article id 102378Article in journal (Refereed) Published
Abstract [en]

We consider propagation of leaky waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green’s function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. Conditions under which a finite number of waves can propagate are obtained and the intervals of localization of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiments, two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation regimes are discovered.

Keywords
Goubau line, Leaky TE waves, Nonhomogeneous dielectric waveguide, Nonlinear permittivity, Numerical method
National Category
Physical Sciences
Identifiers
urn:nbn:se:hig:diva-30786 (URN)10.1016/j.wavemoti.2019.102378 (DOI)
Available from: 2019-10-14 Created: 2019-10-14 Last updated: 2019-10-14Bibliographically approved
Smolkin, E., Snegur, M. & Shestopalov, Y. (2018). Diffraction of TM Polarized EM Waves by a Nonlinear Inhomogeneous Dielectric Cylinder. In: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama): . Paper presented at 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 1-4 August 2018, Toyama, Japan (pp. 66-70).
Open this publication in new window or tab >>Diffraction of TM Polarized EM Waves by a Nonlinear Inhomogeneous Dielectric Cylinder
2018 (English)In: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, p. 66-70Conference paper, Published paper (Refereed)
Abstract [en]

In this work, we consider the diffraction of TM waves by a nonlinear inhomogeneous dielectric cylinder. Numerical experiments are carried out for the nonlinearity with saturation. The physical problem is reduced to solving a nonlinear boundary value problem for a system of ordinary differential equations. Numerical results are obtained using a modification of the shooting method which makes it possible to determine and plot the amplitude of the reflected field with respect to the amplitude of the incident field. Comparison between the nonlinear problem and the corresponding linear setting is performed.

Keywords
Electromagnetics, Optical waveguides, Nonhomogeneous media, Dielectrics, Electromagnetic scattering, Permittivity
National Category
Electrical Engineering, Electronic Engineering, Information Engineering Mathematics
Identifiers
urn:nbn:se:hig:diva-29194 (URN)10.23919/PIERS.2018.8598028 (DOI)000458673700007 ()2-s2.0-85060956964 (Scopus ID)978-4-88552-315-1 (ISBN)
Conference
2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 1-4 August 2018, Toyama, Japan
Funder
Swedish Institute
Note

Funding:

- RFBR 18-31-00109- University of Gävle

Available from: 2019-02-25 Created: 2019-02-25 Last updated: 2019-08-12Bibliographically approved
Shestopalov, Y., Smirnov, Y. & Smolkin, E. (2018). New Propagation Regimes of Symmetric Hybrid Waves in a Nonlinear Metal-Dielectric Waveguide. In: IET Conference Publications 2018: . Paper presented at 2018 12th European Conference on Antennas and Propagation (EUCAP), 9-13 April 2018, London, UK. Piscataway, New Jersey, USA: IEEE, CP741, Article ID 1570402136.
Open this publication in new window or tab >>New Propagation Regimes of Symmetric Hybrid Waves in a Nonlinear Metal-Dielectric Waveguide
2018 (English)In: IET Conference Publications 2018, Piscataway, New Jersey, USA: IEEE, 2018, Vol. CP741, article id 1570402136Conference paper, Published paper (Refereed)
Abstract [en]

The propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear metal-dielectric waveguide is considered. The physical setting is reduced to a transmission eigenvalue problem for a system of ordinary differential equations which is new type of nonlinear eigenvalue problem where spectral parameters are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Place, publisher, year, edition, pages
Piscataway, New Jersey, USA: IEEE, 2018
Series
IET Conference Publications ; CP741
Keywords
Nonlinear metal-dielectric waveguide, azimuthal symmetric hybrid waves, Maxwell equations, Cauchy problem
National Category
Other Mathematics
Identifiers
urn:nbn:se:hig:diva-28592 (URN)2-s2.0-85057322030 (Scopus ID)
Conference
2018 12th European Conference on Antennas and Propagation (EUCAP), 9-13 April 2018, London, UK
Available from: 2018-11-22 Created: 2018-11-22 Last updated: 2018-12-10Bibliographically approved
Smolkin, E., Snegur, M. & Shestopalov, Y. (2018). Nonlinear Hybrid Waves in a Cylindrical Anisotropic Metal-Dielectric Waveguide. In: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama): . Paper presented at 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 1-4 August 2018, Toyama, Japan (pp. 1948-1954).
Open this publication in new window or tab >>Nonlinear Hybrid Waves in a Cylindrical Anisotropic Metal-Dielectric Waveguide
2018 (English)In: 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 2018, p. 1948-1954Conference paper, Published paper (Refereed)
Abstract [en]

The propagation of hybrid waves in a cylindrical anisotropic nonlinear metal-dielectric waveguide is considered. The physical setting is reduced to a transmission eigenvalue problem for a system of ordinary differential equations which is new type of nonlinear eigenvalue problem where spectral parameters are the wave propagation constants. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Keywords
Electromagnetic waveguides, Electromagnetics, Eigenvalues and eigenfunctions, Mathematical model, Dielectrics, Electromagnetic scattering, Permittivity
National Category
Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:hig:diva-29191 (URN)10.23919/PIERS.2018.8597676 (DOI)000458673700357 ()2-s2.0-85060952276 (Scopus ID)978-4-88552-315-1 (ISBN)
Conference
2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), 1-4 August 2018, Toyama, Japan
Funder
Swedish Institute
Note

Funding:

- University of Gävle- RFBR 18-31-00109 

Available from: 2019-02-25 Created: 2019-02-25 Last updated: 2019-08-12Bibliographically approved
Shestopalov, Y., Smolkin, E. & Snegur, M. (2018). Numerical Study of Multilayer Nonlinear Inhomogeneous Goubau Lines. In: Proceedings of the 2018 International Conference on Electromagnetics in Advanced Application (ICEAA): . Paper presented at 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), September 10-14, 2018, Cartagena de Indias, Colombia (pp. 126-129). Piscataway, New Jersey, USA: IEEE conference proceedings, Article ID 8520464.
Open this publication in new window or tab >>Numerical Study of Multilayer Nonlinear Inhomogeneous Goubau Lines
2018 (English)In: Proceedings of the 2018 International Conference on Electromagnetics in Advanced Application (ICEAA), Piscataway, New Jersey, USA: IEEE conference proceedings, 2018, p. 126-129, article id 8520464Conference paper, Published paper (Refereed)
Abstract [en]

We consider propagation of surface TE waves in a circular metal-dielectric waveguide filled with nonlinear (Kerr nonlinearity) multilayered inhomogeneous medium. Analysis is reduced to solving a nonlinear transmission eigenvalue problem for an ordinary differential equation; eigenvalues of the problem correspond to propagation constants of the waveguide. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Place, publisher, year, edition, pages
Piscataway, New Jersey, USA: IEEE conference proceedings, 2018
National Category
Other Mathematics
Identifiers
urn:nbn:se:hig:diva-28587 (URN)10.1109/ICEAA.2018.8520464 (DOI)2-s2.0-85057425398 (Scopus ID)978-1-5386-6763-7 (ISBN)978-1-5386-6762-0 (ISBN)978-1-5386-6761-3 (ISBN)
Conference
2018 International Conference on Electromagnetics in Advanced Application (ICEAA), September 10-14, 2018, Cartagena de Indias, Colombia
Available from: 2018-11-22 Created: 2018-11-22 Last updated: 2018-12-10Bibliographically approved
Smirnov, Y., Smolkin, E. & Shestopalov, Y. (2018). On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular metal-dielectric waveguide filled with nonlinear radially inhomogeneous medium. Journal Electromagnetic Waves and Applications, 32(11), 1389-1408
Open this publication in new window or tab >>On the existence of non-polarized azimuthal-symmetric electromagnetic waves in circular metal-dielectric waveguide filled with nonlinear radially inhomogeneous medium
2018 (English)In: Journal Electromagnetic Waves and Applications, ISSN 0920-5071, E-ISSN 1569-3937, Vol. 32, no 11, p. 1389-1408Article in journal (Refereed) Published
Abstract [en]

Propagation of monochromatic nonlinear symmetric hybrid waves in a cylindrical nonlinear inhomogeneous metal–dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations where spectral parameters are the wave propagation constants. The setting under study is reduced to a new type of nonlinear eigenvalue problem. An analytical method for solving this problem is elaborated. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Place, publisher, year, edition, pages
Taylor & Francis, 2018
Keywords
Goubau line, Kerr nonlinearity, Maxwell’s equations, non-polarized azimuthal-symmetric electromagnetic waves, nonlinear inhomogeneous waveguide, numerical method, two-parameter eigenvalue problem, Circular waveguides, Control nonlinearities, Dielectric waveguides, Differential equations, Electromagnetic wave polarization, Electromagnetic waves, Maxwell equations, Nonlinear equations, Numerical methods, Ordinary differential equations, Problem solving, Wave propagation, Waveguides, Metal-dielectric waveguide, Nonlinear eigenvalue problem, Nonlinear inhomogeneous, Radially inhomogeneous medium, System of ordinary differential equations, Eigenvalues and eigenfunctions
National Category
Other Mathematics
Identifiers
urn:nbn:se:hig:diva-26209 (URN)10.1080/09205071.2018.1438929 (DOI)000433979500006 ()2-s2.0-85041931654 (Scopus ID)
Available from: 2018-03-06 Created: 2018-03-06 Last updated: 2018-06-25Bibliographically approved
Shestopalov, Y., Smolkin, E. & Kuzmina, E. (2018). Spectra of Nonselfadjoint Eigenvalue Problems for Elliptic Systems in Mathematical Models of the Wave Propagation in Open Waveguides. Lobachevskii Journal of Mathematics, 39(8), 1117-1129
Open this publication in new window or tab >>Spectra of Nonselfadjoint Eigenvalue Problems for Elliptic Systems in Mathematical Models of the Wave Propagation in Open Waveguides
2018 (English)In: Lobachevskii Journal of Mathematics, ISSN 1995-0802, E-ISSN 1818-9962, Vol. 39, no 8, p. 1117-1129Article in journal (Refereed) Published
Abstract [en]

Statements and analysis are presented of nonselfadjoint eigenvalue problems for ellipticequations and systems, including singular Sturm–Liouville problems on the line, that arise inmathematical models of the wave propagation in open metal-dielectric waveguides. Existence ofreal and complex spectra are proved and their distribution is investigated for canonical structurespossessing circular symmetry of boundary contours.

Place, publisher, year, edition, pages
New York: , 2018
Keywords
Wave propagation, singular, Sturm–Liouville, open waveguides, nonlinear media
National Category
Mathematics
Identifiers
urn:nbn:se:hig:diva-28006 (URN)10.1134/S1995080218080097 (DOI)000447747900008 ()2-s2.0-85055278125 (Scopus ID)
Available from: 2018-10-07 Created: 2018-10-07 Last updated: 2018-12-06Bibliographically approved
Shestopalov, Y., Smolkin, E. & Snegur, M. (2018). TE-polarized Wave Diffraction by a Cylinder Covered with Nonlinear Dielectric Layer. In: Proceedings of 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP): . Paper presented at 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 5-8 August 2018, Auckland, New Zealand (pp. 321-322).
Open this publication in new window or tab >>TE-polarized Wave Diffraction by a Cylinder Covered with Nonlinear Dielectric Layer
2018 (English)In: Proceedings of 2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 2018, p. 321-322Conference paper, Published paper (Refereed)
Abstract [en]

The problem of diffraction of TE polarized EM waves by an open dielectric waveguide with a nonlinear inhomogeneous filling is under consideration. In such problems a nonlinear eigenvalue problem for a system of differential equations is arised. For the numerical solution a method based on the solution of the auxillary Cauchy problem is proposed. Numerical results are presented.

Keywords
Diffraction, Dielectrics, Electromagnetic waveguides, Nonhomogeneous media, Mathematical model, Electromagnetic scattering
National Category
Electrical Engineering, Electronic Engineering, Information Engineering Mathematics
Identifiers
urn:nbn:se:hig:diva-28698 (URN)10.1109/APCAP.2018.8538309 (DOI)2-s2.0-85059361999 (Scopus ID)978-1-5386-5649-5 (ISBN)978-1-5386-5648-8 (ISBN)978-1-5386-5647-1 (ISBN)
Conference
2018 IEEE Asia-Pacific Conference on Antennas and Propagation (APCAP), 5-8 August 2018, Auckland, New Zealand
Available from: 2018-11-28 Created: 2018-11-28 Last updated: 2019-02-25Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-0168-0282

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