Abstract:
The problem of plane monochromatic TM waves propagating in a layer with an arbitrary nonlinearity is considered. The layer is placed between two semi-infinite media. Surface waves propagating along the material interface are sought. The physical problem is reduced to solving a nonlinear eigenvalue transmission problem for a system of two ordinary differential equations. A theorem on the existence and localization of at least one eigenvalue is proven. On the basis of this theorem, a method for finding approximate eigenvalues of the considered problem is proposed. Numerical results for Kerr and saturation nonlinearities are presented as examples.
Key words:
nonlinear eigenvalue transmission problem, Maxwell equations, Cauchy problem, approximate method for computation of eigenvalues.
Citation:
D. V. Valovik, E. V. Zarembo, “The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for TM waves propagating in a layer with arbitrary nonlinearity”, Zh. Vychisl. Mat. Mat. Fiz., 53:1 (2013), 74–89; Comput. Math. Math. Phys., 53:1 (2013), 78–92
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\paper The method of cauchy problem for solving a nonlinear eigenvalue transmission problem for TM waves propagating in a layer with arbitrary nonlinearity
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2013
\vol 53
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\jour Comput. Math. Math. Phys.
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\vol 53
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Linking options:
https://www.mathnet.ru/eng/zvmmf9796
https://www.mathnet.ru/eng/zvmmf/v53/i1/p74
This publication is cited in the following 12 articles:
Valeria Martynova, Dmitry Valovik, “Nonlinearized nonlinear electromagnetic guided waves in a circle cylindrical waveguide filled with nonlinear dielectric medium”, Journal of Differential Equations, 367 (2023), 804
Tohfeh M., Rajaei L., Miraboutalebi S., Matin L.F., “Transmission of Electromagnetic Waves Through a Nonlinear Over-Dense Plasma Slab”, J. Theor. Appl. Phys., 14:4 (2020), 349–357
M. A. Moskaleva, “Ob obosnovanii chislennogo metoda resheniya nekotorykh nelineinykh zadach na sobstvennye znacheniya teorii volnovodov”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2018, no. 4, 39–49
E. Smolkin, Yu. Shestopalov, “Nonlinear Goubau line: analytical-numerical approaches and new propagation regimes”, J. Electromagn. Waves Appl., 31:8 (2017), 781–797
I. S. Panyaev, D. G. Sannikov, “Dispersive properties of optical tm-type surface polaritons at a nonlinear semiconductor-nanocomposite (blig/ggg) interface”, J. Opt. Soc. Am. B-Opt. Phys., 33:2 (2016), 220–229
E. A. Marennikova, “Zadacha na sobstvennye znacheniya, opisyvayuschaya rasprostranenie elektromagnitnykh TE-voln v ploskom dielektricheskom volnovode, zapolnennom nelineinoi neodnorodnoi sredoi”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2015, no. 3, 72–87
Yury G. Smirnov, Eugenii Yu. Smol'kin, Dmitry V. Valovik, “Nonlinear Double-Layer Bragg Waveguide: Analytical and Numerical Approaches to Investigate Waveguiding Problem”, Advances in Numerical Analysis, 2014 (2014), 1
E.A. Marennikova, Yu. G. Smirnov, D.V. Valovik, Proceedings of the International Conference Days on Diffraction 2014, 2014, 181
D. V. Valovik, Yu. G. Smirnov, E. Yu. Smol'kin, “Nonlinear transmission eigenvalue problem describing TE wave propagation in two-layered cylindrical dielectric waveguides”, Comput. Math. Math. Phys., 53:7 (2013), 973–983
D. V. Valovik, E. Yu. Smol'kin, “Calculation of the propagation constants of inhomogeneous nonlinear double-layer circular cylindrical waveguide by means of the cauchy problem method”, J. Commun. Technol. Electron., 58:8 (2013), 762–769
D. V. Valovik, E. A. Marennikova, Yu. G. Smirnov, “Nelineinaya zadacha sopryazheniya na sobstvennye znacheniya, opisyvayuschaya rasprostranenie elektromagnitnykh Te-voln v ploskom neodnorodnom nelineinom dielektricheskom volnovode”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2013, no. 2(26), 50–63
D. V. Valovik, E. A. Marennikova, Yu. G. Smirnov, “Nelineinaya zadacha sopryazheniya na sobstvennye znacheniya, opisyvayuschaya rasprostranenie elektromagnitnykh TE-voln v ploskom neodnorodnom nelineinom dielektricheskom volnovode”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2013, no. 2, 50–63
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