Numerical solution of the problem of propagation of TM-polarized electromagnetic waves in a nonlinear two-layered dielectric cylindrical waveguide

Smolkin, Eugene; Валовик, Д. В.

doi:10.1109/mmet.2012.6331288

Cited by 16 publications

(2 citation statements)

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“…A background study concerning nonlinear guided waves in media with Kerr and Kerr-like nonlinearities can be found in [14,15,20,24]. In papers [16,17,18,19,21,22] numerical study in layered nonlinear dielectric and metal-dielectric waveguides is performed. Numerical results are obtained with the help of a version of the shooting method (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Propagation of Leaky Te-Polarized Electromagnetic Waves in a Metamaterial Goubau Line

Smolkin

Smirnov

2021

Mathematical Modelling and Analysis

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Propagation of leaky TE-polarized electromagnetic waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear metamaterial medium is studied. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Propagation of Leaky Te-Polarized Electromagnetic Waves in a Metamaterial Goubau Line

Smolkin

Smirnov

2021

Mathematical Modelling and Analysis

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“…A background study concerning nonlinear guided waves in media with Kerr and Kerr‐like nonlinearities can be found in Smirnov and Smolkin (2018), Smolkin and Shestopalov (2017), Smolkin and Valovik (2015), and Smirnov et al (2019). In papers (Smirnov et al, 2014; Smolkin, 2017; Smolkin et al, 2017; Smolkin & Shestopalov, 2015; Smolkin & Valovik, 2012) numerical study of the surface wave propagation in layered nonlinear dielectric and metal‐dielectric waveguides is performed. Numerical results are obtained with the help of a version of the shooting method (see, e.g., Smirnov et al, 2014; Smolkin & Valovik, 2013).…”

Section: Introductionmentioning

confidence: 99%

Surface Waves in a Nonlinear Metamaterial Rod

2020

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We consider propagation of surface Transverse Electric (TE) waves in a rod filled with nonlinear metamaterial medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear surface TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.

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Coupled electromagnetic transverse-electric–transverse magnetic wave propagation in a cylindrical waveguide with Kerr nonlinearity

Smirnov

Валовик

2013

Journal of Mathematical Physics

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Nonlinear coupled electromagnetic TE-TM wave propagation in a cylindrical nonlinear dielectric waveguide with circular cross section is considered. Nonlinearity inside the waveguide is described by Kerr law. Physical problem is reduced to a nonlinear two-parameter eigenvalue problem for a system of (nonlinear) ordinary differential equations. It is proved that TE and TM waves that form (nonlinear) coupled TE-TM wave can propagate at different frequencies ωE and ωM, respectively. It is shown that nonlinear coupled TE-TM wave propagates at different frequencies ωE, ωM and with different propagation constants γE, γM in the waveguide. Frequencies ωE, ωM can be chosen independently. Existence of coupled surface TE-TM waves is proved. Intervals of localization of coupled eigenvalues (γE, γM) are found.

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Numerical solution of the problem of propagation of TM-polarized electromagnetic waves in a nonlinear two-layered dielectric cylindrical waveguide

Cited by 16 publications

References 1 publication

Nonlinear Propagation of Leaky Te-Polarized Electromagnetic Waves in a Metamaterial Goubau Line

Nonlinear Propagation of Leaky Te-Polarized Electromagnetic Waves in a Metamaterial Goubau Line

Surface Waves in a Nonlinear Metamaterial Rod

Coupled electromagnetic transverse-electric–transverse magnetic wave propagation in a cylindrical waveguide with Kerr nonlinearity

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