Guided Electromagnetic Waves Propagating in a Two-Layer Cylindrical Dielectric Waveguide with Inhomogeneous Nonlinear Permittivity

Smolkin, Eugene; Валовик, Д. В.

doi:10.1155/2015/614976

Cited by 32 publications

(11 citation statements)

References 18 publications

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“…Using Propositions 1 and 2, it can be shown (see Smolkin & Valovik, 2015) that the following theorems hold.…”

Section: Proposition 1 Under the Conditionmentioning

confidence: 98%

“…It can be shown (see Smolkin & Valovik, 2015) that the following assertions are valid, which will be used below.…”

Section: Consider the Cubic Equation ||N||xmentioning

confidence: 99%

“…From the results of Smolkin and Valovik (2015) it follows that the nonlinear operator

S (u) : = \int_{0}^{r} N (ρ, s; λ) u^{3} (ρ) d ρ + f (s),

where

N false(ρ, s; λ false) : = - α ρ G false(ρ, s; λ false)

is completely continuous on each bounded subset of C [0, r ].…”

Section: Nonlinear Integral Equationmentioning

confidence: 99%

“…Consider the cubic equation

false‖ normalN false‖ x^{3} + false‖ f false‖ = x

, where

‖ N ‖ = \max_{s \in [0, r]} \int_{0}^{r} |N (ρ, s)| d ρ and ‖f‖ = \max_{s \in [0, r]} |f (s)| .

It can be shown (see Smolkin & Valovik, 2015) that the following assertions are valid, which will be used below.…”

Section: Nonlinear Integral Equationmentioning

confidence: 99%

“…This framework has not been addressed in the literature, to the best of our knowledge. 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.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Using Propositions 1 and 2, it can be shown (see Smolkin & Valovik, 2015) that the following theorems hold.…”

Section: Proposition 1 Under the Conditionmentioning

confidence: 98%

“…It can be shown (see Smolkin & Valovik, 2015) that the following assertions are valid, which will be used below.…”

Section: Consider the Cubic Equation ||N||xmentioning

confidence: 99%

“…From the results of Smolkin and Valovik (2015) it follows that the nonlinear operator