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Schürmann, H.W. & Serov, V. Eur. Phys. J. D (2019) 73: 204.

Guided TE-waves in a slab structure with lossless cubic nonlinear dielectric and magnetic material : parameter dependence and power flow with focus on metamaterials

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Author: Schürmann, Hans Werner1; Serov, Valery2
Organizations: 1Department of Physics, University of Osnabrück, Osnabrück, Germany
2Department of Mathematical Sciences, University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1.2 MB)
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Language: English
Published: Springer Nature, 2019
Publish Date: 2019-10-23


The parameter dependence and power flow of guided TE-waves in a lossless cubic nonlinear, dielectric, magnetic planar three-layer structure is studied as follows. Using a travelling wave ansatz with stationary amplitude, Maxwell’s equations are transformed to a system of ordinary nonlinear differential equations. The solutions of the system are presented compactly (in terms of hyperbolic and elliptic functions).The nonnegative and bounded (“physical”) solutions are determined by using a phase diagram condition (PDC) that is applied to express the continuity (transmission) conditions at the interfaces leading to the dispersion relation (DR).Based on the PDC, the parameter dependence and stability of the solutions to the DR and corresponding power flow are studied numerically for permittivities and permeabilities that may be appropriate to describe metamaterial.

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Series: The European physical journal. D, Atomic, molecular, optical and plasma physics
ISSN: 1434-6060
ISSN-E: 1434-6079
ISSN-L: 1434-6060
Volume: 73
Issue: 9
Article number: 204
DOI: 10.1140/epjd/e2019-100258-y
Type of Publication: A1 Journal article – refereed
Field of Science: 114 Physical sciences
Funding: Open access funding provided by University of Oulu including Oulu University Hospital.
Copyright information: © The Author(s) 2019. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.