University of Oulu

Hans Werner Schürmann, Valery Serov, Parameter dependence and stability of guided TE-waves in a lossless nonlinear dielectric slab structure, Optics Communications, Volume 426, 2018, Pages 110-118, ISSN 0030-4018,

Parameter dependence and stability of guided TE-waves in a lossless nonlinear dielectric slab structure

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Author: Schürmann, Hans Werner1; Serov, Valery2
Organizations: 1Department of Physics, University of Osnabrück, Germany
2Department of Mathematical Sciences, University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.8 MB)
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Language: English
Published: Elsevier, 2018
Publish Date: 2020-11-01


The nonlinear Schrödinger equation is the basis of the traditional stability analysis of nonstationary guided waves in a nonlinear three-layer slab structure. The stationary (independent of the propagation distance) solutions of the nonlinear Schrödinger equation are used as “initial data” in this analysis. In the present paper, we propose a method to investigate the dependence of these solutions on the experimental parameters and discuss their stability with respect to the parameters. The method is based on the phase diagram condition (PDC) and compact representation (in terms of Weierstrass’ elliptic function and its derivative) of the dispersion relation (DR). The problem’s parameters are constrained to certain regions in parameter space by the PDC. Dispersion curves inside (or at boundaries) of these regions correspond to possible physical solutions of Maxwell’s equations as ”start” solutions for a traditional stability analysis. Numerical evaluations of the PDC, DR, and power flow including their parameter dependence are presented.

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Series: Optics communications
ISSN: 0030-4018
ISSN-E: 1873-0310
ISSN-L: 0030-4018
Volume: 426
Pages: 110 - 118
DOI: 10.1016/j.optcom.2018.05.042
Type of Publication: A1 Journal article – refereed
Field of Science: 114 Physical sciences
Copyright information: © 2018 Elsevier B.V. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license