Propagation of electromagnetic waves in an open planar dielectric waveguide filled with an nonlinear medium. I: TE waves

DOI10.1134/S0965542519060137zbMath1427.78023OpenAlexW2955037308WikidataQ127594808 ScholiaQ127594808MaRDI QIDQ2337151

Dmitry V. Valovik

Publication date: 19 November 2019

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542519060137

zbMATH Keywords

comparison theoremMaxwell's equationsnonlinear eigenvalue problemasymptotics of eigenvaluesnonlinear Sturm-Liouville problemnonlinear permittivityplanar dielectric waveguide

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Sturm-Liouville theory (34B24) Antennas, waveguides in optics and electromagnetic theory (78A50) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Waves and radiation in optics and electromagnetic theory (78A40)

Related Items (7)

Perturbation method in the theory of propagation of two-frequency electromagnetic waves in a nonlinear waveguide. I: TE-TE waves ⋮ Maxwell’s Equations with Nonlinear Inhomogeneous Constitutive Relation: Guided Waves in a Film Filled with Inhomogeneous Kerr Medium ⋮ Nonlinearized nonlinear electromagnetic guided waves in a circle cylindrical waveguide filled with nonlinear dielectric medium ⋮ Nonclassical perturbation approach to a nonlinear multiparameter eigenvalue problem arising in electromagnetics ⋮ Propagation of electromagnetic waves in an open planar dielectric waveguide filled with a nonlinear medium. II: TM waves ⋮ On the integral characteristic function of the Sturm-Liouville problem ⋮ Maxwell's equations with arbitrary self-action nonlinearity in a waveguiding theory: guided modes and asymptotic of eigenvalues

Cites Work

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• On the eigenvalues of a nonlinear spectral problem
• On the existence of infinitely many eigenvalues in a nonlinear Sturm-Liouville problem arising in the theory of waveguides
• Dual variational methods in critical point theory and applications
• On the existence of infinitely many nonperturbative solutions in a transmission eigenvalue problem for nonlinear Helmholtz equation with polynomial nonlinearity
• The existence of periodic solutions of systems of differential equations

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