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On a Nonlinear Spectral Problem for a Dielectric Waveguide with Kerr Nonlinearity

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Abstract

The frequency dependence of the propagation constants of plane layered dielectric waveguides with the Kerr nonlinearity is considered. An explanation to the possible difference of their behavior from the linear case, related exclusively to a fixed value of an eigenfunction at the boundary of the layer, is given. Explicit formulas for calculating the dispersion curves are obtained. Their behavior for different ways of defining the eigenfunction of the nonlinear problem is analyzed.

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Funding

A.L. Delitsyn’s work was supported by the Russian Science Foundation at the Institute for Information Transmission Problems of the Russian Academy of Sciences (project no. 14-50-00150).

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Authors and Affiliations

  1. Institute for Information Transmission Problems, Russian Academy of Sciences, 127051, Moscow, Russia

    A. L. Delitsyn

  2. National Research University Higher School of Economics, 125319, Moscow, Russia

    A. L. Delitsyn

  3. Main Scientific Research Test Center of Robotics, Ministry of Defense of the Russian Federation, 119001, Moscow, Russia

    A. L. Delitsyn

  4. Lomonosov Moscow State University, 125009, Moscow, Russia

    L. L. Delitsyn

  5. Moscow State Institute of Culture, 125319, Khimki, Moscow oblast, Russia

    L. L. Delitsyn

Authors
  1. A. L. Delitsyn
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  2. L. L. Delitsyn
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Correspondence to A. L. Delitsyn or L. L. Delitsyn.

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Translated by E. Chernokozhin

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Delitsyn, A.L., Delitsyn, L.L. On a Nonlinear Spectral Problem for a Dielectric Waveguide with Kerr Nonlinearity. Comput. Math. and Math. Phys. 59, 718–730 (2019). https://doi.org/10.1134/S0965542519050063

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  • DOI: https://doi.org/10.1134/S0965542519050063

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