Abstract
We describe the application of the phase plane method to analyze the behavior of stationary harmonic plane electromagnetic waves. The phase plane method allows one to describe qualitatively all possible solutions of the Helmholtz nonlinear differential equation without performing a numerical integration. All types of phase portraits for waves in the media with self-action are presented and their physical interpretation is discussed. The consideration is carried out on the model of cubic nonlinearity without specifying the physical mechanism of this nonlinearity. The features of the nonlinear case are discussed. The phenomenon of the self-limitation of the transmitted wave power in a medium with negative nonlinearity is described.
Similar content being viewed by others
REFERENCES
Andronov, A.A., Vitt, A.A., and Khaykin, S.E., Theory of oscillations, New York: Dover, Inc., 1987.
Jordan, D.W. and Smith, P., Nonlinear Ordinary Differential Equations, Oxford, 2007.
Baghdasaryan, H.V. and Knyazyan, T.M., Optical and Quantum Electronics, 1999, vol. 31, p. 1059.
Baghdasaryan, H.V., Basics of the Method of Single Expression: New Approach for Solving Boundary Problems in Classical Electrodynamics. Yerevan, Chartaraget, 2013, 164 p.
Baghdasaryan, H.V., Knyazyan, T.M., and Mankulov, A.A., Proceedings of 2004 6th International Conference on Transparent Optical Networks, Wroclaw, 2004, p. 363.
Daryan, A.V., Baghdasaryan, H.V., and Knyazyan, T.M., IRPhE2014, Proceedings of the International Conference on ‘Microwave and THz Technologies and Applications’, Armenia: Gitutiun, 2014, p. 106.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare no conflict of interest.
Additional information
Translated by V. Musakhanyan
About this article
Cite this article
Baghdasaryan, H.V., Vardanyan, V.A. & Daryan, A.V. Phase-Plane Analysis of Solutions of the Helmholtz Equation for Electromagnetic Waves in Media with Self-Action. J. Contemp. Phys. 55, 299–305 (2020). https://doi.org/10.3103/S1068337220040052
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1068337220040052