Surface Electromagnetic TM Waves along the Boundary between Two Nonlinear Anisotropic Dielectrics

Authors:

Yuri P. Rybakov,Bijan Saha,

DOI NO:

https://doi.org/10.26782/jmcms.2019.03.00042

Keywords:

Maxwell’s Equations,Surface Waves,Dielectric Permittivity ,KerrDielectrics,

Abstract

It is shown that the Maxwell’s equations for surface electromagnetic TM waves, propagating along the plane boundary between two nonlinear dielectrics with arbitrary diagonal tensor of dielectric permittivity, depending on 2 | | E  , can be integrated in quadratures. For the TM plane wave the magnetic intensity has only the transverse component, but the electric intensity has both transverse and longitudinal ones. This fact permits one to find the first integral of the Maxwell’s equations and eliminate the magnetic intensity. The resulting equations for the electric intensity can be simplified and integrated, if one uses the transverse permittivity as the independent variable. Finally, we consider the Kerr dielectrics, with the permittivity being a quadratic function of the electric intensity. In this case the quadratures can be reduced to the elliptical integrals.

Refference:

I.Abdulhalim I., Zourob M., Lakhtakia A. (2008). Surface plasmon resonance for bio-sensing:a mini-review. Electromagnetism, 28: 214-242.Available online: http://www.tandfonline.com/doi/abs/10.1080/02726340801921650

II.Agranovich V.M., Chernyak V.Y. (1982). Perturbation theory for weakly nonlinear P-polarized surface polaritons. Solid State Communications, 44(8): 1309-1311.Available online: https://www.sciencedirect.com/science/article/pii/0038109882911115

III.Agranovich V.M., Darmanyan S.A., Dubovsky O.A., Kamchatnov A.M., Ogievetsky E.I., Reineker P. (1996). Fermi resonance solitary wave on the interface between two layers of organic semiconductors. Physical Review B: Condensed Matter, 53(23): 15451-15454.Available online: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.53.15451

IV.Agranovich V.M., Darmanyan S.A., Kamchatnov A.M., Leskova T.A., Boardman A.D. (1997). Variational approach to solitons in systems with cascaded 2xnonlinearity. Physical Review E –Statistical, Nonlinear, and Soft Matter Physics, 55(2): 1894-1898.Available online: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.55.1894

V.Agranovich V.M., Mills D.L. (1985). Surface polaritons -Electromagnetic waveson interface surfaces and boundaries. NASA STI/Recon Technical Report A86:36694.Available online: https://www.researchgate.net/publication/238534155_Surface_polaritons_-_Electromagnetic_waves_on_interface_surfaces_and_boundaries

VI.Boardman A.D. (1982). Electromagnetic Surface Modes. John Wiley & Sons Ltd, New York.

VII.Fedyanin V.K., Minalache D. (1982). P-polarized nonlinear surface polaritons in layered structures. Zeitschrift für Physik. B: Condensed Matter, 47(2): 167-173.Available online: https://link.springer.com/article/10.1007/BF01441299

VIII.Gaspar-Armenta J.A., Villa-Villa F. (2013). Electromagnetic surface waves at a metal 2D photonic crystal interface. Journal of the Optical Society of America, 30B(8): 2271-2276.Available online: https://www.osapublishing.org/josab/abstract.cfm?uri=josab-30-8-2271

IX.Mackay T.G., Lakhtakia A. (2010). Electromagnetic Anisotropy and Bi-anisotropy: AField Guide. World Scientific, Singapore.

X.Minalache D., Mazilu D., Bertolotti M., Sibila C., Fedyanin V.K. (1988). Nonlinear TE-polarized surface guided waves in a dielectric “anti-waveguide”. Solid State Communications, 66(5): 517-520.Available online: https://www.sciencedirect.com/science/article/pii/0038109888909726

XI.Minalache D., Nazmitdinov R.G., Fedyanin V.K. (1984). P-polarized nonlinear surface waves insymmetric layered structures. Physica Scripta, 29(3): 269-274.Available online: http://iopscience.iop.org/article/10.1088/0031-8949/29/3/014

XII.Minalache D., Nazmitdinov R.G., Fedyanin V.K. (1989). Nonlinear optical waves in layered structures. Soviet Journal of Particles and Nuclei, 20(1): 86-93.Available online: https://elibrary.ru/title_about.asp?id=25707

XIII.Neidlinger Th., Reineker P., Agranovich V.M. (1997). Influence of static disorder on the dynamics of Fermi resonance solitary waves at the interface between two molecular layers. Journal of Luminescence, 72-74: 804-805.Available online: https://www.sciencedirect.com/science/article/pii/S0022231396003377

XIV.Polo J., Mackay T., Lakhtakia A. (2013). Electromagnetic Surface Waves: AModern Perspective. Elsevier Inc., New York.

XV.Sarid D., Challener W. (2010). Modern Introduction to Surface Plasmons: Theory, Mathematical Modeling and Applications. Cambridge University Press, London.

XVI.Strashko A.A., Agranovich V.M. (2011). To the theory of surface plasmon-polaritons on metals covered with resonant thin films. Optics Communications, 332: 201-205.Available online: https://docslide.com.br/documents/to-the-theory-of-surface-plasmon-polaritons-on-metals-covered-with-resonant.html

XVII.Uvarova L.A., Fedyanin V.K. (1996). Asymptotic solutions for electromagnetic waves in a nonlinear optical cylinder. Theoretical and Mathematical Physics, 106(1): 68-75.Available online: https://link.springer.com/article/10.1007/BF02070764

View | Download