Nonperturbative nonlinear effects in the dispersion relations for TE and TM plasmons on two-dimensional materials

Vera Andreeva, Mitchell Luskin, and Dionisios Margetis
Phys. Rev. B 98, 195407 – Published 7 November 2018

Abstract

We analytically obtain the dispersion relations for transverse-electric (TE) and transverse-magnetic (TM) surface plasmon-polaritons in a nonlinear two-dimensional (2D) conducting material with inversion symmetry lying between two Kerr-type dielectric media. To this end, we use Maxwell's equations within the quasielectrostatic, weakly dissipative regime. We show that the wavelength and propagation distance of surface plasmons decrease due to the nonlinearity of the surrounding dielectric. In contrast, the effect of the nonlinearity of the 2D material depends on the signs of the real and imaginary parts of the third-order conductivity. Notably, the dispersion relations obtained by naively replacing the permittivity of the dielectric medium by its nonlinear counterpart in the respective dispersion relations of the linear regime are not accurate. We apply our analysis to the case of doped graphene and make predictions for the surface plasmon wavelength and propagation distance.

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  • Received 7 August 2018
  • Revised 16 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.195407

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Vera Andreeva1,2,*, Mitchell Luskin2, and Dionisios Margetis3

  • 1Physics Department and International Laser Center, Lomonosov Moscow State University, Moscow 119991, Russia
  • 2School of Mathematics, University of Minnesota, Minneapolis 55455, USA
  • 3Institute for Physical Science and Technology, Department of Mathematics, and Center for Scientific Computation and Mathematical Modeling, University of Maryland, College Park, Maryland 20742, USA

  • *Corresponding author: andr0616@umn.edu

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Issue

Vol. 98, Iss. 19 — 15 November 2018

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