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

TL;DR

This paper derives analytical dispersion relations for TE and TM surface plasmons on nonlinear 2D materials, revealing how dielectric and material nonlinearities differently affect plasmon wavelength and propagation, with specific predictions for doped graphene.

Contribution

It provides the first analytical treatment of nonlinear effects on surface plasmon dispersion relations in 2D materials, highlighting the importance of correct nonlinear modeling.

Findings

Dielectric nonlinearity reduces plasmon wavelength and propagation distance.

Material nonlinearity effects depend on the sign of third-order conductivity.

Predictions made for doped graphene's plasmon properties.

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 lying between two Kerr-type dielectric media. To this end, we use Maxwell's equations within the quasi-electrostatic, 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 TM-polarized surface plasmon wavelength and propagation distance.