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.
Bibliographical noteFunding Information:
We acknowledge support by ARO MURI Award No. W911NF-14-0247 (V.A., M.L., D.M.) and NSF Grant No. DMS-1412769 (D.M.). D.M. acknowledges the support of the Institute for Mathematics and its Applications (NSF Grant DMS-1440471) for several visits, and we acknowledge discussions with Prof. Tony Low and participants at the Institute for Mathematics and its Applications Workshop on Theory and Computation for Transport Properties in 2D Materials.
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