Exact dispersion relation for nonlinear plasmonic waveguides

Abstract

We derive an exact dispersion relation for the surface plasmon polaritons of a nonlinear plasmonic waveguide using exact field decomposition of TM waves. Our approach generalizes the known linear dispersion relations to the case of a medium nonlinearity of the form ε NL = ε L + α|E| 2n. We apply the unique dispersion relation to a plasmonic waveguide with a Kerr-type nonlinearity (n = 1) and show that it enables backward-propagating modes. It also introduces critical points in the energy spectrum of surface plasmon polaritons that result in enhanced interaction of nonlinear modes with each other and external electromagnetic fields.

Guided Plasmon Modes of a Graphene-Coated Kerr Slab

“…11 reduces to the dispersion relation of the SPs supported by a simple nonlinear slot waveguide. In addition, as it has been proven for a plasmonic waveguide [24,25], we recover the dispersion relation of a symmetric graphene-covered PPW with a linear core medium when α → 0.…”

“…Therefore, considering graphene as a material with a nonlinear optical response [19], nonlinear propagation of light in a monolayer [20] and a double-layer [16] of graphene have been studied theoretically. It has been also found through pure analytical and numerical studies that using a Kerr-type nonlinear medium as the substrate, cladding or core medium in a metallic waveguide considerably affects the characteristics of SPs supported by such structures [21][22][23][24][25]. These characteristics of a graphene sheet on a Kerr-type nonlinear substrate [26] and a graphene PPW bounded by the Kerr media [27] have been recently studied while neglecting the nonlinear optical response of graphene.…”

“…[24,25], we derive an exact dispersion relation for the TM SPs of a symmetric slot waveguide formed by a nonlinear Kerr slab of width d and permittivity ε 1 = ε l 1 + α|E| 2 , which is sandwiched between two graphene monolayers at x = ±d/2 (see Fig. 1).…”

Hybrid plasmon–phonon polariton bands in graphene–hexagonal boron nitride metamaterials [Invited]

“…Owing to this property, finite-thickness slabs of hBN act as multimode waveguides for the propagation of hyperbolic phonon polariton collective modes that originate from the coupling between photons and electric dipoles in phonons [7][8][9]. On the other hand, graphene has been demonstrated to be a good candidate to support surface plasmon polaritons for tunable plasmonics in the mid-infrared and terahertz ranges, owing to the possibility of electrostatic doping and its ability to produce higher confinement and lower losses compared to the noble metals [10][11][12][13][14][15][16]. Since both graphene plasmons and hBN phonons reside in the mid-IR, the optical properties of graphene-hBN heterostructures would allow one to marry the advantage of their constituents: electrical tunability in the former and high quality factor of the latter.…”

“…Similar to the natural hyperbolic materials, e.g., hBN, hyperbolic metamaterials (HMMs) [13][14][15][16][17][18] can also support modes with infinitely large wave vectors (high-k modes). Indispersion of TM-polarized propagating waves.…”