Effective medium response of metallic nanowire arrays with a Kerr-type dielectric host

Abstract

We derive an effective medium model to characterize the macroscopic electromagnetic response of metallic nanowire arrays embedded in a host dielectric with a Kerr-type nonlinear permittivity function. It is shown that the macroscopic electromagnetic fields are coupled to the conduction current in the nanowires and to an additional quasi-static potential through a system of nonlinear equations. We prove that a weak nonlinearity leads to an electromagnetic response closer to that of an indefinite medium, and to isofrequency contours with increased hyperbolicity. For high-field intensities the negative refraction of electromagnetic waves at an air − nanowire material interface is enhanced when the nanowires are embedded in a self-focusing Kerr medium.

Theory of spatial optical solitons in metallic nanowire materials

“…Our numerical simulations, based on the spatial evolution of Eq. (12), also seem to indicate that the profile of the solitary waves is stable to perturbations. It is interesting to note that the considered spatial-solitons cannot, as a result of some perturbation, be collapsed into an increasingly narrower beam because at a scale length of the order of the period a the effective medium approximation ceases to work.…”

“…The analysis is based on the effective medium model derived in Ref. [12], which describes the electrodynamics of the wire medium in terms of the state vector satisfies a nonlinear first order partial-differential system. It is however possible to…”

“…36]: As a consequence of the nonlinear response of the host medium (described by the parameter α ), the effective parameters Ref. [12]. The system of equations (1) is our starting point for the calculation of the spatial-solitons supported by the nanowire array based on the effective model.…”

Plasmonic bistability in the nonlinear cylindrical metal-dielectric multilayers

“…10,11 Moreover, if the nonlinearity is introduced someway, the nonlinear plasmonic modes are also available. As a fact, several kinds of the plasmonic solitons have been reported in the plasmonic waveguide arrays and can control the light at the subwavelength scale, such as the discrete solitons in the planar metal-dielectric multilayers, 12-15 the fundamental and the vortical lattice solitons in arrays of metallic nanowires, [16][17][18] the ring-like solitons in metal-dielectric fiber waveguides, 19 etc.…”

Phase matching in hyperbolic wire media for nonlinear frequency conversion

“…To this effect, we require a linear calculation of modes of wire media, and can use existing analytic expressions of the homogenized dispersion relation to start our investigations [16]. Assessing the full conversion efficiency then also requires the calculation of the effective nonlinear properties, for example as discussed, or using microscopic modelling specific to particular implementations [17][18][19][20], beyond the scope of this study. We limit our study to the infrared part of the spectrum, where the real part of the permittivity of metals is large and negative and the losses are not too large [21]: in this regime, the permittivity orthogonal to wires is positive and non-resonant, which also restricts the number of cases to be considered.…”