Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity

Abstract

We consider a sub-wavelength periodic layered medium whose slabs are filled by arbitrary linear metamaterials and standard nonlinear Kerr media and we show that the homogenized medium behaves as a Kerr medium whose parameters can assume values not available in standard materials. Exploiting such a parameter availability, we focus on the situation where the linear relative dielectric permittivity is very small thus allowing the observation of the extreme nonlinear regime where the nonlinear polarization is comparable with or even greater than the linear part of the overall dielectric response. The behavior of the electromagnetic field in the extreme nonlinear regime is very peculiar and characterized by novel features as, for example, the transverse power flow reversing. In order to probe the novel regime, we consider a class of fields (transverse magnetic nonlinear guided waves) admitting full analytical description and we show that these waves are allowed to propagate even in media with $\epsilon <0$ and $\mu >0$ since the nonlinear polarization produces a positive overall effective permittivity. The considered nonlinear waves exhibit, in addition to the mentioned features, a number of interesting properties like hyper-focusing induced by the phase difference between the field components.

12 pages, 7 figures

References in corpus (5)

• Epsilon-Near-Zero (ENZ) Metamaterials and Electromagnetic Sources: Tailoring the Radiation Phase Pattern
• Nonlinear properties of left-handed metamaterials
• Tunable split-ring resonators for nonlinear negative-index metamaterials
• Spatial solitons in nonlinear left-handed metamaterials
• Transverse power flow reversing of confined waves in extreme nonlinear metamaterials

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