Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity

TL;DR

This paper explores the extreme nonlinear regime in metamaterials with very small linear dielectric permittivity, revealing novel electromagnetic behaviors such as power flow reversal and hyper-focusing, enabled by tailored nonlinear Kerr effects.

Contribution

It demonstrates how engineered metamaterials can achieve extreme nonlinear responses with unique features like power flow reversal and allows propagation of nonlinear guided waves in media with negative permittivity.

Findings

Observation of power flow reversing in extreme nonlinear regime

Propagation of nonlinear guided waves in media with negative permittivity

Hyper-focusing effects due to phase differences in field components

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.