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 ǫ < 0 and µ > 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.

Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties

“…7,51 Multi-valued solutions of transmittance, reflectance and absorptance at the fundamental frequency are retrieved by using the graphical method outlined in Ref. 52.…”

“…5,6 This non-resonant enhancement occurs at oblique incidence for transverse magnetic (TM) polarization and is triggered by the continuity of the component of the displacement field normal to the interface. 10 At low irradiance levels, subwavelength ENZ slabs exhibit anomalous multistability and directional hysteresis, 7 so that even a weak nonlinearity can dominate the optical response. Although ENZ conditions occur naturally near the plasma frequency of any material (at visible and UV wavelengths for metals and semiconductors, and in the infrared range for dielectrics), artificial materials are advantageous because ENZ conditions may be engineered at virtually any wavelength.…”

“…3,4 ENZ materials may also be used to achieve enhanced harmonic generation, 5,6 optical bistability, 7,8 and soliton excitation . 9 The efficiency of harmonic generation is boosted in subwavelength ENZ slabs because the electric field is enhanced at the interface with a higher-index substrate.…”

Optical hollow-core waves in nonlinear Epsilon-Near-Zero metamaterials

“…and parameter is obtained by averaging along the y-axis the layer local quantities over the period d) [10]. All effective parameters appearing in the relation (2) can be tailored by choosing the underlying constituents; for example the averaging of the dielectric permittivity can be used to obtain an efficient loss management (using gain and loss media as underlying layers) [12] and/or an epsilon-near-zero metamaterials (exploiting negative and positive dielectric layers) [4].…”

“…On the other hand, a simple strategy for making available the nonlinearity is to reduce the linear polarization. Following this strategy, Ciattoni et al [10] suggested a simple composite structure to achieve very small value of dielectric permittivity where the nonlinear contribution to the dielectric response is not a mere perturbation of the linear one (extreme nonlinear regime). Authors considered a nanoscaled layered structure consisting of alternating metal and dielectric slabs and, in the effective medium scheme, characterized by effective constitutive relations formally coinciding with those of a standard Kerr medium and with response parameters assuming values not available in standard media (nonlinear metamaterials).…”