We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order. Specifically, by resorting to a suitable multiscale technique, we show that medium effective permittivity tensor and the first and second order tensors describing spatial dispersion can be evaluated by averaging suitable spatially rapidly-varying fields each satysifing electrostatic-like equations within the metamaterial unit cell. For metamaterials with negligible second-order spatial dispersion, we exploit the equivalence of first-order spatial dispersion and reciprocal bianisotropic electromagnetic response to deduce a simple expression for the metamaterial chirality tensor. Such an expression allows us to systematically analyze the effect of the composite spatial symmetry properties on electromagnetic chirality. We find that even if a metamaterial is geometrically achiral, i.e. it is indistinguishable from its mirror image, it shows pseudo-chiral-omega electromagnetic chirality if the rotation needed to restore the dielectric profile after the reflection is either a 0• or 90• rotation around an axis orthogonal to the reflection plane. These two symmetric situations encompass two-dimensional and one-dimensional metamaterials with chiral response. As an example admitting full analytical description, we discuss one-dimensional metamaterials whose single chirality parameter is shown to be directly related to the metamaterial dielectric profile by quadratures.

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.

We suggest that electromagnetic chirality, generally displayed by 3D or 2D complex chiral structures, can occur in 1D patterned composites whose components are achiral. This feature is highly unexpected in a 1D system which is geometrically achiral since its mirror image can always be superposed onto it by a 180 deg rotation. We analytically evaluate from first principles the bianisotropic response of multilayered metamaterials and we show that the chiral tensor is not vanishing if the system is geometrically onedimensional chiral; i.e., its mirror image cannot be superposed onto it by using translations without resorting to rotations. As a signature of 1D chirality, we show that 1D chiral metamaterials support optical activity and we prove that this phenomenon undergoes a dramatic nonresonant enhancement in the epsilonnear-zero regime where the magnetoelectric coupling can become dominant in the constitutive relations. The term chirality is generally used to express the asymmetric property of a 3D object which cannot be superimposed onto its mirror image by translations or rotations. 3D chirality is an important feature in many organic molecules (for example, 19 of the 20 common amino acids that form proteins are chiral) and its associated phenomena have an enormous impact in several branches of science encompassing molecular biology, life science, optics, crystallography, and particle physics. The concept of 2D chirality also exists and a planar object is said to be chiral if it cannot be superposed onto its mirror image unless it is lifted from the plane. Although the 3D chirality is widespread in nature, examples of 2D chiral structures are very few [1].In the context of metamaterial science, artificial chiral structures, whose underlying constituents exhibit intrinsic chiral asymmetry, have been investigated theoretically and experimentally by several groups in 3D [2][3][4][5] and 2D configurations [6][7][8][9][10]. Chiral metamaterials have attracted a good deal of attention since they can yield strong chiral bianisotropic response (due to cross-coupling between the magnetic polarization and the electric one), giant optical activity, asymmetric transmission [11], repulsive Casimir force [12], and negative refractive index [13][14][15][16]. It is worth noting that electromagnetic chirality can also be present in the case where underlying constituents are not intrinsically chiral. In this case, the magnetoelectric coupling results from the geometric chirality of the whole structure and the effect is driven by the radiation wave vector contributing to the overall chiral asymmetry (extrinsic chiralilty). 2D extrinsic chiral metamaterials have been first proposed by E. Plum et al. [17] and, in the considered media, authors have observed large optical activity which is indistinguishable from that occuring in media whose constituents are intrinsically chiral.In this Letter, we show that 1D systems can support a peculiar reciprocal bianisotropic response in the long wavelength regime. We evaluate the chiral tensor...

We investigate propagation of a transverse magnetic field through a nonlinear metamaterial slab of sub-wavelength thickness and with a very small and negative linear dielectric permittivity. We prove that, for a given input intensity, the output intensity is a multi-valued function of the field incidence angle so that the transmissivity exhibits angular multi-stability and a pronounced directional hysteresis behavior. The predicted directional hysteresis is a consequence of the fact that the linear and nonlinear contributions to the overall dielectric response can be comparable so that the electromagnetic matching conditions at the output slab boundary allow more than one field configurations within the slab to be compatible with the transmitted field.Optical hysteresis behavior and bistability are fascinating nonlinear phenomena which have attracted a large research interest in the last decades [1] mainly for their potential photonic applications as optical memories, logic gates and optical computing devices [2]. The possibility of engineering the dielectric permittivity and the magnetic permeability offered by metamaterials [3] has recently allowed to prove that the feedback mechanism supporting bistability is facilitated by the the opposite directionality of the phase velocity and the energy flow in the negative index metamaterial [4]. Nonlinear propagation of light through alternating slabs of positive and negative refractive index materials characterized by a vanishing average refractive index has been considered and bistable switching [5] and gap soliton formation [6] have been predicted. Metal-dielectric multilayer structures have also proved to be media exhibiting interesting bistable behavior [7] since the small average dielectric permittivity combined with the nonlinearity allows the sign of the effective overall dielectric constant to be dependent on the optical intensity [8,9].In this Letter, we investigate electromagnetic transmission through a metamaterial slab of sub-wavelength thickness, characterized by a very small and negative linear dielectric permittivity and exhibiting focusing Kerr nonlinearity. We numerically solve Maxwell equations for the problem of reflection and transmission of an inclined incident transverse magnetic (TM) plane wave and we show that the slab transmissivity is, for a given input intensity, a multi-valued function of the field incidence angle. The novel directional hysteresis behavior is due to the fact that the slab can host the extreme nonlinear regime where the linear and nonlinear contributions to the overall dielectric response can be comparable [8] so that the electromagnetic matching conditions at the output slab boundary allows more than one possible field configurations compatible with the transmitted field.Consider a transverse magnetic (TM) monochromatic field (with time dependence exp(−iωt)) E z (x, z)ê z and H = H y (x, z)ê y propagating through the metamaterial slab, embedded in vacuum, reported in Fig.1(a) of sub-wavelength thickness (along the zaxis) L ...

In recent years, unconventional metamaterial properties have triggered a revolution of electromagnetic research which has unveiled novel scenarios of wave-matter interaction. A very small dielectric permittivity is a leading example of such unusual features, since it produces an exotic static-like regime where the electromagnetic field is spatially slowly-varying over a physically large region. The so-called epsilon-near-zero metamaterials thus offer an ideal platform where to manipulate the inner details of the "stretched" field. Here we theoretically prove that a standard nonlinearity is able to operate such a manipulation to the point that even a thin slab produces a dramatic nonlinear pulse transformation, if the dielectric permittivity is very small within the field bandwidth. The predicted non-resonant releasing of full nonlinear coupling produced by the epsilon-near-zero condition does not resort to any field enhancement mechanisms and opens novel routes to exploiting matter nonlinearity for steering the radiation by means of ultra-compact structures.

We show that a homogeneous and isotropic slab, illuminated by a circularly polarized beam with no topological charge, produces vortices of order two in the opposite circularly polarized components of the reflected and transmitted fields, as a consequence of the difference between transverse magnetic and transverse electric dynamics. In the epsilon-near-zero regime, we find that vortex generation is remarkably efficient in sub-wavelength thick slabs up to the paraxial regime. This physically stems from the fact that a vacuum paraxial field can excite a nonparaxial field inside an epsilon-near-zero slab since it hosts slowly varying fields over physically large portion of the bulk. Our theoretical predictions indicate that epsilon-near-zero media hold great potential as nanophotonic elements for manipulating the angular momentum of the radiation, since they are available without resorting to complicated micro/nano fabrication processes and can operate even at very small (ultraviolet) wavelengths.Spin-orbit interaction (SOI) of light is a very important research topic since it provides a tool for manipulating the spatial degrees of freedom of the radiation by acting on its circular polarization state [1]. A remarkable SOI effect is the generation of optical vortices from circularly polarized beams, a process accompanied by spin to orbital angular momentum conversion. Standard procedures to achieve vortex generation are focusing by high-numerical aperture lens [2,3], scattering by small particles [3], propagation along the optical axis of a uniaxial crystal [4,5] and propagation through semiconductor microcavities [6]. Similar SOI effects involving Bessel beams have been considered in uniaxial crystals [7] and at reflection and transmission by a planar interface between two homogeneous media [8]. The advent of metamaterials has further increased the SOI research effort [9], mostly in the use of ultra-thin metasurfaces for manipulating the angular momentum of light [10,11] and for vortex generation [12,13].Epsilon near zero (ENZ) media are nowadays attracting an increasing research interest due to the very unconventional way they affect the electromagnetic radiation. The effective wavelength in ENZ media is much larger than the vacuum wavelength and this entails a regime quite opposite to geometrical optics where the field is slowly-varying over relatively large portions of the bulk. Such feature has been exploited for squeezing electromagnetic waves at will [14], for tailoring the antenna radiation pattern [15] and for enhancing nonlinear response of matter [16][17][18][19][20]. In the context of light SOI, it has recently been proposed that a thin epsilon-near-zero slab can enhance the spin Hall effect of transmitted light [21].In this letter we show that a homogeneous, isotropic and ultra-thin (sub-wavelength thick) slab can support vortex generation. We prove that such genuine SOI effect is physically due to the mutual difference between the dynamics of transverse magnetic and transverse electric fields upon refl...

We theoretically consider infrared-driven hyperbolic metamaterials able to spatially filtering terahertz radiation. The metamaterial is a slab made of alternating semiconductor and dielectric layers whose homogenized uniaxial response, at terahertz frequencies, shows principal permittivities of different signs. The gap provided by metamaterial hyperbolic dispersion allows the slab to stop spatial frequencies within a bandwidth tunable by changing the infrared radiation intensity. We numerically prove the device functionality by resorting to full wave simulation coupled to the dynamics of charge carries photoexcited by infrared radiation in semiconductor layers.Manipulating terahertz (THz) radiation is generally a difficult task since the most of standard materials simply do not respond to such frequencies. However, the advent of metamaterials has allowed to partially reduce this difficulty since their electromagnetic properties can be artificially manipulated 1 through a suitable design of the underlying constituent unit cells. At the same time a number of setups have been proposed for steering the THz radiation 2 and reconfigurable electrically 3 or opticallydriven metamaterials have been exploited for conceiving active THz devices 6 . The most of the proposed active THz devices are tunable frequency-domain filters since it is relatively simple to control the metamaterial dispersion properties through external stimuli. In this Letter we theoretically propose a way for achieving active and spatial filtering of the THz radiation by means of a suitable hyperbolic metamaterial whose THz response can be tuned by an auxiliary infrared field. Hyperbolic or indefinite media 7 are uniaxially anisotropic metamaterials having principal permittivities of different signs, a remarkable feature leading extraordinary plane waves to be ruled by a hyperbolic dispersion relation. Hyperbolicity is the main physical ingredient leading to unusual optical effects as negative refraction 8 and hyperlensing 9 and supporting a number of proposed devices as beam splitters 10 , spatial 11 and angular filters 12 and optical switches 13 . The tunable hyperbolic metamaterial we consider in the present Letter, together with the fields geometry, is sketched in Fig.1. The metamaterial slab of thickness L is obtained by stacking along the x-axis alternating layers of an intrinsic semiconductor 14 (sc) and a negative dielectric (nd) of thicknesses d sc and d nd , respectively and it is illuminated by an infrared (IR) plane wave linearly polarized along the y-axis and normally impinging onto the slab interface at z = 0. The THz field (TH) is a transverse magnetic (TM or p-polarized) monochromatic plane impinging with incidence angle θ onto the interface.The infrared field within the semiconductor layers photoexcites electrons to the conduction band which dynamically recombine so that the resulting electron density N is described by the rate equationwhere is the Planck constant divided by 2π, ǫ 0 is the absolute vacuum permittivity, ǫ sc (ω IR ) is ...

Epsilon-Near-Zero materials exhibit a transition in the real part of the dielectric permittivity from positive to negative value as a function of wavelength. Here we study metal-dielectric layered metamaterials in the homogenised regime (each layer has strongly subwavelength thickness) with zero real part of the permittivity in the near-infrared region. By optically pumping the metamaterial we experimentally show that close to the Epsilon-Near-Zero (ENZ) wavelength the permittivity exhibits a marked transition from metallic (negative permittivity) to dielectric (positive permittivity) as a function of the optical power. Remarkably, this transition is linear as a function of pump power and occurs on time scales of the order of the 100 fs pump pulse that need not be tuned to a specific wavelength. The linearity of the permittivity increase allows us to express the response of the metamaterial in terms of a standard third order optical nonlinearity: this shows a clear inversion of the roles of the real and imaginary parts in crossing the ENZ wavelength, further supporting an optically induced change in the physical behaviour of the metamaterial.