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 deduce the expressions for the two circularly polarized components of a paraxial beam propagating along the optical axis of a uniaxial crystal. We find that each of them is the sum of two contributions, the first being a free field and the second describing the interaction with the opposite component. Moreover, we expand both components as a superposition of vortices of any order, thus obtaining a complete physical picture of the interaction dynamics. Consequently, we argue that a left-hand circularly polarized incoming beam, endowed with a circular symmetric profile, gives rise, inside the crystal, to a right-hand circularly polarized vortex of order 2. The efficiency of this vortex generation is investigated by means of a power exchange analysis. The Gaussian case is fully discussed, showing the relevant features of the vortex generation.

We show an alternative path to efficient second-and third-harmonic generation in proximity of the zero crossing points of the dielectric permittivity in conjunction with low absorption. Under these circumstances, any material, either natural or artificial, will show similar degrees of field enhancement followed by strong harmonic generation, without resorting to any resonant mechanism. The results presented in this paper provide a general demonstration of the potential that the zero-crossing-point condition holds for nonlinear optical phenomena. We investigate a generic Lorentz medium and demonstrate that a singularity-driven enhancement of the electric field may be achieved even in extremely thin layers of material. We also discuss the role of nonlinear surface sources in a realistic scenario where a 20-nm layer of CaF 2 is excited at 21 μm, where ε ∼ 0. Finally, we show similar behavior in an artificial composite material that includes absorbing dyes in the visible range, provide a general tool for the improvement of harmonic generation using the ε ∼ 0 condition, and illustrate that this singularity-driven enhancement of the field lowers the thresholds for a plethora of nonlinear optical phenomena.

o Dip.to di Scienze Fisiche e Chimiche -Via Vetoio -67010 Coppito (AQ), Italy Optical parametric amplification is a second-order nonlinear process whereby an optical signal is amplified by a pump via the generation of an idler field. It is the key ingredient of tunable sources of radiation that play an important role in several photonic applications. This mechanism is inherently related to spontaneous parametric down-conversion that currently constitutes the building block for entangled photon pair generation, which has been exploited in modern quantum technologies ranging from computing to communications and cryptography. Here we demonstrate singlepass optical parametric amplification at the ultimate thickness limit; using semiconducting transition-metal dichalcogenides, we show that amplification can be attained over a propagation through a single atomic layer. Such a second-order nonlinear interaction at the 2D limit bypasses phase-matching requirements and achieves ultrabroad amplification bandwidths. The amplification process is independent on the in-plane polarization of the impinging signal and pump fields. First-principle calculations confirm the observed polarization invariance and linear relationship between idler and pump powers. Our results pave the way for the development of atom-sized tunable sources of radiation with applications in nanophotonics and quantum information technology.