We present a theoretical approach to the study of second- and third-harmonic generation from metallic structures and nanocavities filled with a nonlinear material in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We study the effects of incident TE- and TM-polarized fields and show that a simple reexamination of the basic equations reveals additional, exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.

Two-dimensional transition-metal dichalcogenides (TMDCs) with intrinsically broken crystal inversion symmetry and large second-order nonlinear responses have shown great promise for future nonlinear light sources. However, the sub-nanometer monolayer thickness of such materials limits the length of their nonlinear interaction with light. Here, we experimentally demonstrate the enhancement of the second-harmonic generation from monolayer MoSe₂ by its integration onto a 220-nm-thick silicon waveguide. Such on-chip integration allows for a marked increase in the interaction length between the MoSe₂ and the waveguide mode, further enabling phase matching of the nonlinear process. The demonstrated TMDC–silicon photonic hybrid integration opens the door to second-order nonlinear effects within the silicon photonic platform, including efficient frequency conversion, parametric amplification and the generation of entangled photon pairs.

We experimentally demonstrate efficient third harmonic generation from an indium tin oxide nanofilm (λ/42 thick) on a glass substrate for a pump wavelength of 1.4 μm. A conversion efficiency of 3.3 × 10⁻⁶ is achieved by exploiting the field enhancement properties of the epsilon-near-zero mode with an enhancement factor of 200. This nanoscale frequency conversion method is applicable to other plasmonic materials and reststrahlen materials in proximity of the longitudinal optical phonon frequencies.

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 CaF2 is excited at 21 $\mu${}m, where $\epsilon${} $\sim${} 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 $\epsilon${} $\sim${} 0 condition, and illustrate that this singularity-driven enhancement of the field lowers the thresholds for a plethora of nonlinear optical phenomena.

We investigate local-field enhancement phenomena in subwavelength, $\epsilon${}-near-zero (ENZ) slabs that do not exploit Fabry-P\'erot resonances. In particular, we study the linear response of engineered metamaterial slabs of finite thickness based on plasmonic nanoshells that show an ENZ band in the visible range, and naturally occurring materials (e.g., SiO${}_{2}$) that also display ENZ properties, under oblique, TM-polarized plane-wave incidence. We then introduce active gain material in engineered metamaterial slabs that adds peculiar spectral and angular features to transmission, reflection, and absorption properties, and leads to a further local-field enhancement. These findings are supported by two theoretical studies: First, a simple interface between two semi-infinite media, namely free space and a generic ENZ medium; then, an ENZ slab of finite thickness, with the aim of understanding the system's behavior when varying the ENZ properties as well as the incident angle. For either case we report three distinct physical conditions for which we explain spectral and angular features that might result in strong field enhancement. The gain-assisted metamaterial implementation has the potential of triggering and enhancing low-threshold nonlinear phenomena thanks to the large local fields found at specific frequency and angular bands.

A one-dimensional dielectric grating, based on a simple geometry, is proposed and investigated to enhance light absorption in a monolayer graphene exploiting guided mode resonances. Numerical findings reveal that the optimized configuration is able to absorb up to 60% of the impinging light at normal incidence for both TE and TM polarizations resulting in a theoretical enhancement factor of about 26 with respect to the monolayer graphene absorption (≈2.3%). Experimental results confirm this behavior showing CVD graphene absorbance peaks up to about 40% over narrow bands of a few nanometers. The simple and flexible design points to a way to realize innovative, scalable and easy-to-fabricate graphene-based optical absorbers.