We report comparative experimental and theoretical studies of second and third harmonic generation from a 20nm-thick indium tin oxide layer in proximity of the epsilonnear-zero condition. Using a tunable OPA laser we record both spectral and angular dependence of the generated harmonic signals close to this particular point. In addition to the enhancement of the second harmonic efficiency close to the epsilon-near-zero wavelength, at oblique incidence third harmonic generation displays unusual behavior, predicted but not observed before. We implement a comprehensive, first-principles hydrodynamic approach able to simulate our experimental conditions. The model is unique, flexible, and able to capture all major physical mechanisms that drive the electrodynamic behavior of conductive oxide layers: nonlocal effects, which blueshift the epsilon-near-zero resonance by tens of nanometers; plasma frequency redshift due to variations of the effective mass of hot carriers; charge density distribution inside the layer, which determines nonlinear surface and magnetic interactions; and the nonlinearity of the background medium triggered by bound electrons. We show that by taking these contributions into account our theoretical predictions are in very good qualitative and quantitative agreement with our experimental results. We show that by taking these contributions into account our theoretical predictions are in very good qualitative and quantitative agreement with our experimental results. We expect that our results can be extended to other geometries where ENZ nonlinearity plays an important role.; in ε and out ε are the dielectric constants inside and outside the medium, respectively; z in E and z out E are the corresponding longitudinal components of the electric field amplitude, and require oblique incidence to excite the ENZ point. Therefore, if in ε decreases, then z in E increases and nonlinear optical phenomena are enhanced, including nonlinear index of refraction [1], harmonic generation, optical bistability, and soliton excitation [2-13].While ENZ materials can be made artificially, all natural bulk materials that display a Lorentz-like response also exhibit a real part of the dielectric permittivity that crosses zero, in

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We study electromagnetic pulse propagation in an indium tin oxide nanolayer in the linear and nonlinear regimes. We use the constitutive relations to reconstruct the effective dielectric constant of the medium, and show that nonlocal effects induce additional absorption resonances and anisotropic dielectric response: longitudinal and transverse effective dielectric functions are modulated differently along the propagation direction, and display different epsilon-near-zero crossing points with a discrepancy that increases with increasing intensity. We predict that hot carriers induce a dynamic redshift of the plasma frequency and a corresponding translation of the effective nonlinear dispersion curves that can be used to predict and quantify nonlinear refractive index changes as a function of incident laser peak power density. Our results suggest that large, nonlinear refractive index changes can occur without the need for epsilon-near-zero modes to couple with plasmonic resonators. At sufficiently large laser-pulse intensities, we predict the onset of optical bistability, while the presence of additional pump absorption resonances that arise from longitudinal oscillations of the free electron gas give way to corresponding resonances in the second and third harmonic spectra. A realistic propagation model is key to unraveling the basic physical mechanisms that play a fundamental role in the dynamics.

Phase-locked second and third harmonic generation in the opaque region of a GaAs wafer is experimentally observed and analyzed both in transmission and reflection. These harmonic components, which are generated close to the surface, can propagate through an opaque material as long as the pump is tuned to a region of transparency or semitransparency and correspond to the inhomogeneous solutions of Maxwell's equations with nonlinear polarization sources. We show that measurement of the angular and polarization dependence of the observed harmonic components allows one to infer the different nonlinear mechanisms that trigger these processes, including not only the bulk nonlinearity but also the surface and magnetic Lorentz contributions, which usually are either hidden by the bulk contributions or assumed to be negligible. The experimental results are compared with a detailed numerical model that takes into account these different effects, including for the first time combined linear and nonlinear material dispersions in a nonlinear Lorentz oscillator model of the bulk nonlinearities. Our results suggest that the intensity of the second harmonic signal generated by the surface can be more intense than the signal generated by the bulk. These findings have significant repercussions and are consequential in nanoscale systems, which are usually investigated using only dispersionless bulk nonlinearities, with near-complete disregard of surface and magnetic contributions and their microscopic origins.

Understanding how light interacts with matter at the nanoscale is pivotal if one is to properly engineer nano-antennas, filters and other devices whose geometrical features approach atomic size. We report experimental results on second and third harmonic generation from 20 nm- and 70 nm-thick gold layers, for TE- and TM-polarized incident light pulses. We discuss the relative roles that bound electrons and an intensity dependent free electron density (hot electrons) play in third harmonic generation. While planar structures are generally the simplest to fabricate, metal layers that are only a few nanometers thick and partially transparent are almost never studied. Yet, transmission offers an additional reference point to compare experimental measurements with theoretical models. Our experimental results are explained well within the context of the microscopic hydrodynamic model that we employ to simulate second and third harmonic conversion efficiencies. Using our experimental observations we estimate ∣ χ 1064 n m ( 3 ) ∣≈ 10 − 18   ( m/V ) 2 , triggered mostly by hot electrons.