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We report comparative experimental and theoretical studies of second andthird harmonic generation from a 20nm-thick indium tin oxide layer in proximityof the epsilon-near-zero condition. Using a tunable OPA laser we record bothspectral and angular dependence of the generated harmonic signals close to thisparticular point. In addition to the enhancement of the second harmonicefficiency close to the epsilon-near-zero wavelength, at oblique incidencethird harmonic generation displays unusual behavior, predicted but not observedbefore. We implement a comprehensive, first-principles hydrodynamic approachable to simulate our experimental conditions. The model is unique, flexible,and able to capture all major physical mechanisms that drive the electrodynamicbehavior of conductive oxide layers: nonlocal effects, which blueshift theepsilon-near-zero resonance by tens of nanometers; plasma frequency redshiftdue to variations of the effective mass of hot carriers; charge densitydistribution inside the layer, which determines nonlinear surface and magneticinteractions; and the nonlinearity of the background medium triggered by boundelectrons. We show that by taking these contributions into account ourtheoretical predictions are in very good qualitative and quantitative agreementwith our experimental results. We show that by taking these contributions intoaccount our theoretical predictions are in very good qualitative andquantitative agreement with our experimental results. We expect that ourresults can be extended to other geometries where ENZ nonlinearity plays animportant role.

Study of second and third harmonic generation from an indium tin oxide nanolayer: influence of nonlocal effects and hot electrons