Free electrons in heavily doped semiconductors operate in the hydrodynamic regime, where oscillating velocity, current and electromagnetic field terms can mix and produce relatively strong nonlinear effects in the mid-infrared and terahertz ranges, where the material behaves as a free-electron system. We have designed and realized electron-doped InGaAs nanoantennas with the aim of measuring the efficiency of Third Harmonic Generation (THG) and comparing it with the nonlinearity coefficients predicted by a hydrodynamic model. To observe THG from nanoantennas, we used a difference-frequency generation source of mid-infrared short pulses with center-wavelength tunable between 12 and 6 micrometers. Four different doping levels and several dipole antenna lengths were investigated. The volume-normalized THG efficiencies of free-electrons are much higher than those of the crystal host, as directly shown by analysis of an undoped sample. The THG efficiency is found to peak at a mid-infrared excitation wavelength that depends on the free electron concentration, mirroring the decrease of the plasma wavelength with increasing carrier concentration.
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