Interference Induced Complex Nonlinearities in Metal-ITO Metasurfaces
We combine modeling and experiments to investigate second- and third-harmonic generation (SHG/THG) in metal-indium tin oxide (ITO) metasurfaces. Linear optics at normal incidence show moderate field enhancement near the ITO epsilon-near-zero (ENZ) wavelength, steering the focus toward intrinsic, material driven nonlinear response rather than simple linear field boosting. Wavelength resolved SHG requires a Lorentz dispersive \chi^{2} for ITO to match spectra; a static \chi^{2} fails. Angle resolved SHG/THG cannot be reproduced with purely real coefficients; grouped contributions to \chi^{3} (and effective \chi^{2}) must be complex. Using a hydrodynamic model for the metal and ITO with linear dispersion plus dispersive \chi^{2} and \chi^{3}, we show that these complex phases arise from coherent interference of nonlinear sources in the metal, ITO, and interfaces, each weighted by distinct, complex local field and radiation factors. Experimentally, we fabricated split ring resonator metasurfaces on ITO films atop a metallic ground plate and measured linear reflectance and angle resolved SHG/THG in reflection geometry. The measurements quantitatively confirm the modeling: dispersive \chi^{2} is necessary to capture SHG spectra, and complex, interference induced effective coefficients are essential to reproduce angular SHG/THG patterns. Together, these results provide a unified, physically grounded interpretation of nonlinear emission from metal-oxide metasurfaces without relying on ENZ field enhancement.