Interference-Engineered Metal-ITO Metasurfaces for Tailored Second- and Third-Harmonic Emission

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 shows 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 χ(2) for ITO to match spectra; a static χ(2) fails. Angle-resolved SHG/THG cannot be reproduced with purely real coefficients; grouped contributions to χ(3) (and the effective χ(2)) must be complex. Using a hydrodynamic model for the metal and ITO with linear dispersion plus dispersive χ(2) and χ(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 fields, 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 χ(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. This interference-based picture enables inverse design of metal-ITO ENZ metasurfaces with tailored SHG/THG angular patterns for compact frequency converters, directional nonlinear emitters, and on-chip spectroscopy.