Large reduction in second and third harmonic signals is measured when a sub-nanometer-to-nanometer thick insulator film is deposited over a gold substrate. Such reduction in signal reveals the spilled-out electronic states in the insulator region at the vicinity of the metal-insulator (MI) interface, which are dubbed metal insulator gap states. For metal-insulator-metal (MIM) structures, we observe electric-field enhancement saturation and quenching of the third harmonic efficiencies well above the efficiencies for MI samples. The measured harmonics of incident light scattered from the MI and MIM systems are compared with detailed simulations that account for the nonlinear interactions of free electrons spilled out into the insulator and the nonlocality and electron quantum tunneling effects. Two insulator materials (ZnO and Al2O3) are used in the experiments, and atomic layer deposition is used to cover the gold substrate with variable thickness of the insulator films. On the basis of our simulations, we conclude that the observed MIM third-harmonic signal enhancement (and quenching) effects are primarily due to the nonlocal phenomena in an electron gas. As a consequence of our findings, second- and third-harmonic scattering signals can be analyzed to extract the spill-out electron density in the insulator.

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