We experimentally and theoretically investigate the influence of alumina coating on the second-harmonic generation (SHG) from split-ring resonator shaped air apertures engraved in a gold film, which are also termed as complementary split-ring resonators (CSRRs). By coating the CSRR arrays with alumina film of certain thickness, we precisely tune their electric diploe resonances (EDRs) to overlap the fundamental wavelength (FW) and realize the EDR enhanced SHG process. On this basis, by shortening the arm length of the CSRRs and then coating them with a certain thickness of the alumina film, we have achieved an SHG enhancement of nearly 1.2-fold in experiment and 8-fold in simulation compared to the CSRR array with an unshortened arm length. We attributed it to the improvement of the magnitude of the effective nonlinear source due to the realization of a doubly-resonant condition. As a flexible method, dielectric coating not only is beneficial to precisely and dynamically optimize the linear and nonlinear properties of the as-fabricated nanoscale devices but also can play the role of a protective layer, which can partially improve the damage threshold of these plasmonic nanoscale devices.
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