The generation process of second-harmonic radiation from holes periodically arranged on a metal surface is investigated. Three main modulating factors affecting the far-field distribution and the transmission efficiency are identified: the near-field distribution at the wavelength of the driving source (fundamental harmonic), how second-harmonic light couples to the diffraction orders of the lattice, and its propagation properties inside the holes. It is shown that light generated at the second harmonic can excite electromagnetic modes otherwise inaccessible in the linear regime under normal incidence illumination, a singularity of second-harmonic fields that affects the radiation process. For instance, the least decaying transversal electric mode accessible to the external beam is able to generate a superposition of high-order modes ( and ) at the second harmonic. It is demonstrated that the emission of second-harmonic radiation is only allowed along off-normal paths precisely due to that symmetry. In this work, two different regimes are studied in the context of extraordinary optical transmission, where enhanced linear transmission either occurs through localized electromagnetic modes or is aided by surface plasmon polaritons (SPPs). While localized resonances in metallic hole arrays have been previously investigated, the role played by surface plasmons in second-harmonic generation has not been addressed so far. In general, good agreement is found between our calculations (based on the finite difference time domain method) and the experimental results on localized resonances, even though no free-fitting parameters were used in describing the materials. It is found that second-harmonic emission is strongly modulated by enhanced fields at the fundamental wavelength (either localized or surface plasmon modes) on the glass–metal interface. This is so in the transmission side but also in reflection, where emission can only be explained by an efficient tunneling of second-harmonic photons through the holes from the output to the input side. Finally, the existence of a dark SPP at the fundamental field is identified through a noninvasive method for the first time, by analyzing the efficiency and far-field pattern distribution in transmission at the second harmonic.
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