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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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L. Carletti, D. Rocco, A. Locatelli, C. D. Angelis, V. F. Gili, M. Ravaro, I. Favero, G. Leo, M. Finazzi, L. Ghirardini, M. Celebrano, G. Marino, and A. V. Zayats, “Controlling second-harmonic generation at the nanoscale with monolithic AlGaAs-on-AlOx antennas,” Nanotechnology 28, 114005 (2017).

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[Crossref]

M. Scalora, M. A. Vincenti, D. de Ceglia, and J. W. Haus, “Nonlocal and quantum-tunneling contributions to harmonic generation in nanostructures: electron-cloud-screening effects,” Phys. Rev. A 90, 013831 (2014).

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Note that these nonlocal corrections originate from the composite nature of the plasmonic metamaterial and not from the optical response of its components, which is assumed to be described by local εAu and εh.

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We assume that the fields propagate in xz plane; s-polarized light has non-zero components of Ey,Hx,Hz, while the p-polarized light has components of Ex,Ez,Hy fields. We limit our study to the regime when the metamaterial is excited by a single electromagnetic wave that is either p or s polarized. The detailed investigation of more complicated excitation geometries and the analysis of tensorial properties of χα;βγ(2) will be the subject of future work.

The commercial software (COMSOL, www.comsol.com) implements a model of a periodic Au nanorod array with εAu given by Drude model, εAl2O3≈2.74, and geometrical parameters (r, a) deduced from the structures used in the experiments.