Quantitatively extracting the contribution of asymmetric local-field to χ (2) in cross-shaped Ag nanoholes

We systematically study the contribution of local-field distribution to second-harmonic generation (SHG) in cross-shaped Ag nanohole arrays, which is usually covered by resonance enhancement effect. By increasing one arm-length of the centrosymmetric cross-shaped Ag nanohole, the local-field distribution varies from centrosymmetric to non-centrosymmetric, while the localized surface plasmon resonance peak is red-shifted to the wavelength of the pumping laser accordingly. Both experimental and stimulated results indicate that the contribution of the asymmetric local-field distribution to SHG is quantitatively separated from a strong resonance enhancement effect. It shows that the pure effective second-order nonlinear susceptibility increases as the asymmetric degree of local-field distribution increases, and the largest effective second-order nonlinear susceptibility is ~2.5 times to that in a centrosymmetric local-field distribution. Our results provide evidence for optimizing the design of nonlinear plasmonic nanoantennas and metasurfaces.