Volume electric dipole origin of second-harmonic generation from metallic membrane with non-centrosymmetry patterns

In this article, we analytically study second harmonic (SH) generation from thin metallic films with subwavelength, non-centrosymmetry patterns. Because the thickness of the film is much smaller than the SH wavelength, retardation effects are negligible. The far-field SH intensities are thus dominated by an effective electric dipole. These analytical observations are further justified numerically by studying the effect of polarization of the fundamental field on both the SH signal and the electric dipole. It is demonstrated that bulk SH polarization density is comparable with its surface counterpart. The electric dipole, consequently, originates from the entire {volume of the metallic membrane, in contrast to the fact that SH generation from metal surface is generally dominated by a surface dipole.