  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.
