Second harmonic generation from centrosymmetric thin films by a focused beam with arbitrary transverse structure

We study the scattering of optical second harmonic (SH) radiation from a homogeneous centrosymmetric thin composite film illuminated by a focused beam with arbitrary transverse mode structure. The transverse field distribution of the incident beam is described by combinations of linearly polarized Hermite-Gauss modes. A distinctive feature of the calculated SH radiation angular patterns is the possibility of scattering along the forward direction if a proper combination of different cross-polarized modes is present in the incoming beam. This is in contrast to what was found in previous theories of SH light scattering from small spheres and in experiments with colloidal particles and spherical nanocrystals excited by simple beams.