Far-field radiation patterns of second harmonic generation from gold nanoparticles under tightly focused illumination

We study far-field angular radiation patterns of second harmonic generation (SHG) from gold nanosphere, nanocube, nanorod, and nanocup illuminated by tightly focused linearly and radially polarized beams, respectively. It is found that under linearly polarized illumination, far-field forward-scattering SHG (FSHG) dominates second harmonic (SH) responses generated by those gold particles. On the contrary, it is amazing that significant backward-scattering SHG (BSHG) can be observed when those gold nanoparticles are excited by a focused radially polarized beam. For the case of gold nanosphere, the effective point dipole systems are developed to reasonably elucidate this interesting difference. Our investigations suggest that for SHG microscopy with backward detection scheme, tightly focused radially polarized beam could be a promising excitation field to improve the backward SH signal.