Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material

We describe the electromagnetic theory of second-harmonic generation from the surface of a sphere that is small compared to the wavelength of light. In a leading-order expansion, the second-harmonic radiation is emitted in nonlocally excited electric dipole and locally excited electric quadrupole modes. We analyze the problem with particular emphasis on experimental aspects, such as the radiation pattern, polarization selection rules, determination of nonlinear susceptibilities, radiation efficiency, and spectral characteristics.