Optical second-harmonic scattering from cylindrical particles

The theory of optical second-harmonic (SH) scattering from finite cylinders of arbitrary size, orientation, and crystallographic structure is developed within the Rayleigh-Gans-Debye approximation for plane-wave excitation. Both cases of particles comprised of noncentrosymmetric and centrosymmetric media are examined. For particles comprised of noncentrosymmetric media, all nonlinear susceptibility elements share a common "linear" scattering form factor. For centrosymmetric media, the various nonlinear susceptibility components arising from the surface response experience different scattering form factors. Regardless of the type of media, SH scattering from finite cylinders may be described in terms of an effective nonlinear susceptibility tensor for the particle. Several essential aspects of the SH scattering process are analyzed, such as the radiation patterns and their dependence on particle orientation and input polarization, its chiral response, as well as the size and wavelength scaling for small particles.