Nonlinear Mie theory for second-harmonic and sum-frequency scattering

We present a theory for second-order nonlinear light scattering from spherical particles using source waves of arbitrary frequency and direction based on a combination of linear Mie scattering and reciprocity theory. The theory presented in this work extends existing theory applied to second-harmonic scattering by allowing noncollinear excitation waves of unequal frequency. The absence of an intrinsic symmetry axis was overcome by using a nonstandard expansion for the linear interaction. Numerical results obtained for water droplets in air show an increase in the number of observed maxima in the sum-frequency scattering pattern compared to index-matched theories, as well as a strong backscatter peak, which eventually dominates the scattering pattern. Our method opens up possibilities for studying increasingly complex colloidal systems with nonlinear light scattering spectroscopy.