Sum-frequency generation from a thin spherical layer: I. Analytical solution

In the tensor form, using the generalized Rayleigh–Gans–Debye approximation, the problem of the sum-frequency generation from a thin nonlinear layer deposited on a dielectric spherical particle placed in a dielectric medium is solved. The second-order nonlinear dielectric susceptibility tensor is chosen in a general form containing chiral components. In the vector and tensor forms, expressions are obtained that describe the spatial distribution of the sum-frequency radiation field generated by two plane electromagnetic elliptically polarized waves. Limiting expressions that describe the spatial distribution of the sum-frequency harmonic at small and large radii of the spherical layer are obtained. It is revealed that, at small radii of the spherical layer, the radiation due to the chiral anisotropy coefficients makes a dominant contribution to the generation.