Second harmonic–sum frequency generation in a thin spherical layer. III. Properties of the solution

Mathematical properties of functions characterizing symmetries of spatial distribution of second harmonic–sum frequency radiation are determined. The conditions at which there occurs no generation and the conditions at which the polarization of the generated radiation is linear are found. The revealed properties are systematized by their manifestations in the directivity patterns of the generated radiation. Methods based on these properties for determining the components of the nonlinear dielectric susceptibility tensor are proposed. The relationship is described between the revealed properties as well as conditions and previously found similar properties and conditions for the phenomena of second–harmonic generation and sum–frequency generation.