Second-order cascading in third-order nonlinear optical processes

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Abstract
Because cascaded second-order processes make substantial qualitative and quanitative differences to the results of third-order nonlinear optical experiments, a formalism for their treatment is presented. The symmetry dictates concerning the occurrence and relationships of magnitudes of cascading are tabulated for the higher symmetry crystal classes. Angular momentum considerations are applied to the situations allowing circularly polarized light waves.