The coupled-wave theory is used in the analysis of the interactions among optical waves of different frequencies. In the analysis of the coupling of waveguide modes, coupled-mode theory has to be used. In general, both the interaction among different optical frequencies and the characteristics of the waveguide modes have to be considered for a nonlinear optical interaction in an optical waveguide. In the first section, a combination of coupled-wave and coupled-mode theories is formulated for the analysis of nonlinear optical interaction in a waveguide. In the second section, the coupled equations for a parametric nonlinear interaction in a waveguide are formulated by using three-frequency parametric interaction, second-harmonic generation, and the optical Kerr effect as three examples. In the third section, the coupled equations for a nonparametric nonlinear interaction in a waveguide are formulated by using stimulated Raman scattering and two-photon absorption as two examples.
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