Section-wise-exact coupled-mode theory of waveguide quasi-phase-matched second-harmonic generation

We derive exact mathematical expressions for both the amplitude and phase evolution of optical waves due to linear and nonlinear interactions in a waveguide device and propose a section-wise-exact coupled-mode theory analysis for quasi-phase-matched second-harmonic generation in the waveguide. Section-wise-exact coupled-mode theory is readily applicable to nonuniform quasi-phase-matched gratings and can be useful as a quantitative method in their analysis and design. Using the method, several numerical results are presented for second-harmonic generation in periodically poled LiNbO/sub 3/ channel waveguides. In addition, we introduce a split-step method which takes propagation losses into account and which can include linear and two-photon absorption and waveguide losses.