Exact coupled-mode theory of waveguide quasi-phase-matched second harmonic generation

Quasi-phase-matched (QPM) devices have received considerable attention as efficient short-wavelength generating devices. With the advance of periodic nonlinearity modulation techniques, efficient QPM harmonic generation has been achieved. Among the QPM devices, channel waveguide QPM ones are the most efficient and important because they can effectively guide nonlinear interactions through a long propagation length while preserving high intensities. On the other hand, the analysis of QPM frequency conversion has been predominantly accomplished via coupled-mode theory and non-depleted pump wave approximation. That is, for the purpose of obtaining physical and qualitative concepts, many useful and qualitatively approximated approaches have widely been used even though exact solutions exist. At this point, an exact and quantitative study is also required for the precise analysis and design of QPM devices. Considering the importance of the waveguide QPM device, an exact formulation is truly necessary. We derive exact mathematical expressions for nonlinear interactions in waveguide device and propose an exact coupled-mode theory analysis for the waveguide QPM second harmonic generation.