Analysis of cascaded second-order nonlinear interaction based on quasi-phase-matched optical waveguides

Wavelength conversions based on the cascaded second-order nonlinear interaction in nonlinear optical medium with periodical structures are studied both theoretically. Analytical expressions with clear physical insights are, for the first time, derived for the converted light by the step-by-step method. It is shown that the obtained expressions are valid in large ranges of device parameters, and have features such as simple form, high accuracy, and less computing time. Simulations using the obtained expressions are compared with the experimental results of a MgO-doped LiNbO₃ quasi-phase matched waveguide. It is found that our simulations are consistent well with the experimental results