Optimal design and applications for quasi-phase-matching three-wave mixing

Solutions of quasi-phase-matching three-wave mixing (TWM) for a nonuniform grating structure with phase-shifted segments are derived by use of a matrix operator, for the first time to the authors' knowledge, under the small-signal approximation. Compared with iterative methods of coupled-mode equations, using these expressions can significantly shorten the calculation time, and they can be effectively applied to all-optical signal processing in TWM. The signal and pump bandwidths of wavelength conversion in difference-frequency mixing, as well as the all-optical gating bandwidth in sum-frequency mixing, are optimized with the matrix solutions. By comparison with loss-free waveguide, the propagation loss alpha of the waveguide decreases the conversion efficiency eta, but has little influence on the bandwidth. Numerical results show that alpha can be ignored for nonlinear lengths L < 20 mm, and the optimal bandwidth Δλ is sensitive to η and the variation in the grating period, but not to α.