Influence of stochastic deviations of domain boundary and varying effective index on difference frequency mixing in quasi-phase-matching waveguides

Influence of stochastic deviations of domain boundary and varying effective index on the conversion efficiency of difference frequency mixing (DFM) in quasi-phase-matching waveguides are analyzed. By simplifying the coupled equations of DFM in waveguide according to the actual situation, we provide analytical expressions of the conversion efficiency for the first time. Four models for random errors of domains and variations of effective index are investigated. The results demonstrate that, when the effective index varies regularly along the waveguide, the normalized conversion efficiency ηˆ of DFM is dramatically reduced and the curves of ηˆ on phase mismatch are no longer sinc2 function but ripple profiles, which is different from the situation in bulk crystals. With the same magnitude, random period error cast much larger effect on ηˆ than random duty cycle error, which is similar with the case in bulk crystals.