Effect of pump depletion on second harmonic generation in multiple quasi-phase-matching gratings

Second harmonic generation (SHG) from the aperiodic optical superlattice (AOS) in considering the pump depletion is investigated. It is found the domain configuration designed in undepleted pump approximation (UPA) can also be used to achieve multiple wavelength SHGs with high enough conversion efficiency for an exact solution. The applicable scope of UPA was estimated by a relative tolerance based on the related SHG conversion efficiency calculated in UPA and an exact solution. Results reveal that the relative tolerance is solely determined by the conversion efficiency, and unrelated to the sample configuration, pump intensity, incidental wavelength and nonlinear media. A model to evaluate an exact solution is proposed, and it is suggested that the SHG conversion efficiency can be easily assessed by the developed model. These results can be used to provide direct guidance for practical application, and can also make the estimation of practical samples more convenient.