Theoretical analyses of multiple quasi-phase-matched third-harmonic generation for all configurations

A general theory for multiple quasi-phase-matched third-harmonic generation is investigated systematically. We find that there are up to 24 configurations for third-harmonic generation by cascaded two-parametric processes. All these configurations can be divided into three categories based on the coupling types of the harmonic fields. Each category has a set of coupled wave equations that describe its characteristics. The analytical solutions reveal some features, such as the polarization tuning and quasi-phase-matched gap effect.