Quadratic Cascading in Quasi-Phase-Matching: An Alternative Route to Efficient Third-Harmonic Generation

We report on the theoretical/numerical investigation of simultaneous second- and third-harmonic generation from a single wavelength input in quasi-phase-matched crystals. The presented technique consists of a quadratic crystal with two first-order quasi-phase-matched sections: one designed for quasi-phase-matching to second-harmonic generation and the other for quasi-phase-matching to third-harmonic generation via sum-frequency generation. We identify an optimal length ratio (optimal number of domains) for these sections in order to enhance the conversion to the third harmonic, achieving nearly complete energy transfer. The advantages of the method are demonstrated both numerically and analytically, with a specific example using periodically poled lithium niobate. Quadratic cascading with quasi-phase-matching proves to be an effective approach for achieving cubic-like effects with high conversion efficiencies.