Spatial–temporal evolution of ultrashort laser pulse second harmonic generation in β-barium borate (β-BBO) crystal

Abstract

We establish an effective and efficient theoretical approach called the spatial–temporal broadband nonlinear coupled wave theory (ST-BNCWT) to evaluate the spatial and temporal evolution behaviors of femtosecond laser pulse second harmonic generation (SHG) in a nonlinear medium. In this method, all the frequency components comprising the fundamental-wave laser pulse participate in a series of complicated three-wave mixing nonlinear coupling, including sum-frequency generation, difference-frequency generation, and the usual SHG, to create a second harmonic wave pulse. The contribution from each three-wave mixing process is strongly influenced by the corresponding phase matching or mismatching. We have used this method to analyze systematical transmission evolution characteristics of ultrashort laser pulses in a β-barium borate crystal and disclose the variation of a number of critical physical quantities. Our ST-BNCWT methodology can greatly facilitate the deep understanding of the SHG and various pulse transmission characteristics of ultrashort laser pulses and provide great support and guidance for experimental prediction. Moreover, our scheme opens up a promising path to explore and visualize novel nonlinear optical interactions in solid-state materials spanning the spatial and temporal domain, which are very helpful for building versatile ultrafast lasers in various spectral windows via powerful nonlinear frequency conversion technology against a basic high-performance ultrafast laser such as a Ti:sapphire femtosecond laser.