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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.

In nonlinear optical systems, the optical superposition principle breaks down. The system's response (including electric polarization, current density, etc) is not proportional to the stimulus it receives. Over the past half century, nonlinear optics has grown from an individual frequency doubling experiment into a broad academic field. The nonlinear optics has not only brought new physics and phenomena, but also has become an enabling technology for numerous areas that are vital to our lives, such as communications, health, advanced manufacturing, et al. This Roadmap surveys some of the recent emerging fields of the nonlinear optics, with a special attention to studies in China. Each section provides an overview of the current and future challenges within a part of the field, highlighting the most exciting opportunities for future research and developments.

Nonlinear Raman–Nath diffraction (NRND) offers an effective way to realize multiple noncollinear parametric processes based on the partially satisfied transverse phase-matching conditions in quadratic nonlinear media. Here, the realization of ultrabroadband NRND (UB-NRND) driven by a high-peak-power ultrashort femtosecond pump laser in two types of nonlinear crystals is reported: periodically poled lithium niobate (PPLN) and chirped PPLN (CPPLN). Multi-order ultrabroadband Raman–Nath second-harmonic (SH) signal outputs along fixed diffraction angles are simultaneously observed. This distinguished transversely phase-matched supercontinuum phenomenon is attributed to the synergic action of natural broad bandwidth of an ultrashort femtosecond pump laser and the third-order nonlinear effect induced spectral broadening, in combination with the principal ultrabroadband noncollinear second-harmonic generation processes. The NRND process with multiple quasi-phase matching (QPM) interactions from CPPLN leads to the SH output covering a wide range of wavelengths between 389 and 997 nm and exhibiting an energy conversion efficiency several orders of magnitude higher than previous studies. This UB-NRND scheme would bring better techniques and tools for applications ranging from ultrashort pulse characterization and nondestructive identification of domain structures to accurate parameter monitoring of second- and third-order nonlinear susceptibilities within solid-state nonlinear microstructured materials.