Significance Nonlinear optical crystals exhibit secondary or higher- order nonlinear optical effects under strong laser fields and are commonly used for wavelength/frequency conversion of lasers. They have played a vital role in various fields, such as nonlinear optics, laser communication, laser technology, and military medicine. Common nonlinear optical crystals include lithium niobate (LiNbO3, abbreviated as LN), lithium tantalate (LiTaO3, abbreviated as LT), and potassium titanium phosphate (KTiOPO4, abbreviated as KTP). Key indicators for evaluating the performance of nonlinear crystal materials include large nonlinear optical coefficients, wide transparency range, and high damage threshold. Modulation of nonlinear coefficients is crucial for enhancing the performance of these materials. For instance, by periodically adjusting the nonlinear coefficients (i. e ., spontaneous polarization or ferroelectric domains) of the multifunctional ferroelectric LiNbO3 crystal, nonlinear photonic crystals (NPCs) could be fabricated, significantly improving the conversion efficiency of processes like frequency doubling and spontaneous parametric down conversion. Currently, the primary techniques for fabricating NPCs in LiNbO3 crystals are electrical poling and optical poling. While electrical poling yields excellent performance and is commercialized, its technological process is complex and requires custom masks for each NPC design, increasing manufacturing costs. Traditional electrical poling techniques have demonstrated unique strengths in creating one- dimensional (1D) and two-dimensional (2D) NPCs. However, it encounters significant hurdles when attempting to fabricate three-dimensional (3D) NPCs, presenting substantial experimental challenges within the field of nonlinear optics over the past two decades. There are two primary types of optical poling techniques: light- assisted poling and all- optical poling. Light- assisted poling is characterized by the use of ultraviolet laser irradiation to facilitate the poling process. In contrast, all- optical poling employs either continuous or pulsed lasers to accomplish the poling procedure. By focusing a femtosecond laser into LiNbO3 crystals using a lens or microscope objective, the material's nonlinearity at the focal point can be effectively modulated. If material nonlinearity is modulated throughout a three-dimensional space, the fabrication of 3D NPCs can be achieved. This all- optical poling technique has become extensively adopted in precision material processing, referred to as femtosecond laser direct writing. The utilization of femtosecond laser direct writing overcomes the obstacles associated with manufacturing 3D NPCs, significantly contributing to achieving high- efficient nonlinear frequency conversion and nonlinear beam shaping. Progress Femtosecond laser direct writing technique offers rapid processing speed, high processing accuracy, and flexibility, enabling fast and efficient fabrication of 3D micro-/nanoscale photonic structures. The modulation of nonlinear optical coefficients depends not only on the selected femtosecond laser parameters but also on the intrinsic properties of nonlinear optical crystals, such as bandgap and dispersion. In 2018, with femtosecond laser direct writing technique, Xu et al. fabricated 3D NPCs in ferroelectric barium calcium titanate (Ba0.77Ca0.23TiO3, abbreviated as BCT) crystals by inducing ferroelectric domain inversion (Fig. 1) using femtosecond laser direct writing. Similarly, Wei et al. induced ferroelectric domain erasure in LiNbO3 crystals to fabricate 3D NPCs (Fig. 7). These studies mark the earliest reports on 3D NPC fabrication using femtosecond laser direct writing, turning the exploration of 3D NPC capabilities into a research focus in nonlinear optics. In the past five years, the notable achievement of femtosecond-laser-induced nanodomains has significantly advanced the field of femtosecond laser modulation of ferroelectric crystal domains (Fig. 3). Additionally, in the domain of femtosecond laser modulation of quartz- crystal nonlinear coefficients, the introduction of the additional periodic phase (APP) theory (Fig. 11) has enabled the generation of high- efficiency deep- ultraviolet lasers. Furthermore, the experimental demonstration of second- to- fifth harmonic generations (Fig. 12) marks substantial progress. The utilization of femtosecond laser direct writing technique in fabricating NPCs has overcome a significant challenge in producing 3D NPCs in nonlinear optics over the previous two decades. This development has not only extended the application range of femtosecond laser direct writing but also reinforced its crucial role in nonlinear optics. Conclusions and Prospects With femtosecond laser direct writing, we can periodically modulate the optical nonlinearity of nonlinear crystals leading to the formation of 1D, 2D, and 3D NPCs. This capability is of great significance for achieving high- efficient nonlinear frequency conversion and nonlinear beam shaping applications. Our study succinctly summarizes recent advancements in modulating the nonlinear properties of ferroelectric and quartz crystals using femtosecond laser direct writing. For ferroelectric crystals, the main focus lies on domain inversion, domain erasure, and domain modification. We elucidate the connections and differences among these processes and highlight their potential applications in nonlinear frequency conversion, nonlinear holography, and nonlinear beam shaping. In the case of quartz crystals, we primarily utilize APP phase matching as a key technique to introduce the applications of laser- written APP quartz crystals. These applications include the generation of ultraviolet lasers and the production of high- order harmonics. As our understanding of the interactions between femtosecond lasers and nonlinear crystals deepens, along with the emergence of new nonlinear optical materials and beam- shaping- based femtosecond laser direct writing, further groundbreaking results are anticipated in the field of femtosecond laser modulation of crystal optical nonlinearity.
