Light carries information and energy simultaneously. Manipulating light for communication and energy conversion significantly promotes the progress of human society. Initially, different types of lenses and mirrors are used to help people view further and smaller through telescopes and microscopes. Phenomena such as reflection, refraction, interference, and diffraction are well studied. Among these, the polarization density (P) within a medium is proportional to the electric field (E) of excitation light. As light intensity increases (specifically when a high-power laser is invented and introduced to optical research and production), interactions between medium and intense light fields normally show results that are different from those under traditional conditions. The concepts and applications of nonlinear optics are currently at the optical research stage.

Nonlinear optics, which describes the nonlinear interactions between light and nonlinear medium (i.e., P depends nonlinearly on E), is a significant component of modern optics for both fundamental research and technical applications. Nonlinear interactions involve various processes such as harmonic generation, spontaneous parametric downconversion, the Kerr effect, and the electro-optic effect. Utilizing these processes, we can expand the usable laser wavelength range from deep ultraviolet to terahertz bands and create light sources carrying quantum information. Various types of instruments based on nonlinear optics are available in optical laboratories and factories. Mode-locked lasers produce ultrashort laser pulses for time-resolved measurements and laser manufacturing. Optical parametric oscillators and optical parametric amplifiers can be used to produce wavelength-tunable lasers. Quantum light sources create entangled photon pairs for quantum communication. In these applications, the core components are efficient nonlinear processes. However, weak nonlinear interactions between most medium and phase mismatches result in low conversion efficiency. There are two main ways to improve the overall efficiency: finding materials with high nonlinear coefficients and exploring a highly efficient corresponding phase matching method.

Various high-performance optical crystal materials, including organic and inorganic materials, are studied and are still being widely pursued. Simultaneously, suitable phase matching methods are required for high conversion efficiency, which is crucial for practical applications. Phase matching methods are typically developed for a series of optical crystal materials with common properties. For example, birefringent phase matching is used for crystals with strong birefringent properties, whereas quasi-phase matching is suitable for polarized crystals. Therefore, the search for new types of high-performance nonlinear optical crystals must be accompanied by the corresponding phase matching methods. With the emergence of diverse materials with different properties, optical crystal material families and phase matching methods are being replenished.

Different types of nonlinear crystals and their corresponding phase matching methods have been developed over the past few decades. The most commonly used phase matching method is birefringent phase matching, which is first proposed in 1962. Here, a birefringent crystal separates the fundamental wave and second-harmonic generation (SHG) wave along different optical axes. A carefully selected incident polarization angle and cut angle of the crystal are required for precise refractive-index matching between the fundamental wave and SHG wave (Fig. 3). Utilizing birefringent phase matching, deep-ultraviolet laser generation is achieved with high conversion efficiency. Next, quasi-phase matching with inversion-poled domains is studied based on polarized materials such as lithium niobate crystals. The wavevector mismatch between the fundamental wave and the SHG wave is filled by a predesigned superlattice (Fig. 5). Through a unique periodic structure design, phase matching for third- and higher-order harmonic generation is realized, demonstrating the flexibility of quasi-phase matching (Fig. 6). Two-dimensional optical crystal materials attract significant attention because of their high nonlinear coefficients and excellent integration abilities (Fig. 7). However, traditional phase matching methods, such as birefringent and quasi-phase matching, cannot be applied to two-dimensional materials directly. The newly developed twist phase matching method can be used on layered materials, which exhibits high conversion efficiency and flexibility for two-dimensional materials such as rhombohedral boron nitride and one-dimensional materials such as multiwalled boron nitride nanotubes (Fig. 8).

In conclusion, different types of nonlinear optical crystals and their corresponding phase matching methods are developed for various applications. Nowadays, new families of optical crystals are under study for higher conversion efficiencies, broader wavelength ranges, and novel functionalities. New phase matching mechanisms for highly efficient and universally applicable nonlinear crystal materials are also being pursued. In the future, optical crystals together with corresponding phase matching methods working in the extreme wavelength range (i.e., deeper ultraviolet and longer terahertz wavebands), generating ultrahigh output power, integrating with on-chip photonic circuits, and carrying quantum information are predicted to remain in high demand.