High-power tunable mid-infrared (MIR) and far-infrared (FIR) lasers in a range of 3-20 μm, especially in the atmospheric windows of 3-5 μm and 8-12 μm are essential for the applications, such as in remote sensing, minimally invasive surgery, telecommunication, national security, etc. At present, the technology of MIR and FIR laser have become a research hotspot. As the core component of all-solid-state laser frequency conversion system, nonlinear optical (NLO) crystals for coherent MIR and FIR laser are urgently needed by continuously optimizing and developing. However, compared with several outstanding near infrared, visible, and ultraviolet NLO crystals, such as <i>β</i>-BaB<sub>2</sub>O<sub>4</sub>, LiB<sub>3</sub>O<sub>5</sub>, LiNbO<sub>3</sub>, KTiOPO<sub>4</sub>, and KBe<sub>2</sub>BO<sub>3</sub>F<sub>2</sub>, the generation of currently available NLO crystals for 3-20 μm laser is still underdeveloped. Traditional NLO oxide crystals are limited to output wavelengths ≤ 4 μm due to the multi-phonon absorption. In the past decades, the chalcopyrite-type AgGaS<sub>2</sub>, AgGaSe<sub>2</sub> and ZnGeP<sub>2</sub> have become three main commercial crystals in the MIR region due to their high second-harmonic generation coefficients and wide IR transparency ranges. Up to now, ZnGeP<sub>2</sub> is still the state-of-the-art crystal for high energy and high average power output in a range of 3-8 μm. Unfortunately, there are still some intrinsic drawbacks that hinder their applications, such as in poor thermal conductivity and low laser damage threshold for AgGaS<sub>2</sub>, non-phase-matching at 1.06 μm pumping for AgGaSe<sub>2</sub>, and harmful two-photon absorption at 1.06 μm for ZnGeP<sub>2</sub>. In addition, ZnGeP<sub>2</sub> has significant multi-phonon absorption in an 8-12 μm band, which restricts its applications in long wavelength MIR. With the development of research, several novel birefringent crystals, as well as all-epitaxial processing of orientation-patterned semiconductors GaAs (OP-GaAs) and GaP (OP-GaP), have been explored together with attractive properties, such as large NLO effect, wide transparency ranges, and high resistance to laser damage.<br/>In this paper, from the angle of the compositions of NLO crystal materials, several kinds of phosphide crystals (ZnGeP<sub>2</sub> CdSiP<sub>2</sub>) and chalcogenide crystals (CdSe, GaSe, LiInS<sub>2</sub> series, and BaGa<sub>4</sub>S<sub>7</sub> series) are summarized. In addition, the latest achievements of the orientation-patterned materials such as OP-GaAs and OP-GaP are also reviewed systematically. In summary, we review the above-mentioned attractive properties of these materials such as in the unique capabilities, the crystal growth, and the output power in the MIR and FIR region.
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