1. Introduction

Ultrafast intense lasers can generate unprecedented extreme physical conditions in a laboratory, enabling frontier studies in fields such as inertial confinement fusion, laser-driven particle acceleration, laboratory astrophysics, and laser plasma physics, etc. [1–3]. In particular, an ultrashort intense laser can ionize electrons from the atoms and stimulate high-harmonic generation (HHG) [4] for emitting attosecond pulses [5,6]. For example, in the HHG process, the photon emitted is given by the rule: $h{v_{SA}}_{\textrm{cutoff}} = {I_p} + 3.17{U_p}$ and ${U_p} \propto {I_L}{\lambda _L}^2$ is the quiver energy of the liberated electron in a laser intensity I_L and wavelength λ_L [7]. The extension of wavelength can effectively bright HHG to a soft x-ray region. Ultra-intense and ultrafast coherent mid-infrared (mid-IR) radiation sources have therefore become the focus of laser research because of their potential for application in particle acceleration [8,9], high-field physics [10], brighter hard X-rays and shorter attosecond pulse generation [11].

Owing to a lack of a mid-IR laser gain medium, the generation of mid-IR lasers usually depends on nonlinear frequency conversion pumped by a near-IR laser, including difference frequency generation (DFG) and optical parametric amplifiers (OPAs), which support the generation of ultrashort mid-IR pulses. Moreover, the optical parametric chirped-pulse amplification (OPCPA) technology offers the potential to generate intense mid-IR pulses [12,13]. Nonlinear optical (NLO) crystals play an important role in these nonlinear frequency conversion processes. An excellent mid-IR NLO crystal should have a wide transmission range (from near-IR into mid-IR beyond ∼5 µm), high laser damage thresholds (LDTs), an adequate nonlinear coefficient, large birefringence, and a large crystal aperture [14]. Commonly used mid-IR NLO crystals are usually divided into two categories: oxides and semiconductors. Oxide NLO crystals usually possess a high LDTs owing to their large energy gaps (preferably beyond 3.5 eV) [15] compared with those of semiconductor NLO crystals (usually below 3.0 eV) [16]. For example, the typical LDTs of the mature nonlinear optical crystals β-BBO (β-Ba₂B₂O₄), LBO (LiB₃O₅), KDP (KH₂PO₄), KTP (KTiOPO₄), and LN (LiNbO₃) are 4.5 GW/cm² (1.064 µm @ 10 ns @ 10 Hz) [17], > 0.9 GW/cm² (9 ns @ 1064 nm @ 10 Hz) [18],3–7 GW/cm²(1.064 µm @ 10 ns) [19], 1.5–2.2 GW/cm²(1064 nm @ 11 ns @ 2 Hz) [20], and 0.5−2 GW/cm² (1.064 µm @ 10 ns) [21], respectively. However, owing to multi-phonon absorption, the transmittances of these typical oxide NLO crystals are limited at the mid-IR edge of the spectrum, particularly in the region beyond 5 µm [22]. For example, the transmission ranges of β-BBO, LBO, KDP, KTP, LN are 0.189–3.5µm [23], 0.155–3.2µm [24],0.176–1.4µm [25],0.35–4.5µm [26],0.4–5.5µm [27], respectively. Semiconductor NLO crystals such as ZnGeP₂ (0.74−12 µm) [28], AgGaS₂ (0.47−13 µm) [29], LiGaS₂ (0.32–11.6µm) [30], GaSe (0.62−20 µm) [31], and BaGa₄Se₇ (0.47−18 µm) [32] usually have a large infrared cut-off that extends up to 20 µm. However, certain disadvantages, such as low LDTs, two-photon absorption, and limited crystal size, constrain their high-intensity application [33]. Therefore, mid-IR NLO crystals with excellent performance are urgently required for the generation of ultraintense and ultrafast mid-IR pulses.

Since the discovery of the langasite family of crystals with the Ca₃Ga₂Ge₄O₁₄ (CGG) [34] structure in the 1980s, more than 200 langasite-type crystals have been synthesized [35]. Certain langasite crystals, such as La₃Ga₅SiO₁₄ (LGS) [36], La₃Nb_0.5Ga_5.5O₁₄ (LGN) [37], La₃Ta_0.5Ga_5.5O₁₄ (LGT) [38], Ca₃NbGa₃Si₂O₁₄ (CNGS) [39], Sr₃NbGa₃Si₂O₁₄ (SNGS) [39], Ca₃TaGa₃Si₂O₁₄ (CTGS) [40], Sr₃TaGa₃Si₂O₁₄ (STGS) [41], and others [42] have been grown as single bulk crystals and applied to optoelectronic fields. For nonlinear optical applications, Stade et al. first proposed the possibility of second-harmonic generation (SHG) in LGN and LGT [43]. In 2014, Boursier et al. conducted a comprehensive study of the nonlinear optical characteristics of LGT [44], which motivated recent worldwide interest in mid-IR nonlinear optical applications using the langasite family of crystals [45–47]. Linear and nonlinear optical properties described by the Sellmeier equation, phase-matching curves, the nonlinear coefficient, and damage thresholds have since then been comprehensively studied. Mid-IR laser outputs with nJ-level femtosecond and µJ-level nanosecond pulses have subsequently been realized in LGN crystals [48,49]. Both theoretical studies and experimental results indicate that the LGN crystal is a promising mid-IR NLO crystal for OPA and OPCPA applications [10,45]. In this review, the nonlinearity contribution of each anion group was analyzed using first-principles calculations, and an optimized starting melting composition and temperature field for large-size crystal growth was also proposed. Linear and nonlinear optical properties such as transmission spectra, the Sellmeier equation, and nonlinear coefficients were studied in detail. Tunable mid-IR pulsed nanosecond and femtosecond DFG based on LGN crystals was discussed in detail. Finally, a 0.13 TW, seven-cycle, 5.2 µm OPCPA system using the LGN crystal was proposed for the generation of ultrashort and ultraintense laser sources.

2. Crystal structure and large-size growth of LGN crystal

2.1 LGN crystal structure

Langasite-group crystals with 32 point group were made up of four different kinds of polyhedral, described by the general formula A₃BC₃D₂O₁₄ In the LGN crystal, the AO₈ dodecahedra are filled by La³⁺ ions, the BO₆ octahedra are half filled by Nb⁵⁺ and Ga³⁺ ions, and the CO₄ and DO₄ tetrahedra are fully filled by Ga³⁺ ions, as shown in Fig. 1(a). The origin of the NLO effect in LGN crystals has been revealed using first-principle calculations [22]. The AO₈ dodecahedra contribute more than 80% of the overall second order nonlinear coefficient; the BO₆ octahedra make a small contribution and are able to respond to an external optoelectronic field in a more “flexible” manner to increase the nonlinear optical response. The CO₄ and DO₄ tetrahedra have negligibly small NLO effects owing to a three-fold rotation symmetry operation (C3) and two-fold rotation symmetry operation (C2), which offset the microscopic dipole moments of these tetrahedra. A structure-composition-property map for the langasite family was constructed to clarify the influence of the chemical element at the A and B sites, as illustrated in Fig. 1(b) [22]. The La³⁺ ions are the most beneficial with respect to improving the SHG response (pink region), and the heavy ions at the B site further increase the second order nonlinear optical effect (yellow region).

 

Fig. 1. (a) Polyhedral structure of LGN, and (b) structure-composition-property maps of langasites with different elemental compositions at the A and B sites. Adapted with permission from [ref 22] ©2018 American Chemical Society.

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2.2 Large-size crystal growth

Mid-IR nonlinear optical applications require a large-aperture crystal with a considerably high optical homogeneity to reduce loss, which is still a challenge in this field [37,50]. LGN crystals are normally obtained by the Czochralski pulling method and benefit from its congruent melting property. However, the production of large-size single crystals still presents certain difficulties, such as component supercooling derived from the co-occupancy of Nb⁵⁺ and Ga³⁺ in the B site, the volatilization of Ga₂O₃, and the presence of cracks owing to the inappropriate temperature gradient around the crystal-melt interface. The peritectic reaction frequently occurs, owing to melt-component deviation between the congruent melting component and the stoichiometric ratio. Takeda et al. examined the effect of melt components on crystal quality by measuring the variation in chemical composition and lattice parameters along the growth axis [51]. Yu et al. found that an addition of 1.0−1.5 wt% Ga₂O₃ is beneficial for high-quality LGN crystal growth [52]. An accurate subsolidus phase diagram for the LGN crystal was constructed by a solid-state reaction, as shown in Fig. 2(a) [53]. Thus, a critical starting polycrystalline composition range may be determined using the subsolidus phase relationship of the La-Ga-Nb-O system, to avoid a peritectic reaction and compensate for the volatilization of Ga₂O₃.

 

Fig. 2. (a) Subsolidus phase relations of La-Ga-Nb-O system. (b) The as-grown LGN crystal with a 60 mm diameter. Adapted with permission from [ref 53] ©2021 The Royal Society of Chemistry.

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According to the critical condition of component supercooling as depicted in Ref. [50], the large thermal gradient in the furnace can avoid the supercooling but lead to high thermal stress, especially in the shoulder part of crystal. The small temperature gradients decrease the Von Mises stress but increase the risk of constitutional supercooling. Thus the temperature field and growth parameters must be optimized for growing large-aperture LGN crystals. The temperature field of the solid–liquid interface can be adjusted by the type and thickness of the thermal insulation materials according to the simulation results based on the CGSim code [53]. Different furnace material thicknesses were applied to adjust the temperature gradient, as shown in Fig. 3(a)–(c). The von Mises stress distribution is shown in Fig. 3(d)–(f) and could be used to determine the risk of cracking under different temperature gradients. Therefore, the furnace material with appropriate temperature gradient and a low thermal stress was finally designed to solve the problem of component supercooling and cracking, as shown in Fig. 3(b) and 3(e). High-optical-quality LGN crystals with a diameter of 60 mm were recently obtained in our laboratory, as shown in Fig. 2(b).

 

Fig. 3. (a)–(c) Temperature gradient of the furnace (ΔT = 30 K), (d)–(f) Von Mises stress distribution of the LGN crystal. Reprinted with permission from [ref 53] ©2021 The Royal Society of Chemistry.

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3. Optical properties and mid-IR nonlinear optical applications

3.1 Optical properties of LGN

Linear and nonlinear optical properties such as the Sellmeier equation [43], nonlinear coefficient, and coherence lengths [54] and were simply characterized by Stade and Kaminskii et al. Additionally, a comprehensive and detailed characterization of the optical properties of LGN crystals was presented by our group [55]. The transmission range of LGN (0.28−7.4 µm) is wider than that of KTiOPO₄ (0.176−1.4 µm), KTiOAsO₄ (0.35−5.2 µm), and LiNbO₃ (0.4−5.5 µm) [56]. In an LGN crystal, the vibrations of the D-O bonds exhibit the highest phonon frequency (820 cm⁻¹), as shown in Fig. 4(b). The first-order infrared cut-off edge of the LGN crystal was determined to be 12.2 µm from the perspective of phonon energy [53]. The infrared absorption of crystals is strongly influenced by crystal structure and symmetry. In LGN crystals, the (DO₄) tetrahedron with a 3-fold rotation symmetry operation (C3) is closely connected with the (AO₈) dodecahedra and (CO₄) tetrahedron. The polarization along the c-axis was prohibited by D sites (Wyckoff position 2d) with a 2-fold rotation symmetry operation (C2). The second-order infrared absorption can be reduced by the special symmetry of polyhedrons. In addition, the polarization in the a-b plane was precluded by adjacent polyhedrons at A and C sites (Wyckoff positions 3e and 3f) that were constrained by the 3-fold rotation symmetry operation (C3). In addition, the second-order infrared absorption was impressed by the special symmetry of DO₄ polyhedrons. Thus, the infrared transmission edge of LGN crystal can be extended to 7.4 µm due to the reduction of two-phonon absorption [53].

 

Fig. 4. (a) Transmission spectrum of LGN, and (b) Raman spectrum of the LGN (1000) plane. Reprinted with permission from [ref 53] ©2021 The Royal Society of Chemistry.

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The Sellmeier equations of the LGN crystals were refined by directly measuring the phase-matching angles using an LGN sphere, as shown in Fig. 5(a) [57]. The phase-matching tuning curves of the Type-I SHG ($1/\lambda _{2\omega }^o = 1/\lambda _\omega ^e + 1/\lambda _\omega ^e$), Type- I DFG ($1/\lambda _i^e = 1/\lambda _p^o - 1/\lambda _s^e$) in the (y, z) plane, and Type- II DFG ($1/\lambda _i^o = 1/\lambda _p^\textrm{o} - 1/\lambda _s^e$) in the (x, z) plane are depicted in Fig. 5. The Sellmeier equations of the LGN were then corrected through the simultaneous fitting of all the experimental data. It should be noted that there are some discrepancies between the calculations and experimental data, especially above 2.3 µm, which were caused by the limits of measurements of refractive index.

 

Fig. 5. (a) Image of the LGN crystal sphere, (b) SHG phase matching in the (y, z) plane, (c) DFG phase matching in the (y, z) plane, and (d) DFG phase matching in the (x, z) plane. Wavelength accuracy is within the size of the dots. Adapted with permission from [ref 57] ©2018 The Optical Society.

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The nonlinear coefficient is an important performance parameter for assessing the capacity of nonlinear frequency conversion. The second-order nonlinear coefficient of LGN was measured using the Maker fringe setup [55]. In 2018, the d₁₁ of LGN was determined from the angle critical phase-matched Type-I SHG in the (y, z) plane using KTiOPO₄ (KTP) $d_{24}^{KTP}\textrm{ = }({{\lambda_{2{\omega_2}}} = 0.66\mu m} )= 2.37 \pm 0.17pm/V$ as a Ref. [57]. The coefficient $d_{24}^{KTP}$ governs the Type-II SHG ($1/\lambda _{{\omega _2}}^e + 1/\lambda _{{\omega _2}}^o = 1/\lambda _{2{\omega _2}}^o$) in the (x, z) plane of the KTP, the corresponding effective coefficient being $d_{eff}^{KTP} = d_{24}^{KTP}({{\lambda_{2{\omega_2}}}} )\sin [{{\theta_{P{M_2}}} - {\rho^e}({{\theta_{P{M_2}}},{\lambda_{2{\omega_2}}}} )} ]$ with ${\theta _{P{M_2}}}\textrm{ = }58.5^\circ$ and ${\rho ^e}({{\theta_{P{M_2}}},{\lambda_{2{\omega_2}}}} )\textrm{ = }2.57^\circ$ at the fundamental wavelength, ${\lambda _{2{\omega _2}}}\textrm{ = }1.32$µm. To maintain a fundamental wavelength consistent with KTP, we cut an LGN slab $({{\theta_{P{M_2}}}\textrm{ = }70.4^\circ , {\varphi_{P{M_1}}}\textrm{ = }90^\circ } )$ according to our refined Sellmeier equations [57]. Figure 6 depicts the corresponding SHG conversion efficiency ratio $\eta _I^{LGN}/\eta _{II}^{KTP}$ recorded as a function of the fundamental wavelength ${\lambda_{\mathrm{\omega}}}$ by measuring the fundamental beam and SHG energies. The peak wavelength was ${\lambda _{{\omega _1}}}\textrm{ = }1.317$µm for the LGN, which was extremely close to the target value ${\lambda _{{\omega _2}}}$. Under these conditions, we calculated $d_{eff}^{LGN}$ relative to $d_{eff}^{KDP}$, according to Equations (1–3):

 

Fig. 6. The calculated and measured conversion efficiency in LGN, relative to KTP crystal. Adapted with permission from [ref 57] ©2018 The Optical Society.

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Finally, we found that $|{{d_{11}}({0.659\mu m} )} |\textrm{ = }2.9 \pm 0.5\textrm{pm/V }$ and ${\delta _{11}}\textrm{ = }0.284 \pm 0.049pm/V$, which corroborates the value determined by the Marker fringes.

It should be noted that the LDTs of the LGN crystals have been measured using a pulsed laser with different pulse widths and repetition frequencies in terms of the International Standard Organization 11254-149-52 [58]. The value of LDTs was measured to be 1.41 GW/cm² under a 10-ns and 1-Hz pulse [55]. The LDTs value of 2.8 ± 0.7 GW/cm² were also determined with the width of 5 ns, repetition rate of 10 Hz and the energy of 500 ± 10 µJ [57]. This high LDTs value is rather helpful in withstanding high-intensity pumping light for ultra-intense and ultrashort mid-IR pulse generation.

3.2 Mid-IR nonlinear optical applications

LGN crystals with a wide transmission range, high LDTs, and superior phase-matching characteristics can meet the requirements of mid-IR nonlinear optical applications. We systematically calculated the phase-matching curves of SHG, SFG, and DFG using the refined Sellmeier equation in 2016 [55]. The Type-II optical parameter generation (OPG) with pumping at 1.064 µm was implemented using an LGN slab cut along the special direction ($\theta_{\textrm{PM}}$ = 52°, $\varphi_{\textrm{PM}}$ = 90°) [55]. LGN crystals are considered to be excellent potential NLO crystals for use in mid-IR nonlinear optical applications, particularly in high-intensity and ultrafast laser fields.

In 2021, we demonstrated tunable DFG with LGN crystals pumped by near-IR nano-second lasers pulses [49], and calculated the angle tuning curves for Type-I (o-ee) and Type-II (o-eo) phase matching as well as the corresponding effective nonlinear coefficients $d_{eff}^{o \to ee} = {d_{11}}{\cos ^2}\theta$ for the (y, z) plane and $d_{eff}^{o \to e\textrm{o}} = {d_{11}}\cos \theta$ for the (x, z) plane. The Type-II input-output results at different wavelengths change with the energy of pump beam laser, as shown in Figure.7. The measured and calculated output values marked in the red and blue lines, respectively, are depicted in Figs. 7(c) and 7(d). We find that the output values of Type -II were larger than Type-I due to the larger nonlinear coefficient in the (x, z) plane. It is worth noting that the DFG efficiency gradually drops by an order with the increasing wavelength from 4.6 µm to 5.6 µm due to the reduced d_eff and increased linear absorption in the LGN. The nanosecond mid-IR light source with high accuracy can achieve good application in gas detection.

 

Fig. 7. (a) Used LGN samples, (b) mid-IR Type-II DFG energy at different wavelengths, (c) measured and calculated output energy for Type-I DFG and (d) measured and calculated output energy for Type-II DFG. The insets of (c) and(d) show the fluctuated energy of the input signal at different signal wavelengths. Adapted with permission from [ref 49] ©2018 The Optical Society.

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Few-cycle femtosecond pulses that were tunable by intrapulse DFGs were reported with LGN crystals by Liu et al. [48]. To achieve the largest efficiency-bandwidth product (EBP), the dependences of both conversion efficiency and mid-IR idler bandwidth on crystal length were recorded, as shown in Figs. 8(a)–(d). With a 2-mm-thick LGN, the conversion efficiency was higher than 1‰ for the intrapulse DFG. The efficiencies are comparable to those obtained using a KTiOAsO₄ crystal [59], but are higher than those obtained using a LiIO₃ crystal [60]. In additions, the properties of the generated mid-IR spectra under different phase-matching angles θ were studied in detail. The mid-IR spectra of the Type-II intrapulse DFG exhibited a longer central wavelength than that of the Type-I case.

 

Fig. 8. (a), (b) Measured mid-IR idler spectra for Type-I (Type-II) intrapulse DFG with different crystal lengths. (c), (d) Conversion efficiency and (EBP) as a function of crystal length for Type-I (Type-II) intrapulse DFG. Adapted with permission from [ref 48] ©2020 The Optical Society.

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To generate ultra-intense and ultrafast mid-IR pulses, OPA and OPCPA should be adopted to convert the intense near-IR range into a mid-IR range. In 2019, the promising nonlinear crystal LiGaS₂ with a broad transmission range to 9 µm and large nonlinear coefficients (d₃₁= 5.8 pm/V, d₂₄= 5.1 pm/V, d₃₃=−10.7 pm/V) has been utilized in the 9 µm OPCPA system, generating a peak power of 0.1 GW [61]. However, comparing with the LGN crystal, the peak power could be limited by almost one order of magnitude lower damage threshold. In the meantime, the much stronger incongruent evaporation of the volatile components could lead to smaller aperture (7 mm × 7 mm currently) [62] in the LiGaS₂ crystal, limiting the application in the high-power OPCPA system [12]. Most recently, the OPCPA system that could generate 5.2 µm and terawatt-class seven-cycle pulses based on the large-sized LGN crystal has been designed by Ma et al. [12], after theoretically evaluating the phase-matching performance of LGN in mid-IR OPA and OPCPA [45]. As depicted in Fig. 9, LGN crystals are key elements in both seed pulse generation and multi-stage amplification processes. The octave-spanning Ti:sapphire laser and a Yb:YAG thin-disk pump laser play a significant role in the system.

 

Fig. 9. Schematic setup of OPCPA system based on LGN crystals. Adapted with permission from [ref 12] ©2019 Cambridge Core.

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Liu et al. simulated the amplification process of the pulses in the three-stage OPCPA system [12]. As shown in Fig. 10(a), three OPCPA stages based on LGN crystals amplify the 90-nJ mid-IR seed to 0.1, 2.8, and 16.5 mJ respectively, with a conversion efficiency of approximately 8%. Figures 10(b) and 10(c) show the evolution of the mid-IR chirped-pulse duration and spectrum, respectively. Finally, as shown in Fig. 10(d), the amplified mid-IR spectrum could support a 5.2 µm, 120 fs pulse duration. In addition, the dispersion of the system was strictly analyzed in detail. The designed mid-IR OPCPA system using LGN crystal will become an excellent ultrashort and ultra-intense laser source in the future.

 

Fig. 10. Simulation results for the proposed three-stage OPCPA. The evolution of (a) mid-IR pulse energy, (b) mid-IR pulse duration and (c) mid-IR spectrum. (d) Fourier transformation limited (FTL) pluse after OPCPA-3. Adapted with permission from [ref 12] ©2019 Cambridge Core.

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4. Conclusion

Herein, we reviewed the crystal structure, large-size growth, optical properties, and mid-IR nonlinear applications of LGN crystals. The large-diameter and high-optical-quality LGN crystals may be obtained by overcoming difficulties related to melt composition control and temperature field contribution. The mechanism of wide transparency was explained from the perspective of the intrinsic symmetrical structure of the crystal. The Sellmeier equation was refined by measuring the phase-matching angles of SHG and DFG. Tunable DFG mid-IR pulsed lasers based on LGN crystals pumped by nanosecond pulses were also described. Moreover, femtosecond pulses tunable in the range of 3−7 µm were achieved in two types of intrapulse DFGs. Finally, the usability of the LGN crystals in the intrapulse DFG and OPCPA was demonstrated through numerical simulations. All the results suggest that the LGN crystal is promising in the development of ultrashort mid-IR OPCPA systems, which are expected to promote the advancement of strong-field physics. For practically applying in the mid-infrared OPCPA system, the LGN crystal with larger size and higher optical quality should be fabricated in the future, and the influence of the microscopic defects in the crystal on the damage threshold needs to be further clarified as well. At the same time, the design of laser resonance should be optimized comprehensively to improve the conversion efficiency and output energy of the mid-infrared laser.