Barium Chalcogenide Crystals: A Review

Abstract

In recent decades, new nonlinear optical materials have been actively developed to create coherent tunable light sources in the mid-infrared (mid-IR) part of the spectrum used in a variety of scientific fields. In the present review, the main attention is focused on barium chalcogenide crystals, including their linear and nonlinear optical properties, laser-induced damage threshold (LIDT), and frequency down-conversion.

1. Introduction

The growing significance of mid-IR tunable coherent sources is becoming more apparent due to the constant advancements in modern technologies, medicine, industry, and science. This progress necessitates the use of more precise and reliable tools for diagnostics, control, and measurements. This specific part of the spectrum encompasses the main transparency windows of the atmosphere. These windows exhibit the characteristic absorption lines of vibrational–rotational transitions of various gases, including H₂O, CO₂, CH₄, NO, N₂O, and others [1]. Moreover, the mid-IR range includes transparency regions for many biological objects and compounds of a biological origin, as well as optical and semiconductor materials. As a result, such sources find a wide range of applications, including atmospheric monitoring systems [2,3], noninvasive medical diagnostics [4,5], thermography (thermal imaging) [6], laser surgery [7,8], and various other applications. In various applications, particularly gas analysis applications, the mid-IR range sources listed below are commonly used: CO and CO₂ gas lasers [3,7] along with their frequency-doubled radiation [9,10]; hydrogen fluoride (HF) and deuterium fluoride (DF) chemical lasers [11]; solid-state lasers utilizing crystals doped with transition metals and rare earth ions [12]; III-V diode and IV-VI lead salt diode lasers [13]; tunable quantum cascade lasers (QCLs) [14,15]; and frequency down-converters, like optical parametric oscillators (OPOs) and difference frequency generators (DFGs) [16,17].

The employment of a CO laser enables the discrete tuning of the radiation wavelength within the spectral range spanning from 4.9 $\mathsf{\mu }$m to 7.5 $\mathsf{\mu }$m. Furthermore, it is feasible to produce radiation based on transitions of the first vibrational overtone within the spectral range of 2.5–4.2 $\mathsf{\mu }$m [18]. A discretely tunable CO₂ laser generates radiation within a range of 9.2 $\mathsf{\mu }$m to 10.6 $\mathsf{\mu }$m [19]. Using the isotopes of carbon dioxide molecules as an active medium, the spectral range that encompasses the frequencies of the primary lines of a CO₂ laser can be significantly extended to 8.9–12.3 $\mathsf{\mu }$m [18]. In addressing gas analysis challenges, the feasibility of utilizing CO and CO₂ lasers hinges on the precise alignment of the laser emission lines with the absorption lines of the gases being studied. Since absorption lines of substances may lie between the generation lines of gas lasers, nonlinear frequency converters driven by CO and CO₂ gas lasers are deployed to generate radiation between these lines [20].

The application of HF and DF chemical lasers that produce radiation between 2.7 $\mathsf{\mu }$m and 5 $\mathsf{\mu }$m is constrained by the discrete emission spectra, the strong corrosiveness and harmful nature of fluorides, and the requirement for high-voltage power sources [21].

Presently, the wavelength range of radiation produced by lasers utilizing crystals doped with transition metals and rare earth elements is capped at 5 $\mathsf{\mu }$m [22]. Interband cascade lasers also serve as mid-infrared sources. However, radiation generation beyond 5 $\mathsf{\mu }$m was achieved at cryogenic temperatures [23,24]. QCLs have the capability to produce radiation within the mid-IR spectrum. The wavelength of the light emitted from these lasers spans from 3.5 to 24 $\mathsf{\mu }$m [25]. To achieve a broad range of wavelength tuning, multiple QCLs are simultaneously employed within a single enclosure. One notable disadvantage of quantum cascade lasers is the relatively limited beam quality, a characteristic shared with semiconductor lasers.

Frequency down-conversion is a useful method to broaden the operating range of existing lasers. A significant benefit is the potential to develop solid-state laser systems that offer continuous wavelength tuning across a wide spectrum. Although there are numerous nonlinear crystals suitable for OPOs, only a limited selection is commonly employed due to the lack of essential characteristics required to achieve a high output energy and performance. These crucial properties include having a transparency window within the desired spectral region, a high optical quality (with an absorption coefficient below 0.01 cm⁻¹), an appropriate nonlinear coefficient, a laser-induced damage threshold (LIDT) of at least 0.3 J/cm² for nanosecond pulses, minimal nonlinear losses and excellent thermo-mechanical characteristics.

Oxide crystals with a regular domain structure, such as PPLN, PPKTP, and PPKTA, are commonly used for OPOs in the 2–5 $\mathsf{\mu }$m range [26]. When aiming to produce radiation at longer wavelengths, nonoxide semiconductor crystals become essential as their transmission range surpasses that of oxide crystals. Semiconductor crystals have narrower bandgaps compared to oxides, resulting in an increased quadratic susceptibility and a reduced LIDT [27]. The first semiconductor crystal where optical parametric oscillation was first demonstrated was the proustite Ag₃AsS₃ [28]. The main constraint hindering the extensive application of proustite was its low LIDT of 0.21 J/cm² (at 1.064 $\mathsf{\mu }$m, 17.5 ns, 2 Hz, 1000 pulses) [29]. Since the 1990s, there has been significant progress in the field of a periodic pattern of domain orientation in semiconductors, such as GaAs, GaP, InAs, InP, InSb, ZnSe, and others [30,31]. Currently, the development of periodic structures using these materials remains a challenging and pressing technological objective.

Among semiconductor crystals, commercially available crystals, such as the silver thiogallate AgGaS₂ (AGS) [32], the silver selenogallate AgGaSe₂ (AGSe) [33], and the zinc germanium phosphide ZnGeP₂ (ZGP) [34], are frequently used. The technologies for growing and processing these crystals are highly advanced. However, ongoing research efforts focus on improving the optical characteristics of these crystals through the incorporation of dopants during growth or through specific post-growth treatments [35,36,37]. Among these nonlinear materials, only the AGS crystal is suitable for the frequency down-conversion of the commonly used 1 $\mathsf{\mu }$m solid-state laser to the mid-IR range. This crystal exhibits transparency within the wavelength range of 0.47 to 13 $\mathsf{\mu }$m, with a clear transparency limit at approximately 8.5 $\mathsf{\mu }$m. However, it shows a relatively low LIDT of 0.2 J/cm² (1.064 $\mathsf{\mu }$m, 12 ns, 1 kHz) [38]. To pump frequency down-conversion devices based on ZGP and AGSe crystals, laser radiation sources emitting wavelengths between 1.5 and 2 $\mathsf{\mu }$m are required [39,40]. The ZGP crystal, which is widely utilized, possesses remarkable properties, including a high quadratic nonlinearity coefficient of approximately 75 pm/V and a high thermal conductivity of 36 W/mK [41]. However, its transmission is quite restricted; it is transparent within the range of 0.72–12.3 $\mathsf{\mu }$m but exhibits a significant absorption dip at 9.0 $\mathsf{\mu }$m, making it challenging to utilize this crystal for generating radiation beyond 8–8.5 $\mathsf{\mu }$m [41], which is similar to AGS. In contrast, the AGSe crystal offers a noticeably broader transmission range (0.71 to 19 $\mathsf{\mu }$m) [41] compared to its sulfur-containing counterpart AGS and the ZGP crystal. Furthermore, the AGSe crystal has a relatively lower thermal conductivity of 1 W/mK [42] and a low LIDT of 0.65 J/cm² (2.05 $\mathsf{\mu }$m, 50 ns, 50 Hz) [43].

The aforementioned points highlight the importance of developing novel nonoxide nonlinear crystals considering their diverse potential applications. The selection of a suitable nonlinear crystal should be based on a comprehensive evaluation of all of its physical properties relevant to the specific requirements of a given task. In applications involving the generation of high-power pulsed or continuous-wave radiation, a critical characteristic of crystals is their high thermal conductivity. Conversely, for applications necessitating a broad spectral range of wavelength tuning, factors such as the transparency range, nonlinear coefficient, and phase-matching conditions are crucial. In scenarios demanding a high pulse energy, such as in laser surgery, it is imperative for the nonlinear crystal to exhibit a high LIDT.

Over the past decade, the attention of researchers has been focused on chalcogenide crystals, including alkali and alkali earth metals such as Li and Ba [44]. Technology has been advanced to grow lithium chalcogenides, such as LiGaTe${ }_2$ (LGT), LiInS₂, LiInSe₂, LiGaSe₂, and LiGaS₂ (LGS), as a substitute for the commonly used AGS, AGSe, and ZGP crystals. All ternary chalcogenides containing lithium are classified in the crystallographic class $mm2$, except LGT, which falls into the $\overline{4}2m$ class. These compounds exhibit a relatively wide bandgap, ranging from 2.41 to 3.76 eV [44]. Among these materials, the LGS crystal has gained popularity due to its LIDT of 3.3 J/cm² (at 1.064 $\mathsf{\mu }$m, 14 ns, 100 Hz) [45] and its compatibility with radiation sources emitting wavelengths below 1 $\mathsf{\mu }$m, specifically Ti:sapphire laser systems operating at 800 nm for frequency down-conversion in femtosecond and picosecond regimes [46,47]. One method to enhance the properties of nonlinear crystals involves altering their chemical composition by passing from ternary to quaternary compounds [44]. Additionally, recent research efforts have focused on developing novel lithium-containing systems such as Li/Ag In/Ga/Ge/Se/Te. For example, compounds such as Li_xAg_1−xInSe₂ and Li_xAg_1−xGaSe₂ have been successfully produced and characterized [48,49].

Ba-containing ternary and quaternary chalcogenides have emerged as potential substitutes for AGS, AGSe, and ZGP crystals. In the period from 2009 to 2012, the synthesis of two promising wide-bandgap ternary chalcogenide crystals, BaGa₄S₇ (BGS) [50,51] and BaGa₄Se₇ (BGSe) [52,53], was successfully achieved. These crystals exhibit broad mid-IR transparency ranges, spanning from 0.35 to 12 $\mathsf{\mu }$m for BGS and from 0.47 to 18 $\mathsf{\mu }$m for BGSe at 0% transparency. Shortly thereafter, the quaternary barium chalcogenide compounds BaGa₂GeS₆ (BGGS) and BaGa₂GeSe₆ (BGGSe) were produced [54,55]. In 2016, these crystals were grown in large sizes with a high optical quality using the Bridgman–Stockbarger technique [56]. More recently, in 2022, a novel crystal, Ba₂Ga₈GeS₁₆ (B2GGS), was also synthesized [57,58].

The present paper focusses on the optical, nonlinear, and thermo-mechanical properties of the barium compounds listed above. Particular attention will be paid to LIDT research and frequency down-conversion devices based on these crystals.

2. Crystal Growth

2.1. Ternary Chalcogenides

As previously stated, between 2009 and 2012, BGS crystals were grown effectively using the Bridgman–Stockbarger technique [50,51]. At this time, the selenium-based counterpart BGSe was also synthesized in sufficiently large dimensions for the determination of birefringence and dispersion dependence [52,53]. These parameters are crucial to anticipating the characteristics of phase-matching interactions. High-purity raw materials utilized for charge synthesis included 6Ns for Ga, S, and Se, along with 96% purity for Ba. Taking into account the well-established chemical activity of Ba, the synthesis was conducted using graphite and pyrolytic boron nitride (PBN) containers. The initial components were weighed on the basis of the chemical formulas of the desired compositions and then placed into crucibles made of PBN or graphite. These crucibles were then inserted into a quartz ampule, which was connected to a vacuum system and pumped to a residual pressure of $2\times {10}^{-5}$ mbar. Subsequently, the ampule was sealed. The temperature within the synthesis furnace was gradually raised to 1150 ${ }^{°}$C at a speed of 200 ${ }^{°}$C per h. Subsequently, the ampoule containing the materials was maintained at this temperature for several hours to ensure homogenization. Following this, the synthesis furnace was turned off and allowed to cool down to ambient temperature.

The obtained charge was transferred to the quartz ampule for crystal growth, which had dimensions of 18 mm in diameter and 150 mm in length. The ampule was then evacuated to a residual pressure of $2\times {10}^{-5}$ mbar and placed in a furnace for crystal growth using the Bridgman–Stockbarger technique. The temperature increased to 1130–1140 ${ }^{°}$C (BGS) and to 1070–1080 ${ }^{°}$C (BGSe). In order to prevent the melt from coming into contact with quartz, the inner part of the ampoule was lined with graphite. It was determined that the melting point was 1105 ± 5 ${ }^{°}$C for BGS and 1050 ± 5 ${ }^{°}$C for BGSe. Following multiple initial experiments, the most suitable parameters for the growth procedure were established by evaluating the optical properties of the crystals produced: the crystallization rate fell within the interval of $8\pm 2$ mm/day, while the temperature gradient in the crystallization area was $20\pm 2$ ${ }^{°}$C/cm. The typical duration of growth is between 12 and 15 days [52]. Images of boules and plates of ternary barium chalcogenide crystals grown by the Bridgman–Stockbarger technique are displayed in Figure 1.

Currently, several research teams are growing these crystals using the Bridgman–Stockbarger technique [50,52,53,59]. However, Schunemann et al. also reported the growth of BGS and BGSe crystals using the horizontal gradient freeze technique [60]. In [60,61], the synthesis of single-phase ternary chalcogenide compounds was carried out by combining high-purity elemental starting materials using a two-temperature vapor transport method in sealed, heavy-walled quartz ampoules. The obtained single-phase ingots were placed back into PBN boats, along with oriented seed crystals. Subsequently, the ampule was sealed. The boats and ampoules were then subjected to heating in multi-zone horizontal transparent tube furnaces with an axial temperature gradient of 1–3 ${ }^{°}$C/cm to melt the charge and partially re-melt the seed crystal. Afterwards, the ampule was gradually cooled to achieve directional solidification at a rate of approximately 0.5 mm per h.

2.2. Quaternary Chalcogenides

The Bridgman–Stockbarger technique is also employed for the growth of quaternary barium chalcogenides [56]. The binary compounds Ga₂S₃, Ga₂Se₃, GeS₂, and GeSe₂ were synthesized at elevated temperatures by combining high-purity chemical elements Ba (98%), Ga (99.999%), Ge (99.999%), S (99.999%), and Se (99.999%) in quartz ampoules under vacuum conditions of ${10}^{-5}$ mbar. The BGGS(e) crystal was produced by synthesizing a mixture of BaS(e), Ga${ }_2$S(e)${ }_3$, and GeS(e)${ }_2$ in a graphitized quartz ampoule with a 1:1:1 molar ratio. A similar procedure was followed for the B2GGS crystal, but with a molar ratio of 2:4:1. The ampoules were then vacuum-sealed (${10}^{-5}$ mbar) and placed in a two-zone horizontal furnace, where they were heated to 1050 ${ }^{°}$C for 36 h. Subsequently, the resulting melt was maintained at this temperature for an additional 24 h and stirred until complete homogenization was achieved. The melting points of the compositions were assessed through differential thermal analysis. The heating and cooling rate was 30 ${ }^{°}$C/min. The recorded melting temperatures were 983 ${ }^{°}$C for BGGS, 877 ${ }^{°}$C for BGGSe, and 1008 ${ }^{°}$C for B2GGS [56,57].

The crystals of the quaternary compositions were grown using the Bridgman–Stockbarger technique in a vertical furnace with a temperature gradient of 10 ${ }^{°}$C/cm in the crystallization zone, while the melt was elevated to a temperature 30–40 ${ }^{°}$C higher than the melting point. The growth speed was 6 mm/day, and the crystals exhibit congruent melting behavior. Annealing is not required for these compositions. Photographs showing boules and plates of quaternary barium chalcogenide crystals are presented in Figure 2.

3. Characterization

3.1. Crystallographic Data

Both Ba-containing ternary compounds exhibit biaxial properties. However, although they have similar chemical compositions, BGSe crystallizes in the monoclinic m point group, whereas BGS belongs to the $mm2$ orthorhombic point group as mentioned above. The Ba-containing quaternary compounds are uniaxial. Moreover, BGGS and BGGSe are representatives of the trigonal crystal system (crystal class 3), while the new crystal B2GGS belongs to the $6mm$ point group (hexagonal crystal system).

Table 1. The lattice parameters.

Crystal	Lattice Parameters
BGS	a = 6.237 Å, b = 14.774 Å, c = 5.934 Å [61] (using the convention c < a < b [63])
BGSe	a = 7.6252 Å; b = 6.5114 Å; c = 14.702 Å; $\beta$ = 121.24° [50] a = 14.702 Å, b = 6.5114 Å, c = 7.6252 Å, $\beta$ = 121.24° [61] (using the convention c < a, b—monoclinic axis [63])
BGGS	a = 9.5967 Å; c = 8.671 Å [55]
BGGSe	a = 10.0438 Å; c = 9.114 Å [55]
B2GGS	a = 10.886 Å, c = 11.915 Å [62]

presents data on barium chalcogenides lattice parameters measured using X-ray diffraction by different authors [50,55,61,62].

3.2. Optical Properties

Ba-containing sulfides have better transmission in the visible region than selenide compounds, and the lowest short-wave cut-off edge of 340 nm possesses a crystal BGS. However, they are only transparent up to 12–12.5 $\mathsf{\mu }$m at the 0% level. Selenides, in contrast, have longer mid-IR cut-off wavelengths, up to 18 $\mathsf{\mu }$m. The transmission spectra of 2 mm thick BGS (black curve), BGGS (red curve), B2GGS (blue curve), BGSe (green curve), and BGGSe (purple curve) plates are given in Figure 3. Transmission spectra of barium chalcogenides were recorded using a Photon RT spectrophotometer in the UV to near IR, whereas in the mid-IR we used an Infralum 801 Fourier transform spectrometer.

The transparency ranges at the 0% transmission level for plates of BGS, BGGS, and B2GGS with a thickness of 2 mm are 0.34–13.3, 0.38–12.4, and 0.41–12.7 $\mathsf{\mu }$m, respectively. The sulfides have larger bandgaps compared to the selenides. Specifically, the bandgap values for BGS, BGGS, and B2GGS crystals are 3.59, 3.37, and 3.07 eV, respectively [57,64]. In contrast, the BGSe crystal has a band gap of 2.73 eV, while the BGGSe crystal has a band gap of 2.38 eV [59,64]. At room temperature, for a 2 mm thick BGSe plate, the transparency range at the 0% level is 0.46–18 $\mathsf{\mu }$m. Yelisseyev et al. [59] demonstrated that a BGSe plate with a thickness of 200 $\mathsf{\mu }$m exhibits transparency in the wavelength range of 0.465–22 $\mathsf{\mu }$m. Additionally, they investigated the variation in the bandgap with temperature. It was observed that when the sample temperature was lowered to 80 K, the bandgap increased to 2.91 eV, with dEg/dT = −8.07 × 10${ }^{-}$${ }^4$ eV/K. An intense residual absorption peak around 14.5–15 $\mathsf{\mu }$m in BGSe is similar to those observed in other nonlinear crystals such as AGSe. In [65], the authors investigated the structural characteristics of residual absorption and identified that the absorption bands at approximately 665 cm${ }^{-}$${ }^1$ were caused by deformation vibrations of the Ga-O-Ga bonds within the crystal. This phenomenon occurs as a result of the formation of an O substitution defect in the Se (O${ }_{Se}$) position during the growth process of the BGSe crystal. Figure 3 illustrates that the BGGSe transmission starts at a wavelength of 0.56 $\mathsf{\mu }$m and extends up to nearly 18 $\mathsf{\mu }$m at the 0% level.

3.3. Dispersion Characteristics

The auto-collimation method was used to measure the refractive indices of BGS crystals in the spectral range of 0.42–9.5 $\mathsf{\mu }$m. Prisms were employed for this purpose, and the resulting data were approximated to the Sellmeier equations [52]. Subsequently, Kato et al. presented improved Sellmeier equations derived from phase-matched nonlinear processes, such as second-harmonic, sum-frequency and difference-frequency generation [66]. These equations are valid within a wavelength range of 0.633–8.018 $\mathsf{\mu }$m. This work also presents equations for thermo-optic dispersion.

The initial investigation of the dispersion dependence of the BGSe crystal was conducted using prisms [52,67]. Later, enhanced Sellmeier equations that are obtained through nonlinear frequency conversion were introduced [68,69]. The study [68] investigated the phase-matching conditions by employing the sphere method within the wavelength range of 2–11 $\mathsf{\mu }$m. To achieve this, a crystal was shaped into a polished sphere with a diameter of 7.55 mm. The temperature-dependent behavior of the refractive indices of the BGSe crystal was investigated within two spectral ranges: 0.546–2.325 $\mathsf{\mu }$m (25–125 ${ }^{°}$C) [70] and 0.901–14.201 $\mathsf{\mu }$m (20–120 ${ }^{°}$C) [71]. In study [56], in which the authors first reported the successful growth of large-sized BGGS and BGGSe crystals with good optical quality, the dispersion dependences of both crystals were studied using the minimum deviation of a prism technique. Kato et al. later created improved Sellmeier equations that are applicable to the wavelength range of 0.8–10.6 $\mathsf{\mu }$m [72,73]. The researchers employed a similar methodology to that used for BGS and BGSe [66,71]. Additionally, they derived thermo-optical dispersion formulas for BGGS and BGGSe crystals [72,74].

Initially, the dispersion characteristics of the B2GGS crystal were studied using a prism [57,58]. Subsequently, the Sellmeier equations were improved through phase-matching processes, and the temperature variations of refractive indices were investigated within the temperature range of 20 to 150 ${ }^{°}$C [75].

3.4. Nonlinear Optical Characteristics

Table 2 presents the formulas for the effective nonlinearity of barium chalcogenide crystals, which are provided for biaxial crystals in the principal planes of the dielectric frame.

In a BGS crystal, the second-order symmetry axis aligns with the principal dielectric axis x; the relationship between the crystallographic and dielectric coordinate systems in this crystal can be expressed as xyz ≡ cab given the conditions n${ }_x$ < n${ }_y$ < n${ }_z$ and c < a < b. The angle between the optical axis and the principal dielectric z axis, as measured experimentally, is $45.6^{°}$ [52].

In monoclinic crystals, the b-crystallographic axis always aligns with one of the principal dielectric axes. Experimental results from X-ray, conoscopic, and refractive index measurements indicate that in the case of BGSe, the monoclinic axis x ≡ b is normal to the a–c plane, z ≡ c, and the experimental angle between the optical axis and the z-principal dielectric axis $\Omega$ is $26.3^{°}$[52]. For a dielectric-frame BGSe with orthogonal axes (x, y, z) defined by the relationship n${ }_x$ < n${ }_y$ < n${ }_z$, the x-axis is perpendicular to the mirror plane m. In a study [76], the b-axis was also designated as parallel to the x-axis and the z-axis as parallel to the a-axis. Consequently, the y-axis forms an angle of $31.{24}^{°}$ with the c-axis. The same researchers previously observed that the dielectric frame does not rotate around the x-axis based on the wavelength [77]. The orientation of the (x, y, z) axes with respect to the mirror plane m determines the six non-zero and independent components of the second-order dielectric susceptibility tensor, as outlined in Table 2. Detailed discussions on the applicability of the principal dielectric axes system x, y, z to describe components of the nonlinearity tensor instead of the crystallo-physical frame recommended by the standard [63] are presented in [64].

The expressions for the effective nonlinearity of BGGS and BGGSe crystals are provided in the orthogonal right-handed coordinate system x, y, z where x ≡ a and z ≡ c, which represents the third-order symmetry axis. Therefore, in this scenario, x, y, z can be viewed as a crystallo-physical frame. The BGGSe components of the nonlinearity tensor are provided in reference [78]. Unfortunately, the data regarding the BGGS crystal have not been published.

The second harmonic generation in the B2GGS crystal was demonstrated in reference [58], where the estimation of the $d_{15}$ component value was detailed. In this research, the a-axis, like in the instances of BGGS and BGGSe, was defined to be parallel to the x-axis, while the z-axis was aligned with the c-axis.

Table 2. The expressions for the effective nonlinearity of barium chalcogenide crystals. The symbols o and e denote the ordinary and extraordinary waves, respectively, in the order of ${\lambda }_1{\lambda }_2-{\lambda }_3$, where ${\lambda }_1\ge {\lambda }_2>{\lambda }_3$; $\Omega$ is the angle between the optical axis of the crystal and the Z axis; and $\theta$ and $\phi$ are the polar and azimuthal angles.

Crystal	Effective Nonlinearity Expressions	d${ }_{\mathit{i}\mathit{l}}$, pm/V
BGS	x-y: $d_{eff(oo-e)}=d_{32}sin\phi$; y-z: $d_{eff(ee-o)}=d_{32}{sin}^2\theta +d_{31}{cos}^2\theta$; x-z, $\theta <\Omega :d_{eff(ee-o)}=d_{31}cos\theta$; x-z, $\theta >\Omega :d_{eff(oe-o)}=d_{eff(eo-o)}=d_{31}cos\theta$;	$d_{15}$ = $d_{31}=5.1$; $d_{24}=d_{32}=5.7$; $d_{31}/d_{32}>0$; @532 nm [51]
BGSe	x-y: $d_{eff(oo-e)}=d_{23}cos\phi$; x-y: $d_{eff(oe-e)}=d_{eff(eo-e)}=-d_{15}{sin}^2\phi -d_{24}{cos}^2\phi$; y-z, $\phi =\pm {90}^{°}:d_{eff(oe-o)}=d_{eff(eo-o)}=\pm d_{16}cos\theta -d_{15}sin\theta$; x-z, $\theta <\Omega :d_{eff(oo-e)}=d_{24}sin\theta$; x-z, $\theta <\Omega :d_{eff(oe-e)}=d_{eff(eo-e)}=d_{16}{cos}^2\theta +d_{23}{sin}^2\theta$; x-z, $\theta >\Omega :d_{eff(ee-o)}=d_{16}{cos}^2\theta +d_{23}{sin}^2\theta$; x-z, $\theta >\Omega :d_{eff(oe-o)}=d_{eff(eo-o)}=-d_{24}sin\theta$;	$d_{21}=d_{16}=5.3$; $d_{23}=d_{34}=-14.2$; $d_{15}=d_{31}=1.5$; $d_{24}=d_{32}=-5.0$; $d_{22}=\pm 6.2$; @532 nm [76]
BGGS	$d_{eff(ee-o)}=(d_{11}sin3\phi +d_{22}cos3\phi ){cos}^2\theta$; $d_{eff(oe-o)}=d_{eff(eo-o)}=(d_{11}cos3\phi -d_{22}sin3\phi )cos\theta +d_{31}sin\theta$;	$d_{15}=d_{31}$; No data
BGGSe		$d_{15}=d_{31}=18.3$; $d_{11}=23.6$; $d_{22}=-18.5$; @5.3 $\mathsf{\mu }$m [78]
B2GGS	$d_{eff(oo-e)}=d_{15}sin\theta$;	$d_{15}$ = $d_{24}$ = $d_{31}$ = $d_{32}$ =13; @1.86 $\mathsf{\mu }$m [57]

Table 2. The expressions for the effective nonlinearity of barium chalcogenide crystals. The symbols o and e denote the ordinary and extraordinary waves, respectively, in the order of ${\lambda }_1{\lambda }_2-{\lambda }_3$, where ${\lambda }_1\ge {\lambda }_2>{\lambda }_3$; $\Omega$ is the angle between the optical axis of the crystal and the Z axis; and $\theta$ and $\phi$ are the polar and azimuthal angles.

Crystal	Effective Nonlinearity Expressions	d${ }_{\mathit{i}\mathit{l}}$, pm/V
BGS	x-y: $d_{eff(oo-e)}=d_{32}sin\phi$; y-z: $d_{eff(ee-o)}=d_{32}{sin}^2\theta +d_{31}{cos}^2\theta$; x-z, $\theta <\Omega :d_{eff(ee-o)}=d_{31}cos\theta$; x-z, $\theta >\Omega :d_{eff(oe-o)}=d_{eff(eo-o)}=d_{31}cos\theta$;	$d_{15}$ = $d_{31}=5.1$; $d_{24}=d_{32}=5.7$; $d_{31}/d_{32}>0$; @532 nm [51]
BGSe	x-y: $d_{eff(oo-e)}=d_{23}cos\phi$; x-y: $d_{eff(oe-e)}=d_{eff(eo-e)}=-d_{15}{sin}^2\phi -d_{24}{cos}^2\phi$; y-z, $\phi =\pm {90}^{°}:d_{eff(oe-o)}=d_{eff(eo-o)}=\pm d_{16}cos\theta -d_{15}sin\theta$; x-z, $\theta <\Omega :d_{eff(oo-e)}=d_{24}sin\theta$; x-z, $\theta <\Omega :d_{eff(oe-e)}=d_{eff(eo-e)}=d_{16}{cos}^2\theta +d_{23}{sin}^2\theta$; x-z, $\theta >\Omega :d_{eff(ee-o)}=d_{16}{cos}^2\theta +d_{23}{sin}^2\theta$; x-z, $\theta >\Omega :d_{eff(oe-o)}=d_{eff(eo-o)}=-d_{24}sin\theta$;	$d_{21}=d_{16}=5.3$; $d_{23}=d_{34}=-14.2$; $d_{15}=d_{31}=1.5$; $d_{24}=d_{32}=-5.0$; $d_{22}=\pm 6.2$; @532 nm [76]
BGGS	$d_{eff(ee-o)}=(d_{11}sin3\phi +d_{22}cos3\phi ){cos}^2\theta$; $d_{eff(oe-o)}=d_{eff(eo-o)}=(d_{11}cos3\phi -d_{22}sin3\phi )cos\theta +d_{31}sin\theta$;	$d_{15}=d_{31}$; No data
BGGSe		$d_{15}=d_{31}=18.3$; $d_{11}=23.6$; $d_{22}=-18.5$; @5.3 $\mathsf{\mu }$m [78]
B2GGS	$d_{eff(oo-e)}=d_{15}sin\theta$;	$d_{15}$ = $d_{24}$ = $d_{31}$ = $d_{32}$ =13; @1.86 $\mathsf{\mu }$m [57]

Nonlinear absorption and nonlinear refraction occurring in crystals when exposed to intense laser radiation can cause alterations in the transverse intensity profile of the laser beam within the crystal. This can result in self-focusing effects and optical cavity detuning and ultimately decrease the efficiency of frequency down-conversion. Hence, it is crucial to consider these factors when developing optical setups for highly efficient optical parametric oscillators that are tunable in the mid-infrared spectrum.

The nonlinear absorption and nonlinear refraction results shown in

Table 3. Nonlinear absorption and nonlinear refraction of barium chalcogenide crystals.

Crystal	Measurement Conditions	n2·10−14, cm2/W	$\mathit{\beta }$, cm/GW
BGS	1.053 $\mathsf{\mu }$m; 5.1 ns; 100 Hz; 700 MW/cm2; 2.03 mm long;	0.85	Not observed
	1.028 $\mathsf{\mu }$m; 180 fs; 100 Hz and 100 kHz; 8 GW/cm2; o- and e-pol., 4.8 mm long; [80]	0.72–0.83	Not observed
	1.028 $\mathsf{\mu }$m; 180 fs; 100 Hz and 100 kHz; 2.3 GW/cm2; o- and e-pol., 8.3 mm long; [81]	1.0	Not observed
BGSe	1.053 $\mathsf{\mu }$m; 5.1 ns; 100 Hz; 245 MW/cm2; o- and e-pol.; 2.31 mm long	1.55–1.81	Not observed
	1.064 $\mathsf{\mu }$m; 30 ps; 10 Hz; occurs at 1.3 GW/cm2; 4 mm long; [82]	No data	Observed
BGGS	1.053 $\mathsf{\mu }$m; 5.1 ns; 100 Hz; 700 MW/cm2; 2.05 mm long	0.78	Not observed
BGGSe	1.053 $\mathsf{\mu }$m; 5.1 ns; 100 Hz; 245 MW/cm2; o- and e-pol.; 2.04 mm long	7.4–14	1.3–2.2
B2GGS	1.053 $\mathsf{\mu }$m; 5.1 ns; 100 Hz; 700 MW/cm2; 2.6 mm long	1.93	Not observed

were obtained through the Z-scan technique introduced by Sheik-Bahae et al. [79]. In the years 2019–2020, Mero et al. measured nonlinear refractive indices ($n_2$) of several nonlinear crystals, including LGS and BGS crystals, by exposing the samples to femtosecond pulses at a wavelength of 1.028 $\mathsf{\mu }$m [80,81]. Experiments carried out in identical conditions reveal that the nonlinear refractive index of the BGS crystal is nearly double that of the LGS crystal (∼$0.4\times {10}^{-14}$ cm${ }^2$/W). Both crystals showed a weak dependence of response on the polarization of the laser radiation and the absence of nonlinear absorption at these intensities, and there was no presence of nonlinear absorption at the specified peak intensities. In the study by reference [82], which focused on constructing a picosecond optical parametric amplifier using a BGSe crystal, researchers observed nonlinear absorption within the crystal. This phenomenon initiates at a peak intensity of 1.3 GW/cm${ }^2$ and increases further at 2.38 GW/cm${ }^2$.

Table 3 also includes data measured by us and not published before. Nonlinear absorption ($\beta$) was observed and measured exclusively in the BGGSe crystal, characterized by the smallest bandgap (2.38 eV), among all the crystals tested, when irradiated by nanosecond pulses at a wavelength of 1.053 $\mathsf{\mu }$m (245 MW/cm${ }^2$). This could be attributed to the close proximity of the laser photon energy $\hslash \omega$ = 1.18 eV to half the bandgap energy value E${ }_g$/2 = 1.19 eV (o-wave). The nonlinear absorption coefficient was measured to be between 1.3 and 2.2 cm/GW. This crystal also demonstrates a higher nonlinear refractive index compared to other crystals of 7.4–14 $\times {10}^{-14}$ cm${ }^2$/W. In our study, nonlinear absorption in the BGSe crystal was not detected at intensities roughly one-tenth of those reported in [82]. BGS and BGGS crystals exhibit minimum nonlinear refractive indices, approximately ∼$0.8\times {10}^{-14}$ cm${ }^2$/W, which aligns well with the data for BGS reported by Mero et al. [80,81]. We intend to carry out a comprehensive investigation in the upcoming period on the nonlinear absorption and nonlinear refraction of barium chalcogenide crystals. This study will encompass a range of intensities, pulse repetition rates for pulsed lasers, and a CW regime.

3.5. Thermophysical Characteristics

The practical use of nonlinear crystals strongly relies on the thermophysical properties of materials.

Table 4. Thermophysical characteristics of barium chalcogenides along the three crystallographic directions.

Crystal	Thermal Conductivity, Wm−1K−1				Thermal Diffusivity, mm2s−1				Thermal Expansion, 10−6K−1
	a	b	c		a	b	c		a	b	c
BGS [83]	1.46	1.58	1.68	@323 K	0.74	0.80	0.93	@323 K	No data	No data	No data
	1.54	1.46	1.52	@373 K	0.66	0.72	0.82	@373 K
	1.57	1.45	1.44	@423 K	0.64	0.68	0.78	@423 K
BGSe [84]	0.74	0.64	0.56	@298 K	0.50	0.42	0.38	@298 K	9.24	10.76	11.70	@293–573 K
BGGS [85]	0.91		1.10	@298 K	1.10–0.6		0.9–0.5	@184–473 K	12.1		6.93	@300 K
BGGSe [85]	0.63		0.76	@298 K	0.8–0.4		0.65–0.35	@ 184–473 K	12.2		3.84	@300 K
B2GGS	No data	No data	No data		No data	No data	No data		No data	No data	No data

presents data regarding the thermal conductivity, thermal diffusivity, and thermal expansion of barium chalcogenide crystals. As far as we know, no such studies have been published for the B2GGS crystal up until now.

Out of these compounds, the BGS crystal exhibits the highest thermal conductivity, surpassing that of the AGS crystal (1.143–1.162 Wm${ }^{-1}$K${ }^{-1}$ at 298 K [86] and 1.4–1.5 Wm${ }^{-1}$K${ }^{-1}$[42]). Selenide compounds exhibit a lower thermal conductivity. Barium selenides have a thermal conductivity that is approximately 30% lower than that of the commonly used sulfide AGSe crystal (0.95–1.03 Wm${ }^{-1}$K${ }^{-1}$ at 298 K [87] and 1.0–1.1 Wm${ }^{-1}$K${ }^{-1}$[42]). In the year 2021, the thermal conductivity coefficients for BGGS and BGGSe crystals were reported to be in the ranges of 1.7–1.95 Wm${ }^{-1}$K${ }^{-1}$ and 1.88–2.17 Wm${ }^{-1}$K${ }^{-1}$, respectively, according to [88]. However, subsequent research conducted by the co-authors of the aforementioned study extensively examined the thermo-mechanical properties of these crystals [85]. They concluded that the thermal conductivity values presented in [88] were clearly overestimated and were accompanied by errors in determining the specific heat capacity. As previously stated, the thermal conductivity of nonlinear crystals is crucial in producing high-average-power radiation sources. Unlike the ZGP crystal (36 Wm${ }^{-1}$K${ }^{-1}$ [41]) utilized in high-power OPOs, barium chalcogenides exhibit a considerably lower thermal conductivity. Nevertheless, their high LIDT, as demonstrated below, coupled with their broad transmission range, makes these crystals highly suitable for generating radiation with a high pulse energy [89] or a wide range of wavelength tuning [90].

3.6. Mechanical Characteristics

Information on the mechanical characteristics of nonlinear crystals is crucial for their widespread use. This knowledge is essential for various processes such as cutting, polishing, cleaning, the anti-reflection coating of optical surfaces, and evaluating the impact of thermal stress. The data in

Table 5. Hardness and Young’s modulus of of barium chalcogenides.

Crystal		Hardness, GPa	Hardness VHN, kg/mm2	Young’s Modulus, GPa	Temperature, K	Thermal Drift, nm/s
BGS [91]		6.00	556	80.0	291.75	0.26
BGSe [91]		3.63	336	57.6	289.85	0.33
BGGS [85]	a-cut	4.99	463	65.1	293.7	0.3
	c-cut	4.66	432	71.3	294.5	0.17
BGGSe [85]	a-cut	4.10	380	53.5	294.2	0.19
	c-cut	4.25	394	61.1	294.2	0.14
B2GGS		No data	No data	No data	No data	No data

provide information on the hardness and Young’s modulus of barium chalcogenide crystals. To our knowledge, no publications have been published on the B2GGS crystal.

Among these compounds, the BGS crystal demonstrates the greatest hardness, measuring at 6.00 GPa (Vickers hardness number of 556 kg/mm${ }^2$), and a Young’s modulus of 80.0 GPa [91]. In the first study published in 2009, which focused on the crystal’s growth, a hardness of 327.5 kg/mm${ }^2$ was reported [50]. This difference in hardness could be attributed to the significant advancements in crystal growth technology over the past decade, allowing for the production of more homogeneous crystals with a high optical quality. Barium chalcogenide crystals, whose mechanical properties were studied (refer to Table 5), demonstrate greater hardness levels when compared to AGS (285 kg/mm${ }^2$) and AGSe (170 kg/mm${ }^2$) crystals [92].

4. LIDT

The laser-induced damage threshold is a key parameter in optical components as well as in nonlinear crystals. This parameter depends on various factors, such as the wavelength, pulse duration, pulse repetition rate, surface quality, presence of coatings, etc. The LIDT is defined in the ISO 21254 standard as the “highest quantity of laser radiation incident upon the optical component for which the extrapolated probability of damage is zero” [93]. Under the influence of short laser pulses $\tau$ < 10⁻⁷, damage to the material can occur due to dielectric breakdown and nonlinear (two-photon absorption, self-focusing) and thermal processes, and it can also combine all these components [94,95]. The thermal processes are insignificant for ultrashort pulses of about 10 ps or less. In this case, the damage is prevalent in nonlinear processes such as multi-photon absorption and multi-photon, tunnel, and avalanche ionization [96].

For pulsed sources, the LIDT is defined as the peak-on-axis fluence and expressed in [J/cm²], as this provides the best metric for such sources. There is no need to specifically calculate it to match it to the size of the spot, as a known damage threshold can be applied to any beam diameter [97]. However, in most real transparent optical materials, there is a size dependence of the LIDT associated with the presence of absorbing defects in the material that initiate destruction [98]. The presence of absorbing defects and inclusions, which are typically found in different amounts in real optical materials, often serves as a primary cause of both surface and bulk damage to the materials, leading to a notable reduction in the threshold intensity. Typically, such defects refer to various irregularities, such as cracks, scratches, dents, or contamination, due to which the optical element fails more quickly or at a significantly lower power density than originally intended. As the beam size increases, the probability that a defect will be present in the irradiated area increases noticeably, resulting in a reduced LIDT compared to situations with smaller beam sizes.

Damage caused by continuous-wave (CW) lasers is typically due to thermal effects occurring by absorption in the optical coatings or substrate and is expressed in the peak-on-axis intensity measured in [W/cm²]. The effective size of the Gaussian beam is also related to the energy density. As this density increases, most of the beam width is energetic enough to cause laser damage. According to the ISO 21254 standard, the effective area of a Gaussian beam is defined as $\pi {\omega }^2/2$. To recalculate the LIDT value from one pulse duration to another, the following equation is used [99]:

$$LIDT\left({\tau }_2\right)\approx LIDT\left({\tau }_1\right)\times \sqrt{\frac{{\tau }_2}{{\tau }_1}},$$

(1)

where $\tau$ is the pulse duration. It is important to emphasize that this equation is applicable for pulse durations ranging from 1 to 100 ns and variations in pulse duration should not exceed threefold.

Table 6. LIDT of barium chalcogenide crystals.

Wavelength	10 $\mathsf{\mu }$m	2 $\mathsf{\mu }$m		1 $\mathsf{\mu }$m
Pulse Duration	ns	ns	fs	ns	ps
BGS	52.4 J/cm2 (9.58 $\mathsf{\mu }$m, 100 ns, 1 Hz) [83]	10 J/cm2 (2.1 $\mathsf{\mu }$m, 15 ns, 1 Hz) * [83]		2.4 J/cm2 (1.064 $\mathsf{\mu }$m, 15 ns, 1 Hz) [50] 3.7/2.9 J/cm2 (1.064 $\mathsf{\mu }$m, 14/1 ns, 0.1/0.5 kHz) [51] 7.4/6.4 J/cm2 (1.053 $\mathsf{\mu }$m, 5.1 ns, 0.1/1 kHz) [100]
BGSe	36.6 J/cm2 (10.6 $\mathsf{\mu }$m, 100 ns, 1 Hz) [101]	4.8/3.3/2.1 J/cm2 (2.091 $\mathsf{\mu }$m, 15 ns, 2/5/10 kHz) [102] 2.46 J/cm2 (2.091 $\mathsf{\mu }$m, 15 ns, 0.5 kHz) * [103] 1.37 J/cm2 (2.091 $\mathsf{\mu }$m, 15 ns, 0.5 kHz) * [104]	81 GW/cm2 (2.4 $\mathsf{\mu }$m, 28 fs, 69 MHz) [105]	2/1.4/1.1 J/cm2 (1.053 $\mathsf{\mu }$m, 5.1 ns, 0.1/0.5/1 kHz) * [106] 2.9/2.9/2.6 J/cm2 (1.053 $\mathsf{\mu }$m, 8.3 ns, 0.1/0.15/0.2 kHz) * [107] 1.4/1 J/cm2 (1.064 $\mathsf{\mu }$m, 14/1 ns, 0.1/0.5 kHz) [90] 5.6 J/cm2 (1.064 $\mathsf{\mu }$m, 5 ns, 1 Hz) [84]	0.18 J/cm2 (1.064 $\mathsf{\mu }$m, 30 ps, 10 Hz) [108]
Doped BGSe		6.6/5.1/2.5 J/cm2 (2.091 $\mathsf{\mu }$m, 15 ns, 2/5/10 kHz) [102]		2.5/2.3/2.3/2 J/cm2 (1.053 $\mathsf{\mu }$m, 5.1 ns, 0.1/0.5/1/2 kHz) * [109]
BGGS	14 J/cm2 (10.6 $\mathsf{\mu }$m, 100 ns, 1 Hz) [56]			6.8/7 J/cm2 (1.053 $\mathsf{\mu }$m, 5.1 ns, 0.1/1 kHz) [100]
B2GGS				6.9/7 J/cm2 (1.053 $\mathsf{\mu }$m, 5.1 ns, 0.1/1 kHz) [110]
BGGSe	11 J/cm2 (10.6 $\mathsf{\mu }$m, 100 ns, 1 Hz) [56]	6.5/4.3/2.7 J/cm2 (2.091 $\mathsf{\mu }$m, 15 ns, 2/5/10 kHz) [102]		1.9/1.6/1.3 J/cm2 (1.053 $\mathsf{\mu }$m, 5.1 ns, 0.1/0.5/1 kHz) * [106]

* Scaled data. Refer to the relevant publications for more detailed information.

shows the LIDT of barium chalcogenide crystals under the influence of radiation sources of various durations, wavelengths, and pulse repetition rates. All values are expressed in terms of the peak-on-axis fluence, with the exception of the data for the femtosecond source. Some data, for a more visual comparison, were scaled using the formula above; for more detailed information, we recommend reference to the relevant publications.

BGSe crystals exhibit cleavage planes, which cannot be eliminated by annealing because of their connection with the features of the crystal structure. By varying the composition of additives used to grow BGSe crystals in the laboratory of advanced technologies at Kuban State University, it was feasible to reduce the occurrence of this phenomenon. The composition of the sample was modified by the isomorphic insertion of Ga₂Se₃ in amounts of up to 7.8 mol.%. The LIDT of BGSe crystals, both in their pure form and with a modified composition, was evaluated using nanosecond pulses at 2 $\mathsf{\mu }$m and 1 $\mathsf{\mu }$m [102,109]. According to data from [102], the damage threshold of modified BGSe was approximately 30% higher at pulse repetition rates of 2 kHz and 5 kHz, but this difference decreased to 16% at a higher pulse repetition rate (10 kHz). A similar result was obtained in a study [109] where the LIDT of the modified BGSe was approximately 24% higher than that of the nominally pure BGSe.

In general, all barium chalcogenide crystals considered demonstrate a high LIDT. Particularly, barium sulfide crystals have an LIDT that is more than three times higher than their selenium-containing counterparts, indicating their potential for applications requiring high peak energy. Selenium-containing crystals are also known for their increased nonlinearity and broader transparency range, making them appealing for addressing spectroscopic challenges.

5. Frequency Down-Conversion to the Mid-IR Range

As previously stated, barium chalcogenide crystals show great potential for nonlinear conversion due to several characteristics, such as their transmission range, LIDT, and effective nonlinearity coefficient. This section of the article focuses on the use of these crystals for frequency down-conversion to the mid-IR range. Table 7 presents examples of utilizing the barium chalcogenide crystals for frequency down-conversion to the mid-IR range, along with the resulting radiation properties.

5.1. BGS

To our knowledge, among all barium sulfide compounds, only the BGS crystal was used for frequency down-conversion, being the first one to be successfully grown. BGS was the first barium chalcogenide crystal used for nanosecond OPO applications [111]. A Nd:YAG laser was employed as the pumping source, producing pulses around 7.5 ns at a rate of 10 Hz at a wavelength of 1.064 $\mathsf{\mu }$m. The developed source produced idler pulses less than 6 ns, with energies reaching up to 0.5 mJ at a wavelength of 6.217 $\mathsf{\mu }$m and an average power of around 50 mW. Optical parametric amplifiers using ultrashort pulses (ps and fs) were successfully demonstrated in this crystal at a later date, specifically in 2020 [112,113].

In [113], the first demonstration of a mid-IR optical parametric amplifier (OPA) was published. The BGS-OPA was pumped by a Nd:YAG laser with a pulse duration of 30 ps at 1064 nm and 10 Hz. Achieving a maximum idler pulse energy of approximately 130 $\mathsf{\mu }$J at 7.25 $\mathsf{\mu }$m required a pump energy of around 6.9 mJ, resulting in a pump-to-idler quantum conversion efficiency of about 13%. The wavelength tuning was demonstrated in the 6.3–8.8 $\mathsf{\mu }$m spectral range. In reference [112], an OPA was showcased with pumping by a Yb:KGd(WO₄)₂ laser operating at 1028 nm with a pulse duration of 180 fs and a rate of 100 kHz. The average output power was measured at 59 mW at 10 $\mathsf{\mu }$m and 81 mW at 8.1 $\mathsf{\mu }$m. The tuning of the wavelength was demonstrated in the range of 7.6–11.5 $\mathsf{\mu }$m.

5.2. BGSe

Currently, the BGSe crystal stands out as one of the most extensively researched among all barium chalcogenides. Researchers have successfully utilized this crystal to develop OPOs, OPAs, and DFGs with varying pump wavelengths and pulse durations, along with achieving difference frequency generation in a CW regime. In 2016, we presented the first nanosecond OPO using a BGSe crystal pumped by a 1 $\mathsf{\mu }$m laser [114]. When using the I-type interaction, the idler wavelength exhibited a tuning range of 2.93–9.3 $\mathsf{\mu }$m, while for the II type, it was 5–5.4 $\mathsf{\mu }$m. The peak energy reached 4–10 $\mathsf{\mu }$J at a pulse repetition rate of 100 Hz within the 4–5 $\mathsf{\mu }$m range. Subsequently, in our study [90], the use of a pump laser with an increased pulse energy and the use of crystals of superior optical characteristics led to the achievement of an unprecedented wide tuning range of 2.7–17 $\mathsf{\mu }$m for BGSe-I and 3.6 to 9.6 $\mathsf{\mu }$m for BGSe-II. The maximum idler wave energy generated by an OPO utilizing BGSe-II reached 4.7 mJ at a 5.3 $\mathsf{\mu }$m wavelength, while for an OPO based on BGSe-I, the maximum energy output was 3.7 mJ at a 7.2 $\mathsf{\mu }$m wavelength, using a pump energy of 63 mJ and a pulse repetition rate of 100 Hz. An extremely high OPO output energy was, 21.5 mJ at 3816 nm with the I type of interaction and a repetition rate of 20 Hz [89]. Also, using a nanosecond Nd:YAG laser as a pump source, an intracavity mixing of the signal (1.85 $\mathsf{\mu }$m) and idler (2.51 $\mathsf{\mu }$m) of an Rb:PPKTP OPO in the BGSe crystal was realized [115]. An output pulse energy of approximately 0.7 mJ is produced at ∼7 $\mathsf{\mu }$m with a repetition rate of 100 Hz. The tuning of the mid-IR radiation is implemented through the heating of the Rb:PPKTP crystal.

Table 7. Frequency down-conversion devices based on barium chalcogenide crystals.

Crystal Type, ($\mathit{\theta }$, $\mathit{\phi }$)	Device Type	Length, mm	Pump Source	Pulse Duration and Rep. Rate	Tuning Range	Energy/Power
BGS I type (9.2°, 0°) [111]	OPO	14.1	Nd:YAG, 1064 nm	8 ns 100 Hz	5.5-7.3 $\mathsf{\mu }$m	0.5 mJ @6.2 $\mathsf{\mu }$m
BGS I type (12.5°, 0°) [113]	OPA	15		30 ps 10 Hz	6.3–8.8 $\mathsf{\mu }$m	66 $\mathsf{\mu }$J @6.3 $\mathsf{\mu }$m
BGS I type (13.1°, 0°) [112]	OPA	8.3	Yb:KGd(WO${ }_4$)${ }_2$, 1028 nm	180 fs 100 Hz	7.6–11.5 $\mathsf{\mu }$m	59 mW @10 $\mathsf{\mu }$m 81 mW @8 $\mathsf{\mu }$m.
BGSe-I type (45°, 0°) [114]	OPO	11.8	Nd:YLF, 1053 nm	15 ns 100 Hz	2.9–9.3 $\mathsf{\mu }$m	4–10 $\mathsf{\mu }$J @4–5 $\mathsf{\mu }$m
BGSe-I type (45°, 0°) [107]	OPO	11.8			2.6–10.4 $\mathsf{\mu }$m	45 $\mathsf{\mu }$J @3.3 $\mathsf{\mu }$m
BGSe-II type (33°, 90°) [114]	OPO	10			5–5.4 $\mathsf{\mu }$m	14 $\mathsf{\mu }$J @8.1 $\mathsf{\mu }$m
BGSe-I type (46°, 0°) [90]	OPO	14.6	Nd:YAG, 1064 nm	8 ns 10 Hz	2.7–17 $\mathsf{\mu }$m	3.7 mJ @7.2 $\mathsf{\mu }$m
BGSe-II type (33.5°, 90°) [90]	OPO	13.6			3.6–9.6 $\mathsf{\mu }$m	4.7 mJ @5.3 $\mathsf{\mu }$m
BGSe-I type (53.4°, 0°) [116]	OPO	18.8		8 ns 10 Hz	4.1–4.5 $\mathsf{\mu }$m	1.92 mJ @4.3 $\mathsf{\mu }$m
BGSe-I type (54.7°, 0°) [117]	OPO	17.3		16 ns 10 Hz	3.1–5.2 $\mathsf{\mu }$m	2.56 mJ @4.1 $\mathsf{\mu }$m
BGSe-I type (53.2°, 0°) [118]	OPO	10		6.7 ns 10 Hz		1.03 mJ @4.3 $\mathsf{\mu }$m
BGSe-I type (55.9°, 0°) [89]	OPO	16		11.4 ns 20 Hz	3.6–3.8 $\mathsf{\mu }$m	21.5 mJ @3.8 $\mathsf{\mu }$m
BGSe-I type (42.5°, 0°) [119]	OPO	15		10 ns 10 Hz	8–14 $\mathsf{\mu }$m	1.05 mJ @11 $\mathsf{\mu }$m
BGSe-I type (56.3°, 0°) [120]	OPO	15		13 ns 1 Hz	±5 nm	0.49 mJ @3.5 $\mathsf{\mu }$m
BGSe-I type (55.3°, 0°) [121]	OPO	15		11.6 ns 300 Hz	3.2–4.2 $\mathsf{\mu }$m	1.03 W @3.7 $\mathsf{\mu }$m
BGSe-I type (42.5°, 0°) [122]	OPO	16		13.6 ns 250 Hz	3.42–4.73 $\mathsf{\mu }$m	1.3 mJ @4.1 $\mathsf{\mu }$m
BGSe-I type (53.2°, 0°) [123]	OPO	15		13.7 ns 500 Hz		1.52 mJ @4.4 $\mathsf{\mu }$m
BGSe-I type (56.3°, 0°) [124]	OPO			13 ns 1 Hz	2.76–4.64 $\mathsf{\mu }$m
BGSe-I type (47.1°, 0°) [125]	OPO	25		18 ns 10 Hz		6.8 mJ @6.45 $\mathsf{\mu }$m
BGSe-I type (46°, 0°) [115]	DFG	14.6	OPO, 1.85 + 2.51 $\mathsf{\mu }$m	8 ns 10 Hz	7–8.2 $\mathsf{\mu }$m	711 $\mathsf{\mu }$J @7 $\mathsf{\mu }$m
BGSe I type (40.8°, 0°) [103]	OPO	30	Ho:YAG, 2091 nm	27 ns 500 Hz	4.3–5.2 $\mathsf{\mu }$m	1.47 mJ @4.4 $\mathsf{\mu }$m
BGSe-II type (6°, 90°) [104]	OPO	30		16 ns 1 kHz	8–9 $\mathsf{\mu }$m	314 $\mathsf{\mu }$J @8.9 $\mathsf{\mu }$m
BGSe-II type (23.5°, 90°) [126]	OPO	33		29.3 ns 1 kHz	3.82–4 $\mathsf{\mu }$m	520 $\mathsf{\mu }$J @3.94 $\mathsf{\mu }$m
BGSe-I type (40.8°, 0°) [127]	OPO	30		28 ns 1 kHz	4.5–5.3 $\mathsf{\mu }$m	1.8 mJ @4.5 $\mathsf{\mu }$m
BGSe-I type (39.4°, 0°) [128]	OPO	31	Cr, Er:YSGG, 2.79 $\mathsf{\mu }$m	21 ns 10 Hz	5.6–9.5 $\mathsf{\mu }$m	3.5 mJ @5 $\mathsf{\mu }$m
BGSe-I type (45°, 0°) [129]	DFG	8	Yb:YAG, 1030 nm	2 ps 10 Hz	6.5–8.6 $\mathsf{\mu }$m	60 $\mathsf{\mu }$J @7 $\mathsf{\mu }$m
BGSe I type (54.7°, 0°) [108]	OPA	8	Nd:YAG, 1064 nm	30 ps 10 Hz	3–5 $\mathsf{\mu }$m	830 $\mathsf{\mu }$J @3.9 $\mathsf{\mu }$m
BGSe I type (44°, 0°) [67]	OPA	8			6.4–11 $\mathsf{\mu }$m	38 $\mathsf{\mu }$J @11 $\mathsf{\mu }$m
BGSe-I type (40.2°, 0°) [82]	OPA	10			8–14 $\mathsf{\mu }$m	140–230 $\mathsf{\mu }$J
BGSe-I type (47°, 0°) [130]	OPA	10	Yb:KGW, 1030 nm	290 fs 50 kHz	3.7–17 $\mathsf{\mu }$m	10 mW @16 $\mathsf{\mu }$m
BGSe [131]	OPA	1	Yb:YAG, 1.03 $\mathsf{\mu }$m + 1.15–1.8 $\mathsf{\mu }$m	550 fs 10 kHz	2.5–10 $\mathsf{\mu }$m	6 $\mathsf{\mu }$J @3 $\mathsf{\mu }$m
BGSe-I type (67°, 0°) [132]	DFG	15	Ti:sapphire, 730–970 nm	CW	3.2–7.92 $\mathsf{\mu }$m	1.41 $\mathsf{\mu }$W @5 $\mathsf{\mu }$m
BGGSe II type (27.5°, 0°) [133]	OPO	9.3	cascaded OPO, 1.85 + 2.51 $\mathsf{\mu }$m	8 ns 10 Hz	4.4–13 $\mathsf{\mu }$m	750 $\mathsf{\mu }$J @8 $\mathsf{\mu }$m
BGGSe II type (27.5°, 0°) [134]	OPO	9.3	cascaded OPO, 1.95 + 2.55 $\mathsf{\mu }$m	8 ns 100 Hz	6.6–11.3 $\mathsf{\mu }$m	1.45 mJ @8.2 $\mathsf{\mu }$m
BGGSe I type (25°, 30°) [135]	DFG	2.6	mode-locked Er:fiber oscillator	59 fs 100 MHz	5.8–8.5 $\mathsf{\mu }$m	21 pJ
BGGSe I type (30°, 28°) [136]	DFG	4.4	SPOPOs, 1035 nm	130 fs 40 MHz	up to 10 $\mathsf{\mu }$m	54 mW

Table 7. Frequency down-conversion devices based on barium chalcogenide crystals.

Crystal Type, ($\mathit{\theta }$, $\mathit{\phi }$)	Device Type	Length, mm	Pump Source	Pulse Duration and Rep. Rate	Tuning Range	Energy/Power
BGS I type (9.2°, 0°) [111]	OPO	14.1	Nd:YAG, 1064 nm	8 ns 100 Hz	5.5-7.3 $\mathsf{\mu }$m	0.5 mJ @6.2 $\mathsf{\mu }$m
BGS I type (12.5°, 0°) [113]	OPA	15		30 ps 10 Hz	6.3–8.8 $\mathsf{\mu }$m	66 $\mathsf{\mu }$J @6.3 $\mathsf{\mu }$m
BGS I type (13.1°, 0°) [112]	OPA	8.3	Yb:KGd(WO${ }_4$)${ }_2$, 1028 nm	180 fs 100 Hz	7.6–11.5 $\mathsf{\mu }$m	59 mW @10 $\mathsf{\mu }$m 81 mW @8 $\mathsf{\mu }$m.
BGSe-I type (45°, 0°) [114]	OPO	11.8	Nd:YLF, 1053 nm	15 ns 100 Hz	2.9–9.3 $\mathsf{\mu }$m	4–10 $\mathsf{\mu }$J @4–5 $\mathsf{\mu }$m
BGSe-I type (45°, 0°) [107]	OPO	11.8			2.6–10.4 $\mathsf{\mu }$m	45 $\mathsf{\mu }$J @3.3 $\mathsf{\mu }$m
BGSe-II type (33°, 90°) [114]	OPO	10			5–5.4 $\mathsf{\mu }$m	14 $\mathsf{\mu }$J @8.1 $\mathsf{\mu }$m
BGSe-I type (46°, 0°) [90]	OPO	14.6	Nd:YAG, 1064 nm	8 ns 10 Hz	2.7–17 $\mathsf{\mu }$m	3.7 mJ @7.2 $\mathsf{\mu }$m
BGSe-II type (33.5°, 90°) [90]	OPO	13.6			3.6–9.6 $\mathsf{\mu }$m	4.7 mJ @5.3 $\mathsf{\mu }$m
BGSe-I type (53.4°, 0°) [116]	OPO	18.8		8 ns 10 Hz	4.1–4.5 $\mathsf{\mu }$m	1.92 mJ @4.3 $\mathsf{\mu }$m
BGSe-I type (54.7°, 0°) [117]	OPO	17.3		16 ns 10 Hz	3.1–5.2 $\mathsf{\mu }$m	2.56 mJ @4.1 $\mathsf{\mu }$m
BGSe-I type (53.2°, 0°) [118]	OPO	10		6.7 ns 10 Hz		1.03 mJ @4.3 $\mathsf{\mu }$m
BGSe-I type (55.9°, 0°) [89]	OPO	16		11.4 ns 20 Hz	3.6–3.8 $\mathsf{\mu }$m	21.5 mJ @3.8 $\mathsf{\mu }$m
BGSe-I type (42.5°, 0°) [119]	OPO	15		10 ns 10 Hz	8–14 $\mathsf{\mu }$m	1.05 mJ @11 $\mathsf{\mu }$m
BGSe-I type (56.3°, 0°) [120]	OPO	15		13 ns 1 Hz	±5 nm	0.49 mJ @3.5 $\mathsf{\mu }$m
BGSe-I type (55.3°, 0°) [121]	OPO	15		11.6 ns 300 Hz	3.2–4.2 $\mathsf{\mu }$m	1.03 W @3.7 $\mathsf{\mu }$m
BGSe-I type (42.5°, 0°) [122]	OPO	16		13.6 ns 250 Hz	3.42–4.73 $\mathsf{\mu }$m	1.3 mJ @4.1 $\mathsf{\mu }$m
BGSe-I type (53.2°, 0°) [123]	OPO	15		13.7 ns 500 Hz		1.52 mJ @4.4 $\mathsf{\mu }$m
BGSe-I type (56.3°, 0°) [124]	OPO			13 ns 1 Hz	2.76–4.64 $\mathsf{\mu }$m
BGSe-I type (47.1°, 0°) [125]	OPO	25		18 ns 10 Hz		6.8 mJ @6.45 $\mathsf{\mu }$m
BGSe-I type (46°, 0°) [115]	DFG	14.6	OPO, 1.85 + 2.51 $\mathsf{\mu }$m	8 ns 10 Hz	7–8.2 $\mathsf{\mu }$m	711 $\mathsf{\mu }$J @7 $\mathsf{\mu }$m
BGSe I type (40.8°, 0°) [103]	OPO	30	Ho:YAG, 2091 nm	27 ns 500 Hz	4.3–5.2 $\mathsf{\mu }$m	1.47 mJ @4.4 $\mathsf{\mu }$m
BGSe-II type (6°, 90°) [104]	OPO	30		16 ns 1 kHz	8–9 $\mathsf{\mu }$m	314 $\mathsf{\mu }$J @8.9 $\mathsf{\mu }$m
BGSe-II type (23.5°, 90°) [126]	OPO	33		29.3 ns 1 kHz	3.82–4 $\mathsf{\mu }$m	520 $\mathsf{\mu }$J @3.94 $\mathsf{\mu }$m
BGSe-I type (40.8°, 0°) [127]	OPO	30		28 ns 1 kHz	4.5–5.3 $\mathsf{\mu }$m	1.8 mJ @4.5 $\mathsf{\mu }$m
BGSe-I type (39.4°, 0°) [128]	OPO	31	Cr, Er:YSGG, 2.79 $\mathsf{\mu }$m	21 ns 10 Hz	5.6–9.5 $\mathsf{\mu }$m	3.5 mJ @5 $\mathsf{\mu }$m
BGSe-I type (45°, 0°) [129]	DFG	8	Yb:YAG, 1030 nm	2 ps 10 Hz	6.5–8.6 $\mathsf{\mu }$m	60 $\mathsf{\mu }$J @7 $\mathsf{\mu }$m
BGSe I type (54.7°, 0°) [108]	OPA	8	Nd:YAG, 1064 nm	30 ps 10 Hz	3–5 $\mathsf{\mu }$m	830 $\mathsf{\mu }$J @3.9 $\mathsf{\mu }$m
BGSe I type (44°, 0°) [67]	OPA	8			6.4–11 $\mathsf{\mu }$m	38 $\mathsf{\mu }$J @11 $\mathsf{\mu }$m
BGSe-I type (40.2°, 0°) [82]	OPA	10			8–14 $\mathsf{\mu }$m	140–230 $\mathsf{\mu }$J
BGSe-I type (47°, 0°) [130]	OPA	10	Yb:KGW, 1030 nm	290 fs 50 kHz	3.7–17 $\mathsf{\mu }$m	10 mW @16 $\mathsf{\mu }$m
BGSe [131]	OPA	1	Yb:YAG, 1.03 $\mathsf{\mu }$m + 1.15–1.8 $\mathsf{\mu }$m	550 fs 10 kHz	2.5–10 $\mathsf{\mu }$m	6 $\mathsf{\mu }$J @3 $\mathsf{\mu }$m
BGSe-I type (67°, 0°) [132]	DFG	15	Ti:sapphire, 730–970 nm	CW	3.2–7.92 $\mathsf{\mu }$m	1.41 $\mathsf{\mu }$W @5 $\mathsf{\mu }$m
BGGSe II type (27.5°, 0°) [133]	OPO	9.3	cascaded OPO, 1.85 + 2.51 $\mathsf{\mu }$m	8 ns 10 Hz	4.4–13 $\mathsf{\mu }$m	750 $\mathsf{\mu }$J @8 $\mathsf{\mu }$m
BGGSe II type (27.5°, 0°) [134]	OPO	9.3	cascaded OPO, 1.95 + 2.55 $\mathsf{\mu }$m	8 ns 100 Hz	6.6–11.3 $\mathsf{\mu }$m	1.45 mJ @8.2 $\mathsf{\mu }$m
BGGSe I type (25°, 30°) [135]	DFG	2.6	mode-locked Er:fiber oscillator	59 fs 100 MHz	5.8–8.5 $\mathsf{\mu }$m	21 pJ
BGGSe I type (30°, 28°) [136]	DFG	4.4	SPOPOs, 1035 nm	130 fs 40 MHz	up to 10 $\mathsf{\mu }$m	54 mW

In the case of nanosecond OPOs utilizing BGSe, longer-wavelength pump sources were also employed, including a Ho:YAG laser operating at 2.09 $\mathsf{\mu }$m [103,127] and a Cr, Er:YSGG laser operating at 2.79 $\mathsf{\mu }$m [128]. In the study by Yang et al. [127], there was a peak output power of 5.12 W with a pump power of 28 W for a Ho:YAG laser system. This output power consisted of 3.44 W of signal wave at 3.9 $\mathsf{\mu }$m and 1.68 W of idler wave at 4.5 $\mathsf{\mu }$m.

In 2013, Yang et al. successfully demonstrated a picosecond OPA based on a BGSe-I crystal for the first time [108]. The pump source utilized was a mode-locked Nd:YAG laser system emitting at 1064 nm with a pulse duration of 30 ps and operating at a repetition rate of 10 Hz. They achieved a quantum conversion efficiency of 56% from 1064 nm to 3.9 $\mathsf{\mu }$m, resulting in a maximum output energy of 830 $\mathsf{\mu }$J at 3.9 $\mathsf{\mu }$m. Additionally, they also presented a tuning curve that spans 3 to 5 $\mathsf{\mu }$m. Subsequently, the authors illustrated the ability to tune the wavelength within the 8–14 $\mathsf{\mu }$m range with an energy output ranging from 140 to 230 $\mathsf{\mu }$J [82]. Tian et al. successfully demonstrated the first tunable femtosecond mid-IR OPA using a BGSe crystal, offering an exceptionally wide spectral range from 3.7 to 17 $\mathsf{\mu }$m [130]. The OPA is pumped by a Yb:KGW laser at 1030 nm, delivering pulses of a 250 fs duration at a rate of 50 kHz. At a wavelength of 16 $\mathsf{\mu }$m with a 290 fs pulse duration, the OPA achieves a maximum output power of 10 mW, corresponding to a quantum conversion efficiency of 5%.

Although the thermal conductivity of the BGSe crystal is not too large, in 2019 a CW DFG was demonstrated for the first time [132]. This was achieved by mixing a CW Ti:sapphire laser with a CW Nd:YAG laser in a 15 mm long BGSe crystal (I type). The experiment resulted in a tunable range from 3.15 to 7.92 $\mathsf{\mu }$m, with a maximum DFG power of 1.41 $\mathsf{\mu }$W recorded at 5 $\mathsf{\mu }$m.

5.3. BGGSe

The employment of the quaternary barium chalcogenide BGGSe for frequency down-conversion into the mid-IR was demonstrated in [133] for the first time. The experimental setup was similar to the one described in [115], although in the second stage an OPO was used instead of a DFG. The wavelength tuning range achieved in this setup was between 4 and 13 $\mathsf{\mu }$m at 100 Hz, delivering a peak energy of 750 $\mathsf{\mu }$J at around 8 $\mathsf{\mu }$m. Later, the configuration was upgraded by incorporating a selective element, a volume Bragg grating (VBG), into the first stage. The highest energy attained around 8 $\mathsf{\mu }$m is 1.1 mJ with a line width of approximately 20 cm${ }^{-1}$ and a pulse duration of ∼7 ns. The total conversion efficiencies from 1 to 8 $\mathsf{\mu }$m for the broad spectrum and with VBG are 31% and 23%, respectively.

The BGGSe crystal was employed for a femtosecond DFG [135,136]. In [136], the authors achieved wavelength tuning down to 10 $\mathsf{\mu }$m with a maximum internal quantum efficiency of 45%. Research carried out by Elu et al. [135] demonstrated that a BGGSe DFG produces a pulse energy of 21 pJ at 100 MHz in a spectral range of 5.8 to 8.5 $\mathsf{\mu }$m. The results unveiled the electric field of the carrier-envelope-phase stable pulse duration of 91 fs, which corresponds to fewer than four optical cycles.

This crystal was also utilized for frequency up-conversion to the mid-IR range. The sum frequency generation within the CO laser cavity was realized using the BGGSe crystal [137]. The laser system functioned at the same time in two spectral regions: the fundamental band of the CO laser (4.9–6.0 $\mathsf{\mu }$m) and its band of sum frequencies (2.45–2.95 $\mathsf{\mu }$m). Various configurations of the laser cavity were evaluated. The maximum powers of the laser pulses in the fundamental and sum frequency bands were 2 kW and 10 W, respectively.

6. Conclusions

This review focuses on Ba-containing ternary (BGS and BGSe) and quaternary (BGGS, BGGSe, and B2GGS) chalcogenides. With the exception of thermal conductivity, these crystals seem to outperform the commonly used AGS and AGSe crystals. All of the crystals discussed exhibit a high LIDT, while sulfide crystals demonstrate an LIDT greater than 3 times that of their selenium-containing counterparts, suggesting their suitability for applications requiring a high peak energy. However, selenides are recognized for their enhanced nonlinearity and wider transparency range, making them attractive for spectroscopic tasks. Currently, the most popular crystals are BGS, BGSe, and BGGSe. These crystals have been used effectively by researchers to create OPOs, OPAs, and DFGs with different pump wavelengths and pulse durations. The outcomes of utilizing crystals in frequency down-conversion devices suggest that barium chalcogenide crystals could emerge as a promising nonlinear crystal for generating mid-IR in the femtosecond, picosecond, and nanosecond regimes with an exceptionally broad tuning spectral range.