1. INTRODUCTION

The ongoing development of new highly efficient nonoxide nonlinear crystals for the mid-IR part of the spectrum (3–30 µm) has been mainly driven by frequency downconversion of advanced all-solid-state laser sources operating in the near-IR [1]. The latter include Nd- and Yb-laser systems operating near 1 µm, Tm- and Ho- (including co-doped) laser systems operating near 2 µm, and to a lesser extent Er-laser systems operating near 1.6 µm and slightly below 3 µm. The useful nonoxide compounds employed in second-order, $\chi ^ {(2)}$ or three-wave nonlinear processes include phosphides (P), sulfides (S), selenides (Se), arsenides (As), and tellurides (Te), for which the mid-IR cutoff wavelength determined by multi-phonon absorption follows the relations ${\rm{S}} \lt {\rm{Se}} \lt {\rm{Te}}$ (chalcogenides) and ${\rm{P}} \lt {\rm{As}}$ (pnictides). Note that the longer this cutoff wavelength, the narrower the bandgap, for which the opposite relations ${\rm{S}} \gt {\rm{Se}} \gt {\rm{Te}}$ and ${\rm{P}} \gt {\rm{As}}$ hold, which means that longer pump wavelengths are required to avoid two-photon absorption (TPA), a higher-order nonlinear loss process. On the other hand, narrower bandgap is normally associated with increased nonlinear susceptibility which is a highly desirable property. Note that the above relations are strictly fulfilled only within a certain family of nonlinear crystals, e.g., for the ${\rm I}{\text -}{\rm III}{\text -}{\rm VI}_2$ type silver chalcopyrites ${\rm{Ag}}B{C_2}$ where $B = {\rm{Ga}}$, In and $C = {\rm{S}}$, Se, Te, which exhibit $\bar 4 2m$ tetragonal symmetry (point group). However, not all of these acentric crystals possess sufficient birefringence for phase-matching to be useful in nonlinear optics. Thus, only few of them have become commercially available and widely spread. In the first place, these are ${\rm{AgGa}}{{\rm{S}}_2}$ (AGS) and ${\rm{AgGaS}}{{\rm{e}}_2}$ (AGSe), which represent the benchmarks for laser pumping near 1 and 1.6 µm, respectively, to generate longer wavelengths in the mid-IR, i.e., in frequency downconversion. In addition, AGSe is the primary choice for second-harmonic generation (SHG) of 10.6-µm ${{\rm{CO}}_2}$ gas lasers which is an example of an opposite, upconversion nonlinear process of frequency doubling. Both of them show, however, a number of limitations which hinder their application in practice, in the first place the chemical instability of the polished surface in air. In addition, the thermal conductivities and the optical damage thresholds are one of the lowest. For these reasons, wherever possible, these crystals have been substituted by better performing ones. The best example is ${\rm{ZnGe}}{{\rm{P}}_2}$ (ZGP) which is a ${\rm{II}} {\text -} {\rm{IV}}{\text -} {{\rm{V}}_2}$ type chalcopyrite with the same $\bar 4 2m$ symmetry, and also mature and commercially available. ZGP is chemically stable and possesses much higher nonlinearity, thermal conductivity, and damage threshold. Consequently, it has become the primary choice when pumping near 2 or 3 µm; however, there are some exceptions. As a phosphide, the mid-IR transmission of ZGP is inferior, with a clear transparency limit around 8.5 µm, which is comparable to AGS but much shorter than AGSe. On the other hand, due to its narrower bandgap, TPA would not allow ZGP to be pumped near 1 µm like AGS; in practice linear residual absorption in ZGP does not permit pumping even near 1.6 µm where AGSe can be used. There is an additional technological issue which limits the volume of useful AGS and AGSe samples with optical quality: annealing at high temperature with surface diffusion of ${\rm{A}}{{\rm{g}}_2}{\rm{S}}$ and ${\rm{A}}{{\rm{g}}_2}{\rm{Se}}$ is necessary for long periods to correct the stoichiometry and eliminate scattering defects.

From the above, it is clear that there are plenty of good reasons to develop new nonoxide nonlinear crystals. One such family of crystals comprises the ${\rm{Li}}B{C_2}$ compounds (with the sulfides and selenides having orthorhombic $mm{{2}}$ symmetry and the tellurides exhibiting tetragonal $\bar 4 2m$ symmetry) [1]. Compared to their Ag counterparts, the Li compounds exhibit wider bandgaps and higher thermal conductivity and damage threshold; however, their nonlinear susceptibility is lower, the growth in large sizes is extremely difficult, and sophisticated annealing is required, with only ${\rm LiGaS}_2$ (LGS) being chemically stable. In addition, due to the specific vibrations which determine the mid-IR cutoff wavelength, Li selenides show almost the same upper transparency limit as the sulfides. Nevertheless, due to their exceptionally wide bandgaps and high damage thresholds, the Li compounds have found some unique applications: e.g., the Li sulfides are the only nonoxide mid-IR materials that can be pumped without the onset of TPA even by ultrafast Ti:sapphire laser systems operating near 800 nm [1].

In this work we will review the properties of four Ba compounds that can now be considered to be useful and promising nonoxide nonlinear crystals for the mid-IR part of the spectrum: the orthorhombic ${\rm{BaG}}{{\rm{a}}_4}{{\rm{S}}_7}$ (BGS) with point group $mm{{2}}$, the monoclinic ${\rm{BaG}}{{\rm{a}}_4}{\rm{S}}{{\rm{e}}_7}$ (BGSe) with point group $m$, as well as the trigonal ${\rm{BaG}}{{\rm{a}}_2}{\rm{Ge}}{{\rm{S}}_6}$ (BGGS) and ${\rm{BaG}}{{\rm{a}}_2}{\rm{Ge}}{{\rm{Se}}_6}$ (BGGSe) belonging to crystal class 3. The ternary compounds are biaxial and the quaternary compounds are uniaxial. We review the available data on their transmission, dispersion, birefringence, nonlinearity, etc., measured using large size single crystals of high optical quality, and the schemes of phase-matched frequency conversion nonlinear processes that have already been realized.

2. CHARACTERIZATION

Few dozens of new nonoxide nonlinear crystals have been designed and reported in the last decade, e.g., [2–6]. However, the great majority of them have been only synthesized as powders and characterized only crystallographically, by diffuse powder reflectance measurements and in the best cases with Kurtz–Perry powder SHG tests to confirm their noncentrosymmetric nature and birefringence. Theoretical electronic structure calculations provide some information on the bandgap, refractive indices, and nonlinearity but it is mainly used to decide if further development is justified. The four Ba crystals discussed in the present work belong to the short list of well-characterized nonlinear crystals by which we mean that the basic properties including transparency, dispersion, birefringence, and to some extent nonlinearity, have been measured on high optical quality bulk samples. In fact, they can be considered as the most successful development of such birefringent nonlinear materials in the last decade with advanced growth technology (see Fig. 1), adequate characterization, and demonstrated applications potential. There are only few other examples of such characterized nonoxide crystals from the last decade, e.g., ${\rm{PbG}}{{\rm{a}}_2}{\rm{GeS}}{{\rm{e}}_6}$ [7] or ${\rm{AgLiG}}{{\rm{a}}_2}{\rm{S}}{{\rm{e}}_4}$ [8], but at present it is difficult to identify some unique features for their application.

 

Fig. 1. State-of-the-art as-grown and partially polished boules (left), and antireflection-coated optical elements (right) of BGSe (top) and BGGSe (bottom). Boules with a diameter of 40 mm and a length of the order of 100 mm can be readily grown now.

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The four Ba compounds considered here in fact do not belong to the same family. Their common feature is that both the ternary and quaternary sulfides BGS and BGGS can be considered as a viable alternative to AGS, and both the ternary and quaternary selenides BGSe and BGGSe can be considered as a viable alternative to AGSe. Such reasoning is based on the similar transparency range compared to AGS and AGSe, respectively, because this is the primary criterion when comparing two such materials with respect to possible applications in nonlinear optics, as explained in the example with ZGP given before. As it will be seen, compared to their Ag counterparts, the ternary Ba compounds exhibit roughly 4–5 times lower nonlinear figure of merit (${\rm{FM}} = {d^2}/{n^3}$ where $d$ is some average nonlinear coefficient and $n$ is the average refractive index) [1]. However, their bandgaps are wider, the damage thresholds are higher, and they are chemically stable. The quaternary Ba compounds exhibit similar advantages and disadvantages relative to AGS and AGSe. On the positive side none of the four Ba compounds require post-growth annealing procedures; on the negative side, the biaxial BGSe and the uniaxial BGGS and BGGSe are more difficult to characterize due to their low symmetries.

 

Fig. 2. Unpolarized transmission of BGS, BGSe, BGGS, and BGGSe measured with sample thickness between 10 and 20 mm and recalculated for a uniform thickness of 10 mm with the multiple reflection effect eliminated. The losses do not exceed 1%/cm in the good transparency range where the transmission is determined primarily by the Fresnel reflections. Note that the mid-IR transparency range of BGS and BGGS is similar to other sulfides (AGS, LGS, ${\rm{LiIn}}{{\rm{S}}_2}$, ${\rm{HgG}}{{\rm{a}}_2}{{\rm{S}}_4}$, ${\rm{AgGaGe}}{{\rm{S}}_4}$, ${\rm{A}}{{\rm{g}}_3}{\rm{AsS}}_3$, ${\rm{A}}{{\rm{g}}_3}{\rm{Sb}}{{\rm{S}}_3}$, HgS, ${\rm{InP}}{{\rm{S}}_4}$, etc.) while that of BGSe and BGGSe is similar to other selenides (AGSe, GaSe, CdSe, ${\rm{T}}{{\rm{l}}_3}{\rm{AsS}}{{\rm{e}}_3}$, ${\rm{AgGaG}}{{\rm{e}}_5}{\rm{S}}{{\rm{e}}_{12}}$, etc.).

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Table 1. Information on the Dispersion, Birefringence, and Second-Order Nonlinearity of the Ba Compounds

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The four Ba compounds can be also compared to the orthorhombic (biaxial) ${\rm{Li}}B{C_2}$ crystals ($B = {\rm{Ga}}$, In, $C = {\rm{S}}$, Se). With similar bandgaps, FM, and damage thresholds, the Ba compounds seem easier to grow in larger sizes, exhibit less residual absorption without annealing, and the selenides offer extended transmission into the mid-IR.

The acentric orthorhombic $mm{{2}}$ symmetry of BGS was identified as early as 1983 [9], with lattice parameters (using the convention ${c_0} \lt {a_0} \lt {b_0}$ [10]) ${a_0} = {6.2}\;\mathop {\rm A}\limits^\circ$, ${b_0} = {14.8}\;\mathop {\rm A}\limits^\circ$, and ${c_0} = {5.9}\;\mathop {\rm A}\limits^\circ$. Small single crystals of BGS were first grown in [11] by the Bridgman–Stockbarger technique. The SHG effect was confirmed by the Kurtz–Perry powder test yielding an average nonlinear coefficient comparable to that of AGS and birefringence sufficient for phase-matching. Although only tiny pieces of optical quality were obtained in [11], a short-wave cutoff of 350 nm could be measured (bandgap ${\sim}\;{3.54}\;{\rm{eV}}$) with a 0.7-mm thick sample and the transparency extended up to 13.7 µm at the 0-level which is similar to AGS. A short-wave cutoff of 345 nm (${\sim}{3.59}\;{\rm{eV}}$) was reported later in [12]. In [13] we demonstrated the successful growth of large size boules of high optical quality by the vertical Bridgman–Stockbarger method. The as-grown BGS crystals were colorless, and the transmission is shown Fig. 2. Prisms of high optical quality could be cut which allowed us to measure the refractive indices by the auto-collimation method [13]. The orientation of the dielectric frame was determined from conoscopic pictures using 633-nm laser light and monitoring the three principal dielectric axes $xyz$ (under the convention ${n_x} \lt {n_y} \lt {n_z}$) and the two optic axes. The experimental angle between the latter and the $z$-principal dielectric axis, $\Omega ={45.6}^\circ$, could be well reproduced by the fitted Sellmeier equations [13]. Thus, the biaxial BGS is one of the rare examples of equidistant refractive indices.

From the space group specified in [9,11], the twofold axis of BGS should be the $c$ crystallographic axis. We confirmed this independently by non-phase-matched SHG generation using amplified femtosecond pulses at 1.3 µm and propagation along the three crystallographic axes [13]. From the refractive index measurements, we arrived at the correspondence between the dielectric ($xyz$) and crystallographic ($abc$) axes of $xyz \equiv cab$ [13]. This information is essential for the form of the effective nonlinearity expressions, because traditionally, the tensor components ${d_{{il}}}$ for orthorhombic crystals are given in the $abc$ crystallographic frame [14]. Assuming the Kleinman symmetry condition is satisfied, ${d_{15}} = {d_{31}}$ and ${d_{24}} = {d_{32}}$, in the principal planes we have [14]

Some additional known characteristics of BGS are compiled in Table 3. These include the temperature-dependent (50°C–150°C) thermal conductivity $K$ [32], nonlinear refractive index ${n_2}$ and TPA [33,34], as well as Moh’s hardness [11].

The acentric monoclinic point group $m$ of BGSe, the selenide analog of BGS, was identified in 2010 in [44] where its structure (similar to BGS) was described for the first time and the lattice parameters (using the convention ${c_0} \lt {a_0},\;b$: monoclinic axis, and $\beta \gt {{90}}^\circ$) are ${a_0} = {{14.7}}\;\mathop {\rm A}\limits^\circ$, ${b_0} = {6.5}\;\mathop {\rm A}\limits^\circ$, ${c_0} = {7.6}\;\mathop {\rm A}\limits^\circ$, and $\beta = {{121}}^\circ$ [10]. From a Kurtz–Perry powder test the authors concluded that the average nonlinear coefficient of BGSe is roughly 50% higher compared to AGS. Only millimeter size single crystals could be grown in [44] and the short-wave cutoff at ${\sim}{{470}}\;{\rm{nm}}$ (corresponding to a bandgap of 2.64 eV) was determined from diffuse reflectance measurements. A more recent transmission study with a very thin (0.2 mm) sample gave a direct bandgap value of 2.73 eV (${\sim}{{454}}\;{\rm{nm}}$) at room temperature and 2.91 eV at 80 K [35]. The transparency of BGSe extends up to 18 µm at the 0-level according to [44]; in [35] this limit was estimated to be 22 µm. Almost simultaneously, large size single crystals of high optical quality BGSe were grown in 2010 by the vertical Bridgman–Stockbarger technique in [13]. The as-grown BGSe boules were light yellow in color and their transmission is shown in Fig. 2. BGSe is free of absorption losses at the 10.6 µm ${{\rm{CO}}_2}$ laser wavelength. Similar to BGS, we measured the refractive indices of BGSe by the auto-collimation method using prisms which served to create the initial Sellmeier equations; see Table 1 [13].

Table 2. Sellmeier $n_i^2 = {A_i} + {B_{1i}}/(\lambda^2 - {C_{1i}}) + {B_{2i}}/(\lambda ^2 - {C_{2i}})$ and Thermo-Optic $d{n_i}/dT = ({E_i}\lambda ^{- 3} - {F_i}\lambda ^{- 2} + {G_i}\lambda ^{- 1} + {H_i}) \times {{1}}{{{0}}^{- 5}}\;^\circ {{\rm{C}}^{- 1}}$ Expressions for the Biaxial BGS and BGSe Crystals, Where $i = x,y,z$ and $\lambda$ Is in µm^a

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Table 3. Some Important Characteristics of the Ba Compounds^a

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Other refractive index measurements and Sellmeier equations valid in a limited wavelength range were reported in [19]. The orientation of the dielectric frame was determined like for BGS from conoscopic pictures using 633-nm laser light and monitoring the three principal dielectric axes $xyz$ (under the convention ${n_x} \lt {n_y} \lt {n_z}$) and the two optic axes. The experimental angle between the latter and the $z$-principal dielectric axis, $\Omega = {26.3}^\circ$ (in agreement with the one calculated from the Sellmeier equations), indicated that the biaxial BGSe is optically positive [13].

In monoclinic crystals, one of the principal dielectric axes always coincides with the $b$-crystallographic axis and from x-ray and refractive index/conoscopic measurements we established that for BGSe it is $x \equiv b$ (monoclinic axis).

At 633 nm, we also observed that, within ${{\pm 0.5}}^\circ$ uncertainty, in BGSe $z \equiv c$. Thus, it is possible to define and measure the tensor components of the second-order nonlinearity ${d_{{il}}}$ directly in the $xyz$ frame since it nearly coincides with the crystallo-physical frame (an orthogonal frame for reporting tensor properties, with two axes parallel per definition to the crystallographic $b$ and $c$ axes [10]). While this deviates from the standard [10], we note that it corresponds to the tradition established for the majority of monoclinic nonlinear crystals (e.g., the organic ones [14]). Using the $xyz$ frame for definition of ${d_{{il}}}$ is simpler because this is the frame where also the phase-matching conditions (i.e., the angles $\theta$ and $\varphi$) are defined. The disadvantage is that the $xyz$ frame may rotate about the $x \equiv b$ axis with wavelength and temperature. However, measurements between crossed polarizers indicated that no such rotation takes place in BGSe in the 0.7–1.8-µm wavelength range [24]. Nevertheless, one shall take care to avoid any ambiguity for this monoclinic symmetry. Obviously, there are four possible orientations of the $xyz$ dielectric frame relative to the $abc$ frame with both frames right-handed. Selecting the $x$ axis to be parallel but not antiparallel to the $b$ axis is then essential. The remaining two possibilities (the one shown in Fig. 3 and the one with both $y$ and $z$ axes in opposite direction) are equivalent in the sense of nonlinear optics because due to the inversion symmetry, $d_{{\rm eff}}^2$ exhibits ${\rm{2/}}m$ centric symmetry [45]. For the same reason it is not necessary to define the crystallographic axes sense [10] since the right-handedness of this frame and $\beta \gt 90^\circ$ lead to only two choices which differ by a 180° rotation about the $b$ axis.

 

Fig. 3. Crystallographic ($abc$) and orthogonal dielectric ($xyz$) right-handed frames of BGSe. The monoclinic $b$ axis is per convention normal to the $a - c$ plane (mirror plane $m$) which contains the $y$ axis; ${c_0} \lt {a_0}$ is adopted for the lattice constants. The two optic axes (one of them shown by a green dashed arrow) lie in the $x - z$ plane, symmetric to the $z$ axis (${n_{x\:}} \lt {n_y} \lt {n_z}$).

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Two octants are sufficient to describe unambiguously the effective nonlinearity of a monoclinic crystal. Let us select the first ($+,+,+$) and fourth ($+,-,+$) octants to this aim which means we choose ${-}{{90}}^\circ \le \varphi \le + {{90}}^\circ$ and ${{0}}^\circ \le \theta \le \;{{90}}^\circ$. For the monoclinic point group $m$, with the selected frame correspondence and assuming Kleinman symmetry to hold, i.e., ${d_{21}} = {d_{16}}$, ${d_{23}} = {d_{34}}$, ${d_{24}} = {d_{32}}$, and ${d_{31}} = {d_{15}}$, we have the following expressions for nonvanishing effective nonlinearity in the principal planes [45]:

Note that Eqs. (2d) and (2g) as well as (2e) and (2f) are identical in terms of absolute values. In fact, from phase-matching considerations, the case Eq. (2e) is never realized. Equations (2a)–(2g) involve four independent tensor components. The need for a careful selection of the frame correspondence is obvious from Eq. (2c) because independent of the intrinsic signs of the two tensor components the two terms may add or subtract depending on the octant chosen. More general expressions for propagation outside the principal planes which involve also the diagonal components ${d_{22}}$ and ${d_{33}}$ can be found in [45].

Realizing phase-matched processes in BGSe, the Sellmeier equations were subsequently refined: SHG and SFG were used in [20], and SHG and DFG with an original method employing a sphere were used in [21]; see Tables 1 and 2. Similarly, using phase-matched SHG, the thermo-optic coefficients of BGSe were fitted in [22] and these data are also included in Table 2. Different thermo-optic coefficients for BGSe were published in [23] but they were derived only from prism dispersion measurements in a rather limited (0.546–2.325 µm) spectral range.

The nonlinear coefficients of BGSe were theoretically evaluated in [44]; however, the authors were unable to recover in which orthogonal frame this had been performed. The assumption that this was in a crystallo-physical frame for Table 4 is kind of arbitrary since such a frame and the dielectric $xyz$ frame were introduced only later [13]. With respect to the magnitude of the theoretical results, the reliability is also unclear because the calculated bandgap value and refractive indices based on the same theory deviate substantially from the experimental values. The Maker fringes technique was employed in [25] but it yielded only partial results without relative signs. Both measured coefficients are marked with “±” in Table 4 but the relative sign of ${d_{22}}$ with respect to ${d_{23}}$, ${d_{34}}$ is also unknown. The measurements in [25] were performed in a crystallo-physical frame but converted to the $xyz$ frame for the table, just as those from [44]. The most comprehensive study so far included phase-matched SHG, Maker fringes, and oriented sphere measurements and was performed directly in the dielectric $xyz$ frame [24,26]. Unfortunately, the predicted ${d_{{\rm eff}}}$ from this study seems too low to explain the excellent downconversion performance of BGSe; see Section 3.

Table 4. Tensor Components ${d_{il}}$ [pm/V] of BGSe, with All Results Rescaled to 532 nm

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Although BGSe is at present the most widely studied and, as will be seen in the next section, also the most widely applied nonoxide Ba nonlinear crystal, it cannot be considered as a fully characterized material because of the difficulties related to the determination of its nonlinear tensor components. Any calculations of optimum conversion efficiencies, in particular outside the principal planes of BGSe, are at present mere speculations [46].

Some additional known characteristics of BGSe are compiled in Table 3. These include the anisotropic thermal conductivity $K$ and thermal expansion $\alpha$ [36], observations of TPA [37], photoluminescence [35], phonon spectra [35,38], and THz spectroscopy [39,40]. The maximum phonon energy of ${\sim}{{350}}\;{\rm{c}}{{\rm{m}}^{- 1}}$ indicates that two-phonon absorption eventually determines the practical upper transparency limit for thick samples of BGSe [35]. The absorption peak near 15 µm seen in Fig. 2 can be found with different magnitude in the corresponding literature, an indication of some polarization dependence. A similar absorption peak for BGS can be seen in Fig. 2 near 9.5 µm.

Soon after the discovery of BGSe, four potentially interesting isostructural (point group 3) quaternary Ba chalcogenides were identified: ${\rm{BaG}}{{\rm{a}}_2}{\rm{Si}}{C_6}$ ($C = {\rm{S}}$, Se) [47] and ${\rm{BaG}}{{\rm{a}}_2}{\rm{Ge}}{C_6}$ ($C = {\rm{S}}$, Se) [47,48]. Kurtz–Perry powder SHG tests revealed nonlinearities comparable to those of AGS and AGSe for the sulfides and the selenides, respectively [47,48], and adequate birefringence of the Ge compounds [48]. As for the ternary BGS and BGSe, the respective bandgaps, measured by diffuse reflectance, were wider compared to AGS and AGSe [47]. Bulk samples of a few millimeters in size were grown only for ${\rm{BaG}}{{\rm{a}}_2}{\rm{Ge}}{{\rm{S}}_6}$ (BGGS) in [48] where in addition transmission spectra were recorded. Subsequent work revealed that ${\rm{BaG}}{{\rm{a}}_2}{\rm{SnS}}{{\rm{e}}_6}$ also belongs to this family and exhibits similar properties [49]. From the powder tests it could be concluded that the nonlinearity increases with decreasing bandgap for the entire series. We established that in this family, ${\rm{BaG}}{{\rm{a}}_2}{\rm{Si}}{C_6}$ are chemically unstable compounds and focused our efforts on BGGS and BGGSe. The lattice constants of BGGS are ${a_0} = {9.6}\;\mathop {\rm A}\limits^\circ$ and ${c_0} = {8.7}\;\mathop {\rm A}\limits^\circ$ and those of BGGSe are ${a_0} = {10.0}\;\mathop {\rm A}\limits^\circ$ and ${c_0} = {9.1}\;\mathop {\rm A}\limits^\circ$ [47,48]. The corresponding bandgaps determined from diffuse reflectance are 3.23 eV (380 nm) and 2.22 eV (560 nm) [47]. A similar measurement in [48] gave a higher value of 2.81 eV for BGGSe while from transmission measurements the bandgap of BGGS was estimated to be 3.26 eV (380 nm) and the mid-IR cutoff wavelength was estimated to be 13.7 µm.

In [27] we reported the successful growth of large size high optical quality BGGS and BGGSe crystals by the vertical Bridgman–Stockbarger technique. This allowed us to characterize the transmission, dispersion, birefringence, and partially the nonlinearities. The bandgap values, determined for the ordinary wave with thin (${\lt}{{1}}\;{\rm{mm}}$) $a$-cut samples in polarized light, are 3.37 eV (368 nm) for BGGS and 2.38 eV (522 nm) for BGGSe. The good transparency of thick BGGS extends in the mid-IR up to ${\sim}{7.8}\;{{\unicode{x00B5}{\rm m}}}$ from which point it gradually decays down to the 0-level at ${\sim}{11.8}\;{{\unicode{x00B5}{\rm m}}}$; see Fig. 2. The good transparency of BGGSe extends up to ${\sim}{{11}}\;{{\unicode{x00B5}{\rm m}}}$, covering the important 10.6 µm fundamental wavelength of the ${{\rm{CO}}_2}$ laser, and decays to the 0-level at ${\sim}{{17}}\;{{\unicode{x00B5}{\rm m}}}$ for 1-cm thickness. No phonon absorption peaks are visible in Fig. 2 for the quaternary Ba compounds. As can be seen, they exhibit narrower bandgaps but also lower near band edge absorption compared to their ternary counterparts.

Table 5. Sellmeier Equations $n_i^2 = {A_i} + {B_{1i}}/(\lambda ^2 - {C_{1i}}) - {D_i}{\lambda ^2}$ for BGGS and $n_i^2 = {A_i} + {B_{1i}}/(\lambda ^2 - {C_{1i}}) + {B_{2i}}/(\lambda ^2 - {C_{2i}})$ for BGGSe, and Thermo-Optic $d{n_i}/dT = ({E_i}\lambda ^{- 3} - {F_i}\lambda ^{- 2} + {G_i}\lambda ^{- 1} + {H_i}) \times {{1}}{{{0}}^{- 5}}\;^\circ {{\rm{C}}^{- 1}}$ Expressions for BGGSe, Where $i = o$ or $e$ and $\lambda$ Is in µm^a

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The refractive indices of the two quaternary Ba compounds were measured using prisms to derive initial dispersion relations [27]; see Tables 1 and 5. Both BGGS and BGGSe are optically positive and hence the bandgap for the ordinary wave is the important one with respect to TPA. Unfortunately, the Sellmeier equations were refined by phase-matched nonlinear processes (SHG and SFG) only for BGGSe [28], for which also the thermo-optic coefficients were fitted, based on additional temperature-dependent index measurements with a prism [29]; see Table 5.

Table 6. Damage Thresholds of the Ba Compounds

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In the trigonal point group 3, in general two octants are needed for finding the maximum ${d_{{\rm eff}}}$ in birefringent phase-matching even though the crystals are uniaxial. We have studied the corresponding tensor components only for BGGSe. The four independent nonzero components under Kleinman symmetry are ${d_{11}}$, ${d_{22}}$, ${d_{33}}$, and ${d_{31}} = {d_{15}}$. Only three of them are involved in the formulas for birefringent phase-matching in such a positive crystal:

Using phase-matched SHG and SFG processes with picosecond and nanosecond pulses in samples of BGGSe which were oriented in the $xyz$ frame with known axes sense, and using AGS as a reference material, we found a self-consistent set of solutions: ${d_{11}} = + {23.6}\;{\rm{pm/V}}$, ${d_{22}} = - {18.5}\;{\rm{pm/V}}$, and ${d_{31}} = + {18.3}\;{\rm{pm/V}}$ at 5.3 µm [30]. Note that the relative signs are in agreement with the theoretical calculations in [47] but the preliminary estimation for the absolute value of ${d_{11}}$ in [27] was an overestimation. Thus, BGGSe has been recently also added to the SNLO database [31]; see Table 1. For the sulfur compound BGGS, only theoretical estimations of the nonlinear coefficients have been published, predicting equal relative signs [47].

Although in the specific case of BGGSe, the first octant is sufficient for finding a maximum ${d_{{\rm eff}}}$, to utilize the knowledge about the relative signs, one shall strictly follow the above procedure for determination of this octant in the $xyz$ frame. In the case of Type II phase-matching, Eq. (3b), one can adjust the contribution of all three terms to be additive by selecting a proper azimuthal angle $\varphi$. This optimum angle ($\varphi = {12.7}^\circ$) is in fact constant (as long as we ignore the dispersion of the tensor components) independent of the three-wave interaction process. Consequently, the FM of Type II BGGSe for frequency doubling of 10.6-µm ${{\rm{CO}}_2}$ lasers exceeds that for AGSe. Higher conversion efficiency compared to AGSe can be expected also for frequency downconversion with 1.6- or 2-µm pump laser systems.

Very recently the thermal conductivity of BGGS and BGGSe has been measured and it showed weak anisotropy with values higher compared to AGS and AGSe [41]; see Table 3. The phonon spectra of BGGS and BGGSe have been studied in [42,43], respectively.

The optical damage resistivity is an important property of any nonlinear crystal which depends on many parameters such as wavelength, pulse duration, repetition rate, beam size, evaluation method, surface quality, coatings, etc. In most cases surface damage occurs first but this can happen either on the entrance or on the exit surface. Thus, prior to using them, the data compiled in Table 6 shall be carefully checked in the corresponding publication. For nanosecond pulses we used as a measure the peak on-axis fluence while for picosecond and femtosecond pulses where indirect damage might dominate, we used the peak on-axis intensity.

Finally, it shall be outlined that at present the technology of the selenide compounds seems more advanced and larger boules can be manufactured [13,27,58]; see Fig. 1.

3. APPLICATIONS

All the four Ba compounds possess the phase-matching capability to cover the mid-IR spectral range by downconversion of 1.064 µm laser radiation, show clear transparency, and are free of TPA at this pump wavelength although this is strictly true for the selenides only with nanosecond and longer pulse durations. The selenides are transparent at 10.6 µm and transmit up to 17–18 µm.

Table 7. Optical Parametric Oscillators Realized with Ba Nonoxide Nonlinear Crystals: I (II), Type I (II) Phase-Matching, $L$, Sample Length, ${\lambda _3}$, Pump Wavelength, ${\lambda _1}$, Idler Wavelength, SRO, Singly Resonant OPO, DRO, Doubly Resonant OPO^a

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Optical parametric oscillators (OPOs) operating in the nanosecond regime, pumped at 1.064 µm, are obviously one of the most attractive schemes for generation of high energies/average powers in the mid-IR. BGS was the first crystal studied and showed robust OPO performance [59]. BGSe has been the most widely applied crystal in such OPOs, pumped near 1, 2, and 2.8 µm; see Table 7. Pumping at longer wavelengths is expected to suppress damage related problems, concerning not only the nonlinear crystal but also the OPO optics in general. Singly and doubly resonant OPOs have been studied, pumped in single- and double-pass schemes at repetition rates from 1 Hz to 1 kHz. Temperature tuning has also been demonstrated [60,61]. It should be noted, however, that the output idler wavelength exceeded the upper limit of oxide materials (about 5 µm) only in few cases; see Table 7. Thus, highest energies were produced at 10 Hz in [55] (3.7 mJ at 7.2 µm), see Fig. 4, and in [62] (1.05 mJ at 11 µm). A pump depletion (i.e., quantum efficiency) of 40% was reached in [55] corresponding to a pump to idler conversion efficiency of 5.9%. In most cases, Type I phase-matching in BGSe was employed. Type II phase-matching can ensure broader tunability with a single cut and narrower bandwidth. It has been studied only in [52,55,63] but the octant was unknown, i.e., it is unclear whether the effective nonlinearity has been optimum. BGGSe is expected to provide similar performance with 2-µm pumping but so far it has been studied only in an intracavity configuration, without optimization of the azimuthal angle for maximized effective nonlinearity [64].

In [73] BGSe Type I ($L = {17.54}\;{\rm{mm}}$) was employed for DFG between the 1.064 µm radiation of a nanosecond Nd:YAG laser and the idler pulses of a ${\rm{KTiOPO}}_4$ (KTP) OPO pumped by the same laser at 10 Hz. Maximum energy of 5.72 mJ at 3.58 µm and tuning in the 3.36–4.27 µm range were achieved but such wavelengths can be in principle covered also by an oxide-based OPO. In [74] BGSe Type I ($L = {14.6}\;{\rm{mm}}$) was used for intracavity DFG between the signal and idler of a doubly resonant periodically poled KTP nanosecond OPO pumped by a Nd:YAG laser at 1.064 µm. An average power of ${\gt}{{71}}\;{\rm{mW}}$ was achieved near 7 µm at 100 Hz, equivalent to an overall quantum efficiency of 7.8% (conversion efficiency of ${\sim}{1.2}\%$). In the continuous-wave regime TPA obviously plays no role, and in [75] BGSe Type I ($L = {{15}}\;{\rm{mm}}$) was used at much shorter input wavelengths, mixing Ti:sapphire and Nd:YAG lasers to produce a power of 1.41 µW at 5 µm by DFG, with tunability from 3.15 to 7.92 µm.

BGS and BGSe have been used in the picosecond regime in seeded optical parametric amplifiers (OPAs) pumped by 30-ps Nd:YAG lasers at 10 Hz. Different lengths of BGSe Type I ($L = {{4}}$, 8, 8.7 mm) were compared [19,37,56], providing an idler tunability from 3 to 14 µm with a maximum energy of 230 µJ at 9.5 µm. With picosecond pulse pumping BGSe exhibited some TPA, see Table 3, presumably related to defects. This served as a motivation to try BGS Type I ($L = {{15}}\;{\rm{mm}}$) in the same scheme reaching an idler tunability from 6.3 to 8.8 µm with a maximum energy of 130 µJ at 7.25 µm [76] at rather similar overall conversion efficiencies from 1.064 µm to the idler.

One of the most promising applications of the Ba compounds have been realized in the femtosecond regime, down to few optical cycles where the carrier-envelope phase (CEP) stability becomes a desirable property, e.g., for high-harmonic generation. In this case Type I phase-matching is chosen due to the larger parametric gain bandwidths. The wide bandgap of BGS makes it suitable for pumping with femtosecond pulses without TPA. In [34,77,78] BGS Type I ($L = {8.3}\;{\rm{mm}}$) was employed in white-light continuum (WLC) seeded OPA pumped by 180-fs pulses at 100 kHz from an ${\rm{Yb}}{:}{\rm{KGd}}{({{\rm{WO}}_4})_2}$ laser system emitting at 1.028 µm; see Fig. 5(a). The average idler power reached 59 mW for a pump power of 3.7 W (quantum efficiency: 29%); see Fig. 5(b). The shortest idler pulse duration amounted to 126 fs (3.8 optical cycles). Still some tuning was possible, from 8 to 10.9 µm for the central wavelength. This spectral range is determined by the low group velocity mismatch (GVM) and is shifted to longer wavelengths compared to LGS which was tested simultaneously [77,78]. The idler pulses shall be nominally CEP-stable since the WLC was derived from the same pump source.

In [79] a similar seeded BGGSe (Type I, $L = {4.37}\;{\rm{mm}}$) OPA was studied pumped by a 100-kHz, Tm-fiber laser system providing 275-fs pulses at 1.96 µm. Part of the available pump power of 5.5 W was used to generate tunable seed pulses. Idler tuning from 4 to 12 µm was achieved with a maximum energy of 1.05 µJ (105 mW) at 9 µm. The pulse duration did not exceed 160 fs across the tuning range, e.g., 153 fs at 9.0 µm, corresponding to 5.1 optical cycles.

The same BGGSe sample was employed in [80] for DFG between the signal and idler outputs of a synchronously pumped periodically poled ${\rm{LiNb}}{{\rm{O}}_3}$ OPO, in turn pumped by 130-fs pulses from a 1.035-µm Yb-fiber laser operating at 40 MHz. Tunable femtosecond pulses in the 3.88–17.65 µm range were generated with a maximum energy of 1.34 nJ (${\sim}{{54}}\;{\rm{mW}}$) at 4.8 µm. This represents the highest output from such femtosecond DFG compared to other crystals with conversion efficiency 2 times higher compared to AGSe. The internal DFG quantum efficiency was ${\sim}{{40}}\%$ across the tuning range.

The advantageous dispersive (low GVM) properties of BGGSe enabled the generation of few-cycle CEP-stable pulses at 7 µm with a spectrum spanning over 2400 nm at ${-}{{20}}\;{\rm{dB}}$ [81]. In this case the two output beams from a 100-MHz Er-fiber laser system (Er- and Tm/Ho-fiber amplified outputs) were mixed in BGGSe Type I ($L = {2.6}\;{\rm{mm}}$) producing a mid-IR energy of 21 pJ (2.1 mW). Both in terms of efficiency and spectral acceptance BGGSe turned out to outperform GaSe, notwithstanding its lower FM. Sophisticated electro-optic sampling allowed one to measure directly a pulse duration of 91 fs at 7 µm, corresponding to less than 4 optical cycles [81]. More recently, the same BGGSe sample was employed for intrapulse DFG producing 86-fs pulses (2.5 optical cycles) at 10.3 µm [82] and outperforming GaSe and ZGP as a key component of a novel high-brightness seven-octave and few-cycle CEP-stable light source.

 

Fig. 4. (a) Nanosecond singly resonant OPO based on BGSe with double-pump pass to reduce the threshold: $\lambda /{{2}}$, half-wave plate; P, polarizer; T, telescope; D, diaphragm; BM, bending dichroic pump mirror transmitting the idler; IOC, input–output coupler transmitting pump and idler and reflecting signal; TR, total reflector. Only the nonresonant mid-IR idler is extracted after a double pass through the crystal and characterized behind the long-pass filter F [55]. (b) Performance of the OPO from (a) with Types I and II BGSe for a physical cavity length of 24 mm. The pump repetition rate for this experiment has been reduced to 10 Hz by a shutter [55].

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Fig. 5. Tunable mid-IR OPA based on BGS: (a) schematic layout. PR, partial reflector; WLC, white-light continuum; DM, dichroic mirror; BS, beam sampler; Ge lens, collimating lens for the idler (yellow). (b) Recorded idler spectra corresponding to broadest idler bandwidth (at 9.5 µm) and highest idler energy (at 10.1 µm). Tuning is achieved by tilting the BGS crystal and optimizing the temporal and spatial overlap of the pump (red) and signal (blue) beams.

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Note that in all the above applications the BGGSe samples were cut for Type I phase-matching at $\varphi = {{30}}^\circ$, utilizing only the ${d_{11}}$ tensor component, see Eq. (3a), because optimization by the azimuthal angle would have required knowledge of the relative signs which were only subsequently established.

Intrapulse DFG has been recently studied also with BGSe, pumped by a 28-fs, 69-MHz Cr:ZnS laser system at 2.4 µm [57]. With a Type I ($L = {{1}}\;{\rm{mm}}$) sample the DFG spectrum extended from 6 to 18 µm at ${-}{{30}}\;{\rm{dB}}$ but the pulse duration was not measured.

SFG of discrete lines of $Q$-switched CO lasers (typically 500 ns, 100 Hz) in BGGSe Type I has been studied in [83–86] producing radiation between 2.45 and 2.95 µm by SHG (including intracavity) and between 1.7 and 1.9 µm by SFG ($L = {10.4}$ and 4.7 mm). The efficiency reached 0.7%–1.7% in SHG corresponding to a peak power of up to 100 W; the peak power at the third harmonic reached 0.5 W. While the advantages of BGGSe at such short wavelengths are questionable, DFG of discrete lines of $Q$-switched CO and ${{\rm{CO}}_2}$ lasers in BGGSe Type I ($L = {12.7}\;{\rm{mm}}$) produced discrete radiation in the 14 µm spectral range [87] which seems more interesting.

Finally, narrowband terahertz generation at 1.97 and 2.34 THz with high efficiency was demonstrated in [88,89] using optical rectification in a 0.5-mm thick $b$-cut BGSe excited by 50-fs pulses at 800 nm.

4. CONCLUSION

We present the state of the art with respect to the characterization of four Ba chalcogenide compounds with proven potential for nonlinear optical applications. The compilation of the properties serves two main purposes: (i) one can directly compare these compounds for an optimum choice in a specific application, and (ii) one can avoid ambiguities related to different frames that have been used in the literature so far for reporting different properties. The latter is a consequence of the low symmetry which requires precise definitions of the frame correspondence. This makes the present review quite different from previous attempts to summarize the knowledge about these and other newly developed nonlinear materials for the mid-IR [90–92]. The coverage of the existing relevant literature can be considered complete as of last year 2020. However, aspects, such as crystal growth, crystallographic structure, defect formation and analysis, etc., remained outside the scope of the present paper.