## Abstract

Non-centrosymmetric crystals of BaGa_{2}GeS_{6} and BaGa_{2}GeSe_{6} were grown in large sizes with good optical quality, which enabled the characterization of their linear (transmission, dispersion, and birefringence) and nonlinear (second order susceptibility) properties for the first time.

© 2016 Optical Society of America

## 1. Introduction

The search for new highly efficient non-oxide nonlinear crystals for the mid-IR part of the spectrum is very active in recent years, mainly in relation to frequency down-conversion of advanced all-solid-state laser sources operating in the near-IR [1]. However, only few such crystals are commercially available and widely spread. On the first place, these are the I-III-VI_{2} chalcopyrites AgGaS_{2} (AGS) and AgGaSe_{2} (AGSe) which represent the benchmarks for pumping near 1 µm (Nd- or Yb-laser systems) and near 1.5 µm (Er-laser systems). In addition AGSe is the primary choice for frequency doubling of CO_{2} lasers at 10.6 µm. Both of them show, however, a number of limitations which hinder their application in practice. On the first place this is the chemical instability of the polished surface in air. In addition, the optical damage thresholds are one of the lowest, especially for down-conversion. Moreover, to obtain optically uniform samples, annealing at high temperature is necessary for long periods.

The development of high optical quality BaGa_{4}S_{7} (BGS) and BaGa_{4}Se_{7} (BGSe) crystals as alternatives to AGS and AGSe, can be considered as a successful step since these two compounds are chemically stable and show much larger band-gaps and higher optical damage thresholds at similar transmission windows in the mid-IR [2]. However, both of them are biaxial (BGS is orthorhombic and BGSe monoclinic) which complicates their characterization (e.g. the determination of all tensor components) and hinders their application potential.

Recently, a new class of potentially interesting quaternary Ba chalcogenides has been identified: BaGa_{2}АВ_{6} (А = Si, Ge; В = S, Se) [3,4], that present another alternative to AGS and AGSe. While the second-harmonic generation (SHG) tests with powders reveal nonlinearities similar to those of AGS and AGSe, the corresponding band-gaps are larger and one could expect higher damage thresholds [3]. Further powder tests confirmed that their birefringence should be sufficient for phase-matching [4]. Subsequent work revealed that BaGa_{2}SnSe_{6} also belongs to this family and exhibits even higher nonlinearity [5]. The general trend of increasing nonlinearity with decreasing band-gap remains valid for the entire series. Although the crystallographic studies based on X-ray diffraction data can be considered as complete, the lack of large single crystals restricted the optical studies to powder tests while theoretical models yielded some predictions about the nonlinearity and the birefringence.

We established that in this series, BaGa_{2}SiS_{6} and BaGa_{2}SiSе_{6} are chemically unstable in air whereas the rest of these quaternary compounds (including BaGa_{2}SnS_{6} which we were able to grow for the first time) are stable. For this reason in this work we focus on the Ge compounds, BaGa_{2}GeS_{6} (BGGS) and BaGa_{2}GeSе_{6} (BGGSe). We report on their synthesis, growth, characterization (transmission, dispersion, birefringence, nonlinearity), and first realization of phase-matched SHG with high optical quality samples of BGGS and BGGSe.

## 2. Growth and crystallographic properties

For synthesis of the two quaternary compounds we used pure chemical elements: Ba (99.9%), Ga (99.999%), Ge (99.999%), S (99.999) and Se (99.999%). The binary compounds Ga_{2}S_{3}, Ga_{2}Se_{3}, GeS_{2} and GeSe_{2} were synthesized from these elements in evacuated (10^{−6} mbar) quartz ampoules at high temperature. BGGS was synthesized in a graphitized quartz ampoule filling it with metallic Ba and sulfur (composition BaS), Ga_{2}S_{3} and GeS_{2} in 1:1:1 molar ratio. The ampoule was sealed off under vacuum (10^{−6} mbar) conditions by means of a gas burner. The procedure for BGGSe was analogous. The ampoules were then inserted into a horizontal oven and heated to 1000°C within 16 h. The melt was kept at this temperature for additional 24 h, mixing it until complete homogenization. Finally, the heated ampoules were transferred into the oven for crystal growth by the Bridgman-Stockbarger technique.

The melting temperature of the compounds was determined by differential scanning calorimetry (DSC). The sample to be analyzed (with a mass of 1 g) was loaded into a quartz ampoule and sealed off under vacuum. The heating and cooling speed was 30°C/min. The determined melting temperature of BGGS is 983°C and that of BGGSe is 877°C. The corresponding values reported in [3] are 941°C and 880°C.

The BGGS(e) crystals were grown by the vertical Bridgman-Stockbarger method in an oven with a thermal gradient of 10°C/cm in the crystallization zone by heating the melt to 30-40°C above the melting point. The growth speed was 6 mm/day. BGGS and BGGSe both exhibit congruent melting character. No annealing was necessary for these compounds. Figure 1 shows photographs of fragments of as-grown boules of BGGS and BGGSe.

For preliminary orientation of the crystalline samples we applied conoscopy. Figure 2 shows conoscopic pictures recorded with plates made of the uniaxial BGGSe, placed between two crossed polarizers, for monochromatic light propagation perpendicular (left) and along (right) the ** c**-crystallographic axis which coincides with the optical axis.

The space group of BGGS and BGGSe is *R*3 [3,4] belonging to crystal class (point group) 3. For this enantiomorphic polar crystal class, the scalar gyration parameter is non-zero for light propagation along the optical axis where the birefringence vanishes. That is why two circularly polarized waves propagate along the ** c**-axis, the polarization becomes elliptic for slight deviation from this direction, and finally, for angle values of few degrees birefringence becomes the dominant effect. For this reason, in Fig. 2 (right), isogyres in the form of a dark cross are not observed for light propagation along the optical axis of BGGSe while colored concentric rings (isochromes) are seen in the peripheral regions, which is characteristic of non-gyrotropic crystals. Similar conoscopic pictures were obtained also for BGGS.

X-ray data were collected on a DIFRAY 401 M diffractometer (Scientific Instruments, St. Petersburg, Russia). The identification of the BGGS and BGGSe compounds was based on comparison of the recorded diffractograms (in particular the interplanar spacings and relative intensities) using powder samples with those from the literature [3]. The derived lattice parameters for BGGS are *a* = 9.602 Å, *c* = 8.690 Å, and *ρ* = 3.890 g/cm^{3}, аnd for BGGSe they are *a* = 10.008 Å, *c* = 9.090 Å, and *ρ* = 5.200 g/cm^{3}. The corresponding X-ray diffractograms are shown in Fig. 3.

The final orientation of the crystalline samples was performed by the X-ray diffractometer in terms of azimuthal angle *φ* and polar angle *θ* defined in the orthogonal frame of the optical indicatrix ** xyz**. According to the standards for the point group 3, the

**-axis is chosen to be parallel to one of the crystallographic**

*x***-axes, the**

*a***-axis is parallel to the polar crystallographic**

*z***-axis, and the**

*c***-axis is chosen to form a right-handed orthogonal frame.**

*y*## 3. Transmission and refractive index of BGGS and BGGSe

Transmission spectra in the visible – near-IR and also in the mid-IR were recorded using high quality thick samples with unpolarized light, see Fig. 4. The 0-level transmission of the visible cut-off edge is at 0.41 µm for BGGS and at 0.58 µm for BGGSe. The room temperature band-gap values were determined with thin ** a**-cut samples in polarized light: we obtained 3.37 eV or 0.368 µm (o-wave) and 3.29 eV or 0.377 µm (e-wave) for BGGS, and 2.38 eV or 0.522 µm (o-wave) and 2.31 eV or 0.537 µm (e-wave) for BGGSe. These values are in accordance with the band-gaps determined in [3] from diffuse reflectance spectra, 3.23 eV for BGGS and 2.22 eV for BGGSe but contradict the 2.81 eV estimate for BGGSe by the same method in [4]. It can be concluded that both BGGS and BGGSe can be pumped at 1.064 µm (Nd:YAG laser systems) without two-photon absorption (for o-polarized wave).

The good transparency of BGGS extends in the mid-IR up to ~7.8 µm from which point it gradually decays down to the 0-level at ~11.8 µm. The good transparency of BGGSe extends up to almost 12 µm, covering the important 10.6 µm fundamental wavelength of the CO_{2} laser. Beyond this wavelength the transmission spectrum shows a typical feature for multi-phonon absorption and decays to the 0-level at ~18 µm.

The refractive indices were measured by the minimum deviation technique. Two triangular prisms were fabricated for this purpose, which are shown in Fig. 5. The BGGS prism had an apex angle of 14°25′22″ and entrance surface dimensions of 10.17 (side) × 8.5 (height, along ** c**) mm

^{2}. The BGGSe prism had an apex angle of 14°31′41″ and dimensions of 10.78 (side) × 12.32 (height, along

**) mm**

*c*^{2}.

The dispersion of the two principal refractive indices of BGGS was measured between 0.435 and 10 µm and that of BGGSe between 0.66 and 10 µm, see Fig. 5. BGGS and BGGSe are positive uniaxial crystals (n_{e} > n_{o}): the birefringence of BGGS is in the ~0.05-0.07 range and that of BGGSe is larger, ~0.08-0.11. These values agree fairly well with the theoretical predictions in [3], e.g. 0.068 for BGGS and 0.15 for BGGSe at 1 µm, however, the calculated refractive indices in [3] are overestimated: e.g. at 1 µm they are 2.534-2.602 (BGGS) and 2.89-3.04 (BGGSe). Since the second order nonlinearity to a great extent depends on the linear susceptibility this throws some doubt on the accuracy of the nonlinear coefficients calculated in [3].

The measured refractive indices were fitted by Sellmeier equations with one pole and an IR quadratic correction term in the form n^{2} = A + B / (*λ*^{2} – C) – D*λ*^{2}. The fit parameters are summarized in Table 1 while the calculated refractive indices can be seen in Fig. 5.

## 4. Effective nonlinearity and SHG

There are four independent non-zero tensor components for point group 3 under Kleinman symmetry: *d*_{11}, *d*_{22}, *d*_{33}, and *d*_{31} = *d*_{15}. The effective nonlinearity is given by:

The calculations predict phase-matched SHG in BGGSe at 10.6 µm both for type-I and type-II interaction with very similar *d*_{eff} if *d*_{11} is utilized (*φ* = 30° or 90° and *φ* = 0° or 60°, respectively) and the effect of *d*_{31} is neglected. However, for BGGS, because of the lower birefringence, even type-I SHG is at the limit while type-II is impossible.

The same samples depicted in Fig. 4 were used for SHG tests at 10.6 µm with a CO_{2} laser. The 9.4-mm thick BGGS was cut at *θ* = 76°, *φ* = 30°. The 4.84-mm thick BGGSe was cut at *θ* = 36°, *φ* = 30°. Note that the choice of the azimuthal angle *φ* according to Eqs. (1)-(2) allows one to study both type-I (utilizing *d*_{11}) and type-II (utilizing *d*_{22} and *d*_{31}) interaction if phase-matching can be achieved by adjusting the polar angle *θ*. A 12.45-mm thick type-I AGSe crystal was used as a reference sample, cut at *θ* = 52°, *φ* = 45° (*d*_{eff} = *d*_{36}sin*θ, d*_{36} = 29.5 pm/V [6]). All samples were uncoated.

The TEA CO_{2} laser emitted 100-ns long pulses at 10.6 µm at a repetition rate of 1 Hz. The maximum available energy was 100 mJ. The fundamental radiation was focused with a 1.2-m BaF_{2} lens and the nonlinear crystals were placed in the focal position where the Gaussian beam radius was ~2 mm. Under these conditions SHG was obtained with BGGSe but not with BGGS. The type-I phase-matching angle calculated with Eqs. (1)-(2) is 31.7° while the experimental result was 32°. Also for type-II phase-matching, the experimental angle was larger, by 2.4°, compared to the calculation with the Sellmeier equations. For the chosen nonlinear process, *d*_{eff} of BGGS is very low due to the lower birefringence. To observe SHG we tuned the CO_{2} laser to 9.27 µm and repolished the BGGS sample to a polar angle of *θ* = 66° while the thickness was reduced to 6.1 mm. SHG could be indeed observed under these conditions and the phase-matching angle was in excellent agreement with calculations. All experimental points are shown by symbols in Fig. 6.

It was possible to estimate the effective nonlinearity and from it *d*_{11} of BGGSe from comparison of the conversion efficiency in type-I interaction with AGSe in the small signal limit (<5% SHG efficiency). Since the spectral extent (*Δν* < 0.14 cm^{−1}) and angular convergence of fundamental beam (1.8 mrad full angle at FWHM intensity) were much narrower than the spectral (25 cm^{−1} for BGGSe and 9 cm^{−1} for AGSe) and angular (external full angle exceeds 30 mrad for both crystals) acceptance, respectively, and the birefringence (spatial walk-off) could be neglected, the plane wave approximation is justified. Alternatively, the aperture length (*L*_{a} ≈2.7 *L*_{c} where *L*_{c} is the crystal length) and the effective length of focus (*L*_{f} > 1 m) as defined by Boyd and Kleinman [7] are longer that the actual sample lengths. Assuming a loss coefficient of 1%/cm for both AGSe and BGGSe and taking into account the Fresnel reflections both at the entrance and exit surfaces, the result is *d*_{11} (BGGSe) ~66 ± 15 pm/V. The external SHG efficiency in type-II BGGSe was more than an order of magnitude lower compared to type-I. This leads to the conclusion that both *d*_{22} and *d*_{31} are much lower in magnitude or have the same sign in Eq. (2). For type-II SHG at 10.6 µm, *d*_{eff} = 14.4 pm/V, which is much lower than *d*_{eff} = 47.5 pm/V for type-I. However, without knowledge of the exact octant in which the propagation takes place, and the magnitude and relative sign of the *d*_{22} and *d*_{31} components of the 2nd order nonlinear susceptibility tensor one cannot rule out the possibility of achieving higher *d*_{eff} in both types of interaction.

## 5. Conclusion

In conclusion, high optical quality large size samples of the new non-centrosymmetric chalcogenide crystals BGGS and BGGSe have been grown for the first time which enabled the assessment of their major properties relevant to nonlinear optical applications. BGGS and BGGSe show a number practical advantages compared to the commercial AGS and AGSe crystals applicable in the same spectral ranges, on the first place being chemically stable and free of defects that require post growth treatment. While chemically they are related to the previously studied BGS and BGSe crystals which show also similar transparency ranges, BGGS and BGGSe possess higher symmetry and are optically uniaxial.

As a next step in their characterization we plan to evaluate all the independent nonlinear coefficients in magnitude and sign which will show whether higher effective nonlinearity is not possible by contribution of more than one tensor element through adequate selection of the azimuthal angle and the octant in which the propagation takes place.

No optical damage was observed in the SHG experiments performed. Using the same pump source (single 100-ns pulses at 10.6 µm) we carried out separate damage tests on thin plates of BGGS (2.8 mm) and BGGSe (2.2 mm) with random orientation. The Gaussian beam waist radius in the position of the samples was 0.38 mm. The obtained damage thresholds in terms of peak on-axis values are 14 J/cm^{2} (140 MW/cm^{2}) for BGGS and 11 J/cm^{2} (110 MW/cm^{2}) for BGGSe. Front surface damage was observed in all cases.

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