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Abstract
This paper reports on the refined Sellmeier and thermo-optic dispersion formulas for BaGa4Se7 that provide a good reproduction of the temperature-dependent phase-matching conditions for type-2 difference-frequency generation between the signal and idler outputs of a Nd:YAG laser-pumped KTiOPO4 optical parametric oscillator in the 8.457–9.092 µm and 12.075–14.201 µm spectral ranges at 20–150°C and recent experiments within these wavelength and temperature ranges performed by other authors.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The monoclinic nonlinear optical crystal BaGa4Se7 (BGSe) was discovered more than 10 years ago [1] and cannot be considered any more to be a new material for frequency conversion in the mid-IR part of the spectrum since most of the possible three-wave interaction schemes have been already demonstrated on different time scales [2]. There is no doubt that BGSe, having a similar transmission window up to 18 µm, is a viable alternative to the commercially available chalcopyrite AgGaSe2 (AGSe) [3]. The advantages of BGSe comprise the growth without subsequent annealing, the chemical surface stability, and some thermo-mechanical properties, including damage resistivity, related to its larger bandgap of 2.73 eV [2,4]. This larger bandgap permits, in contrast to AGSe, pumping near 1 µm without the onset of two-photon absorption, which has made BGSe the most successful crystal for Nd:YAG laser-pumped mid-IR optical parametric oscillators (OPOs) [2,5].
One of the difficulties associated with BGSe, related both to the accurate characterization of its properties and practical use is due to the low symmetry (point group m). Thus, the phase-matching properties and the tensor of the 2nd order nonlinearity still show substantial discrepancies in the published literature. In general, it can be stated that the effective nonlinearity should be comparable to that of AGSe. The Sellmeier and thermo-optic dispersion equations have been refined a few times based on phase-matched nonlinear processes [2]. However, the reliability of such relations depends on the type of the process and the wavelength ranges involved. Type-2 interaction has in fact been rarely used in BGSe [2]. In general it can ensure narrower OPO output (signal and idler) bandwidths. A 1.064-µm pumped type-2 BGSe 10-Hz OPO showed a tunability of 3.6-9.6 µm with a maximum energy of 4.7 mJ at 5.3 µm [5]. A 2.091-µm pumped type-2 BGSe 1-kHz OPO was tunable at 4.39–4.62 µm [6] and 7.91–9 µm [7] with an energy of 314 µJ at 8.926 µm. In all cases the interaction was oe-o type in the yz principal plane (φ = 90°) of BGSe [2] which provides information on the nx refractive index at long wavelengths.
Very recently, it has been reported by Yang et al. [8] that our Sellmeier and thermo-optic dispersion formulas for BGSe presented in [9,10] do not fit their experimental points of the temperature-tuned type-2 90° phase-matching conditions along the z-axis for a Ho:YLF laser (2.0513 µm)-pumped OPO in the 9.39–10.63 µm range. Note that these are the longest wavelengths demonstrated for type-2 interaction in BGSe and 90° phase-matching ensures superior accuracy in such measurements. In order to derive more accurate Sellmeier and thermo-optic dispersion formulas, we have measured the phase-matching angles of such a crystal cut for type-2 difference-frequency generation (DFG) between the signal and idler outputs of a Nd:YAG laser-pumped KTiOPO4 (KTP) OPO in the 8.437–9.909 µm and 12.075–13.703 µm ranges at 20°C and their temperature dependence at 8.853 and 14.201 µm by heating the crystal from 20°C to 150°C, and refined our previous dispersion formulas to give the best fit to those new experimental results. Here we report the updated Sellmeier and thermo-optic dispersion formulas that provide a good reproduction of the above-mentioned experimental results of Yang et al. [8] as well as those of type-1 phase-matching wavelengths of Nd:YAG laser-pumped OPOs in the 3.60–3.99 µm range reported by Zhang et al. [11] and Kong et al. [12].
2. Experiments and discussion
The BGSe crystal used in the present experiment was cut normal to the x (= b), y, and z (≈ c) axes, and its xy faces were optically polished with a flatness of λ/10. The dimensions of this crystal are 6, 6, and 7 mm along x, y, and z axes, respectively. The orientation of the c-axis was checked with X-ray diffraction with an accuracy of ±0.05°. This crystal was mounted on a Nikon stepmotor-driven rotation stage having an accuracy of ±0.02° as described in [9,10].
Fig. 1. Schematic of the experimental setup for type-2 DFG (1/λp – 1/λs = 1/λi) in BGSe using the signal and idler outputs of a Nd:YAG laser-pumped KTP OPO as input sources.
Figure 1 illustrates the phase-matching measurements. We used the signal and idler outputs of a Nd:YAG laser-pumped nanosecond KTP OPO operating at 10 Hz as input sources to obtain the DFG output in BGSe under the type-2 phase-matching conditions (oe-o). The phase-matching angles in the yz (φ = 90°) plane were first measured by rotating the crystal in the clockwise and counterclockwise directions about the x-axis at 20°C. For reliable determination of a zero-incidence angle, a He-Ne laser beam reflected from the entrance face of the crystal was aligned on a 0.2 mm slit located 2 m from the crystal. The generated DFG output radiation was monitored by a spectrometer with a HgCdTe detector after blocking the transmitted pump and signal beams by using two ZnSe mirrors having R ≅ 100% around 2 µm. The DFG wavelengths were calculated with energy conservation (1/λp – 1/λs = 1/λi) from the measured pump and signal wavelengths (λp and λs).
The resulting data points (open circles) for type-2 DFG in the 8.437–9.909 µm and 12.075–13.703 µm ranges are shown in Fig. 2 together with the tuning curve (solid line) calculated with the following best-fitted Sellmeier equations:
Fig. 2. Phase-matching curves for type-2 DFG between the signal and idler outputs of a Nd:YAG laser (1.0642 µm)-pumped KTP OPO in the xz (φ = 0°) and yz (φ = 90°) planes of BGSe at 20°C. The solid line is calculated with Eq. (1) presented in the text. Open circles are our experimental points. The dashed line is calculated with the Sellmeier equations of Yang et al. [8].
We next have measured the temperature-dependent phase-matching conditions for the above-mentioned DFG processes to derive the accurate thermo-optic dispersion formula up to ∼14 µm. However, because the temperature variation of the 90° phase-matching conditions strongly depends on the accuracy of both refractive indices and thermo-optic constants, and it is hard to determine the exact 90° phase-matching wavelength and temperature, we decided to measure the temperature variation of the phase-matching angles in the yz plane (φ = 90°) by placing the present BGSe crystal in a temperature-controlled copper oven (accuracy of ±0.1°C) set on the Nikon stepmotor driven rotation stage.
The experimental points (open circles) obtained by using pump wavelengths of λp = 1.9000 µm (λi = 8.853 µm) and λp = 1.9800 µm (λi = 14.201 µm) are shown in Fig. 3 together with the tuning curves (solid lines) calculated with Eq. (1) and the following best-fitted thermo-optic dispersion formula:
Fig. 3. Temperature-dependent phase-matching curves for type-2 DFG between the signal and idler outputs of a Nd:YAG laser-pumped KTP OPO in the yz (φ = 90°) plane of BGSe. The solid lines are calculated with Eqs. (1) and (2) presented in the text. Open circles are our experimental points.
In order to check the utility of Eqs. (1) and (2), we have calculated the type-2 phase-matching angles in the yz (φ = 90°) plane for a Ho:YLF laser (2.0513 µm)-pumped OPO. The resulting tuning curve (solid line) at 20°C is shown in Fig. 4 together with the data points (solid circles) given by Yang et al. [8] at 9.9251–10.0126 µm and the tuning curve (dashed line) calculated with their Sellmeier equations. As can be seen from this figure, our tuning curve reproduces more closely their data points than their tuning curve.
Fig. 4. Phase-matching curves for a Ho:YLF laser (2.0513 µm)-pumped type-2 BGSe OPO in the xz (φ = 0°) and yz (φ = 90°) planes at 20°C. The solid line is calculated with Eqs. (1) and (2) presented in the text. The dashed line is calculated with the Sellmeier equations of Yang et al. [8]. Solid circles are their experimental points (Table 2 of Ref. [8]).
We next have calculated the type-2 phase-matching condition in the yz (φ = 90°) plane of BGSe for the Ho:YAG laser (2.0907 µm)-pumped OPO presented by Zhao et al. [7]. The calculated angles are θpm = 4.83°, 5.60°, 6.37°, and 6.94° at λi = 8.9257, 8.6720, 8.4222, and 8.2440 µm, respectively, which agree well with their experimental values of θpm = 4.71°, 5.48°, 6.16°and 6.65° presented in Table 1 of [7]. Similar results (θpm = 4.70°, 5.46°, 6.24°, and 6.81°) were also obtained by using the Sellmeier equations of Yang et al. [8]. Note that our type-1 tuning curves in the xz plane (φ = 0°) for the pump wavelength of λp = 1.0642 µm predict angles that are –0.1∼0.4°, 0.6∼0.8°, and 0.8∼1.1° smaller than the published OPO data points of Kostyukova et al. [5] and Xu et al. [13], and the DFG data points of Liu et al. [14] measured with differently oriented crystals of θcut = 46°, 42.5°, and 44° in the 8-15 µm range, respectively. Since the Sellmeier equations of Yang et al. [8] give even smaller (by 1.4∼1.6°) phase-matching angles than our tuning curves, we did not use their dispersion relations for the further analysis.
Regarding the utility of Eq. (2), we have checked the temperature variation of the type-2 90° phase-matching conditions for a Ho:YLF laser (2.0513 µm)-pumped OPO [8]. Our tuning curve (solid line) given by Eqs. (1) and (2) is shown in Fig. 5 together with the experimental points (solid circles) of Yang et al. [8]. It can be seen from this figure that our tuning curve reproduces well their data points in the 9.66–10.22 µm range, whereas a somewhat large discrepancy of ΔΤ = 8∼9°C was encountered at 9.40 and 10.63 µm.
Fig. 5. Temperature-dependent 90° phase-matching wavelengths for a Ho:YLF laser-pumped type-2 BGSe OPO along the z-axis. The solid line is calculated with Eqs. (1) and (2) presented in the text. Solid circles are the experimental points of Yang et al. [8].
We successively calculated the temperature variation of the type-1 phase-matching wavelengths in the xz plane (φ = 0°) for Nd:YAG laser-pumped OPOs measured by Zhang et al. [11] and Kong et al. [12]. Our tuning curve (solid line) calculated for θpm = 56.56°, which was determined to obtain λs = 1.5140 µm at 20°C, is shown in Fig. 6 together with the data points (solid circles) of Zhang et al. [11] measured with a θ = 55.9° cut crystal and their tuning curve (dotted line) calculated with the Sellmeier equations of Yang et al. [15] coupled with our previous thermo-optic dispersion formula [10], which differs slightly from our own tuning curve. Their experimental results give dλs/dT = –0.48 nm/°C while our calculated value is dλs/dT = –0.52 nm/°C.
Fig. 6. Temperature-dependent phase-matching curves for a Nd:YAG laser-pumped type-1 BGSe OPO in the xz plane (φ = 0°). The solid line is calculated with Eqs. (1) and (2) presented in the text (θpm = 56.56°). The dotted line is calculated with the Sellmeier equations of Yang et al. [15] coupled with our previous thermo-optic dispersion formula [10] (θpm = 55.96°). Solid circles are the experimental points of Zhang et al. [11] (θpm = 55.9°).
Note that the small discrepancy of dλs/dT in Fig. 6 can be partly attributed to the error of the cutting angle of their crystal [11]. In fact, our tuning curve (solid line) calculated for θ = 56.48° overlaps well with the experimental points (solid circles) of Kong et al. [12] measured with a θ = 56.3° cut crystal (Fig. 7).
Fig. 7. Temperature-dependent phase-matching curve for a Nd:YAG laser-pumped type-1 BGSe OPO in the xz plane (φ = 0°). The solid line is calculated with Eqs. (1) and (2) presented in the text (θpm = 56.48°). Solid circles are the experimental points of Kong et al. [12] (θpm = 56.3°).
3. Conclusion
We have reported the refined Sellmeier and thermo-optic dispersion formulas for BGSe that provide a good reproduction of our new experimental results for type-2 DFG presented in this paper as well as the latest experimental results for type-1 and type-2 OPOs published in the literature. We believe that these formulas are highly useful to investigate the self-induced thermal effects for high average power nanosecond OPOs such as those described in [16]. Temperature tuning for type-2 90° phase-matching in BGSe on the other hand is very attractive for continuous-wave or synchronously pumped OPOs which require tight focusing and have not been realized, yet. Note that the output idler wavelengths in this case still lie within the clear transparency plateau of BGSe below 12 µm [2].
Funding
Deutsche Forschungsgemeinschaft (PE 607/14–1).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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