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Abstract
Temperature tuning of CdSe optical parametric oscillators (OPO’s) is studied by pumping with the 1.8645-µm signal and 2.4793-µm idler outputs of a Nd:YAG laser-pumped CsTiOAsO4 (CTA) OPO. The measured temperature-dependent phase-matching conditions are used to construct new Sellmeier and thermo-optic dispersion formulas for CdSe, which are verified via temperature-tuned sum-frequency generation (SFG) between the fundamental and second harmonic of a transversely excited atmospheric (TEA) CO2 laser operating at 10.2466, 9.5525, and 9.2714 µm.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
CdSe is one of the oldest non-centrosymmetric crystals applied in nonlinear optics. Since the first demonstration of parametric frequency mixing (sum-frequency generation, SFG) by Herbst and Byer in 1971 [1], a lot of research has been carried out on frequency down-conversion of near-IR laser sources to the mid-IR part of the spectrum [2]. This includes optical parametric oscillators (OPO’s), optical parametric generators (OPG’s), and difference-frequency generation (DFG) [3–19].
CdSe is a II-VI semiconducting compound which under normal pressure and temperature conditions crystallizes in a hexagonal closed packed wurtzite structure belonging to the 6 mm point group. Among the non-oxide nonlinear crystals for the mid-IR, it occupies a special position due to its unique properties. On one hand, the thermal conductivity and damage threshold are relatively low, and the nonlinear coefficient is modest with regard to its band-gap. On the other hand, it has a mature growth technology (both from the melt or vapor phase) leading to extremely low density of defects and residual absorption (down to 0.1%/cm at 10.6 µm) and large size of the available (also commercially) optical elements. In addition, among the non-oxide nonlinear crystals, CdSe is the preferable choice when it comes to the longest wavelengths [2]: it is considered to be transparent up to ∼25 µm but DFG up to 28 µm has been experimentally detected even in the presence of phonon absorption [12].
The birefringence of the uniaxial CdSe is relatively low and thus it is not phase-matchable for degenerate interaction such as second-harmonic generation. However, this results also in low spatial walk-off. Only type-2 phase-matching exhibits non-vanishing effective nonlinearity in the optically positive CdSe but non-critical interaction at θ = 90° is possible. Since its sulfur isomorph CdS has even lower birefringence, CdSe remains the single representative of this family in nonlinear optics. However, it shall be mentioned that it finds also other optical applications: for IR wave plates [20] and as a host crystal for Cr2+ [21,22] and Fe2+ [22] tunable solid-state lasers emitting in the mid-IR. Thus, it is important to have an accurate characterization of the linear optical properties of CdSe.
Concerning the thermo-optic coefficients of CdSe, they can be refined by studying the temperature dependence of the phase-matching conditions in parametric frequency conversion. However, we are aware of only one report on the temperature dependent phase-matching in a CdSe OPO [5]. Recent studies of CdSe OPO’s pumped by high-average power Ho:YLF and Ho:YAG lasers revealed that severe thermal lensing effects occur in CdSe crystals [17–19], as previously reported for a Ho:YLF laser-pumped AgGaSe2 OPO [23]. Such a thermally induced local index variation can also result in noticeable phase mismatch, which will strongly affect the conversion efficiency of the frequency-conversion processes. To investigate these deleterious effects, we have studied temperature-tuned CdSe OPO’s by pumping with the 1.8645-µm signal and 2.4793-µm idler outputs of a Nd:YAG laser-pumped CsTiOAsO4 (CTA) OPO and constructed Sellmeier and thermo-optic dispersion formulas of CdSe from the measured temperature-dependent phase-matching conditions. These formulas have been verified by mixing the fundamental and second harmonic of a transversely excited atmospheric (TEA) CO2 laser while tuning the crystal temperature at different operating wavelengths.
2. Experiments and discussion
We first measured the phase-matching angles for a CdSe OPO by pumping with the 1.8645-µm signal output of a Nd:YAG laser-pumped CTA OPO [25] at 20°C. The 4.5-cm-long OPO cavity consisted of two flat mirrors. The fused silica pump mirror highly transmitted the signal output and had 93∼96% reflectivity at 2.2–4.4 µm. The ZnSe output mirror had 87% reflectivity at 1.8645 µm and 88∼95% reflectivity at 2.2–4.6 µm. For pumping with the 2.4793-µm idler output, the pump mirror was replaced by an IR grade fused silica mirror having 92% transmission at 2.4793 µm and a reflectivity of 93∼98% at 3.2–4.3 µm. Thus in both cases double-pass pumping was applied to reduce the OPO threshold. The 2.5-cm-long, θ = 90° and φ = 0° cut CdSe crystal (supplied earlier by Cleveland Crystals Inc., now Gooch & Housego) placed in the OPO cavity was with anti-reflection coating centered at 3 µm.
Since we are only interested in the phase-matching conditions, no attempt was made to optimize the conversion efficiencies. The generated signal and idler wavelengths were indirectly determined from the SFG wavelengths obtained by mixing the signal output with the residual Nd:YAG laser beam in LiNbO3. The pump energies at 1.8645 and 2.4793 µm were ∼5 mJ/pulse at 30 Hz, where the self-heating effect of CdSe is expected to be negligible.
The resulting tuning points for 1.8645-µm excitation are shown by open circles in Fig. 1 together with the theoretical curves calculated with the Sellmeier equations of Bhar [24] (dashed line) and Chenault and Chipman [20] (dotted line), lying 6.3 nm above and 6.7 nm below our measured signal wavelength at θ = 90°, respectively. Similar results were also obtained when pumping at 2.4793 µm.
Fig. 1. Phase-matching curve for a type-2 CdSe OPO pumped by the 1.8645-µm signal output of a Nd:YAG laser-pumped CTA OPO at 20°C. The solid line is calculated with Eq. (1). The dashed and dotted lines are calculated with the Sellmeier equations of Bhar [24] and those of Chenault and Chipman [20], respectively. Open circles are our experimental points.
Meanwhile, we found that the theoretical results calculated by the Sellmeier equations of Bhar [24] give a reasonable agreement with the earlier published data for an OPO pumped by a HF laser (λp = 2.83, 2.87, 2.91 µm) [6], an OPG pumped by a Cr, Er:YSGG laser (λp = 2.797 µm) [10], an OPO pumped by the idler output of a Nd:YAG laser-pumped KTiOAsO4 OPO [11,14], DFG between the fundamental (λp = 1.0642 µm) and the idler output of a frequency-tripled Nd:YAG laser-pumped β-BaB2O4 OPO [12], and DFG between the signal and idler outputs of Nd:YAG laser-pumped Ag3AsS3 (proustite) [7] and LiNbO3 [15] OPO’s. The corresponding idler outputs cover the 8.1–8.3 µm [6], 8.0–13.0 µm [10], 8.0–10.6 µm [11,14], 15–28 µm [12], 9.4–24 µm [7], and 5.8–22 µm [15] spectral ranges in the mid-IR. Thus, we have slightly adjusted only the first and second terms of Bhar’s Sellmeier equations to ensure the best fit to our experimental points of the 90° phase-matching wavelengths (open circles) plotted in Fig. 2 and to also reproduce the data points reported by Herbst and Byer [3] (solid circles) and Watson et al. [13] (solid diamonds).
The refined Sellmeier equations at 20°C are expressed as:
Fig. 2. 90° phase-matching curves for type-2 down-conversion in CdSe at 20°C. The solid, dashed, and dotted lines follow the same notation as in Fig. 1. Solid circle, triangles, squares, and diamonds are OPO data points taken from [3, 4,5, 11,14], and [13], respectively, while crosses are data points for DFG taken from [16]. Open circles are our OPO data points.
Note that Eq. (1) gives somewhat large deviations from the 90° phase-matching points (solid triangles) reported by Davydov et al. [4,5] for a CdSe OPO pumped by a Dy2+:CaF2 laser (λp = 2.36 µm) and those (crosses) reported by Kemlin et al. [16] for DFG with pump wavelengths at 2.72 and 2.79 µm (Fig. 2), but it correctly reproduces the recently published data points (solid and open squares) measured by Chen et al. [18,19] for an injection-seeded CdSe OPO pumped by a Ho:YAG laser (λp = 2.0906 µm) in the 10–12 µm range, as shown in Fig. 3.
Fig. 3. Phase-matching curves for a type-2 CdSe OPO pumped by a Ho:YAG laser at 20°C. The solid, dashed, and dotted lines follow the same notation as in Fig. 1. Solid and open squares are data points taken from [18] and [19], respectively.
We subsequently measured the temperature-dependent 90° phase-matching conditions by mounting the CdSe crystal in a temperature-controlled copper oven having an accuracy of ±0.1°C and heating the crystal from 20°C to 240°C at 20~40°C intervals [25]. The resulting tuning points (open circles) obtained by pumping with the 1.8645-µm signal pulses are shown in Fig. 4 together with the tuning curve (dashed line) calculated with Eq. (1) and the thermo-optic coefficients dn/dT deduced from the Sellmeier equations of Bhar and Ghosh at 100°C and 300°C [26]. As can be seen from the figure, the temperature variation of the signal wavelength of dλs/dT = –0.065 nm/°C given by the calculation is almost two times larger than our experimental value of dλs/dT = –0.035 nm/°C due to the inaccuracy of the deduced thermo-optic coefficients in this wavelength range.
Fig. 4. Temperature-dependent phase-matching curves for a type-2 CdSe OPO pumped by the 1.8645-µm signal and 2.4793-µm idler outputs of a Nd:YAG laser-pumped CTA OPO. The solid lines are calculated with Eqs. (1) and (2). The dashed lines are calculated with Eq. (1) and the thermo-optic coefficients deduced from the Sellmeier equations of Bhar and Ghosh at 100°C and 300°C [26]. Open circles are our experimental points.
Also plotted in Fig. 4 are our data points (open circles) obtained by pumping with the 2.4793-µm idler pulses together with the tuning curve (dashed line) calculated with Eq. (1) and the deduced thermo-optic coefficients [26]. It is seen that the theoretical tuning curve again differs from our experimental points. The temperature variation of the signal wavelength of dλs/dT = –0.082 nm/°C is almost two times smaller than our measured value of dλs/dT = –0.166 nm/°C in contrast to the 1.8645-µm excitation.
To figure out the reasons for the obvious difference between theory and experiment, we fabricated a CdSe prism with an apex angle of 21°23’ from a boule supplied earlier by Cleveland Crystals Inc. and measured the thermo-optic coefficients dno/dT and dne/dT for the ordinary and extraordinary waves at 0.7993, 1.0642, 1.1523, 2.0520, and 3.3913 µm by changing the prism temperature from 20°C to 200°C at 20∼40°C intervals. From these raw data,a tentative thermo-optic dispersion formula has been constructed and iteratively adjusted to give the best fit to our experimental points given in Fig. 4.
The derived thermo-optic dispersion formula valid in the temperature range of 20-240°C is expressed as:
To test the validity of Eq. (2), we measured the temperature variation of the phase-matching angles for SFG between the fundamental and second harmonic of a TEA CO2 laser operating at 10.2466, 9.5525, and 9.2714 µm by heating the crystal from 20°C to 140°C at 20∼40°C intervals. The resulting tuning points (open circles) are shown in Fig. 5 together with the tuning curves (solid lines) calculated with Eqs. (1) and (2). It is found that in contrast to the theoretical results (dashed lines) given by the deduced thermo-optic coefficients [26], the measured temperature dependence of the phase-matching angle dθ/dT is positive, and as a result, this nonlinear process is 90° phase-matchable at ∼120°C when operating the CO2 laser at 10.2466 µm. This experimental observation is well reproduced by using Eqs. (1) and (2), confirming the validity of these dispersion equations in this wavelength range.
Fig. 5. Temperature-tuned phase-matching curves for type-2 SFG between the fundamental and second harmonic of a TEA CO2 laser at 10.2466, 9.5525, and 9.2714 µm in CdSe. The solid and dashed lines follow the same notation as in Fig. 4. Open circles are our experimental points.
Finally, we note that as already shown in Fig. 2, Eq. (1) gives the 90° phase-matched OPO wavelengths of λs = 3.3380 µm and λi = 8.0550 µm at 20°C for the pump wavelength at 2.36 µm, which differ from λs = 3.37 µm and λi = 7.86 µm [4], and λs = 3.36 µm and λi = 7.88 µm [5] reported by Davydov et al. Nonetheless, our calculated value of dλi/dT = +0.923 nm/°C (= –0.143 cm–1/°C) reasonably explain the 29-cm–1 shift of the idler frequency observed by changing the crystal temperature from –123°C to 147°C (∼ 0.107 cm–1/°C) [5].
3. Conclusion
We have reported the Sellmeier and thermo-optic dispersion formulas for CdSe that provide a good reproduction of the temperature-dependent phase-matching conditions for CdSe OPO’s pumped at 1.8645 and 2.4793 µm and those for SFG between the fundamental and second harmonic of a TEA CO2 laser operating at 10.2466, 9.5525, and 9.2714 µm. We believe that these two formulas are highly useful to investigate thermal lensing and dephasing effects in parametric interactions such as those reported in [17–19] and in general, the thermal dependence of the refractive indices of CdSe in other applications including wave plates [20] and tunable solid-state lasers based on Cr2+ and Fe2+ doping [21,22].
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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