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Abstract
For the first time, the temperature stability of second-harmonic-generation (SHG) is reported for the entire space of a YCa4O(BO3)3 (YCOB) crystal for a temperature range of -10 – 520 °C. Both theoretical calculations and experimental data indicate an optimum phase-matching (PM) direction of (θ = 149.2°, ϕ = 0°), which is located in the XZ principle plane (90° < θ < 180°). A special regression phenomenon of the PM angle was found in this direction, which further increased the SHG output at high temperature (> 200 °C). As a result, for SHG of the Nd:YAG laser, the measured temperature bandwidth of a YCOB crystal cut along the optimum PM direction is larger than 490 °C·cm. As demonstrated in this study, among all nonlinear optical crystals, this cut-type is currently the best choice when temperature-insensitive SHG is required.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, rare-earth calcium oxyborate nonlinear optical (NLO) crystals of the form RECa4O(BO3)3 (RECOB, where RE = Tm, Y, Gd, Sm, Nd, or La) have gained increasing prominence owing to their excellent all-round properties and extensive application prospects [1–6]. Two representatives of such crystals, YCOB and GdCOB have similar structures and NLO characteristics, including their symmetry, lattice parameters, the magnitudes of their second-order NLO coefficients (din), and with respect to the spatial distribution disciplines of their effective NLO coefficient (deff) [7]. Unlike other NLO crystals, YCOB and GdCOB have relatively small thermo-optic coefficients, resulting in outstanding temperature stability during frequency conversion processes [8–13]. The thermal rotation effect of the optical principal plane increases the complexity of the temperature bandwidth [2]. In 2019, an overall evaluation of the SHG temperature bandwidth in a GdCOB crystal was performed, yielding a maximum value in excess of 430 °C·cm corresponding to a specific spatial direction (θ = 135°, ϕ = 47.3°) [14]. Whether YCOB crystals exhibit a similar attribute is an interesting question that has yet to be resolved.
This paper presents a systematic investigation of the temperature stability of a YCOB crystal with respect to the SHG of an Nd:YAG laser. Considering the thermal-optic and thermal rotation effects of the principal axes of the refractive index, the temperature bandwidth is no longer symmetrical in the crystal space, and the values in the second octant (90° < θ < 180°) are obviously larger than those in the first octant (0° < θ < 90°). The phase-matching (PM) direction with the largest temperature bandwidth is (θ = 149.2°, ϕ = 0°), which is located in the XZ principle plane for which θ > 90°. This calculated regularity is proved via SHG experiments. In addition, we observed a special regression phenomenon for the PM angle around the (θ = 149.2°, ϕ = 0°) direction when the temperature of the YCOB crystal was higher than 200 °C. Therefore, the practical temperature bandwidth (490 °C·cm) exceeds the theoretical value considerably. Overall, the YCOB crystal exhibits superior temperature stability and practicability relative to GdCOB crystals.
1 Theoretical analyzing
YCOB is a monoclinic crystal belonging to the Cm space group. As a negative biaxial crystal, its crystallography axis b is collinear but opposite to the principal optical axis Y. Its crystallographic axes a and c lie in the optical principal plane XZ, following the relationships ∠aZ = 24.7° and ∠cX = 13.4° [11]. Here, the optical principal axes X, Y, and Z obey the law nX < nY < nZ [1,15]. The direction of light propagation (with wave vector k) is represented by (θ, ϕ), where θ is the deviation angle relative to the Z axis, and ϕ is the azimuth angle in the XY plane [14]. Because the two-fold crystallography axis b is parallel to Y, under above definition, the direction (θ, ϕ) and the direction ($\textrm{180}^{\circ } - \theta,\; 180^{\circ } - $) are equivalent [7].
Based on the second-order NLO coefficients of the YCOB crystal and the Sellmeier equations [12,15], we calculated the PM curve and the corresponding deff for the type-I SHG of the 1064 nm laser, as shown in Fig. 1. Owing to the mmm symmetry of the refractive indices and the 2/m symmetry of deff, the PM distributions of the entire crystal space can be represented by the first (0° < θ < 90°, 0° < ϕ < 90°) and second (90° < θ < 180°, 0° < ϕ < 90°) octants. From Fig. 1, it can be seen that the PM curve (red line) is distributed symmetrically between the two octants, whereas the deff (blue line) is distributed disproportionately. In the XZ plane, the PM angles are (30.8°, 0°) and (149.2°, 0°) corresponding to deff values of 0.57 and 0.98 pm/V, respectively. In the XY plane, the PM angle is (90°, 35.9°) corresponding to a deff value of 0.36 pm/V. Across both octants, the peak deff value is 1.41 pm/V, corresponding to the PM direction (112.7°, 37.4°) in the second octant. In the first octant, the largest deff and the corresponding PM angle are 0.77 pm/V and (64.2°, 37.5°).
Fig. 1. Type-I PM curve (red line) and corresponding deff (blue line) in the first and second octants for the SHG of 1064 nm Nd:YAG laser in a YCOB crystal. The red circle points represent the processing directions of the four kinds of experimental samples, and the blue square points are the corresponding deff values.
The calculation procedure for the temperature bandwidth is similar to that used in Ref. [14], which we briefly introduce here. Under the condition of a small-signal approximation, the practical SHG conversion efficiency η can be written as
where η0 represents the maximum achievable SHG conversion efficiency (i.e., that corresponding to complete PM), l is the crystal length, k = 2πn/λ is the wave vector, and Δk represents the phase mismatch. If Δk = ±π/l, η decreases to 40.5% of η0; the corresponding temperature interval is the acceptance temperature ΔT, with ΔTl denoting the temperature bandwidth. For type-I SHG, the phase mismatch is3. Temperature bandwidth experiments
To examine the trends shown in Fig. 2, we performed temperature bandwidth experiments for different YCOB samples. A YCOB crystal was processed into rectangular samples with a length of 10 mm along four specific directions: (30.8°, 0°), (67.3°, 37.4°), (112.7°, 37.4°), and (149.2°, 0°). Among these directions, (112.7°, 37.4°) is the PM direction with the largest deff across the entire crystal space, which is the direction concerned traditionally. The direction (149.2°, 0°) was used to test the extreme value of the temperature bandwidth presented in Fig. 2, while (67.3°, 37.4°), (30.8°, 0°) are the symmetry directions of (112.7°, 37.4°) and (149.2°, 0°), respectively, in the first octant. The directions of these samples and the corresponding deff values are shown in Fig. 1. The end faces (4 × 4 mm2) of all samples were polished to optical grade but uncoated. The crystal sample was set in a copper billet with two end faces trepanned for light transmission. A temperature controller with a precision of 1 °C was buried in the copper billet to detect the sample temperature. To provide better thermal insulation, two glass sheets with antireflective coatings corresponding to wavelengths of 532 and 1064 nm were fixed at the two ends of the crystal. The experiment was conducted for a temperature range of -10 – 520 °C, and the temperature variation rate was 2 °C/min.
We performed a single-pass SHG experiment using a nanosecond Nd:YAG laser source (Q-smart 850, Quantel Corp., France). The wavelength, pulse width, and repetition rate were 1064 nm, 6 ns, and 10 Hz, respectively. The single-pulse energy was kept at 6 mJ. For these parameters, the maximum SHG conversion efficiency for all samples was no more than 5%, and could be analyzed using the small-signal approximation formulae, i.e., Eq. (1). Figure 3 presents the normalized SHG efficiency as a function of temperature for various YCOB samples. The temperature bandwidth is distributed asymmetrically over the two octants, indicating the existence of the thermal rotation effect. As a consequence, the phase mismatch caused by the thermo-optic effect is partially counteracted in the second octant, with the first octant exhibiting the opposite behavior. Therefore, the temperature bandwidth in the second octant is noticeably larger than that in the first octant. All experimental data were fitted using Eq. (1), with the fitted results shown in Fig. 3 (solid lines).
Fig. 3. Temperature tuning curves for type-I SHG of 1064 nm Nd:YAG laser in different YCOB samples. Discrete points and solid lines represent the experimental data and fitted curves, respectively; the dotted line is a reference to determine ΔTl where the normalized η = 0.405; the dashed line is a reference to determine ΔTFWHM where the normalized η = 0.5.
Of all the YCOB crystals, the (149.2°, 0°) sample exhibits a special performance. For this sample, Eq. (1) fails to describe the experimental data above 160 °C. This can be explained by the following mechanism: the phase mismatching originates primarily from two aspects, that is, the thermo-optic effect and the thermal rotation effect. The former causes variations in the refractive indices, while the latter causes variations in the principal optical axes. When the temperature of the (149.2°, 0°) crystal sample is lower than 180 °C, the thermo-optic effect dominates the thermal rotation effect, and the phase mismatch Δk increases as the temperature is elevated. By contrast, the SHG conversion efficiency decreases. For a crystal temperature of approximately 200 °C, the conversion efficiency reaches its non-zero lowest point. For temperatures ranging from 180–300 °C, the thermal rotation effect basically offsets the thermo-optic effect; therefore, Δk remains at a relatively stable level, and the change in the SHG conversion efficiency is small. At crystal temperatures exceeding 300 °C, the thermal rotation effect overwhelms the thermo-optic effect, Δk gradually reduces to 0, before becoming a negative value. Conversely, the SHG conversion efficiency increases gradually and reaches a peak at approximately 410 °C. To the best of our knowledge, this peculiar phenomenon has never been reported for other NLO crystals. Ultimately, the SHG conversion efficiency of the (149.2°, 0°) YCOB sample always remains above 40.5% from -10 – 480 °C. Therefore, |Δk| ≤π/l in this scope, and the measured temperature bandwidth ΔTl is larger than 490 °C·cm.
The experimental and calculated temperature bandwidths of the four YCOB samples are listed in Table 1 alongside other NLO parameters, including the acceptance angles Δθ and Δϕ, the walk-off angles ρ1 and ρ2, and the acceptance bandwidth of the fundamental wave Δλ. ΔTFWHM, i.e., the acceptance temperature corresponding to the full width at half maximum (η = 50%), is also shown in Fig. 3 and presented in Table 1 for each sample.
Table 1. Nonlinear optical properties for type-I SHG of 1064 nm Nd:YAG laser in different YCOB samples.
For an intuitive comparison, we also include the experimental values of the temperature bandwidth in Fig. 2 (cross-shaped data points). All measured values of ΔTl are larger than the calculated values. From this, we speculate that the thermo-optic coefficients reported in [15], and adopted for the calculations herein, are larger than the actual coefficients. Overall, the experimental data demonstrates good agreement with the theoretically calculated curve accounting for thermal rotation. The maximum temperature bandwidth obtained from the experiment exceeds 490 °C·cm (from -10 – 480 °C), appearing for the (149.2°, 0°) direction in the XZ plane, as predicted by the theoretical curve. This represents a remarkable difference with respect to equivalent analyses for GdCOB crystals, for which the maximum temperature bandwidth has been reported in the specific spatial direction (135°, 47.3°) [14]. These contrasting results can be attributed to the great difference in the thermal rotation effect between YCOB and GdCOB crystals. According to the thermal rotation parameters reported by Umemura et al. [8,9], the thermal rotation angles of both crystals are almost the same at 1064 nm. While at 532 nm, the thermal rotation angle of GdCOB crystals is about two times that of YCOB crystals, with this latter observation responsible for the discrepancy in the temperature bandwidth distribution over the entire crystal space. To verify this, we recalculated the temperature bandwidth of the YCOB crystal substituting the thermal rotation angle (α) of the GdCOB crystal, while preserving the other parameters. This resulted in the orientation with the maximum temperature bandwidth in the YCOB crystal changing from the principal plane to the spatial direction (θ ≈ 133°). This indicates that for RECOB crystals, the main factor influencing the spatial distribution of the temperature bandwidth is the thermal rotation rate of the principal optical plane as opposed to the refractive index, PM angle, or thermo-optic coefficient.
Because the thermal rotation effect of the principal optical plane is very difficult to measure, only a few NLO crystals have been examined up to now, such as YCOB, GdCOB, BIBO, and dLAP. Among these four crystals, YCOB has the smallest thermal rotation rate, which is 0.0137 mrad/°C (532 nm) [9]. For GdCOB, BIBO, and dLAP crystals, the thermal rotation rates are 0.0253 mrad/°C (532 nm) [8], 0.0275 mrad/°C (1064 nm) [16], 0.0340 mrad/°C (1064 nm) [17], respectively.
4. PM angle experiments
To verify the above analysis, we repeated the SHG experiment under the same conditions, and measured the variation in the PM angle θ as a function of the crystal temperature. The furnace controlling the crystal temperature was mounted on a high-precision turntable. The temperature was varied from 25–490 °C. First, the position corresponding to maximum SHG efficiency at 25 °C was established. As the temperature was increased, the SHG efficiency decreased. The sampling interval of the crystal temperature was approximately 50 °C. At each sampling point, we adjusted the position of the turntable to ensure the maximum SHG efficiency was measured, and recorded the external rotating angle Δθext relative to the initial position at 25 °C. Then, Dθext was converted to the inner rotating angle Δθ in the crystal by dividing it by the fundamental refractive index. The deviation of the PM angle θ, i.e., Δθ, is plotted in Fig. 4 as a function of crystal temperature. For the (67.3°, 37.4°) and (112.7°, 37.4°) samples, Δθ increases linearly with the increase in temperature (Figs. 4(a) and 4(b)). Linear fitting to the experimental data was conducted, with the slopes determined to be 5.18 × 10−3 °/°C and 4.43 × 10−3 °/°C for the (67.3°, 37.4°) and (112.7°, 37.4°) samples, respectively.
Fig. 4. Temperature variation of the PM angle for different YCOB samples. (a) (67.3°, 37.4°) sample, (b) (112.7°, 37.4°) sample, (c) (30.8°, 0°) sample, (d) (149.2°, 0°) sample. Discrete points indicate experimental data, solid red lines indicate linear fitting for the entire temperature range, solid blue lines indicate linear fitting for partial temperature ranges.
For the (30.8°, 0°) sample, the variation of Δθ can be divided roughly into three linear stages, which correspond to the gradually increasing slopes, as shown in Fig. 4(c). For the three temperature ranges of 25–130 °C, 130–330 °C, and 330–490 °C, the slopes of Δθ are 1.06 × 10−3 °/°C, 1.63 × 10−3 °/°C, and 2.01 × 10−3 °/°C, respectively. This indicates that with the increase in temperature, the speed at which the phase mismatch is induced by the thermo-optic and thermal rotation effects becomes increasingly faster.
As depicted in Fig. 4(d), the (149.2°, 0°) sample once again demonstrates a remarkable PM performance, similar to that observed in the former temperature bandwidth experiment (Fig. 3). When the sample temperature is below 130 °C, the thermo-optic effect exceeds the thermal rotation effect, and the phase mismatch Δk increases with the increase in temperature, with Δθ increasing accordingly. When the crystal temperature is approximately 200 °C, Δk and Δθ both reach their maximum values. For temperatures ranging from 130–280 °C, the thermal rotation effect essentially compensates for the thermo-optic effect; therefore, Δk remains at a relatively fixed level, and the change in Δθ is slow. By contrast, when the crystal temperature exceeds 280 °C, the thermal rotation effect overwhelms the thermo-optic effect, with Δk reducing to 0 at ∼ 430 °C, and then reversing its direction of change. Similarly, Δθ decreases to 0 when the temperature is ∼ 430 °C, that is, the PM angle θ returns to its initial location at room temperature (i.e., 25 °C). Because (30.8°, 0°) is the symmetry direction of (149.2°, 0°) in the first octant, its corresponding phase mismatch Δk signifies the positive stacking of the thermo-optic and thermal rotation effects, with the continuous enhancement of the thermal rotation effect leading to the gradual increase of the rotation angle-temperature gradient, as demonstrated in Fig. 4(c).
Following the above analysis, it can be observed that the experimental result presented in Fig. 4(d) is basically consistent with that shown in Fig. 3. The PM angle experiment again attests to the remarkable temperature-dependent SHG performance of the YCOB crystal cut along the (149.2°, 0°) direction. As the previous testing proved that the thermo-optic coefficients of the YCOB crystal increase with the increase in temperature [15], this phenomenon can be attributed to the fact that at high temperatures, the increase in thermal rotation is more severe. Gradually, the influence of the thermal rotation effect exceeds that of the thermo-optic effect. As a result, Δk and Δθ present reverse changes, while, concurrently, η and θ experience recovery processes at approximately 410 °C.
5. SHG efficiency experiments
To test the temperature stability of the (149.2°, 0°) sample further, temperature tuning experiments for type-I SHG were performed at different fundamental energies. As demonstrated in Fig. 5, when the single-pulse energy of the fundamental wave was changed from 6 mJ to 90 mJ, the maximum SHG conversion efficiency increased from 3.7% to 40.1% and the measured temperature bandwidth decreased from > 490 °C·cm to 166 °C·cm. In Ref. [13], the temperature stabilities for type-I SHG of 1064 nm were measured to be −0.057%/°C (30–220 °C) and −0.064%/°C (25–160 °C) for Czochralski- and Bridgman-grown YCOB crystals, respectively. The corresponding maximum SHG conversion efficiencies were 55.4% and 67.8%, respectively [13]. A crystal direction of (31°, 180°) was equivalent to the (149°, 0°) direction of the YCOB crystal in this study. The parameters of their fundamental laser are 340 ps, 2.84 mJ, and 100 Hz, corresponding to a peak power of 8.34 MW. In this study, our fundamental light source was a Nd:YAG laser with 6 ns, 10 Hz pulses, producing peak powers of 1–15 MW for pulse energies of 6–90 mJ. Considering that we did not use a convex lens to focus the fundamental beam, the peak power density in the YCOB crystal was far below that used in Ref. [13]; therefore, our SHG conversion efficiencies are lower than those reported by that study. For the experimental data in Figs. 5(a)–5(c), the average gradients of the SHG conversion efficiencies were -0.0116%/°C, -0.0686%/°C, and -0.1553%/°C, respectively, corresponding to a temperature range of 25–200 °C. These results indicate that there is no unified standard for the evaluation of temperature stability, with specific experimental conditions a critical factor. From Fig. 5(d), it is observed that at all of the fundamental energies, the normalized SHG efficiency of the (149.2°, 0°) sample always remains at 20% above when the crystal temperature is no higher than 500 °C. In this respect the (149.2°, 0°) sample outperforms the other samples considerably, as shown in Fig. 3.
Fig. 5. (a)–(c) Measured SHG conversion efficiency as a function of crystal temperature at different fundamental energies for the YCOB sample cut along the (149.2°, 0°) direction. (d) Normalized SHG conversion efficiencies at different fundamental energies.
6. Conclusions
Considering the thermal-optic effect due to the principle axes of the refractive index and the thermal rotation effect due to the principal plane of the refractive index, we calculated the temperature bandwidth (ΔTl) of a YCOB crystal for all type-I SHG PM directions at 1064 nm. To verify the calculation, we tested four YCOB samples whose PM angles were distributed symmetrically over the crystal space. Calculations and experiments both demonstrate that the YCOB crystal has a specific spatial distribution of the temperature bandwidth, that is, ΔTl in the second octant (90° < θ < 180°) is considerably larger than that in the first octant (0° < θ < 90°), with the PM direction with the largest ΔTl being (149.2°, 0°), which is located in the XZ principle plane for which θ > 90°. For the YCOB sample cut along the (149.2°, 0°) direction, we observed a special regression phenomenon of the PM angle when the crystal temperature exceeded 200 °C. This phenomenon was recorded in all of the SHG measurements, including the temperature bandwidth experiments (Fig. 3), PM angle experiments (Fig. 4), and SHG efficiency experiments (Fig. 5). In addition, it has been repeatedly confirmed by multiple experiments on multiple (149.2°, 0°) samples. This apparently unique property results in the measured ΔTl exceeding 490 °C·cm, which is significantly larger than the theoretical value.
For comparison, the basic characteristics of some typical NLO crystals are listed in Table 2. For GdCOB and YCOB crystals, their small thermo-optic coefficients are associated with large temperature bandwidths; simultaneously, the significant thermal rotation effect accentuates this advantage. Compared with the GdCOB crystal, the YCOB crystal exhibits a larger ΔTl and higher deff. Moreover, the most stable SHG PM direction in the YCOB crystal is (149.2°, 0°), which lies in the XZ principle plane. This is more convenient to process than the equivalent spatial direction of (135°, 47.3°) in the GdCOB crystal.
Table 2. Characteristics related to the SHG by a 1064 nm Nd:YAG laser in some NLO crystals.
In summary, the YCOB crystal possesses many excellent properties, such as congruent melting, easy growth, a high laser damage threshold, and a large NLO coefficient. Owing to its remarkable PM angle regression property, it has replaced the GdCOB crystal as the most thermally stable SHG crystal reported to date. For the temperature-insensitive SHG of 1064 nm laser, the temperature bandwidth of 490 °C·cm in YCOB crystal is quite larger than the values ever observed in other NLO crystals, such as 430 °C·cm at (135°, 47.3°) in GdCOB [14], 75 °C·cm at (44°, 45.7°) in potassium titanyl phosphate (KTP) [28], 170 °C·cm at (71.1°, 67°) in KTP [37], and 150 °C·cm at (33.3°, 21.5°) in deuterated l-arginine phosphate (dLAP) [17]. With continued research, further development and optimization of YCOB crystal components for other frequency conversion processes will be realized. Such components should prove highly applicable in many laser devices that require high frequency conversion efficiency and good temperature stability simultaneously, for example, high average power lasers, harsh temperature environment lasers, and high-quality self-frequency doubling lasers.
Funding
National Natural Science Foundation of China (61975096); Shenzhen Fundamental Research Program (JCYJ20180305164316517); Natural Science Foundation of Shandong Province (ZR2017MF031).
Disclosures
The authors declare no conflicts of interest.
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