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Abstract
We report accurate Sellmeier equations at 22℃ for LaBGeO5, which reproduce well our experimental results for the quasi phase-matching conditions with the ee-e, oe-o, eo-o, and oo-e interactions in the 0.2660 − 1.0642 µm spectral range. In addition, the thermo-optic dispersion formula (dn/dT) of this material is also presented.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In 1991, LaBGeO5 (LBGO) was reported by Kaminskii et al. [1] as a nonlinear optical (NLO) crystal for the first time. Although the cutoff wavelength of LBGO is ∼0.195 µm, its small birefringence (B = ne − no = 0.0384 at 1.064 µm) limits the utility of this material to UV generation. However, since Hirohashi et al. recently developed periodically poled LaBGeO5 (PPLBGO) as a new quasi phase-matching (QPM) device, a few groups demonstrated harmonic generation of a Nd:YAG laser at 1.064 µm [2–6].
The optical properties and Sellmeier equations of LBGO were reported by Kaminskii et al. [1]. In addition, the nonlinear optical constant of this material was reported to be d33 = 0.96 pm/V by Honda et al. [7], which is about 2.7 times larger than the value reported in Ref. 1. Owing to its intrinsic physical properties such as no hygroscopicity and chemical stability, PPLBGO is an attractive NLO material for UV generation based on a solid-state laser. In order to predict the grating period of PPLBGO correctly, we attempted to derive the accurate Sellmeier equations for the ordinary and extraordinary waves of PPLBGO. So we measured the QPM wavelengths at 22 ℃ for second-harmonic (SHG) and sum-frequency generation (SFG) in the 0.2660 − 1.0642 µm spectral range with the ee-e, oo-e, eo-o, and oe-o interactions by using the PPLBGO sample with the grating period of Λ = 5.80 µm. Moreover, we measured the temperature-tuned SHG and SFG wavelengths in the same QPM processes between 20 ℃ and 160 ℃ and derived the thermo-optic dispersion formula for LBGO.
2. Experiments and discussion
2.1 QPM conditions
The 10-mm-long, 0.5-mm-thick PPLBGO crystal used in this experiment was provided from Oxide Corp. and was fabricated with the grating period of Λ = 5.80 µm. The nanosecond pulse Nd:YAG laser (HOYA Continuum Surelite II-10) at 1.0642 µm was operating at a repetition rate of 10 Hz in all measurements. By using a KTiOPO4 optical parametric oscillator (OPO) pumped by a frequency-doubled Nd:YAG laser as a pump source, we first measured the SHG and SFG wavelengths in the 1st order QPM processes with the ee-e, oo-e, oe-o, and eo-o interactions. The experimental results at 22 ℃ are tabulated in Table 1 together with the theoretical values calculated with the following Sellmeier equations:
Table 1. Quasi phase-matched SHG and SFG wavelengths in periodically poled LaBGeO5 with a grating period of Λ ∼ 5.80 µm at 22 ℃.
Table 2. Refractive indices of LaBGeO5 at 22 ℃.
2.2 Birefringence phase-matching
In order to check the birefringence phase-matching (BPM) properties of this material, we attempted to measure the type-2 SHG wavelength in the same PPLBGO sample. The SHG signal of the idler output of the aforementioned KTiOPO4 OPO was observed in this experiment. The resulting tuning curves for BPM SHG are shown in Fig. 1 together with the experimental point for the type-2 90° phase-matched SHG wavelength. This experimental value at 22 ℃ is λ1 = 1.2751 µm, which is ∼8.0 nm shorter than the theoretical value of λ1 = 1.2831 µm calculated with Eq. (1). This result indicates that Eq.(1) is unable to reproduce well the phase-matching conditions beyond 1.064 µm. We should note that the additional Sellmeier coefficients in the IR are requested to reproduce the precise phase-matching conditions in the wide spectral range.
Fig. 1. Phase-matching angles for type-1 (ee-o) and type-2 (oe-o) SHG in LBGO. The real and dashed lines are the theoretical curves calculated with Eq.(1) in this text and the Sellmeier equations of Kaminskii et al.[1], respectively. Open circle is our data point for type-2 SHG.
2.3 Temperature-dependent phase-matching conditions
We next measured the temperature-tuned SHG and SFG wavelengths for the 1st order QPM process with the ee-e interaction between 20 ℃ and 160 ℃. The experimental results for the temperature tuning curves in the PPLBGO with the grating period of Λ = 5.80 µm are shown in Fig. 2 (a) and (b) for SHG and SFG, respectively. The experimental data for SFG in Fig. 2 (b) were obtained by mixing the signal output of a frequency-doubled Nd:YAG laser pumped OPO and the fundamental wavelength at 1.0642 µm. The solid lines in Figs. 2(a) and (b) are the theoretical curves calculated with our index formula Eq. (1) and the following thermo-optic dispersion formula for LBGO.
where λ is in micrometers. As can be seen from Fig. 2 (a) and (b), the resulting tuning curves fairly agree with our experimental points.
Fig. 2. Temperature-tuned QPM (a) SHG and (b) SFG wavelengths for the 1st order QPM process with the ee-e interaction in PPLBGO with the grating of Λ = 5.80 µm. Open circles are our experimental points. The solid lines are the theoretical curves calculated with Eqs. (1) and (2) in this text.
Moreover, we measured the thermo-optic constants (dn/dT) at 0.4880, 0.5145, 0.5325 and 0.6328 µm by using a minimum deviation method with the abovementioned LBGO prism. From the raw data (dn/dT) observed between 20 ℃ to 120 ℃, and the experimental data for the temperature bandwidths in harmonic generation of a Nd:YAG laser at 1.064 µm [8], we have derived the thermo-optic dispersion formula (Eq. (2)). For comparison, the experimental points for dn/dT are plotted in Fig. 3 together with the theoretical curves given by Eq. (2). As shown in this figure, the theoretical values agree with the experimental data within an accuracy of less than ± 1×10−6.
Fig. 3. Thermo-optic constants for LBGO. Open circles (ordinary wave) and open triangles (extraordinary wave) are our experimental points obtained by a minimum deviation method. The solid lines are the theoretical curves calculated with Eq. (2) in this text.
Since the thermal expansion coefficient of this material has not been measured in this experiment, we assumed that a gating period was constant for crystal temperature when calculating QPM conditions in this work. However, Eq. (2) can reproduce the experimental results for the temperature-dependent QPM temperatures of harmonic generation of a Nd:YAG laser at 1.064 µm. Figure 4 (a) shows the QPM temperatures for SHG at 0.532 µm in the PPLBGO having the grating periods of Λ = 19.75, 19.80, 19.85, and 19.90 µm. The solid line in this figure is calculated with Eqs. (1) and (2) and agrees well with the experimental data given by Hirohashi et al.[8]. In addition, we checked the QPM temperatures for SHG at 0.266 µm in the 2nd order QPM process. The resulting curve calculated with Eqs. (1) and (2) is also shown in Fig. 4 (b) together with the experimental points obtained by the PPLBGO having the grating periods of Λ = 4.14, 4.16, and 4.20 µm [5,8]. As shown in Fig. 4 (b), our theoretical curve is in good agreement with the experimental points in the deep UV spectral region.
Fig. 4. QPM temperatures for SHG at (a) 0.532 µm and (b) 0.266 µm in PPLBGO. Open triangles are the experimental points taken from [8]. The solid lines are the theoretical curves calculated with Eqs. (1) and (2) in this text.
Furthermore, the temperature phase-matching bandwidth (FWHM) for third-harmonic generation (THG) of a Nd:YAG laser at 1.064 µm was reported to be ΔT·l = 8.4 ℃·cm in [4], which is 14% larger than our theoretical value of ΔT·l = 7.4 ℃·cm. It should be pointed out that our calculated QPM temperatures for THG at 0.355 µm in the PPLBGO with the grating periods of Λ = 6.39, 6.41, and 6.43 µm agree fairly with the experimental points given by Hirohashi et al. (Figure 2 (a) of [4]).
Finally, the temperature tuning rate of the fundamental wavelength in the type-2 BPM 90°phase-matched SHG process was calculated to be dλ1/dT = 0.22 nm/℃ at λ1 = 1.2831 µm (Fig. 1) by using Eqs. (1), (2). This theoretical value agrees with our experimental value of dλ1/dT = 0.20 nm/℃. This result indicates that our thermo-optic dispersion formula Eq. (2) is valid between 0.266 µm and 1.28 µm.
3. Conclusions
We have reported the Sellmeier equations at 22℃ for LBGO that provide a reproduction of the QPM conditions in the 0.2660–1.0642 µm spectral range. In addition, the thermo-optic dispersion formula for LBGO is also presented. These Sellmeier and thermo-optic dispersion formulas are thought to be highly useful to determine a grating period of PPLBGO device and to predict QPM temperatures.
References
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8. J. Hirohashi and Y. Furukawa, personal communication, (2017).
