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The second-order nonlinear optical (NLO) coefficients of the BaGa4Se7 crystal were experimentally determined through the Maker Fringe Technique for the first time. The values of the two major nonlinear tensor elements d11 and d13 were 24.3 and 20.4 pm/V, respectively. These results were in agreement with the ones obtained through theoretical calculations.
© 2015 Optical Society of America
1. Introduction
Middle-Infrared (mid-IR) nonlinear optical (NLO) crystals play an important role in the modern IR laser frequency conversion technology that includes optoelectronic device, resource exploration, long-distance laser communication, etc., owing to their advantages in the production of stable solid-state IR laser devices. Therefore, the exploration and development of mid-IR NLO crystals is of broad scientific and technological importance. Although in the past many NLO crystals have been grown to generate efficient laser output in the mid-IR spectral region, the crystals used are still not good enough to fully meet the demand of laser development. Thus, improved new mid-IR NLO crystals are still needed [1].
BaGa4Se7 (BGSe) is a newly developed IR NLO crystal [2,3]. It is the selenide analogue of the chalcogenide compound BaGa4S7, whose acentric orthorhombic structure was identified in 1983 [4] and the IR NLO effect was reported in 2009 [5]. In 2010, the compound BGSe was synthesized for the first time and its properties were preliminarily investigated. On the whole, BGSe shows a number of intriguing optical properties. For example, the transparent range of this crystal covers from 0.47 to 18 um, which makes it possible to obtain mid-IR coherent light through parametric down-conversion from 1-micron (Nd and Yb) lasers without the two-photo absorption problem plaguing many other IR crystals such as ZnGeP2. Moreover, the BGSe crystal is non-critically phase-matchable and its SHG effect is about 2-3 times that of the benchmark material AgGaS2, which makes it easier to achieve effective frequency conversion, whether is through down-conversion of 1-micron lasers or SHG of 10.6 μm CO2 laser. Besides, the surface laser damage threshold of BGSe is about 3.7 times that of AgGaS2, and this makes it possible to be pumped by higher-energy laser devices [6]. From these, it can be deduced that BGSe is a very promising NLO crystal for practical applications in the mid-IR region, and this has been exemplified by some recent achievements. Based on BGSe, a high efficiency and high peak power picosecond mid-IR optical parametric amplifier (OPA) was demonstrated in 2013 [7]. Pumped by a 30 ps 1064 nm Nd:YAG laser, a 3-5 μm tuning range and a maximum idler output of 830 μJ at 3.9 μm with peak power of ~27 MW was obtained. The maximum photon conversion efficiency from 1064 nm to 3.9 μm reached as high as 56%. Recently, widely tunable picosecond mid-IR OPA with wavelength ranging from 6.4 to 11 µm was also demonstrated [8]. All these achievements are attributed to the excellent optical performances of the BGSe crystal.
Although the nonlinear susceptibility of BGSe has been preliminarily tested by means of powder SHG method [2,9], it is still necessary to determine the nonlinear optical coefficients of this crystal more precisely. The powder SHG method is semi-quantitative and can only give an approximate range for the nonlinearity of crystals. For a crystal which shows good optical performances and has broad application prospect, that is obviously not enough. Furthermore, for low-symmetric crystals such as BGSe, which belongs to the Pc space group (m-point group), the effective nonlinearity in laser frequency conversion is often dependent on several non-zero elements of the second-order NLO tensor, and different relative values between elements will affect the choice of the direction for crystal processing so that optimal conversion efficiency would be obtained. Therefore, determining the exact values of the tensor elements is of great sense for crystal application. In this paper, we will introduce our attempt to measure the NLO coefficients for the BGSe crystal by the Maker fringe technique, and some expected results were obtained.
2. Experiments
Maker fringe technique can data back to a 1962 paper by Maker et al. which reported the observation of a oscillation in the second harmonic power as the angle of a thin quartz plate was rotated to vary the effective thickness, L [10]. Here, denotes the phase mismatch between the input fundamental light and the output harmonic wave . This technique has been used successfully for more than 40 years and is well developed [11–13]. It is a non-phase-matched method and permits any propagation direction of light, so is applicable to NLO crystals with all kinds of symmetry (crystals of various symmetry classes). Moreover, with the proper set of crystal cuts, most of the dij elements in the nonlinear tensor can be determined in theory by analyzing the fringes for different fundamental and harmonic polarizations. Particularly, for crystals with symmetries not lower than those of the orthorhombic system, the value of any individual tensor element can be obtained independently.
Figure 1 shows the experimental setup for Maker fringes measurements. A Q-switched Nd:YAG laser (Spectra-Physics, Model Pro 230) emitting 10 ns pulses at 1064 nm with a repetition rate of 10 Hz was used as the fundamental light source, and the polarization of the laser was controlled by a half wave plate along with a Glan-Taylor polarizer. The second harmonic (SH) signal at 532 nm from the crystal was separated from the fundamental by an IR filter, selectively detected by a photomultiplier tube (Hamamatsu, Model R105), and then recorded to form Maker fringes. During the experiments, the incident fundamental beam diameter was about 1.5 mm and its energy per pulse was ~20 mJ.
In the crystal-physical XYZ coordinate system [3], considering the Kleinman symmetry [14], the second-order NLO tensor d of the BGSe crystal has a form of
with a total of six independent NLO coefficients: d11, d12, d13, d15, d24, d33. Theoretically, we can adopt the arrangements shown in Figs. 2(a)-2(d) to measure the Maker fringes corresponding to d11, d13, d15 and d33, respectively. However, we did not obtain any analyzable fringes for d15 and d33 in experiment. The reason for this may be that the magnitude of the two coefficients is too small and the optical quality of the BaGa4Se7 crystal was not so perfect, which could not provide enough signal-to-noise ratio for measuring. For d11 and d13, experimental fringes are obtained, as shown by the black solid lines in Figs. 3 and 4.
Fig. 2 Orientation of the BaGa4Se7 crystal to measure the Maker fringes corresponding to (a) d11, (b) d13, (c) d15, and (d) d33 coefficients. The corresponds to the fundamental light, and to the SHG light.
As for the coefficients d12 and d24 of BGSe, there is no way to obtain Maker fringes for any individual independently due to the low symmetry of this crystal. In theory, we can adopt the arrangements shown in Figs. 5(a) and 5(b) to measure the synthesized fringes for d12 intertwined with d13, and d24 with d15, respectively. However, no analyzable fringes were obtained for the latter. The experimental fringes for the former were shown in Fig. 6.
Fig. 5 Orientation of the BaGa4Se7 crystal to measure the Maker fringes corresponding to (a) d12 intertwined with d13, (b) d24 with d15. The corresponds to the fundamental light, and to the SHG light.
All the above measurements were based on a Y-cut 8mm × 7mm × 1.76mm BGSe plate. A 1.79 mm thick (110)-cut KH2PO4 (KDP) crystal was also prepared to be used as a reference sample, because the Maker fringe technique is a relative method and the NLO coefficient d36 of KDP has a consensus value of 0.39 pm/V [15, 16]. Both BGSe and KDP crystals were processed to have a parallelism better than 1 minute and were uncoated. The experimental arrangement to measure the Maker fringes for d36 of the KDP crystal and the corresponding results were shown in Figs. 7(a) and 7(b), respectively.
Fig. 7 Maker fringes measurement for the coefficient d36 of the KDP crystal: (a) orientation arrangement; (b) experimental and theoretical fringes.
3. Results and discussion
According to the theory of the Maker fringes technique, the SH output power from crystals under some reasonable approximations is a function of the fundamental incident angle θ:
Here is constant when the incident power Pω is fixed just as in our experiment, and af (θ) depicts the envelope of the Maker fringe; c is the light speed in vacuum, andω0 the radius of the light beam; L is the thickness of the sample; λ is the fundamental wavelength; nω and n2ω are the refractive indices at the fundamental and harmonic wavelengths, respectively, and θω and θ2ω are the corresponding refractive angles.The coefficient dij can be determined by the central-inserted-value of the envelope:
or by the value of a decided by all the maximum values in a Maker fringes pattern:By analyzing the experimental fringes in Figs. 3, 4, and 7(b), we can determine the NLO coefficients d11 and d13 using the Eq. (5), as following
The theoretical Maker fringes were then simulated using the above results, as shown by the red dashed lines in Figs. 3 and 4. It can be seen that they were in good agreement with the experimental fringes, which conversely proved the accuracy of the experimental measurements and further the calculated values for d11 and d13.
For the experimental fringes in Fig. 6, the envelop value at the central location (θ = 0°) characterized the SHG intensity that was contributed by the single coefficient d13 of BGSe crystal. The coefficient d12 also contributes to the SHG signal in the case of fundamental oblique incidence, i.e., at the locations of θ≠0° in Fig. 6. Through careful analysis, it can be concluded that the coefficient d12 has an opposite sign relative to d13, whose value calculated using Eq. (4) is .
It can be seen that the two values of d13 (20.4 vs 19.2 pm/V) agree basically; however, there is still a difference of ~6% between them. Since d13 = 19.2 pm/V was obtained from a synthesized fringes pattern, and only the location of θ = 0° was utilized to calculate, it probably have less accuracy compared with the former result. Thus, the value of the NLO coefficient d13 of the BGSe crystal could be determined to be 20.4 pm/V. This result is also in perfect agreement with that from theoretical calculations (d13 = 20.6 pm/V, see Reference [2]). For d11, the experimental value is in basic agreement with the theoretical result of 18.2 pm/V [2].
The values of the other dij elements may also be determined through Maker Fringe technique when the optical quality of the BGSe crystal is further improved in future. The crystal used at present contains a few microscopically visible defects such as growth patterns and inclusions, which generates noise strong enough to submerge the fringe signal if the latter is too weak due to small dij values. For dij elements with large values like d11 and d13, although the noise would also decrease the signal-to-noise ratio of the fringes, it has little influence on the accuracy of the measured data, as the noise is disordered, irregular, and so weak compared to the regular fringe signals. In fact, no noise can be clearly seen in Figs. 3 and 4.
Although only two of the six NLO tensor elements of the BGSe crystal were successfully determined through Maker fringes technique, it can be inferred from the present results that the BaGa4Se7 crystal has a large nonlinear susceptibility, as whether it is the coefficient d11 or d13, the value is much larger than that of d36 of the practically-used benchmark crystal AgGaS2 (d36 = 11 ~13 pm/V). This demonstrates the preliminary investigation for the SHG effect of this crystal, which was described in the “Introduction” part of this paper.
4. Conclusion
In this paper, we described our work to determine the second-order NLO coefficients of the BGSe crystal. By comparing the experimental Maker fringes for d11 and d13 of BGSe with that of d36 of KDP, the values of d11 and d13 of BGSe were determined to be 24.3 and 20.4 pm/V, respectively. These results show that the BGSe crystal has a large nonlinear susceptibility, and may have a broad prospect for practical applications in the mid-IR spectral region.
Acknowledgments
The work was financially supported by the National Natural Science Foundation of China (No. 51472251) and the Fundamental Research Funds for the Central Universities (ZY1416).
References and links
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