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Abstract
Large-size DKDP crystals are grown by conventional-growth (CG) and rapid-growth (RG) methods and their deuterium homogeneities are measured in situ by Raman spectroscopy. The influence of deuterium homogeneity on third harmonic generation (THG) is also researched. The results indicate that the CG DKDP crystal is in good homogeneity of deuterium content (0.005% cm−1 deviation along the e-axis) and its influence on the third harmonic generation can be neglected, while the RG DKDP crystal shows a more complicated distribution of deuterium content. Its deuterium content decreases gradually, about 0.2% per cm with crystal growing, which will lead to about 5% inhomogeneity of the THG efficiency at 3 GW/cm2 of fundamental radiation.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In high power large-aperture laser system, potassium dihydrogen phosphate (KDP) crystal and its deuterated analog DKDP crystal are the optimal choices for converting high power Nd:glass laser into the ultraviolet for target irradiation, owing to their excellent optical properties and availability in large sizes [1, 2]. Currently, the third harmonic laser is used as the normal working wavelength. And 60%–80% deuterated DKDP crystal performs usually as the tripler in view of avoiding laser damage caused by the transverse stimulated Raman scattering, which usually occurs in KDP crystal [3, 4].
DKDP crystal is usually grown from deuterated aqueous solution by conventional-growth (CG) or rapid-growth (RG) method [5, 6]. In the growing of DKDP crystal, the unavoidable variation of growth parameters such as temperature, supersaturation and deuterium content in solution will induce the inhomogeneity of deuterium content in crystal. Ji et al. [7] discovered 5.4% discrepancy of deuterium content in RG DKDP crystal with sizes of 65 mm × 65 mm × 113 mm. Zhang et al. [8] grew a DKDP crystal with sizes of 100 mm × 105 mm × 96 mm by RG method and the deuterium discrepancy is about 1.4%. Recently, we have researched the deuterium homogeneity of a CG DKDP crystal (150 mm × 150 mm × 190 mm) and the deuterium inhomogeneity is estimated to be 0.12% [9]. Previous research on the deuterium homogeneity is basing on several samples of a DKDP crystal. The spacial distribution of deuterium content remains ambiguity. In addition, the deuterium inhomogeneity will give harmful impact on the third harmonic generation (THG) and the criterion of deuterium inhomogeneity have not be given.
It is reported that with the deuterium content increasing the v1 mode of DKDP crystal, assigned to totally symmetric vibration of the PO4 ion, displays an approximately linear red-shift and 1 cm−1 shift represents about 2.68% deuterated level variation [10–12]. For a large-size DKDP crystal slice, its deuterium content distribution can be mapped accurately without destruction according to this Raman character. In this work, the Raman mapping technique is applied to measure the deuterium homogeneity of large-size DKDP crystal in situ. The deuterium homogeneities of CG and RG DKDP crystals are then compared. Besides, the influence of deuterium homogeneity on THG is studied and a criterion of deuterium inhomogeneity is proposed.
2. Experimental
2.1 Samples’ preparation
A large-size DKDP crystal was grown from about 70% deuterated aqueous solution by CG method. DKDP crystal grew along the Z direction with growth rate of about 1 mm/day with temperature decreasing. The crystal rotated in the mode of “forward-stop-backward” to keep the homogeneity of growth solution. DKDP crystal slice with a size of 430 mm × 430 mm × 9 mm sample was cut for type-II phase matching (Sample 1#). Figure 1(a) shows the cutting schematic diagram and photograph of the sample. We also prepared a CG type-II KDP crystal with a size of 330 mm × 330 mm × 9 mm as a reference (Sample 2#). In addition, another large-size DKDP crystal was grown by RG method and the deuterium content of growth solution is about 80%. The crystal grows along the X/Y and Z directions simultaneously with temperature decreasing shaping prismatic sector and pyramidal sector respectively in 15 days. The size of the as-grown crystal is about 50 mm × 50 mm × 80 mm. Two samples were cut from the crystal as shown in Fig. 1(b) (Sample 3# is X-cut and Sample 4# is Z-cut). As a reference, a RG Z-cut KDP crystal was prepared (Sample 5#). The grown crystals are all in perfect crystallization and no macroscopic defects are detected. Samples were fine polished for measuring. The samples’ parameters are listed in Table 1.
Fig. 1 Cutting schematic diagram and photograph of (a) CG DKDP crystal and (b) RG DKDP crystal samples.
Table 1. Parameters of samples and their homogeneities
2.2 Raman spectrum measurement
A Raman spectroscopy (Renishaw Invia-Reflex) was used for measuring the Raman spectrum with excitation wavelength of 532 nm. Figure 2 displays the schematic diagram of the measuring system. After starting up the measuring system was stabilized for 2 hours to acquire a high repeatability. The spectroscopy is calibrated by the first-order Raman peak of Si monocrystal (520.3 cm−1). The crystal samples are placed on the translation platform which can translate within a plane in two dimension controlled precisely by a computer. Samples were progressively scanned. The distance among every measuring point is 20 mm in the CG KDP/DKDP crystals and 0.4 mm in the RG. The exciting light focus on 1 mm depth beneath the samples’ surfaces to avoid the proton exchange layer profiles in DKDP crystal. Raman spectra were collected from 800 cm−1 to 1000 cm−1 with a step of 1 cm−1. At every measuring point the Raman spectrum is repeated 6 times.
Fig. 2 Schematic diagram of the measuring system used to perform the Raman spectrum measurements of large-size KDP and DKDP crystals.
3. Results and discussion
3.1 Deuterium homogeneity of CG DKDP crystal
Figure 3(a) shows the Raman spectra measured in somewhere of the CG KDP and DKDP crystals. Comparing with KDP crystal, the v1 mode of DKDP crystal shifts to lower wavenumbers and the in-plane-bending mode δ(OD) arises [13]. The measurement of the Raman spectra was repeated 6 times and the results are fitted by Lorentz function to determine the Raman shift of the v1 mode (). As shown in Fig. 3(b), both of the and show a sight fluctuation and the measuring repetition is estimated to be 0.02 cm−1 (root-mean-square). For every measuring point, the chooses the average of the 6 times and the corresponding experimental standard deviation is about 0.008 cm−1.
Fig. 3 (a) Raman spectra of KDP and DKDP crystals, (b) Raman shift of the v1 mode in KDP and DKDP crystals.
The well grown KDP crystal is in good homogeneity and the is expected to be a constant. Figure 4(a) shows the measured spacial distribution of Sample 2# (14 × 15 measuring points). As can be seen, the is in good spacial homogeneity and the slight discrepancy among the measuring points is mainly induced by the measuring error. Furthermore, the average of along o axis and e axis are calculated respectively, which are shown in Fig. 4b. It is clear that the shows no obvious variation tendency along o axis and e axis and the is about (913.340 ± 0.002) cm−1. The result confirms the high measurement accuracy of this measuring system.
Figure 5(a) is the spacial distribution of deuterium content in Sample 1# (18 × 18 measuring points). The result indicates that the deuterium content varies mainly along the e axis. Similar to Fig. 4(b), Fig. 5(b) shows the average of deuterium content along o axis and e axis. As can be seen, the deuterium content remains a constant along the o axis (62.68% ± 0.01%) basically but increases gradually from 62.59% to 62.75% along the e axis. The deuterium gradient is estimated to be 0.005% cm−1. The data along the e axis are well fitted by an exponential formula. The inhomogeneity of deuterium content in this paper is perfectly coincident with our earlier report in Ref [9]. measured by the noncritical phase-matched fourth harmonic generation (0.12% deviation of deuterium content along the e axis for 190 mm size DKDP crystal).
Fig. 5 (a) Spacial distribution of deuterium content in Sample 1#, (b) variation of deuterium content in Sample 1# along o and e axis.
In the growing of DKDP crystal, the deuterium content in crystal is lower than that in solution, i.e. deuterium segregation. The segregation coefficient K, defined as the mole% ratio of deuterium in crystal to the deuterium in solution, can be described by the exponential equation [14]
where M is the mole% deuterium in solution. The CG DKDP crystal grows along the Z direction only with small and steady supersaturation. During the crystal growing the deuterium atoms tend to concentrate in growth solution as a result of deuterium segregation. Thus, higher deuterated DKDP crystal can be got at later growth period according to Eq. (1). Basing on the growth parameters of the DKDP crystal, we simulated the deuterium variation of along the e axis DKDP crystal, which is shown in Fig. 5(b). The calculated result indicates an excellent linear dependence of deuterium content with the e axis position. However, the calculated deuterium content increases faster with the e axis position than the experimental data. As is known, the segregation coefficient is also susceptible to the growth temperature, which is not taken into account in the simulation. Thus, the deuterium discrepancy may be induced by the temperature decreasing in the crystal growing. These results imply that the temperature has a positive correlation with the segregation coefficient. In other words, the temperature deduction will depress the deuterium concentrating in solution as crystal growing.3.2 Deuterium homogeneity of RG DKDP crystal
Figure 6(a) shows the spacial distribution in Sample 5#. As can be seen, the is also in good spacial homogeneity. Comparing with the result in Fig. 4, we find that growth method has no obvious effect on the . Figure 6(b) is the spacial distribution of deuterium content in Sample 3#. It appears that the deuterium content of prismatic sector is lower than that of pyramidal sector at the same growth period. Since the crystal growth takes place at the crystal-solution interface, the atomic structure at this boundary plays a primary role on the deuterium content. The pyramidal face (101) has the K+ ions on the outside of the crystal, while the prismatic face (100) has both the positive K+ ions and the negative (H/D)2PO4- at the interface [14]. The difference in polarity of the layers and, espacially, the differences in size and polarizability of the ions will result in a different surface free energy, which may influence the deuterium segregation [15–17]. Therefore, the structure differences of the prismatic and pyramidal faces are responsible for their deuterium content deviation. In addition, the deuterium content decreases about 1% gradually with crystal growing in both sectors. The deuterium gradient is about 0.2% cm−1. The results are fully consistent with earlier reports [7–9]. Different from the CG process, the supersaturation reduces a lot in the RG process. Thus, the large variation of the supersaturation dominates the deuterium inhomogeneity mechanism of RG DKDP crystal. Figure 6(c) gives the deuterium content distribution in Sample 4#. An interesting feature appears in the distribution. It is clear that the deuterium content along the (110) direction is higher than other prismatic sectors, which is related to the growth hydrodynamics. In the growth process, the crystal rotated in the mode of “forward-stop-backward”. As a result, the velocity of crystal at the corner is bigger and the mass transfer film is thinner, which will have an effect on the segregation coefficient of deuterium atom [18]. Table 1 summarizes the measured homogeneities of all the samples.
Fig. 6 (a) Spacial distribution of in Sample 5#, (b) spacial distribution of deuterium content in Sample 3# and (c) Sample 4#
3.3 Influences on the THG
Generally, the third harmonic laser is realized using cascade type-I/type-II sum-frequency generation [19,20]. The basic scheme is diagrammed in Fig. 7. The first crystal converts the fundamental laser to the second harmonic via type-I phase-matching. The doubling efficiency should be as close to 66.6% as possible. The copropagating second harmonic and residual fundamental beam are then passed through a DKDP tripler creating the THG by type-II phase-matched sum-frequency mixing.
In the process of THG, efficient frequency conversion scheme requires close attainment of the phase-matching condition
where k denotes the wave number, ω is the angular frequency of fundamental laser, n is the refractive index, c is the speed of light in vacuum. For partially deuterated DKDP crystal, its refractive indexes are functions of deuterium content and orientation angle of the optic axis with respect to the field propagation direction [21–23]. Thus, the phase-matching angle (θpm) depends on the deuterium content (D) of tripler. Figure 8a gives the simulated θpm(D) dependence. As can be seen, the θpm is almost in linear with the deuterium content. 1% higher deuterium content will cause 230 μrad (0.013°) increasing of the θpm.Fig. 8 (a) Phase-matching angle of tripler versus deuterium content, (b) dependence of the THG efficiency on the deuterium content deviation. Iω represents the intensity of fundamental laser. The relative reduction of ηTHG at each fundamental intensity for ΔD = 0.5% and 0.2% are plotted in the inset.
As aforementioned, both of the CG and RG DKDP crystals display a non-uniform distribution of deuterium content. The θpm will vary with position correspondingly. To achieve a higher THG efficiency, the large-size DKDP crystal should choose the phase-matching angle that corresponding to the average deuterium content of all positions (D0). Accordingly, the position with deuterium content Di (Di≠D0) will be mismatched in the THG and the corresponding conversion efficiency decreases as a result. The dependence of THG efficiency (ηTHG) on the deuterium content deviation (ΔD = |Di–D0|) is simulated basing on the well-known coupled amplitude equations for sum-frequency generation [24]. The crystal thicknesses used in the simulation are 12 mm for the SHG and 9 mm for the THG. The result is shown in Fig. 8b. The ηTHG(ΔD) dependence is not linear in the interval 0 to 1.5%, ηTHG reducing more rapidly at larger ΔD. The inset of Fig. 8b plots the relative reduction of ηTHG (ΔηTHG) versus fundamental intensity (Iω) at ΔD = 0.5% and 0.2%. As can be seen, the ηTHG shows a linear reduction when driven with increasing fundamental radiation. The ΔηTHG is insignificant when the ΔD is less than 0.2%. For the CG DKDP crystal, the 0.16% inhomogeneity of deuterium content has no obvious effect on the ηTHG. Thus, we can conclude that the CG DKDP crystal is in good homogeneity of deuterium content and the variation is acceptable. However, the RG DKDP crystal in this paper has about 1% deviation of deuterium content and the ΔD is about 0.5%, which will lead to about 5% reduction of the ηTHG at 3 GW/cm2 of 1ω radiation. As reported in Ref [7], the RG DKDP crystal has a 5.4% discrepancy of deuterium content and the reduction of the ηTHG will be more serious. Besides, the non-uniformity of ηTHG deteriorates the homogeneity of 3ω near-field distribution, which aggravates the self-focusing effect in the following optical elements [25]. Thus, measures should be taken to suppress the inhomogeneity of deuterium content in the rapid growing of DKDP crystal.
4. Conclusion
We measured the deuterium homogeneities of large-size CG and RG DKDP crystals in situ by Raman spectroscopy. From our results it follows that the deuterium content of CG DKDP crystal increasing about 0.16% along the e-axis as crystal growing. The deuterium inhomogeneity is induced by the segregation of deuterium atom. However, the RG DKDP crystal shows a different feature from the CG. Its deuterium content of prismatic sector is lower than that of pyramidal sector at the same growth period as a result of their structure differences. And the deuterium content decreases gradually about 1% with crystal growing in both sectors, which is mainly due to the large variation of the supersaturation. In addition, the deuterium content along the (110) direction is higher than other prismatic sector induced by the growth hydrodynamics. Furthermore, the influence of deuterium homogeneity on the THG is analyzed. It is found that the reduction of THG efficiency can be neglected when the ΔD is less than 0.2%. However, 0.5% of ΔD will lead to about 5% reduction of the ηTHG at 3 GW/cm2 of 1ω radiation. Thus, it can be concluded that the CG DKDP crystal is in good homogeneity of deuterium content and its influence on the THG efficiency is insignificant. While the 1% deuterium inhomogeneity of RG DKDP crystal has an apparent infulence on the THG efficiency and the 3ω near-field distribution will deteriorate as a result. For the RG DKDP crystal, the deuterium homogeneity should be, therefore, paid more attention and the growing procedure should be optimized in view of improving the deuterium homogeneity.
Funding
Open Project of State Key Laboratory of Crystal Materials, Shandong University (KF1601); National Natural Science Foundation of China (Grant No. 11404306).
Acknowledgements
We would like to thank the State Key Laboratory of Crystal Materials, Shandong University and Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences for providing DKDP crystals.
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