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High-quality KDP and DKDP crystals with 12%, 70% and 80%-deuterium content were grown by the conventional temperature cooling method. The nonlinear optical characteristics of K(DxH1-x)2PO4 crystals, including nonlinear absorption and refraction, were systematically investigated through the Z-scan method at λ = 532 nm. The results demonstrate the existence of nonlinear absorption and refraction, and a nonlinear refractive index with a positive sign indicates the generation of self-focusing effect. Moreover, the results indicate that nonlinear absorption and refraction were associated with crystal direction and structure, especially the distribution of H2PO4- or D2PO4- groups. For K(DxH1-x)2PO4 crystals, a similar rule of β was z > I > II, while n2 (or χR(3)) was z > II ≈I. These results will evoke more attention to KDP and DKDP applications, especially frequency conversion and electro-optic switch.
© 2017 Optical Society of America
1. Introduction
The pure and deuterated potassium dihydrogen phosphate crystal, KDP and K(DxH1-x)2PO4 (DKDP), are well known for their excellent dielectric, piezoelectric, electro-optical and nonlinear optical properties [1–3]. DKDP and KDP crystals are only nonlinear materials applied as frequency conversion and electro-optical switching devices in large-aperture laser systems, such as the application of National Ignition Facility (NIF) Nd:glass amplifier [3]. Similarly with KDP, DKDP crystals with various deuterium contents are suitable for harmonic generation, especially 70% and 80% deuteration level-DKDP crystals [4]. Moreover, 12% deuteration level-DKDP could increase the efficiency of second harmonic generation (SHG) at the retracing point of phase-matching due to a bandwidth about 20nm [5].
Under nanosecond (picosecond or femtosecond) laser pulses, self-phase modulation (SPM) and cross-phase modulation (XPM) may be introduced by third-order nonlinear susceptibility in medium. The nonlinear effects lead to phase-mismatch, and suppress frequency conversion efficiency [6, 7]. The intensity-dependent refractive index results in self-focusing or defocusing, spatial distribution and pulse broadening. In addition, the generation of nonlinear absorption decreases conversion efficiency and even brings about damage, especially in high-power laser systems. Therefore, laser output power and service life of crystals are restricted by these nonlinear optical effects [8, 9]. So far, rare research has been paid on nonlinear absorption and refraction for various deuteration level-DKDP crystals. In order to enhance the crystal utilization efficiency, better understanding nonlinear characteristics, particularly nonlinear optical absorption and refraction, are essential to the applications of DKDP crystals with 12%, 70% and 80% deuterium contents.
The studies of nonlinear optical characteristics have been performed by various methods, such as three-wave or four-wave mixing [10, 11], nonlinear interferometry [12], time-resolved interferometry [13] and Z-scan [14]. Considering advantages of simplicity and sensitivity, Z-scan method is a widely used method in measurement of nonlinear refraction and absorption. More importantly, nonlinear refractive index together with its sign could be calculated and distinguished. In this paper, Z-san method was utilized to investigate nonlinear optical nonlinearity of 12%, 70% and 80% deuteration level-DKDP crystals. In particularly, nonlinear absorption and refraction with various directions were explored at λ = 532 nm under pico-second laser pulses irradiation.
2. Experiment
Crystal growth and phase identification
KDP and DKDP crystals with different deuterium contents (12%, 70% and 80%) were grown from the deuterated aqueous solutions using the conventional temperature cooling method. Before growth, the solutions, which were prepared from dissolving high purity KH2PO4 with heavy water, were filtered with a 0.22 μm membrane and heated at 80°C for 24 h. On basis of the correspondence temperature and super-saturation, the growth rate along z-direction was maintained at 3 mm/day and the cooling temperature was performed by FP21 (a Shimada controller). In process of crystal growth, the crystal was rotated in a mode of “forward-stop backward” with speed of 77 r min−1. For as-grown crystals, X-ray powder diffraction (XRD) patterns were carried out a D8 Advance diffractometer in 2θ range from 15° to 65°.
Nonlinear optical characterization
In this part, our main purpose is to explore nonlinear characteristic of DKDP crystals with crystal orientation and deuterium content. According to Fig. 1(a), samples of z-cut, I and II-type were obtained from as-grown crystals with dimensions of 10 × 10 × 1.5 (thickness) mm3.
Fig. 1 (a) cutting schematic diagram of samples with different directions (b) Schematic diagram of Z-scan experimental set-up: BS Beam splitter, D1 and D2 Detectors.
The nonlinear optical characteristics were investigated by Z-scan method [14]. Figure 1(b) shows the schematic diagram of close-aperture Z-scan. The aperture does not exist in open-aperture Z-scan. Through this method, the corresponding variations of relative intensity with positions could be presented on a computer in real time. Based on the practical application and laboratory conditions, a mode-locked Nd:YAG laser with wavelength of 1064 nm (pulse duration of 20 ps and repetition rate of 10 Hz) was applied as laser source. The nonlinear optical characteristics of samples were investigated at second harmonic wavelength of 532 nm. The focal length of lens was 25 cm, the radius of beam waist was about 26 μm and laser power intensity at focal point was about 31 GW/cm2. Then nonlinear absorption could be measured separately under the condition of open-aperture (no aperture). Nonlinear refraction (including the sign) was acquired by closed-aperture Z-scan measurement. Based on the obtained results, nonlinear absorption coefficient (β) and nonlinear refractive index (n2) could be theoretically calculated [15, 16].
3. Results and discussion
Single crystals growth and analysis of crystals structure
Figure 2 shows the as-grown crystals with different deuterium contents. From the images, we can see that as-grown K (DxH1-x) 2PO4 crystals are transparent, free of inclusions and no cracks. The powder XRD patterns of as-grown crystals are presented in Fig. 3(a), which demonstrate that crystal structure has changed little with the variation of deuterium content. From Fig. 3(b), the main diffraction peaks of (200) and (112) faces are found to shift downward with increasing of deuterium content. This implied that the corresponding angles of diffraction peaks exhibit a gradual decrease with increasing of deuterium content. The lattice parameters, calculated by the Rietveld Whole Pattern Fitting and cell refinement, are presented in Table 1. The lattice parameters a (b) enhance gradually with an increase of deuterium, while the axial ratios c/a have slightly downgraded because H-O (D-O) bonds are almost parallel to a (b) axes [16]. But the value of c, which is mainly affected by phosphorus-oxygen tetrahedron, has no obvious regularity due to H-O (D-O) bonds perpendicular to c axis.
Fig. 2 Photographs of the as-grown crystals with different deuterium content: (a) KDP (b) 12%-DKDP (c) 70%-DKDP (d) 80%-DKDP.
Table 1. Lattice parameters of DKDP crystals compared to KDP
Nonlinear absorption
Figure 4 shows the normalized transmittance curves of KDP and K(DxH1-x)2PO4 (x = 12%, 70%, 80%) under condition of open-aperture. In this case, the information about nonlinear absorption is not influenced by nonlinear refraction. The sharp valleys at focus point clearly show the existence of nonlinear absorption. In Fig. 4, the dashed lines represent experimental data, and the solid lines are the fitting results which can be expressed as follows [17–19]:
where Leff, L, I0, α0 and β are the effective thickness, thickness, peak intensity, linear absorption coefficient and nonlinear absorption coefficient, respectively. z0 = πω02/λ is diffraction length of focused beam, λ is the wavelength of light beam and z is sample position. According to fitting results and Eq. (1), β can be obtained. Then the imaginary part related with nonlinear absorption can be calculated with following formulas [18, 20]: where is third-order susceptibility, is the real part of , n0 is the linear index of refraction and ω is optical frequency. The nonlinear absorption coefficients β and corresponding with different directions are detailed presented in Table 2. Based on the figures and values, the relationships between nonlinear absorption and directions have been acquired for K(DxH1-x)2PO4 crystals. An obvious common characteristic is that the values of z-direction are larger than other directions, and the relationship of nonlinear absorption coefficients β (or) is z > I > II. In addition, nonlinear absorption along I and II-directions has a fluctuation with variation of deuterium content, however the change along z-direction is not obvious. Compared to 12% and 80%-DKDP crystals, pure and 70%-deuterium doped KDP crystals have a relatively small nonlinear absorption.Fig. 4 Normalized transmittance curves of KDP (Ai), 12%-DKDP (Bi), 70%-DKDP (Ci) and 80%-DKDP (Di) (i = I, II, z) in open-aperture.
Table 2. Calculated results of nonlinear optical parameters of KDP [25] and K(DxH1-x)2 PO4 (x = 12%, 70%, 80%) at λ = 532 nm
Nonlinear refraction
For K(DxH1-x)2PO4 crystals, the normalized transmittance curves of nonlinear refraction are shown in Fig. 5. Because nonlinear absorption as a separate part did not affect nonlinear refraction, the pure nonlinear refraction curves were obtained through the close-aperture dividing by open-aperture results [21, 22]. The symbols of a, b, c and d represent 0, 12%, 70% and 80% deuterium content in DKDP crystals, while I, II and z represent the directions of K(DxH1-x)2PO4 specimen. From the results, the valley-peak configurations indicate that nonlinear refractive index of K(DxH1-x)2PO4 crystals is positive [14]. The dashed and red solid lines correspond to the experimental data and fitting results, respectively. The fitting curves can be presented as follow [22, 23]:
Where △Φ0 is nonlinear phase shift at focus and x = z/z0. z0 = πω02/λ is the diffraction length of focused beam. After fitting, the value of △Φ0 can be received.Fig. 5 Normalized transmittance curves of KDP (ai), 12%-DKDP (bi), 70%-DKDP (ci) and 80%-DKDP (di) (i = I, II, z) in close/open-aperture.
Based on Eq. (6), nonlinear refractive index n2 is easily calculated. Here the wave vector k is equal to 2π/λ. Then the real part (χR(3)) of nonlinear susceptibility χ(3) can be obtained. The detailed calculation procedures are written as below [18,21]:
where c, n0 are the speed of light in vacuum and linear refractive index of materials, respectively. The value of n2(esu) could be determined through Eq. (8), and nonlinear optical parameters of K (DxH1-x) 2 PO4 are listed in Table 3. It can be seen that the values of n2, n2 (esu) and χR(3) are associated with crystal orientations. Under a certain deuterium content, specimen along with the direction of phase matching (I or II-direction) has a relatively small parameter. In addition, no obvious trend is presented with the variation of deuterium, but a small change is observed due to the variation of deuterium in crystal structure. What’s more, the calculated results demonstrate that physical mechanism of the phenomenon may be dominantly assigned to the distortion of electron cloud, especially H2PO4- or D2PO4- groups [24, 25].Table 3. Calculated results of nonlinear optical parameters of KDP [25] and K(DxH1-x)2 PO4 (x = 12%, 70%, 80%) at λ = 532 nm
Meanwhile, a similar rule has been presented that the values of n2 are about II ≈I < z. In other words, the growth of θ results in the decrease of n2. The rule is analogous to the results at wavelength of 1064nm, which has been reported in R.A. Ganeev article [26]. Taking advantage of the calculated, and Eq. (6), the values with which is the absolute value of the complex-valued quantity are obtained and shown in Table 2 [18].
Discussion
From the above measurement and calculated results, nonlinear optical characteristics of K(DxH1-x)2PO4 crystals at λ = 532 nm are clearly exhibited. The most obvious feature is that crystal structure plays crucial role in affecting β and n2. Especially, the difference between crystal orientations is mainly attributed to arrangements of H2PO4- or D2PO4- groups, which is associated with nonlinear optical properties of K(DxH1-x)2PO4 crystals [24, 25]. Compared to I and II-directions, larger nonlinear absorption and refraction along z-direction have been obviously observed, indicating that nonlinear absorption and refraction effects are more inclined to be induced in KDP electro-optical switching devices of high-power laser systems.
Another feature is that no obvious trend is discovered with the change of deuterium content. However, a noticeable modification is induced by the variation of deuterium, especially I and II-directions. Such behavior may be principally related to replacement of hydrogen bonds by deuterium bonds. In processes of crystal growth, hydrogen (deuterium) bonds forming between H2PO4- or D2PO4- groups are crucial to construct the structural framework for KDP-family [27]. Hence, the evolution of crystal structure, such as the decreasing of c/a, is affected by doping deuterium. This implies hydrogen (deuterium) bonds effect may be a contributing factor not being neglected. Moreover, hydrogen (deuterium) bonds are almost perpendicular to z axis, which may be the reason why it has little impact on nonlinear absorption and refraction along z-direction.
In addition, smaller nonlinear optical parameters (β, n2) of KDP and DKDP crystals are in contrast to previously results and other nonlinear optical crystals, such as dye-doped KDP (β = 141 cm/GW, n2 = 7.35 × 10−5 cm2/MW) [28], LiNbO3 (β = 2.1 × 10−10 cm/W, n2 = 14.2 × 10−13 esu) [26] and LiRbB4O7 (n2 = −4.935 × 10−11 cm2/W) [29]. And lower nonlinear absorption effect of KDP at λ = 532 nm is shown with respect to the wavelength of 216nm (β = 6.0 ± 0.5 × 10−10 cm/W) [30]. Since nonlinear absorption may induce thermodynamics of microscopic changes, and even crystal damage for optical components. With regard to nonlinear refraction with a positive sign, self-focusing effect is more inclined to produce phase-mismatching, intensity inhomogeneity near convergent region [31–33], and even decrease the efficiency of frequency conversion [6]. Therefore, pure KDP and DKDP crystals with lower nonlinear absorption and refraction are more specifically suited to applying as frequency conversion devices in high-power laser systems. More importantly, I and II directions as frequency conversion devices [4, 5] are conductive to the utilization efficiency owing to lower nonlinear absorption and refraction. Due to larger nonlinear absorption and refraction effect, z direction as optical switch should be paid attention to application environments.
4. Conclusions
High quality K(DxH1-x)2PO4 (x = 0, 12%, 70% and 80%) crystals were grown by the conventional temperature cooling method. The phase purity and lattice parameters were characterized by X-ray powder diffraction. The results show that axial ratios c/a decreases with the deuterium content increasing. Furthermore, nonlinear optical characteristics of KDP and DKDP crystals have been measured using z-scan method at λ = 532 nm. The results demonstrate that appreciable nonlinear absorption and nonlinear refraction are detectable. The sign of nonlinear refractive index n2 is positive, indicating self-focusing effect in K(DxH1-x)2PO4 crystals. In addition, the dependences of nonlinear absorption and refraction on specimen directions (I, II and z) have been researched in detailed. The variation caused by directions and doping deuterium suggest that nonlinear absorption and refraction are mainly associated with H2PO4- or D2PO4- groups. Meanwhile, nonlinear absorption coefficient β, nonlinear refractive index n2 and third-order susceptibility are calculated, respectively. Particularly, a similar rule has been presented that the value of β among directions measured is z > I > II, while n2 (or 2χR(3)) is z > II ≈I.
Funding
National Natural Science Foundation of China (51321091, 50721002, 51602174 and 51202131); Natural Science Foundation of Shandong Province (ZR2016EMQ04); SDUST Research Fund and Joint Innovative Center for Safe and Effective Mining Technology and Equipment of Coal Resources; Shandong Province (2014JQJH102).
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