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Abstract
Laser damage threshold (LDT) is critical for optical devices in high-intensity laser applications. Understanding the influence mechanism of a high-intensity laser on optical materials is principal for improving the materials’ LDTs. Here, the LDT of La3Ga5.5Nb0.5O14 (LGN) crystals, the most promising nonlinear optical material for mid-infrared optical parametric chirped-pulse amplification (OPCPA), were studied, and its laser damage mechanism was elucidated. Oxygen vacancies in different ligands have important and distinct effects on LDTs and introduce defect levels, playing primary roles in the reduction of LDTs by the absorption of electrons in the conduction bands. The formation of F-centers also decreases LDTs via two-photon absorption. In addition, the linear absorption of free electrons in the conduction bands contributes more than the two-photon absorption, induced by the defect level, in the nanosecond laser damage process. By annealing in optimized conditions, the 0% laser damage probability of the LGN crystals was measured up to 13.1 J/cm2, which is a 24% improvement compared with that of the as-grown sample, and the highest of the mid-infrared nonlinear optical crystals. The results can not only lead to further improvements in the laser amplification properties in OPCPA systems but also inspire further studies on the application of optical materials in high-intensity lasers.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
High-intensity lasers can provide extreme physical conditions and are employed in numerous applications such as laser fusion [1], electron acceleration [2], and attosecond science [3]. Furthermore, mid-infrared high-intensity lasers are of particular interest because of their exotic performance in light-to-matter interactions, especially in high-harmonic generation [4] and particle acceleration [5,6], which can be realized by the optical parametric chirped-pulse amplification (OPCPA) technique [7]. To date, a 100 TW mid-infrared OPCPA system was designed at a wavelength of 2.2 µm, based on nonlinear optical (NLO) LiNbO3 crystals [8], and represents the highest achievable mid-infrared peak power. Because the traditional NLO oxide crystals usually have a limited infrared cutoff edge of < 5 µm and the ordinary NLO semiconductor crystals have a low LDT of 100 MW/cm2, the wavelength broadening of the OPCPA system is still constrained by the development of NLO crystals with a wide transmission spectrum and high laser damage threshold (LDT) [9,10]. In recent years, a langasite NLO crystal, La3Ga5.5Nb0.5O14 (LGN), has emerged with a high LDT of ∼10 J/cm2 and a transparent range from 0.28 µm to 7.4 µm [11–13]. Furthermore, it has been theoretically evaluated that the LGN crystals have advantages in the broadband and large gains, and they have an amplifiable short pulse width, besides the employable commercial near-infrared pump sources [13]. Given this evaluation, a mid-infrared OPCPA system at wavelengths of up to 5.2 µm was proposed with a pumped intensity of 50 GW/cm2 (2 ps @ mm-level spot size) [14], and a seed pulse of up to 7 µm was experimentally realized [15,16]. As the LDT of LGN crystals determines the maximum achievable amplifiable peak power of the as-applied OPCPA system [17–19], the improvement in the LDT of LGN crystals should fall back on the physical insights regarding LGN crystal structures, however, this is yet to be accomplished.
Herein, we investigate the laser damage mechanism of LGN crystals using experiments and calculations and also improve the LDTs through thermal annealing in different conditions. The two absorption peaks at approximately 355 nm and 480 nm are ascribed to the introduction of oxygen vacancies and F-centers, as determined by first-principles calculations. The introduction of defect levels increases the linear absorption of free electrons and the number of electronic avalanche precursors by the two-photon absorption method, which dramatically reduces the resistance of laser damage. To eliminate the harmful effects of the defects, we optimized the annealing atmosphere and temperature. After annealing in atmospheric air at 700 °C, a high 0% probability damage threshold of 13.1 J/cm2 was achieved under 1064 nm Nd: YAG laser pulses for 10 ns, at 1 Hz. By determining the laser damage mechanism and improving the LDT of the LGN crystals, we developed a high-LDT LGN crystal for use in high-intensity lasers.
2. Experimental section
2.1 Single crystal growth
The polycrystalline materials were synthesized via a solid-state reaction at 1350 °C in air. Single crystals were obtained in a crystal-pulling furnace (Lande Photoelectric Technology Co. Ltd.). The entire growth process was monitored using a weight-and-diameter system with the JPG automatic diameter control program. The polycrystalline materials were melted in an iridium crucible with a diameter of 70 mm and a height of 40 mm. Pure Nitrogen (N2) and Nitrogen combined with 2% oxygen (N2 + 2%O2) were used as growth atmospheres. The pulling speed and rotation were 0.5–0.8 mm/h and 10–12 rpm, respectively.
2.2 X-ray fluorescence spectrum
The LGN crystals grown in different atmospheres were grounded into powders of 250–300 mesh. The contents of various elements were measured using a Rigaku ZSX Primus II X-ray fluorescence spectrometer equipped with an end-window rhodium target X-ray tube (4 kW) and a 30 µm ultra-thin beryllium window. The maximum acceleration voltage and electric current were 60 kV and 160 mA, respectively. The diameter of the channel light bar and sample box mask was 30 mm.
2.2 High-resolution X-ray diffraction
A high-resolution X-ray diffraction was implemented on a Bruker-AXS D5005HR diffractometer equipped with a two-crystal Ge (220) monochromator set for Cu-Kα1 radiation (λ = 1.54056 Å). The accelerating voltage and tube current were 30 kV and 30 mA, respectively, and the step time and step size were 0.1 s and 0.001°, respectively. The rocking curves were measured using (1000) plates polished to optical quality.
2.3 Transmission spectrum
A (1000)-LGN plate with 10 × 10 × 1.5 mm3 dimensions was processed from the as-grown crystal and polished precisely. The transmittance spectrum in the visible and near-infrared range (0.2–2.5 µm) was measured using a Cary 5000 DUV spectrophotometer.
2.4 Computational methods
First-principles calculations were performed using the CASTEP package [20] based on the density functional theory [21]. Optimized ultrasoft pseudopotentials [22] were used to simulate the ion-electron interactions for all constituent elements. A kinetic energy cutoff of 500 eV was chosen with Monkhorst-Pack k-point meshes (4 × 4 × 2) in the Brillouin zone [23]. The generalized gradient approximation using the Perdew-Burke-Ernzerhof functional was adopted [24]. Only the atomic positions in the unit cells of all crystals were fully optimized using the BFGS method [25]. The lattice constants of the as-grown LGN crystals in the N2 + 2%O2 atmosphere were fixed. The convergence thresholds between optimization cycles for energy change, maximum force, maximum stress, and maximum displacement were set to 5.0 × 10–6 eV/atom, 0.01 eV/Å, 0.02 GPa, and 5.0 × 10–4 Å, respectively. The optimization was terminated when all these criteria were satisfied.
2.5 Thermal annealing
Six (1000)-LGN plates with 10 × 10 × 1.5 mm3 dimensions were cut from the as-grown LGN crystals in the N2 + 2%O2 atmosphere. The plates cut from the crystals grown in an oxygen-containing atmosphere were annealed at 700 °C in a vacuum (sample II) and in atmospheric air (III). Then, some plates were annealed at atmospheric-air temperatures of 500, 700, 900, and 1100 °C. The holding time for all samples was 48 h. The preparation conditions of the LGN samples are listed in Table 1.
Table 1. Preparation conditions of the LGN samples
2.6 Weak absorption at 1064 nm
The optical absorption was measured using a photothermal common-path interferometer (PCI) and a laser calorimeter set up at Stanford University, and it was found to have a sensitivity of 10−7 cm−1. The 1064 nm pump beam with a power of 9 W and diameter of 0.5 mm, intersected with the weak probe beam at 633 nm inside the crystal. The refractive index variation resulting from the pump distorted the probe beam before the wavefront and then produced a periodically distorted signal. The signal was recorded by the detector, spontaneously filtrated by a lock-in amplifier, and then sent to a computer. The dimensions of the as-used samples polished inside and outside were 4 × 5 × 6 mm3.
2.7 Nonlinear optical absorption measurements
Nonlinear optical absorption was investigated using the Z-scan method, based on the transmission type. The sample was moved from end-to-end along the axis by the platform, and the corresponding changes in the relative intensity with position were displayed on the computer in real time. An open-aperture Z-scan system was used to characterize the nonlinear absorption properties excited by a femtosecond laser source centered at 1035 nm with a pulse width of 400 fs, repetition rate of 25 kHz, and power instability of 1%. The Rayleigh range z0 and highest power density I0 were 3.72 mm and 260 GW/cm2, respectively.
2.8 Laser damage measurements
The LDTs were studied using a Q-switched (Nd: YAG) laser at 1064 nm (LPS-1064-A) with a 10 ns pulse width and 1 Hz repetition rate. The pulse was focused on the polished (1000) LGN plates with 10 × 10 × 1.5 mm3 dimensions using a lens with a focal length of 300 mm. The radius of the laser speckle was 0.28 mm, as measured by the knife-edge method. The pulse energy was measured directly in front of the plates by a calorimeter (LPE-1A). The error in the laser energy was determined by combining the 3% uncertainties of the energy measurements. Laser conditioning was investigated as a function of frequency using the 1-on-1 approach [26].
3. Results and discussion
3.1 Single crystals grown in different atmospheres
As illustrated in Fig. 1(a), the LGN crystals were firstly grown in different atmospheres using the same polycrystalline component, temperature field, rotation speed, and pulling rate. During the crystal growth process, the evaporation of Ga2O3 grown in the N2 atmosphere was remarkably more intense than that in the N2 + 2% O2 atmosphere, resulting in lower crystalline and optical qualities. This was further demonstrated by the as-measured rocking curves’ full widths at half-maximum (FWHMs) of 42.3″ and 28.9″ for N2 and N2 + 2% O2, respectively. Hence, all the measurements and analyses presented hereafter are based on the samples derived from the LGN crystals grown in the N2 + 2% O2 atmosphere. The ultraviolet and visible transmission spectra of the as-grown LGN crystals in the N2 + 2% O2 atmosphere are illustrated in Fig. 1(c). Two prominent absorption bands are observed at 355 nm and 480 nm in the transmission spectrum, attributing to several point defects or their complexes, as explained in the next section. According to the transmission spectra, the optical bandgaps were calculated using Tauc’s equation, αhv = A(hv-Eg)2, where α is the absorption coefficient and A is an energy-independent constant [27]. The (αhv)1/2 versus hv values were plotted according to the indirect model, and the optical bandgap of sample I was determined to be 4.10 eV at the intersection of the tangent and the x-axis [28], as illustrated in Fig. 1(d).
Fig. 1. (a) Photograph of the as-grown LGN crystal in the N2 and N2 + 2% O2 atmospheres, (b) rocking curves of the (1000)-LGN plates, (c) the transmission spectra from 200-800 nm, and (d) optical energy bandgap of sample I.
Langasite crystals have the structural form A3BC3D2O14, which can be occupied by different elements with the appropriate ionic radii. The LaO8 dodecahedrons (3e position), GaO6 and NbO6 distorted octahedrons (1a position), and two types of GaO4 tetrahedrons (2d and 3f positions) built the LGN structure together [29,30]. Owing to the evaporation of Ga2O3, the gallium oxygen and oxygen vacancy may exist in the crystals, and as measured by XRF, the ratio of Ga3+ to Nb5+ deviates from the stoichiometric ratio. In detail, the LGN crystals grown in the N2 and N2 + 2% O2 atmospheres have the refined composition of La2.99Ga5.37Nb0.53O14 and La3.00Ga5.49Nb0.49O14, respectively, that deviate from the stoichiometric ratio. To investigate the origin and influence of the defects in the LGN crystals, three oxygen vacancy sites and three Ga vacancy sites were considered. VO1, VO2, and VO3 sites and VGa-tetra, VGa-tetra3, and VGa-oct sites as labeled in Fig. 2(a). For the VO2+ or VGa3- contained model, an additional +2 or −3 charge was added to maintain the total charge balance.
Fig. 2. (a) LGN crystal structure models for different defects and (b) electronic states of the stoichiometric LGN crystal with fixed crystallographic sites.
When vacancy defects were involved, new defect levels in the forbidden gap merged, considerably affecting the optical properties and LDTs of the LGN crystals. The electronic band structures of the stoichiometric LGN crystals and those containing vacancy defects were calculated, as illustrated in Figs. 2(b) and 3, respectively. The introduction of vacancy defects causes extra defect levels between the conduction and valence bands. According to the defect formation energies listed in Table 2, three types of oxygen vacancies can exist in the LGN crystals, but the gallium vacancies are difficult to form because of the large positive formation energies. Comparing Fig. 2(b) and Fig. 3(a), the introduction of oxygen vacancy defects leads to an enlargement of the intrinsic optical bandgap (from 3.37 eV to 3.67 eV) and induces defect levels concurrently at 2.51 eV.
Table 2. Defect formation energies
The formation of a defect energy level in the forbidden gap can induce extra absorption in the ultraviolet and visible regions. As illustrated in Fig. 4, oxygen vacancies such as VO12+ (2d), VO22+ (6g), and VO32+ (6g) in the LGN crystal can induce extra absorption in the ultraviolet and visible regions, which is consistent with the experimental results. When the oxygen vacancies captured two electrons to form F-centers, a wide absorption band in the visible region appeared, as illustrated in Fig. 1(b). In LGN crystals, a disordered substitution exists in the BO6 octahedrons. These vacancies are normally generated to maintain charge neutrality when an atom is replaced by another atom with a different valence. The replacement of Nb5+ and Ga3+ requires an additional oxygen vacancy to maintain charge balance. Thus, the absorption peak around 355 nm and 480 nm can be identified as oxygen vacancies and F-centers. Notably, the VO32+-constituting octahedron formed the most easily owing to the smallest defect formation energies, as represented in Table 2. The concentrations of the oxygen vacancies and F-centers have a degree of balance in the LGN crystals, which is related to the oxygen content of the environment [31].
3.2 Annealing in different atmospheres and temperatures
It is well known that thermal annealing is an effective method for improving the quality and properties of crystals [32]. When annealing in a vacuum and air atmosphere, the F-centers were destroyed by the removal of two electrons, causing Ga3+ to recover to Ga+ [33]. The destruction of F-centers weakens the absorption at approximately 480 nm, which explains the difference between the annealed and unannealed samples. Simultaneously, the oxygen vacancies can be partially compensated by the oxygen in the environment. First, we annealed LGN plates in vacuum and air atmospheres, labeled as samples II and III, respectively. As depicted in Fig. 5(a), the intensity of the absorption at 480 nm decreased to varying degrees after annealing. Unlike sample III, the transmittance of sample II decreased in the entire ultraviolet and visible regions. The ultraviolet cutoff edge of sample II shifted to a longer wavelength, and the ultraviolet cutoff edge of sample III moved to a shorter wavelength. Accordingly, the optical bandgaps of these two samples annealed in vacuum and air atmospheres were 4.07 eV and 4.15 eV, respectively, as illustrated in Fig. 5(b).
Thereafter, four (1000)-LGN plates were annealed in atmospheric air at different temperatures (500 °C, sample IV; 700 °C, sample III; 900 °C, sample V; 1100 °C, sample VI) to study the LDT dependencies of the LGN crystals further. As illustrated in Fig. 5(a), the intensities of absorption bands at approximately 480 nm change with the annealing temperature. The optical bandgaps were calculated using the transmittance, revealing slight differences between the samples, as illustrated in Fig. 5(b) (sample IV, 4.12 eV; sample III, 4.15 eV; sample V, 4.13 eV; sample VI, 4.13 eV). Moreover, the measured bandgaps are all larger than the calculated one using the GGA-PBE method, which is in accordance with the typical trend [34].
3.3 Linear absorption of LGN crystals
Free electrons are important precursors in avalanche ionization breakdown [35–37], where density is considered the damage criterion. Once it reaches a critical value of Ncrit, the intense absorption emerges and induces an irreversible damage [38]. The ratio of the number of electrons between the valence and conduction bands follows Boltzmann statistics [39], and it can be calculated as
where, Nv is the number of valence band electrons, Nc is the number of conduction band electrons, ΔE is the energy difference between the valence and conduction components at room temperature, k is the Boltzmann constant, and T is the temperature (T = 298.15 K in our calculations). As illustrated in Fig. 6, the normalized Nc values of samples I–VI were calculated by applying Eq. (1) and assuming the number of electrons in the valence band to be constant. Nc exhibits a negative relationship with the intrinsic optical bandgap; for example, the number of conduction band electrons of sample III is five times larger than that of sample I owing to the difference between their intrinsic optical bandgaps (sample III: 4.15 eV, sample I: 4.10 eV). Nc is the characteristic value of the linear absorption intensity, and the number of conduction band electrons has a negative relationship with the crystal LDTs [40].The linear absorption of samples was determined using PCI technology [41]. As illustrated in Fig. 7, the weak absorption value derived from the middle region of sample I was measured to be approximately 3600 ppm/cm, which is the highest value among all six samples. After thermal annealing, the weak absorption values of samples II-VI decreased to approximately 700, 1200, 2800, 1400, and 1500 ppm/cm, respectively. These reductions can be attributed to decreases in the concentrations of free electrons in the annealed samples.
Fig. 7. Weak absorption values at 1064 nm of the samples, where (a), (b), (c), (d), (e), and (f) correspond to samples I, II, III, IV, V, and VI, respectively.
3.4 Nonlinear absorption induced by defects
According to the transmission spectra in Fig.5a, changes in the absorption band at approximately 480 nm occur in different conditions. The electronic excitation of defects can be achieved by the two-photon absorption of the 1035 nm laser light. Open-aperture Z-scan measurements were performed to investigate the nonlinear absorption responsible for these changes. The nonlinear absorption results of the LGN samples at 1035 nm are illustrated in Fig. 8. In this case, the sharp valleys at the focus point clearly indicate the existence of nonlinear absorption, and the depth directly represents the absorption intensity. On the basis of the mechanism of the Z-scan technique, these findings confirm that the nonlinear absorption of the LGN crystals is reverse-saturable absorption. The dotted and solid lines represent the experimental data and fitting results, respectively. For an open aperture, the normalized transmittance formula is [42]
Fig. 8. TNL(z) curves of the LGN plates of samples I-VI. The points represent the experimental data, and the solid lines represent the fitting curves.
According to the absorption peaks in the transmittance spectra, some defect levels are located between the conduction and valence bands. As illustrated in Fig. 8, the two-photon nonlinear absorption (TPA) coefficients β of the annealed samples are much smaller than those of the unannealed samples. After thermal annealing, the F-center (VO2+ +2e) was thermally annihilated in the air atmosphere. The defect energy levels caused by the F-centers were also destroyed, decreasing the probability of the two-photon absorption. The smallest β was achieved in sample III among the samples annealed in the air atmosphere, which corresponds to the smallest absorption, approximately 480 nm. The two-photon nonlinear absorption coefficients of all samples are listed in Table 3. The free electrons produced by multiphoton ionization can also be used as seed electrons in the avalanche breakdown [35,36,43,44]. The smaller the two-photon absorption coefficients, the smaller the number of free electrons.
Table 3. TPA coefficients of different samples annealed in air and vacuum under different temperatures
3.5 Laser damage threshold and mechanism of the LGN crystals
The LDTs of LGN crystals were measured by an Nd: YAG laser with a 10 ns pulse width and 1 Hz repetition rate. Figure 9 illustrates the damage probability of the annealed LGN samples versus the power fluence. The LDTs of the LGN samples annealed at different temperatures are all improved to varying degrees. The LGN plate annealed at 700 °C exhibits the highest 0% LDT of 13.1 J/cm2 (1.31 GW/cm2). Accordingly, a temperature of 700 °C and the atmospheric air were determined to be the best annealing conditions for improving the LDTs. However, the LDT of sample II decreased to 10.2 J/cm2 owing to the worst optical quality, with a much larger rocking curve FWHM (44.8″) compared with that of sample I (28.9″).
In summary, the linear and nonlinear absorptions induced by defects play important roles in the laser damage processes of LGN crystals. The defect levels induced by the oxygen vacancies increase the number of free electrons, which increases the linear absorption of crystals. Simultaneously, the defect levels promote the occurrence of the TPA, increasing the initial free electrons for avalanche breakdown. The contributions of the two absorption types to the damage threshold changes with the laser power density. For a relatively low intensity, such as the 1 GW/cm2 intensity of the nanosecond laser system discussed in this paper, we found that the linear absorption accounts for a larger proportion of the total absorption, as summarized in Table 4. When a crystal is used in a higher intensity system, the nonlinear absorption plays a more important role in LDT reductions. The LDTs of commonly used mid-infrared NLO crystals under similar test conditions are summarized in Fig. 10, the LGN has the highest LDTs among all the crystals. Here we can see that the LDT of KTA crystal is comparable with that of LGN and the effective nonlinear coefficient deff of KTA (1.99 pm/V) is a little larger than LGN (1.54 pm/V) [13]. However, the KTA crystal is difficult to generate lasers beyond 5 µm due to its limited transparency (0.35-5.2 µm), which is not the case for LGN (0.28-7.4 µm) [45]. More importantly, the LGN exhibits smaller phase mismatch and thus larger gain bandwidth than KTA crystal. Thus, the LGN is considered to be a potential candidate for the nonlinear crystal of the mid-infrared OPCPA system.
Fig. 10. LDTs of commonly used mid-infrared NLO crystals. The LDTs were obtained with 10 ns pulses at 2.05 µm for the ZnGeP2 crystal and approximately 10 ns pulses at ∼1 µm for the other crystals. Most of the data were acquired from the work by Nikogosyan [45]. The data for CdSiP2 were reported by Schunemann et al [46]. and those for BaGa4Se7 and BaGa4S7 were reported by Yao et al. [47] and Ye et al. [48].
Table 4. Linear and nonlinear optical absorptions of sample I -VI
4. Conclusion
To the best of our knowledge, this study presents the first experimental and theoretical demonstration of the laser damage mechanism in LGN crystals. The effects of the defect levels on the band structure of the LGN crystals were revealed by first-principles calculations. The introduction of oxygen vacancies induced defect levels in the forbidden gap. The linear absorption in crystals caused by free electrons in the conduction band increased because of the introduction of oxygen vacancies and F-centers. The defect levels also led to the TPA, which could provide the initial electrons for further avalanche ionization. Compared to nonlinear absorption, linear absorption plays a more important role in nanosecond laser systems. After optimizing the annealing conditions, the 0% probability damage threshold was improved to 13.1 J/cm2 at an atmospheric-air temperature of 700 °C. The laser damage mechanism in LGN crystals can provide reference information for optical materials in high-intensity laser fields. In a mid-infrared OPCPA system, the higher the resistance of the LGN crystals to laser damage, the higher pump and power scaling they can support.
Funding
National Natural Science Foundation of China (51890863, 51902181, 52025021); National Key Research and Development Program of China (2021YFB3601504); Future Plans of Young Scholars at Shandong University.
Disclosures
The authors declare no competing financial interest.
Data availability
Data underlying the results presented in this review are not publicly available at this time but may be obtained from the authors upon reasonable request.
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