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Abstract
Pinpoint damage is the main type of bulk damage in potassium dihydrogen phosphate (KDP) crystals in high-power lasers. Using time-resolved microimaging, we observed the complete dynamic evolution of pinpoint damage in a KDP crystal. We analyzed changes in the patterns of dark zones formed by decreasing probe transmittance in transient images throughout the process. The mechanical properties of stress waves in KDP crystals were further studied by a depolarized shadowgraph experiment and theoretical simulation. The dynamic evolution of mechanical stress waves was observed, and the correlation between mechanical failure due to stress waves and the static characteristic damage morphology was established.
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1. Introduction
Potassium dihydrogen phosphate (KH2PO4, KDP), which has a large electro-optic coefficient and a nonlinear optical coefficient, exhibits good transmission in a wide spectral range and is easily grown to large diameters. KDP is the most commonly used material for electro-optical switching and frequency doubling in high-power solid-state laser devices [1,2]. However, it is brittle and has low toughness, and its melting and boiling points are much lower than those of other optical materials such as fused silica and K9 glass. Bulk damage easily occurs under laser irradiation, causing absorption and scattering of the laser at damage points, and even modulation of local light fields, which can damage downstream components [3]. The KDP crystal is the weakest link in the optical path of high-power solid-state laser devices and greatly limits their load capacity.
Laser-induced damage to KDP crystals is a complex phenomenon involving multiple coupled physical processes. The damage mechanism is not yet thoroughly understood [4–6]. KDP crystals are anisotropic, and the bulk damage morphology is related to the orientation of the observed plane [7,8]. Many studies have shown that under irradiation by a laser with a higher laser fluence than the threshold of the KDP crystal, bulk damage appears as a large number of pinpoint damage sites distributed along the laser irradiation direction. The sites are on the order of several microns to hundreds of microns in size and have characteristic directions. The pinpoint damage density increases exponentially with laser fluence [9,10]. The size of a single pinpoint damage site increases with laser pulse width [11]. The bulk damage threshold depends strongly on the wavelength and polarization of the irradiated laser [7,12]. The size and density of the pinpoint damage sites do not increase significantly with multiple episodes of laser irradiation [13–16]. However, laser-induced damage occurs by multiple transient processes on the order of nanoseconds. Current studies have focused on analyzing the static morphology and pinpoint damage distribution in KDP crystals, which are not sufficient to describe the development of laser-induced damage and the response of the material in the multiscale dynamic time domain.
According to the higher single photon energy, ultraviolet laser pulse causes more serious laser-induced damage to KDP crystal, nonlinear elements, under engineering conditions. In this study, by an ultraviolet laser pulse to approach to the real engineering conditions, we used time-resolved microimaging to capture the response of KDP crystals at various times after irradiation and determined the complete evolution mechanism of the pinpoint damage. Simultaneously, using a depolarized shadowgraph experiment and theoretical simulation, we observed orthogonal patterns of ellipsoidal mechanical stress waves on the xOy plane during damage evolution and identified a correlation between the directions of microcracks at pinpoint damage sites and the maximum tensile stress. These results focused on the thermal and mechanical response can provide research support for understanding the damage mechanism of KDP crystals and revealing its physical nature.
2. Experimental methods
Figure 1 shows the time-resolved pump–probe system. A Q-switched Nd:YAG laser with multi-longitudinal mode is used as the pump to induce laser damage. The operating wavelength is 355 nm after frequency conversion, and the full width at half-maximum (FWHM) is approximately 12 ns with a Gaussian profile. After focusing by a lens with a focal length f of 150 mm, the beam diameter at the rear surface of the KDP sample is approximately 700 μm. The laser fluence is set to 26 J/cm2 in the time-resolved microimaging experiment, which is higher than the threshold of the laser-induced damage and less than the fluence of the self-focusing and the threshold of the intrinsic damage. A charge-coupled device (CCD1) and energy meter (EM) are used to monitor the focused beam profile and energy in real time.
Fig. 1. Schematic diagram of time-resolved microimaging system. HWP: half-wave plate, PBS: polarization beam splitter, QWP: quarter-wave plate, FL: focusing lens, HR: reflector, NBF: narrow-band filter, MS: microscope, EM: energy meter, BS: beam splitter.
Another Q-switched Nd:YAG laser is used as the pump to induce stimulated Brillouin scattering (SBS) [17] in a liquid cell with a length of 60 cm. The operating wavelength is 532 nm after frequency conversion, and the FWHM is approximately 8 ns with a Gaussian profile. Induced Stokes light with a FWHM approximately of 800 ps is obtained by SBS pulse compression technology and used as the probe in the experimental system, in order to improve the time resolution of the pump–probe system. The compression structure is shown in the dotted box in Fig. 1. The turn-back structure [18] can increase the interaction distance between the Stokes light and the pump and improve the pulse compression ratio. The SBS active medium, FC-40, has a short phonon life and high damage threshold, which contribute to pulse compression.
After polarization beam splitting, optical path delay, and polarization beam combination, a sequential dual-probe detection system is used, and the time interval between the double probes, which is recorded as Δτ, is set to 3.8 ns. In an independent damage event, two side-view transient images can be obtained. In order to eliminate birefringence, the probe passes along the optical axis of a z-cut KDP sample with dimensions of 3 cm × 1 cm × 1 cm. The magnification of the microscope is 20×, and the maximum static spatial resolution is 1 μm. As shown in Fig. 1, the delay between the probe peak and the damage-inducing pump peak is controlled by a digital delay generator and recorded as τ (jitter less than 200 ps) by an oscilloscope (not shown in the figure). In addition, because of the photoelastic effect [19] in the transparent optical material, the polarization probe is partially depolarized as it passes through the stress region; thus, it detects the stress in the sample and improves the observation of the dynamic damage process.
3. Experimental results and discussion
3.1 Dynamic development of bulk damage in KDP crystal
Bulk damage in the KDP crystal (Fig. 2) appears as a large number of pinpoint damage sites along the laser transmission direction. Microscopic observation [7,16,20–22] reveals that the typical morphology of pinpoint damage in the KDP crystal is a core with a dense periphery, which is characteristic of impact sites, and a monoclinic crack extending around the core. As indicated by arrows, the cracks have two characteristic directions perpendicular to each other, with angles of approximately 45° relative to the horizontal direction.
Figure 3 shows transient shadowgraphs of the development of bulk damage in the KDP crystal during the rising edge of the pump. The pump–probe delay is marked in each image, and the pump passes through the sample from left to right. As shown in Fig. 3(a1), at τ = −10.4 ns, laser energy is deposited at damage precursors. The absorption regions (circular dark zones in the transient image) are observed after the pump reaches about a few hundreds of picoseconds [23], which are then ionized to form plasma clusters. Figure 4(a) shows the unit cell structure of a KDP crystal, which has three main types of chemical bonds [24–26]. The first two types are K–O ionic bonds called α and β bonds, which are formed by the PO4 tetrahedron and adjacent K+ with different bond lengths and angles. The third type of chemical bond, H(O)···O, is a type of hydrogen bond called a γ bond, which is weaker and connects PO4 tetrahedrons. As shown in Fig. 4(b), the H and O atoms in the hydrogen bond are not in the same plane, but in a relative equilibrium position approximately perpendicular to the z axis. In addition, absorption defects and impurities in the KDP crystal further decrease the damage threshold [27,28] and become damage precursors at which laser energy is deposited during irradiation by the pump.
Fig. 3. Time-resolved shadowgraphs of bulk damage in KDP crystal during rising edge of pump. The timeline indicates the time of the transient image, and subscripts 1 and 2 indicate transient images captured by the probe in the same damage event.
At τ = −6.6 ns, as indicated by the arrows in Fig. 3(a2), subsequent pump energy is deposited in the plasma clusters, which explode sequentially, forming orthogonal elliptical dark zones. The time between energy deposition and plasma explosion is several nanoseconds. The explosion of plasma clusters causes stress waves in bulk materials. The polarization probe is depolarized as it passes through the stressed region and forms the dark zones. The material structure directly determines the stress wave pattern. The KDP crystal is tetragonal with centrosymmetry in the xOy plane, and the stress waves form a specific pattern. The introduction and analysis in detailed for stress wave will be given in Section 3.2.
As shown in Fig. 5, from τ = −1.7 ns to τ = 12.5 ns, when the crystal is still irradiated by the pump, the damage sites not only receive additional laser energy, but also exhibit typical mechanical failure behavior. The transient process can be described as follows. With the development of the orthogonal elliptical dark zones indicating stress waves after the plasma clusters explode, the damage sites crack and form narrow dark zones with tapered ends; their central axes have angles of 45° with respect to the horizontal direction. Transient images taken at various times in this stage show different dark zone patterns. As indicated by the arrow in Fig. 5(a1), at τ = −1.7 ns, the dark zones representing stress waves are small in scale and replace the central tapered dark zones formed by cracking at damage sites. Macroscopic transient images show patterns of orthogonal elliptical dark zones. As indicated by the arrow in Fig. 5(b1), the stress waves spread, and the damage sites undergo further cracking; thus, the dark zones exhibit both stress waves and tapered patterns. As indicated by the arrow in Fig. 5(c1), the stress waves spread further, and the corresponding gray values increase in the shadowgraphs; consequently, brighter dark zones that are more similar to the background are formed. When pumping almost stops, most of the dark zones are narrow with tapered ends.
Figure 6 shows transient shadowgraphs of bulk damage in the KDP crystal after pumping stops. The transient dark zones are narrow and tapered at each end, and the dark zones formed by stress waves almost disappear in the transient images. The bulk damage continues to develop after pumping ends. As shown in Fig. 6(a1)–(a3), the tapered dark zones continue to crack along the central axes for approximately 10 ns after the termination of pumping under the experimental laser fluence. At τ = 25 ns [Fig. 6(b1) –(b3)], the dimensions along the cracking direction are the same in the transient and static images, meaning near the termination of the cracking. In addition, combined with Fig. 5, the tapered dark zones appear to be supported by laser irradiation. The widths of the tapered dark zones, that is, their vertical central axes, continue to increase during pumping, and the values are much larger than those in the static images. While, as shown in damage events (a) and (b), the widths of the tapered dark zones essentially stop increasing after pumping stops. Further, the dark zones gradually come into contract, as shown in damage events (c) and (d). According to the static morphology of pinpoint damage [16], which has a central core and a specific monoclinic crack, the contracting dark zones leading to larger transient scale in the shadowgraphs did not cause substantial damage. Thus, during pumping, the local material around the damage sites was under high-pressure or high-temperature conditions [29,30] that were not sufficient to cause damage but instead absorbed the probe energy and increased the width of the tapered dark zones. After pumping stops, the material gradually recovered from this abnormal state and returned to the initial state of high probe transmittance, causing the dark zones in the shadowgraphs to contract correspondingly. The entire cooling rebound process was relatively long, and the relaxation time was on the order of a few hundreds of nanoseconds or more. The results are consistent with experimental measurements in Ref. 30.
Fig. 6. Time-resolved shadowgraphs of bulk damage in KDP crystal after pumping stops. Static shadowgraphs of a damage event are indicated by a subscript 3.
3.2 Stress waves in KDP crystal
As shown in Fig. 1 (Section 2), depolarized shadowgraphs with a dark background and bright stress waves were obtained by CCD2 by blocking the s-polarized probe to observe the dynamic changes in the stress waves in the KDP crystal. Figure 7 shows the transient development of the stress waves induced by bulk damage in the KDP crystal. The stress waves form orthogonal patterns of ellipsoids. Note that stress parallel or perpendicular to the probe does not cause a photoelastic effect; consequently, four dark zones appear at the ends of the long axes of the ellipsoids, as indicated by the arrow in Fig. 7(a). In addition, as shown in Fig. 7 (a)-(c), The serious phase transformation around damage sites reduces the resolution of the stress waves profiles under pumping. In the same damage event, stress waves are basically the same in scale and expand gradually with time, which are consistent with Ref. 29. In each damage event, the average value of multiple stress envelopes is calculated to reduce error. Figure 8 shows the relationship between the length of the long axis of the elliptical stress waves and the delay in the KDP crystal under different laser fluences. The stress waves induced by bulk damage in the KDP crystal exhibit the same linear development trend under different laser fluences. The slope, 4.5 km/s, indicates the propagation velocity, and the horizontal axis intercept, −6.31 ns, represents the delay in stress wave development induced by plasma cluster explosions. This result is consistent with the feature indicated by arrows in Fig. 3(a2), which is the first dynamic observation of the orthogonal elliptical dark zones.
Fig. 7. Time-resolved depolarized shadowgraphs of stress waves induced by bulk damage in KDP crystal, where (a)–(h) show different damage events.
Fig. 8. Length of long axes of elliptical stress waves induced by bulk damage in KDP crystal under different laser fluences and time delays.
The main factor producing the characteristic final morphology during the formation of pinpoint damage has not been fully determined. Some researchers believe that when damage precursors composed of crystal growth defects and embedded impurities absorb the laser energy, the crystal freely releases stress along the direction of its weakest chemical bonds, cracking and forming microcracks [7,16]. Despite the random locations of damage precursors in the KDP crystal, the behavior of different damage precursors in the images we captured exhibits the same characteristics. In addition, the bond angles on the xOy plane in Fig. 4(b) are not oriented along the cracks in the static images. This calls into question the suggestion that cracking occurs along chemical bonds. Crack formation still needs to be explored in terms of the dynamic behavior and essential properties of pinpoint damage.
Figure 9 shows the results of a simulation of the stress in the KDP crystal using finite element software. The elastic constants of the crystal are listed in Table 1 [31]. The stress wave pattern on the xOy plane in Fig. 9(a) is consistent with the orthogonal ellipses observed experimentally, which arise from the symmetry of the KDP crystal. In addition, the stress is concentrated at the load source. Figure 9(b) shows the corresponding tensile stress distribution results, where the directions of tensile stress are marked by arrows. The strongest tensile stress appears at angles of 45° with respect to the horizontal; this result is consistent with the crack directions in the pinpoint damage.
Fig. 9. Simulation results of KDP crystal on the xOy plane at 30 ns. (a) Stress distribution, (b) tensile stress distribution.
Table 1. Elastic Constants of KDP Crystal [31]
According to the transient images and simulation results, pinpoint damage in a KDP crystal occurs in three stages. First, damage precursors, such as absorbent defects, impurities, or hydrogen bonds with low bond strength, absorb laser energy. This is an ultrafast process, and superheated material is formed after the pump reaches about a few hundreds of picoseconds. With increasing temperature, damage sites are ablated and form cores because of the low melting point of KDP crystals (252.6℃). Then plasma clusters formed by the ionization of the damage sites explode, causing mechanical stress waves in the bulk material. The interval between the times of the observation of the absorption regions and stress waves is about 4 ns in the experiment. Compared to the results in Ref. 23, the interval is related to the laser fluence of the pump. The stress effects the material at the periphery of the cores, forming dense layers. On the xOy plane, the stress wave form patterns of orthogonal ellipsoids. Finally, the stress is concentrated at the ablation cores, resulting in a strong tensile stress on the centers, and the maximum tensile stress occurs at angles of 45° with respect to the horizontal direction. KDP is a brittle material, and KDP crystals have low fracture toughness [32]. The KDP crystal fractures in these directions to form monoclinic or biclinic cracks and forms a characteristic pinpoint damage morphology. In the experiment, the mechanical cracking of pinpoint damages lasted for more than 20 ns. In addition, the intensity and duration of the stress waves are positively correlated with the fluence and width of the irradiated laser, in good agreement with the relationship between the pinpoint damage and irradiated laser parameters. Compared to fused silica, another common ultraviolet optical element in high-power solid-state laser devices, the dynamic response behaviors of laser-induced damage are basically the same. However, according to different material thermodynamic strength, the response time and the damage degree are different. Fused silica is isotropic; consequently, stress waves form circle patterns in bulk material, and mechanical cracks do not have characteristic directions.
4. Conclusion
Using SBS pulse compression to obtain a subnanosecond probe and time-resolved microimaging technology, we captured transient shadowgraphs at various stages during the irradiation of a KDP crystal by a Gaussian laser pulse with a typical electro-optic Q-switched width. The results revealed the complete dynamic evolution of pinpoint damage in the KDP crystal. According to the response and characteristics of the material at different stages, the dynamic evolution of the KDP crystal was divided into three processes: energy deposition, mechanical cracking, and dynamic rebound. A depolarized shadowgraph experiment and theoretical simulation demonstrated the presence of mechanical stress waves appearing as orthogonal ellipsoids during the dynamic evolution and established a correlation between the mechanical failure generated by the stress waves and the static damage morphology. The stress wave pattern is related to the symmetry of the KDP crystal. The tensile stress focused at damage site centers further affects the material, resulting in cracking along the directions of the maximum tensile stress in the KDP crystal and forming monoclinic or biclinic cracks. The existing subnanosecond probe limited the dynamic resolution of the system, and a shorter pulse will be considered to be used to quantify the dynamic response of KDP crystal. In addition, Further study will be focused on measuring dynamic behavior on other observed plane and the stress wave intensity to improve the pinpoint damage mechanism of KDP crystal.
Funding
National Natural Science Foundation of China (61905052).
Disclosures
The authors have no conflicts to disclose.
Data availability
Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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