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Single point diamond turning (SPDT) currently is the leading finishing method for achieving ultra-smooth surface on brittle KH2PO4 crystal. In this work, the light intensification modulated by surface cracks introduced by SPDT cutting is numerically simulated using finite-difference time-domain algorithm. The results indicate that the light intensification caused by surface cracks is wavelength, crack geometry and position dependent. Under the irradiation of 355nm laser, lateral cracks on front surfaces and conical cracks on both front and rear surfaces can produce light intensification as high as hundreds of times, which is sufficient to trigger avalanche ionization and finally lower the laser damage resistance of crystal components. Furthermore, we experimentally tested the laser-induced damage thresholds (LIDTs) on both crack-free and flawed crystal surfaces. The results imply that brittle fracture with a series of surface cracks is the dominant source of laser damage initiation in crystal components. Due to the negative effect of surface cracks, the LIDT on KDP crystal surface could be sharply reduced from 7.85J/cm2 to 2.33J/cm2 (355nm, 6.4ns). In addition, the experiment of laser-induced damage growth is performed and the damage growth behavior agrees well with the simulation results of light intensification caused by surface cracks with increasing crack depths.
© 2014 Optical Society of America
1. Introduction
Owing to the unique nonlinear optical and electro-optical properties, potassium dihydrogen phosphate (KH2PO4, mostly known as KDP) has been extensively used in inertial confinement fusion (ICF) drivers such as NIF (National Ignition Facility, in US), LMJ (Laser MegaJoule, in France) and Shenguang Laser Facility (in China) [1–3]. In these ICF drivers, KDP boules are accurately cut from desired crystal angles to achieve Pockels cell switch crystals, second harmonic generation (SHG) crystals and third harmonic generation (THG) crystals [4, 5]. During the past decade, rapid growth technique has been successfully developed to efficiently produce large-size and high-quality crystal boules, which largely alleviated the challenge of high KDP optics demand in ICF. However, due to the weak mechanical and physical properties of KDP crystals (e.g., soft and brittle, extremely water soluble, thermally sensitive, prone to fracture and scratch [6]), the ICF projects are undergoing another challenge in volume production of large-aperture crystal optics with ultra-smooth surfaces [5].
Single point diamond turning (SPDT), also named diamond fly-cutting is considered to be the state-of-art for KDP crystal finishing to obtain ultra-smooth surfaces required in ICF laser systems. However, when exposed to intense lasers, SPDT finished crystals are susceptible to suffer from laser-induced damage, which may grow dramatically under the irradiation of following laser pulses [7–9]. And now, low laser-induced damage threshold (LIDT) of KDP optics remains a strong limitation in the development of high power laser systems [10]. Exploring the mechanisms of laser-induced damage has been an active field for nearly two decades, and till now two major underlying mechanisms have been commonly accepted: extrinsic mechanisms associated with pre-existing absorbing inclusions [11–14], and intrinsic ones based on electron ionization [12, 15, 16]. Under the stimulation of previous work, new techniques (e.g., laser conditioning [13, 17], thermal annealing [18, 19] and crystal-growth conditions controlling [20]) have been developed to increase the laser damage resistance of KDP crystals. However, the actually measured LIDT for KDP crystals is still much lower than the theoretically calculated value [15, 21], which results from insufficient consideration of the complex facts affecting laser damage resistance. Due to the weak mechanical and physical properties, it is prone to generate flaws (e.g., cracks and scratches) on finished KDP surfaces. Currently, surface parameters like surface roughness Ra and micro-waviness (power spectra density, PSD) [4] are mostly concerned for achieving high-precision surfaces on ICF optics. Nevertheless, the effect of surface-flaw-related parameter on laser damage resistance, which is unavoidable and critical, has rarely been well considered. Thus, taking a detailed investigation of the effect of surface cracks on laser-induced damage resistance of KDP crystal cannot only provide insights into further understanding of laser damage mechanisms, but also contribute to the comprehensive evaluation of the finished surfaces on optical components.
So far, some work have correlated laser damage resistance with surface defects originated from grinding and polishing for fused silica. The light intensification (square of electric field, |E|2) has always been employed in simulations to explain the effect of surface flaws on LIDT [22–25]. Previous studies have shown that the light intensification caused by surface cracks is only several times and someone debates that this is insufficient to launch an intrinsic optical breakdown [26]. However, latest research using more accurate simulation models shows that the light intensity can be enhanced by several hundreds of times with the presence of some specific kinds of surface defects, which may definitely trigger optical breakdown [26, 27]. Besides, the localized light intensification caused by surface cracks can also result in local energy deposition, which is physically associated with both the extrinsic and intrinsic mechanisms of laser-induced damage. On the other hand, micro-indentation and laser damage test have been applied to experimentally figure out the leading factor lowering the LIDT of flawed optical surface [28].
In this work, surface cracks on SPDT finished KDP surfaces are characterized by atomic force microscope (AFM). Then, the models of three typical kinds of surface cracks (lateral, radial and conical cracks) are employed to numerically simulate the crack-induced light intensification by using finite-difference time-domain (FDTD) algorithm. The dependence of light intensification on laser wavelength, crack position and geometry are discussed in detail, respectively. Further, the surface cracks on KDP crystals are classified according to the magnitude of crack-induced light intensification, which can be applied to evaluate the surface quality of finished crystal optics. Finally, a combination of micro-indentation and laser damage testing are presented to experimentally verify the effect of surface cracks on laser damage resistance. The experimental results are well consistent with the simulation results and some potential mechanisms for laser-induced damage and its growth have been proposed.
2. Surface cracks on diamond flycut KDP crystal and simulation models
When SPDT works, the diamond tool firmly embedded at the edge of a large plate spins following the rotation of the spindle and the raw KDP surface is cut steadily as the sample feeds horizontally [21]. The process of SPDT flycutting and magnified view of diamond tool are shown in Fig. 1(a). As mentioned above, the weak mechanical and physical properties of KDP crystal make it prone to bring in cracks and scratches on the finished surface. From the tested AFM results in Figs. 1(b) and 1(c), an evident crack is created on the finely finished surface. However, the surface roughness Ra is shown to be roughly 15nm, which is almost at the same order of magnitude of surface quality required by ICF laser systems [4, 5]. Thus, it is of great practical importance to investigate the effect of surface cracks on laser damage resistance for KDP crystals. According to a large amount of testing results on the finished KDP surfaces, it is shown that the generated cracks are tens of nanometers to several micrometers in dimension, based on which several crack models are built for the following FDTD simulations. It should be noted that this work focuses on the surface cracks arising from brittle fracture, which are different from shallow scratches introduced by diamond cutter marks as shown in Fig. 1(b).
Fig. 1 (a) Cutting process of KDP crystal finished by SPDT with a diamond tool. The inset is a magnified view of the tool tip. (b) The finished surface characterized with AFM. An evident crack is introduced on the KDP surface, though surface roughness Ra is about 15nm. (c) AFM section profile of KDP surface with crack. (d) Schematic of three typical kinds of cracks caused by static indentation and crack models used for the following simulations.
Similar to the surface cracks on fused silica processed by polishing and grinding, the crack formation on KDP crystal can be also approximately equivalent to the process of repeated indentation of mechanically loaded hard indenter (diamond tip) on crystal surface during flycutting [28, 29]. According to the distribution of localized stress field, the cracks can be typically classified into three types (radial, lateral and conical cracks [30]) as shown in Fig. 1(d). Radial and lateral cracks are generally created from a sharp indenter, which is often the case for sharp diamond tools. As shown in Fig. 1(d), radial cracks are planar cracks perpendicular to the surface and initiated during loading process [25]. While, lateral cracks travel mostly parallel to the surface and finally arrive at the surface to balance the internal stress during unloading process. Conical cracks are cone cracks caused by blunt indenter [29]. Sometimes, as sharp diamond tool softens due to cutting heat, the tool tip may wear and become blunt with a large edge radius as shown in Fig. 1(d). The models of these three types of cracks including their respective geometrical parameters are demonstrated in Fig. 1(d) for the following FDTD simulations.
As stated above, light intensity enhancement caused by surface cracks is a crucial factor initiating laser-induced damage on optical materials. The crack-induced light intensification is simulated by numerically solving Maxwell equations with FDTD algorithm to theoretically investigate the effect of surface cracks on laser damage resistance of KDP crystals [31, 32]. The FDTD simulations and the optical parameters for KDP crystal are described in detail in [31]. Since LIDT is wavelength dependent [15, 33] and laser-induced damage on front and rear surfaces behave differently [7, 9], the effects of crack position (on the front or rear surface) and laser wavelength are both considered. The crack-induced light intensification on Pockels cell switch, SHG and THG crystals are investigated respectively through specific combinations of crack position and laser wavelength (1064nm, 532nm and 355nm). To guarantee the calculation accuracy and reduce numerical dispersion in FDTD algorithm, the grid sizes are set to be less than λ/12 among all the simulations [31]. Further, the variations of light intensification with respect to geometrical parameters of cracks are also exhibited in detail and explanations for such behaviors are given respectively.
3. Simulation results and discussions
The light intensifications caused by surface cracks are analyzed to theoretically investigate their effect on laser damage resistance of KDP crystal. Light intensity enhancement factor (LIEF) is introduced to quantitatively characterize the localized light intensification caused by surface cracks [25, 28, 31]. In this work, the light intensity inside defect-free crystal is calculated first, and the LIEF is defined as the ratio between maximal light intensity enhancement caused by surface cracks and light intensity inside defect-free crystal. As shown in Fig. 1(d), front- and rear-surface cracks are realized by changing the propagation direction of the input wave. The light intensification under the irradiation of 1064nm, 532nm and 355nm lasers are simulated respectively to study the laser damage resistance of specifically applied KDP optics (Pockels cell switch and frequency converters). All the simulation results are eventually summarized to figure out which kind of cracks is the dominating factor that lowers down the capacity of laser damage resistance for SPDT finished crystal components.
3.1 Localized light intensification caused by radial cracks
The simulation model for radial cracks is shown in Fig. 1(d). As described above, radial crack is planar crack perpendicular to surface, so 2D FDTD simulation is sufficient to fully model the scenario of its induced light intensification. For simplicity sake, we use a plane incident wave with TE mode (polarized in y direction) and the initial amplitude is normalized to 1 V/m. Figure 2 shows the simulated distribution of light intensification caused by radial crack located on both front and rear surfaces. The crack is 6μm wide and 3μm deep and the wavelength of the incident wave is 355nm.
Fig. 2 Distribution of light intensification modulated by radial surface cracks with the irradiation of 355 nm laser. The radial cracks are 6μm wide and 3μm deep, located on front (a) and rear (b) surfaces.
From Fig. 2, it can be seen that the initial plane wave is largely modulated by the radial crack no matter where the crack is located. The profiles of light intensification and their underlying physics shown in Figs. 2(a) and 2(b) differ from each other. For the front-surface radial crack, the light intensification is generated through three physical mechanisms: diffraction originated from the intersection point of the crack wall and crystal surface, standing wave caused by reflected light inside the crack, and interference ripples between transmitted lights from both the crack walls and rear surface as indicated in Fig. 2(a). The standing wave and diffraction effects make dominant contribution to the maximum light intensification. The profile of diffraction ripples is very similar to that caused by front-surface particle, which is calculated by use of Fresnel diffraction theory [24]. The LIEF in Fig. 2(a) is only 3.32. While for rear-surface radial crack, though the profile of the intensified light is less complex, the LIEF is 14.47, which is more than 4 times larger than that caused by front-surface crack. This result provides an explanation to the reported experimental phenomenon that rear surface is more susceptible to suffer from laser-induced damage than front surface [25]. The much higher LIEF modulated by rear-surface crack can be attributed to the constructive interference between the incident wave and the totally reflected wave at the crack wall. The constructive interference results in a series of hot spots parallel to the rear surface as shown in Fig. 2(b). This is consistent with the reported light intensity distribution caused by rear-surface features on other optical materials [25, 28].
Figure 3 shows the variation of LIEFs with respect to the depth of front- and rear-surface radial cracks under the irradiation of 1064nm, 532nm and 355nm lasers. It is seen that for the three wavelengths, the LIEFs caused by rear-surface cracks are generally larger than those caused by front-surface cracks. With the increase of crack depth, the rear-surface crack induced LIEFs increase sharply first, then keep roughly stabilized and finally drop slightly. While for front-surface cracks, the LIEFs present a monotonic increase in the whole range of simulated crack depths. Different underlying physics should be responsible for the difference between front-and rear-surface cracks. For cracks on front surfaces, with the increase of crack depth, the incident angle increases and the amount of light reflected at the crack wall increases as well according to Fresnel’s reflection theory, resulting in the formation of stronger standing wave inside the crack as shown in Fig. 2(a). As a result, the localized LIEFs increase globally as a function of the crack depth. However, for cracks on rear surfaces, with the increase of depth, the propagating behavior of incident light experiences four stages: partially reflected at the crack shown in Fig. 3(b), totally reflected at the crack shown in Fig. 3(c), totally reflected at both crack wall and rear surface shown in Fig. 3(d), and totally reflected at the crack wall while partially reflected at rear surface as shown in Fig. 3(e). As discussed in [31], the occurrence of double total reflection can cause the largest light intensification for rear-surface cracks. Hence, the LIEFs caused by rear-surface crack with respect to the crack depth increases sharply first, and slightly decreases thereafter. It is also indicated in Fig. 3(a) that the crack-induced LIEF illuminated with 355nm laser is higher than those illuminated with 532nm and 1064nm lasers, especially for the rear-surface cracks. This is well consistent with the experimental results that terminal optics (running under 355nm laser irradiation) in ICF suffer from the most severe threat of laser damage susceptibility [15, 33].
Fig. 3 (a) Variation of LIEF as a function of depth for radial cracks located on front and rear surfaces. The wavelengths of 1064nm, 532nm and 355nm are all considered. The insets on the right are the distributions of light intensification modulated by rear-surface cracks with depths of 1.0μm (b), 3.0μm (c), 6.0μm (d) and 8.0μm (e). The crack width is constant at 6.0μm for the simulations.
The dependencies of LIEFs caused by radial cracks on crack width and angle are shown in Fig. 4. It is presented in Fig. 4(a) that with the increase of crack width, the variation of LIEFs caused by front- and rear-surface exhibits similar trend: the curves rise up first and then decrease gradually. Again, the mechanisms discussed above (standing wave for front-surface crack and total reflection for rear-surface crack) could be applied to account for the variation tendency. For front-surface when the crack width is large enough to generate a standing wave, the intensity of the reflected light decreases with the increase of crack width, resulting in the formation of weaker standing wave. And, for rear-surface the double total reflections can occur when the width of radial crack is in moderate size, ranging from 4.0μm to 8.0μm for crack depth of 4.0μm. To verify the role of total reflection in the rear-surface crack induced light intensification, the variation of LIEFs caused by oblique cracks with respect to crack angle are summarized in Fig. 4(b). Compared with Fig. 4(a), it is shown that the dependency of LIEF on crack angle exhibits the same tendency to the dependency of LIEF on crack width for rear-surface cracks. There is a peak around 30°, regardless of the laser wavelength in Fig. 4(b). This is because the occurrence of total reflection is primarily determined by the crack angle [25, 31, 34]. For all the three wavelengths, the condition for the occurrence of total reflections at both the crack wall and rear surface is: 21.1°<θr<45°, which has been discussed in details in previous work [31]. From the results above, it can be confirmed that the total reflections at the crack wall and surface are the intrinsic factor that determines the evolution of light intensification caused by rear-surface cracks with various geometrical parameters.
Fig. 4 (a) Plot of LIEFs with respect to width of radial cracks on both front and rear surfaces under the irradiation of 1064nm, 532nm and 355nm lasers. The crack depth is 4.0μm for the simulations. (b) Variation of LIEFs as a function of crack angle for oblique radial cracks on rear surface. The width and depth of the oblique crack are 1.0μm and 6.0μm, respectively.
According to all the simulation results in Figs. 3 and 4, for front- and rear-surface radial cracks, it is summarized that the LIEFs caused by rear-surface cracks are much larger than those caused by front-surface cracks, especially under the irradiation of 355nm laser. The light intensification caused by rear-surface radial cracks is as large as 20, while for front surface, it is only 5. Therefore the rear surfaces of THG crystal components undergo the worst laser damage resistance, when the effect of radial surface cracks is considered.
3.2 Localized light intensification caused by lateral cracks
In actual finishing process of KDP crystal, lateral cracks generally spread to the surface when they are brought in by sharp diamond tip. The formation of lateral cracks largely leads to material removal for brittle components [29]. The applied lateral model is sketched in Fig. 1(d). Due to the non-ignorable dimensions in all X, Y and Z directions for lateral cracks, FDTD simulations in this case must be performed using 3D algorithm to model the practical scenario as close as possible. Figure 5 depicts the light intensification profile modulated by lateral crack on front and rear surfaces. The parameters of the crack are: length 2al = 4μm, open width wl = 0.5μm and depth dl = 2μm, respectively. The wavelength of incident laser is 355nm.
Fig. 5 Distribution of light intensification by lateral cracks. The crack dimensions are: 2al = 4μm, wl = 0.5μm and dl = 2μm. The upper pictures are the cross-sectional profiles containing the maximum light intensification in Y (a), X (b) and Z (c) directions for front-surface cracks, while the lower pictures are the sectional profiles containing the maximum light intensification in Y (d), X (e) and Z (f) directions for rear-surface cracks.
By comparing the light intensification caused by front- and rear-surface lateral cracks in Fig. 5, it is found that the LIEF caused by front-surface crack is much larger than that caused by rear surface crack. The LIEF by rear-surface crack is 5.7, while the LIEF by front-surface crack is 43.0, which is almost 8 times higher. Such big difference arises from different mechanisms of the light intensification. For rear surface shown in Figs. 5(d-f), similar to the case of radial cracks, light intensity is mainly enhanced by totally reflected light in partial region of the crack wall close to the surface, which will result in constructive interference when interacting with the incident light. The enhanced ripples can be definitely found parallel to the crack wall as shown in the inset in Fig. 5(d). However, for front surface shown in Figs. 5(a-c), due to the specific geometry, the lateral crack acts like a concave lens [28], which will tightly focus the incident light to a limited volume, resulting in much stronger light intensification. The strongly focused hot spots are apparently presented along the axis of symmetry of the crack as shown in the inset of Fig. 5(a). It should be noted that the diffraction related enhancement ripples are also generated in Figs. 5(a)-5(c), though the enhancement is smaller than that caused by tight concentration of the input light.
The lateral cracks induced LIEFs as a function of crack open width is displayed in Fig. 6 with the irradiation of 1064nm, 532nm and 355nm lasers. The curves in Fig. 6 exhibit different variation tendencies for front- and rear-surface cracks. For the front surface, it is shown in Figs. 6(a)-6(c) that the LIEFs show a similar trend for all the three laser wavelengths. The LIEF gradually rises first and goes down when the open width reaches a certain value. This is because the diffraction effect caused by tiny crack should become weaker as the open width increases. As a result, the amount of incident light that can be tightly focused may increase, leading to the larger light intensification. However, when the crack size is so large that the diffraction effect can be ignored, the concaving profile of the lateral crack would become gentle and the focusing effect may be weakened, resulting in reduced LIEFs even the width increases.
Fig. 6 Variation of LIEFs caused by lateral cracks as a function of crack open width. The upper graphs are for the front-surface cracks under the irradiation of 1064nm (a), 532nm (b) and 355nm (c) lasers, while the lower graphs are for the rear-surface cracks under the irradiation of 1064nm (d), 532nm (e) and 355nm (f) lasers. In the simulations, the crack length is 2al = 4μm and the depths of 1μm, 2μm and 3μm are considered.
On the contrary, the trend for rear surfaces shown in Figs. 6(d)-6(f) is quite different. One sees that the LIEFs gradually ascend with the increasing crack open width. The diffraction effect plays an important role again. Since the depth of lateral cracks remains constant as the open width increases in the simulations, the total reflection determined by the geometry of the internal crack wall keeps unchanged either. Only the diffraction effect can affect the light intensification caused by lateral cracks with the increasing open widths. The diffraction effect should be weakened with the increase of open width, leading to the steadily increasing tendency of LIEF as shown in Figs. 6(d)-6(f). Unlike in the case of radial cracks, the light intensification caused by lateral cracks on front surfaces is always much higher than that caused by rear-surface cracks.
Figure 7 presents the variation of LIEFs with respect to the depth of both front- and rear-surface lateral cracks under the irradiation of 1064nm, 532nm and 355nm lasers. Again, the LIEFs caused by front-surface cracks are much larger than those caused by rear-surface cracks. The former also experiences more evident rise with the increase of crack depth, particularly for 355nm laser irradiation as shown in Fig. 7(a). For example, a small increase of crack depth from 1μm to 3μm results in a sharp increase of LIEF from 25 to 144 for front-surface crack irradiated with 355nm laser. According to Figs. 7(b) and 7(c), it is found that the more tightly focused regions with larger crack depths contribute to the sharp increase of LIEFs. However, the variation of LIEF caused by rear-surface crack presents no obvious change with the increase of crack depth. All the simulated LIEFs caused by rear-surface cracks are no higher than 20 as shown in Fig. 7(a).
Fig. 7 (a) Variation of LIEFs as a function of depth for lateral cracks on front and rear surfaces. The wavelengths of 1064nm, 532nm and 355nm are all considered. The insets on the right are the distribution of light intensification modulated by front-surface lateral cracks with depths of 1.0μm (b) and 3.0μm (c). The crack open width and length are wl = 0.5μm and 2al = 4μm.
To summarize, the LIEFs modulated by front-surface lateral cracks are generally much higher than those caused by cracks on rear surfaces. Besides, the light intensification is wavelength dependent and it is higher for shorter wavelengths. For instance, the LIEFs caused by the irradiation of 355nm and 532nm lasers are as high as 160 and 60, respectively, while for 1064nm laser irradiation, it is only 20. Thus, the front surfaces of THG crystal components (running under 532nm laser irradiation) undergo relatively lower laser damage resistance, when considering the effect of lateral surface cracks.
3.3 Localized light intensification caused by conical cracks
In practical SPDT finishing of KDP crystal, conical cracks are generally produced by blunt diamond tool, which is formed through the wear of the sharp cutting edge as shown in Fig. 1(d) [29]. Previous studies of laser-induced damage related to conical cracks mainly focus on polishing- or grinding-related surfaces for fused silica and phosphate glass [24–28]. In this part, we will show the influence of surface conical cracks on laser damage resistance of SPDT finished KDP crystals. The FDTD models for conical cracks are shown in Fig. 1(d) as well. Similar to lateral cracks, the simulations for conical cracks are based on 3D FDTD algorithm. In the simulations, the crack angle θc is set to be 30° in order to trigger the double total reflections at the crack wall and crystal surface [31]. The profiles of the enhanced light intensity caused by conical cracks on front- and rear-surface are demonstrated in Fig. 8. The dimensions of the conical crack are: length 2ac = 2μm, open width wc = 0.5μm and depth dc = 2μm. The wavelength of incident laser is 355nm.
Fig. 8 Distribution of light intensification caused by conical surface cracks. The dimensions of the crack are: 2ac = 2μm, wc = 0.5μm and dc = 2μm. The upper pictures are the cross-sectional profiles containing the maximum light intensification in Y (a) and Z (b) directions for front-surface cracks, while the lower pictures are the cross-sectional profiles containing the maximum light intensification in Y (c), and Z (d) directions for rear-surface cracks.
From the distribution of light intensity in Fig. 8, it is seen that the incident beams are both strongly concentrated to some small regions with the presence of conical cracks on front and rear surfaces. As shown in Figs. 8(a) and 8(b), the localized focal hot spots caused by front surface cracks arise from the constructive interference between transmitted lights at the internal crack walls. The internal walls of the crack act as a convex lens due to the lower refractive index of air inside, resulting in a region of hot spots inside crystal. The hot spots can be focused to several or tens of micrometers beneath the surface, which may explain the experimentally observed laser-induced bulk damage and the formation of filamentation inside crystal [2, 8]. For the rear-surface conical cracks, the hot spots are much more severe than those of front surface. The localized light intensity depicted in Figs. 8(c) and 8(d) is dramatically enhanced due to the double internal total reflections [25, 34], similar to the case of rear-surface radial cracks shown in Fig. 2(b). The difference between conical crack and radial crack on rear surfaces is that the internal shape of conical crack is closed. It can confine the totally reflected lights to interfere within a limited area. An array of hot spots indicated in red color is obviously presented parallel to the surface in the inset of Fig. 8(c). It should be noted that a series of diffraction ripples in Fig. 8 are also generated by the conical cracks though not so obvious when compared with the focused hot spots.
The variation of conical cracks induced LIEFs as a function of crack open width and depth are demonstrated in Figs. 9 and 10 under the irradiation of 1064nm, 532nm and 355nm lasers. From Fig. 9, it is shown that when the crack open width increases, the variations of LIEFs caused by front- and rear-surface cracks are very different. For the conical cracks on rear surfaces in Fig. 9(b), the LIEFs gradually increase first and then saturate after the width reaches a certain value. This trend comes from the evolution of light diffraction at different crack open width. When the crack width is small, strong diffraction would be initiated, resulting in less light reflections. As the open width increases, the diffraction becomes weaker and tends to saturate. Therefore the total reflection of the incident laser grows first and keeps stable to a certain extent. A firm proof of the above mechanism can be seen in Fig. 9(b). For all the three wavelengths, it is when the open width is slightly larger than the laser wavelength that the saturation begins. A main difference for the front surface is that besides the contribution of diffraction, the increase of open width would also lead to a higher amount of incident light travelling inside the crack as shown in the geometry of conical crack in Fig. 1(d), which will be concentrated by the convex crack wall. Therefore, the LIEFs exhibit a sharp increase with the increase of crack width as shown in Fig. 9(a).
Fig. 9 Variation curves of LIEFs as a function of open width for conical cracks located on both front (a) and rear (b) surfaces. During the variation of crack width, the other parameters keep constant at 2ac = 2μm and dc = 2μm.
Fig. 10 Variation curves of LIEFs as a function of depth for conical cracks located on both front (a) and rear (b) surfaces. During the variation of crack depth, the other parameters keep constant at 2ac = 2μm and wc = 0.5μm.
As displayed in Fig. 10(a), the evolution of LIEFs with respect to crack depth shows slight increase first and keeps almost unchanged afterward. This is because the localized hot spots caused by front-surface conical cracks are primarily determined by the open width, while the depth only affects the diffraction. In contrast to front surface, the LIEFs in Fig. 10(b) increase acutely at the beginning. For rear-surface conical cracks, as the crack depth increases, the amount of input light reaching the crack walls and being totally reflected will sharply increase, which results in the acute increase of LIEF. However, the LIEF will keep stable when the constructive interference between totally reflected lights is saturated finally.
From all the simulation results in Figs. 9 and 10, it is summarized that the LIEFs caused by both front- and rear-surface conical cracks are very large due to the tightly focusing of the incident light. The light intensification caused by front-surface conical cracks is mainly determined by crack open width. For 355nm laser irradiation, front-surface conical cracks with large open width can induce LIEF as high as 80. The light intensification caused by rear-surface conical cracks is much larger, which is more crack depth dependent. For 355nm laser irradiation, rear-surface conical cracks can generate LIEF as high as 500. Therefore, the surfaces (especially the rear surfaces) of THG crystals are always suffering from more susceptibility of laser-induced damage when the effect of conical surface cracks is considered.
3.4 Summary of simulation results: light amplification caused by surface cracks
The FDTD simulation results discussed above indicate that the LIEFs caused by various surface cracks are not only crack position and geometry dependent, but also laser wavelength dependent. To show it more clearly, the LIEFs caused by three typical kinds of surface cracks under illumination of 1064nm, 532nm and 355nm lasers are summarized in Table 1. For completeness, the downstream components behind THG crystal are also listed. The magnitude of light intensification required for potential laser-induced breakdown was approximately estimated by Feit et al. on the basis of avalanche-related laser damage mechanism [16, 26]. As estimated in [26], light intensity enhancement of more than 30 times is necessary to launch an avalanche for the typical laser intensity used in NIF (5GW/cm2 or less).
Table 1. Summary of all the LIEFs caused by three typical kinds of surface cracks on KDP crystals under the irradiation of 1064nm, 532nm and 355nm lasers
Considering the estimated light intensification for launching avalanche in [26], it is found in Table 1 that the laser damage resistance of SPDT finished KDP crystals can be evidently lowered by lateral cracks on front surface and conical cracks on both front and rear surfaces. The LIEFs caused by lateral and conical cracks are laser wavelength dependent that shorter wavelengths result in higher LIEFs. The LIEFs caused by rear-surface conical cracks are at the magnitude of hundreds of times and the LIEFs induced by front-surface lateral cracks can also reach more than 100 times for 355nm laser irradiation, which is more than sufficient to lower the laser damage resistance of KDP crystals. However, for light intensification caused by radial cracks, it is not high enough to produce intrinsic optical damage. One should keep in mind that the insufficient intensification may increase the absorption of particles hidden inside cracks, which is another mechanism for laser-induced damage [26]. On the other hand, the LIEFs caused by front-surface lateral cracks keep increasing with respect to crack depth as shown in Fig. 7 and the LIEFs caused by conical cracks keep rising with both crack depth and open width as shown in Figs. 9 and 10, which implies that the LIEFs caused by surface cracks could be certainly higher than those shown in Table 1 for actual KDP surfaces. Based on the discussions above, it can be summarized that: for conical cracks, the laser damage resistance can be negatively affected when they are located on both surfaces of THG crystals and the rear surfaces of Pockels cell switch and SHG crystals; While for lateral cracks, the laser damage resistance can be largely reduced only for the front surface of THG crystal. These results indicate that in order to reduce the negative effects of surface cracks, it is of great implication to control the population and geometrical dimensions of surface cracks in the actual application of KDP crystals. Recently, new techniques (e.g., laser conditioning [17] and micro-machining [31]) have been proposed and proven to be the promising methods to achieve crack closure or remove the surface defects for retrieving the damage resistance of KDP crystals. It is worth noting that though the LIEFs caused by front-surface lateral and conical cracks are not large enough as shown in Table 1, they can probably reach 30, when the crack dimensions become large enough as implied in Figs. 7(a) and 9(a). All the simulations above on light intensification caused by surface cracks cannot only provide potential mechanism explaining the lower laser damage threshold of actual KDP components, but also contribute to future comprehensive evaluation of SPDT finished KDP crystal surfaces.
4. Laser damage experiments on KDP crystal
The effect of surface cracks on laser damage resistance of KDP crystal is experimentally investigated by testing and comparing the laser damage thresholds of crack-free and flawed KDP surfaces. Micro-indentation is an effective method to study the process of crack formation on brittle materials [6, 27, 29]. And in this work, it is applied to produce flawed KDP surfaces with plastic indentation or brittle fracture, which consists of surface cracks. The setup used to test the LIDTs of KDP surface is sketched in Fig. 11. In this setup, an Nd:YAG SAGA laser is employed and runs steadily at 355nm wavelength, 10Hz repetition rate and 6.4ns pulse duration. The pump laser is highly focused on the front surface of KDP samples, which is mounted at the electrically controlled stage. Meanwhile, the change of surface morphology after each laser pulse irradiation is detected in situ using a CCD camera. Other experiment parameters and the testing procedure applied in our experiments can be found in detail in [31]. In summary, an R-on-1 test is performed on 10 sites with pulse fluence ramping up until damage occurs. The LIDT is defined as average value of the lowest fluences triggering laser damage for all tested sites. The occurrence of laser damage is online detected by CCD device and double checked with optical microscope afterwards. The 355nm laser is considered in the experiment, since surface cracks produce the largest light intensification at this wavelength according to the simulation results above.
The tested damage thresholds for crack-free and mechanically cracked KDP surfaces are presented in Fig. 12. For flawed surfaces, KDP samples with plastic and brittle indentations are both tested to figure out the dominant factor lowering the actual laser damage resistance of crystal components. It is shown that the LIDT of crystal surface with plastic indentation is 6.54J/cm2, which is slightly lower compared to that of crack-free surface. However, for the surfaces with brittle indentations, the LIDTs are greatly reduced to 2.33J/cm2 and 2.27 J/cm2, which are about only a third of the LIDT for initial crack-free surface. The surfaces with brittle indentation before and after laser irradiation are shown in Figs. 12(b) and 12(c). A load of 400mN is applied to create brittle indentation. Besides plastic deformation, a fracture area containing a series of cracks is chiseled on KDP crystal surface as shown in Fig. 12(b). The mechanically generated open cracks on the flawed surface are several micrometers wide and hundreds of nanometers deep, which are consistent with the scales of numerically simulated surface cracks. As to the cracks beneath the flawed surface, new techniques need to be developed for accurately measuring their geometrical information in the future. After the irradiation of 355nm laser with 2.40J/cm2, the indentation site becomes severely damaged as shown in Fig. 12(c). While for cracked indentation with lower load, only pure plastic deformation is generated on the surface and the LIDT is not so dramatically decreased. This result implies that brittle fracture with cracks rather than pure plastic deformation is the dominant factor decreasing the laser damage resistance for finished KDP crystal. This is well consistent with the experimental results for fused silica components [27].
Fig. 12 Experimentally tested LIDTs for crack-free and flawed KDP surfaces (a) and the morphologies of mechanically produced indentations on KDP surface before (b) and after (c) 355nm laser irradiation.
Some of the simulation results discussed above can be further verified by the experiments of laser-induced damage growth. Figure 13 shows the growing variation of laser damage size with the increase of laser pulses and the variation of LIEFs caused by front-surface lateral cracks with the increase of crack depth. It is exhibited in Fig. 13(a) that once the damage is launched, its size grows exponentially when the number of laser pulses increases. Similar behavior has been observed experimentally for surface damage on fused silica. It is known that following the increase of pulse numbers, crack depth would increase monotonically as the damage aggravates. Thus, the crack depth shows a positive correlation with the number of laser pulses. Assuming the cracks should be responsible for the growth of laser damage, one can expect the evolution of damage size with respect to pulse number to be characterized by the variation of LIEFs with regard to crack depth in the simulations. Indeed, the simulation results indicate that the evolution of LIEFs as a function of crack depth depicted in Fig. 13(b) presents an exponential tendency, which agrees well with the experimentally observed damage growth behavior as shown in Fig. 13(a). This theoretically validates that the surface cracks should be mainly responsible for the growth of damage sites under subsequent laser shots. Additionally, laser conditioning has been experimentally proven to be an effective action to achieve crack closure (decreasing the crack width) on optical surfaces for enhancing the laser damage resistance [27]. The simulation results shown in Figs. 4, 6 and 9 demonstrate that the decreasing of crack width actually leads to the reduction of light intensification caused by surface cracks. Based on this, the light intensification caused by cracks with respect to crack width can provide potential underlying mechanism for laser conditioning strategy.
Fig. 13 Experimentally obtained evolution of damage size as the increase of laser pulse number (a) and numerically simulated variation of LIEFs as a function of lateral crack depth (b). The depth of a damage spot increases monotonically with the increase of pulse number.
5. Conclusion
Using AFM tested crack information on SPDT finished KDP surface, the light intensifications caused by three typical kinds of surface cracks (radial, lateral and conical cracks) are investigated by employing 2D and 3D FDTD algorithms. Light intensifications modulated by surface cracks exhibit wavelength, crack geometry, and position dependent. Lateral cracks on front surfaces and conical cracks on both surfaces can produce light intensification as high as hundreds of times, which is sufficient to launch an avalanche ionization reducing the laser damage resistance of KDP crystals. Various underlying mechanisms like total internal reflections, diffraction and standing wave effects are successfully proposed to explain the light intensification induced by surface cracks and its variation with respect to crack geometrical parameters. By conducting laser damage experiments for various KDP samples (crack-free or flawed surfaces), it is found that brittle fracture with a series of surface cracks is the dominant source lowering the laser damage threshold of KDP crystal, which is consistent with the simulation results. The LIDT (355nm, 6.4ns) on flawed KDP surfaces could be reduced to nearly one third of that on crack-free surfaces by the negative effect of surface cracks. What’s more, the experimentally obtained incremental variation of laser damage size with the increase of pulse numbers agrees well with the numerically simulated variation of light intensification caused by surface cracks with the increase of crack depth. The light intensity enhancement modulated by surface cracks can be expected to provide potential insights into understanding the mechanisms of laser-induced damage growth and laser conditioning for improving laser damage resistance of KDP crystal components.
Acknowledgment
The authors gratefully acknowledge the National Natural Science Foundation of China (Grant No. 51275113) and the National Science and Technology Major Project of China (Grant No. 2013ZX04006011-215) for their financial support of this work.
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