3.1 Experimental results

The damage probabilities of HR coatings without and with LSPP are shown in Figure 2, which evidently showed a decrease in damage probability and an increase in damage threshold for coatings that had undergone LSPP with appropriate process parameters. When the overlapping rate was 30%, as shown in Figure 2(a), the laser-induced damage resistance of HR coatings was increasingly enhanced with processed laser energy which varied from 0.4 to 0.6 J. When the laser energy was at the maximum 0.6 J, the laser-induced damage threshold (LIDT) had increased to 27.8 J/cm² and the maximum damage probability decreased to only 30% at 74.9 J/cm². When the overlapping rate was improved to 50% as shown in Figure 2(b), although the laser-induced damage resistance had always been improved as the processed laser energy in the range of 0.2–0.4 J, the LIDT and the damage probability began to decrease and increase with laser energy, respectively. When the laser energy was of the minimum 0.2 J, the LIDT had achieved the maximum value of 36.7 J/cm², and the maximum damage probability also decreased to about 30% at 76.5 J/cm². Compared with the coatings without LSPP which had a low LIDT of 8 J/cm², the reason for the enhancement of laser damage resistance after LSPP was possibly because of the comprehensive modification of the intrinsic defects and the mechanical properties which made defects less susceptible to excitation.

Figure 2 The one-on-one damage probabilities of coatings without and with LSPP at overlapping rates of (a) 30% and (b) 50%.

3.2 Microstructures and microcharacteristics

As the XRD pattern shown in Figures 3(a) and 3(b), though no new phase was generated after LSPP, the peaks were broadened and shifted (such as the example of the (020) peak shown in Figures 3(c) and 3(d)). According to the full width at half maximum (FWHM) and diffraction angle obtained by fitting of XRD line profiles with the Pearson VII function^[Reference Yella, Venkateswarlu, Buddu, Ravi, Rao, Kiran and Rajulapati^20], the microstress was acquired by the Williamson–Hall plots method^[21–23], as shown in Figure 4. The microstress in the figure was negative, indicating that the stress direction was perpendicular to the surface and downward, which illustrated that the existing microstress was in the form of compressive stress. As the inherent stress in the coatings was very small and tended towards zero, the microstress herein could be considered as the value of the residual stress. It was clear the residual stress of coatings with LSPP of reasonable parameters exhibited considerable increment, as shown by the dotted line in Figure 4, which indicated the enhancement of mechanical properties such as bonding force between interfaces. The microstress soon reached an extreme value which basically remained unchanged as the shock energy or overlapping rate increased further, and thus the LIDT was mainly affected by defects at this time. The LIDTs manifested an increasing trend until a maximum value at an overlapping rate of 50% with laser energy of 0.2 J first and then a decreasing trend as laser energy continued to increase. When the laser energy was 0.4 J with an overlapping rate of 50%, the LIDT had decreased to 10.7 J/cm², which was similar to that of coatings without LSPP. The different variation trends between microstress and LIDT indicated defects had a major role in affecting the laser-induced damage resistance of coatings, compared with mechanical properties. However, the enhancement of the mechanical properties could also decrease the probability of defect excitement and improve the laser-induced damage resistance, which requires further study in the future to confirm. In addition, the fact that the LIDT also had low values with high microstress in some cases indicated that the excessive laser energy used in the LSPP process may have no positive effect or possibly a negative effect on defects. Compared with the existing post-processing techniques, LSPP has been found to have a comprehensive modification of intrinsic defects and mechanical properties, which may overcome the limitations of the current techniques on improving the laser-induced damage resistance of coatings. Beyond that, the benefit of LSPP on the packing density and water absorption of the porous HR coatings, as well as the applications on various coatings, will be systematically studied in future work.

Figure 3 XRD patterns of coatings with LSPP at overlapping rate of (a) 30% and (b) 50%, with (c) and (d) showing the corresponding specific XRD patterns of the (020) peak.

Figure 4 Statistical chart of the microstress and LIDT.

3.3 Morphology and depth of damage sites

Since the laser-induced damage resistance of coatings was affected by the combined effects of mechanical properties and damage defects, damage morphologies and depth characteristics of 1064 nm HR coatings with and without LSPP were studied to discover and clarify the process and effect of LSPP on the damage precursors. It was found that there were two typical damage morphologies^[Reference Liu, Wei, Wu, Yu, Cui, Yi and Shao^19]: large-area plasma scald without damage pits in the center (marked as type I) as shown in Figure 5(a); and large-area plasma scald with micrometer-sized pits in the center (marked as type II) as shown in Figure 5(e). It is well known that damages of coatings are induced by defects in nanosecond-pulse regime. As the inset shown in Figure 5(a), because no pits are observed at the original position of the plasma scald under scanning electron microscopy (SEM) at a higher magnification but a maximum depth of about dozens of nanometers, the most likely precursors for damage morphology of type I are assumed to be the submicrometer-sized defects distributed within the outermost layer, making the actual existing pits of too small size be observable. An analysis of the morphology of damage sites (Figures 5(b)–5(d)) and the corresponding FIB cross-sections (Figures 5(f)–5(h)) for coatings with or without LSPP found the bottoms of the micrometer-sized pits, namely the locations of the precursors, were randomly distributed at the relatively shallow interfaces, but always at or below the sixth interface which was of relatively high electric-field intensity^[Reference Liu, Wei, Wu, Yu, Cui, Yi and Shao^19].

Figure 5 The two typical damage morphologies of coatings with LSPP processed by an energy of 0.6 J at overlapping rate of 30% tested by SEM at (a) 31.8 J/cm² and (e) 74.9 J/cm², respectively. SEM and FIB images of the central pits of coatings: (b) and (f) without LSPP damaged at 74.1 J/cm²; (c) and (g) with LSPP processed by energy of 0.6 J at overlapping rate of 30%, and damaged at 74.9 J/cm²; (d) and (h) with LSPP processed by energy of 0.2 J at overlapping rate of 50%, and damaged at 76.5 J/cm².

The size distributions of the surrounding plasma scald of coatings with and without LSPP are depicted in Figure 6. As the laser irradiated at an oblique angle of 45°, the shape of the scalding was elliptical^[Reference Liu, Zhao, Li, Hu, Gao, Fan and Shao^24], the size or diameter of which was defined as its major axis. For a single coating without or with LSPP of same processing parameters, the scald diameter increased almost linearly with the incident laser fluence from 100 μm or so to about 1 mm, while varying by hundreds of micrometers at one laser fluence. It was found that LSPP almost had no effect on the size distribution of scalds which were mainly determined by the properties of damage precursors.

Figure 6 Size distribution of plasma scalds versus laser fluence of coatings: (a) without LSPP; (b)–(d) processed at an overlapping rate of 30%; (e)–(g) processed at an overlapping rate of 50%.

Although the LSPP process looked as if it had almost no influence on the damage morphology and damage depth, the individual minimum laser fluences to induce damage morphology of type I or type II for coatings with or without LSPP were obviously different as indicated in Table 1. Damage morphologies of type I were mainly distributed in the laser fluence of the close-threshold region, and only when the irradiated laser fluence increased above a certain value did damage morphologies of type II begin to appear. The variation tendency of the minimum laser fluence that induced type I damage morphology, which was consistent with that of the LIDTs shown in Figure 4, verified the LSPP process with optimized parameters had a distinct modification of absorbing defects distributed especially within the outermost layer. As indicated by Table 1, the improvement of the minimum laser fluence inducing type II damage morphology was more probably due to the enhancement of mechanical properties as we discussed previously. However, the more definitive synergetic and comprehensive modification process of intrinsic defects, mechanical property and microstructure requires further study in the future. From Figure 4 and Table 1, it was clear that there was a critical shock pressure for the LSPP process, at which the LIDT and the minimum laser fluence inducing type I and type II damage morphologies reached the maximum values of 36.7, 41.4, and 57.5 J/cm², respectively. Once the shock pressure is greater than the critical value, the promotion effect of LSPP on the laser-induced damage resistance becomes weakened and could even decrease. Thus, there was a corresponding interval for the LSPP parameters to achieve optimal improvement of the laser-induced damage resistance.

Table 1 The minimum laser fluence inducing type I and type II damage morphologies for coatings without and with LSPP of different parameters.

3.4 The plasma pressure model

3.4.1 Establishment of the plasma pressure model

Many plasma pressure models^[25–28] of LSP have been proposed and researched so far, such as the Fabbro model^[Reference Fabbro, Fournier, Ballard, Devaux and Virmont^25], which is the current most widely recognized model in the application fields of metals and alloys. On account of the experimental fact that the effect of LSPP on dielectric coatings was affected by the coupling of various factors such as the detailed characteristics of absorbing layer and pulse waveform, a plasma pressure equation was established based on a more suitable model proposed by Liu et al. ^[Reference Liu, Yang and Yu^29] to achieve the optimal LSPP parameters and further reveal the improvement mechanism. As shown in the inset in Figure 1(a), during the laser shockwave-forming process, the absorbing layer of the coatings absorbed laser energy and explosively vaporized and evaporated to form a plasma, which formed a three-phase coexistence of gas, liquid, and solid in the treated area. Considering the influence of pulse waveform, the material of confining layer, the peak plasma pressure ${P}^{\prime }$ in LSPP process was expressed by the relation^[Reference Liu, Yang and Yu^29]

(1)\begin{align}{P}^{\prime }={\kappa}_1{\kappa}_2\frac{\sqrt{R^{\ast }T}\left(\sqrt{\gamma }+1/\sqrt{\gamma}\right)}{\varepsilon +{R}^{\ast }T\left(1+\gamma /2\right)}{I}_0,\end{align}

where ${\kappa}_1$ and ${\kappa}_2$ are influence coefficients of pulse waveform and the confining layer, respectively; ${R}^{\ast }$ is the molar gas constant divided by the molecular molar mass of the substance; $\gamma$ is the specific heat ratio of the gas; $\varepsilon$ is the specific energy of coatings; ${I}_0$ is the incident pulse laser intensity, ${I}_0=\frac{E}{\tau S}$; $E$ is the laser shock energy, $\tau$ is the pulse width, and $S$ is the incident cross-sectional area; $T$ is the temperature of the film surface, $T=\frac{2A\varPhi \sqrt{t}}{\sqrt{\pi \lambda \rho c}}+{T}_0=\frac{2A\varPhi}{\lambda}\sqrt{\frac{\alpha t}{\pi }}+{T}_0$; $\alpha$ is the thermal diffusivity, $\alpha =\frac{\lambda }{\rho c}$; $\lambda$ is the thermal conductivity, $\rho$ is the density, and $c$ is the specific heat capacity; ${T}_0$ is the initial temperature of the film surface, because $T\gg {T}_0$, ${T}_0$ is generally ignored; $A$ is the absorption rate of the absorbing layer to the laser; $\varPhi$ is the laser power density, $\varPhi =\frac{E}{\tau \pi {r}^2}$; $r$ is the spot radius; and $t$ is the temperature propagation time.

The peak plasma pressure ${P}^{\prime }$ described in Equation (1) is the maximum pressure generated within the duration of a laser pulse. As the experiments involve raster scan processes where pulses are spatially overlapped, test locations are exposed to multiple pressure pulses, even for a single scan. We postulate that these repeated pressure pulses create a cumulative effect in the optical coating, and we therefore calculate the total pressure $P$ for each scan. Based on the experimental fact that the processed laser energy $E$, spot overlapping rate $\eta$, and the number of scans $\delta$ could all influence the post-processing effect, ${I}_0$ is instead by the more reasonable average laser intensity $En/\tau {S}^{\ast }$, where ${S}^{\ast }$ is the laser shock area, $n$ is the total number of pulses irradiated on the treated area which is equal to the product of ${n}_1$ and ${n}_2$ (the shot numbers in each line and column), $a=D+D\left(1-\eta \right)\left({n}_1-1\right)$ and $b=D+D\left(1-\eta \right)\left({n}_2-1\right)$ are the length and width of the treated area, $\eta =\Delta L/D$, $\Delta L$ is the length of the overlap between adjacent spots, and $D$ is the spot diameter. Based on Equation (1) and neglecting the infinitesimal factor $\varepsilon /\sqrt{R^{\ast }T}$, the formula of the total pressure $P$ can be obtained as follows:

(2)\begin{align}P={\sum}_{i=1}^{\delta }{\omega}_i{\kappa}_1{\kappa}_2\frac{\sqrt{\gamma }+1/\sqrt{\gamma }}{\left(1+\gamma /2\right)\sqrt{2A{R}^{\ast }{\left(\alpha t\right)}^{1/2}/\lambda {\pi}^{3/2}}}\frac{\sqrt{E} nr}{\sqrt{\tau }{S}^{\ast }},\end{align}

where ${\omega}_i$ is the absorption coefficient of the absorbing layer under the ith scan, which is a variable because the absorbing layer will be consumed after each scan. Notably, when the number of scans $\delta =1$, ${\omega}_i={\omega}_1=1$; when $\delta >1$, $0<{\omega}_{\delta }<\cdots <{\omega}_{i+1}<{\omega}_i<{\omega}_{i-1}<\cdots <{\omega}_1=1$. Making $\beta ={\kappa}_1{\kappa}_2\frac{\sqrt{\gamma }+1/\sqrt{\gamma }}{\left(1+\gamma /2\right)\sqrt{2A{R}^{\ast }{\left(\alpha t\right)}^{1/2}/\lambda {\pi}^{3/2}}}$, Equation (2) is simplified to

(3)\begin{align}P={\sum}_{i=1}^{\delta }{\omega}_i\beta \frac{\sqrt{E} nr}{\sqrt{\tau }{S}^{\ast }}.\end{align}

From the total pressures of LSPP processes under different processing parameters listed in Table 2, the total pressure $P$ was found to increase gradually from $0.23\beta\ \mathrm{to}$  $0.41\beta$, as the pulse energy or overlapping rate increased. Although the LIDT increased with increasing $P$ at first, there was an optimum LSPP total pressure $0.29\beta$ beyond which the LIDT actually went back down. Therefore, there must be an optimum $P$ of $0.29\beta$, which well confirmed the conclusions speculated from Figures 4 and 5 that there existed a critical pressure of the LSPP process. A considerable promotion effect of LSPP needs reasonable choice of the processing parameters to generate a rational pressure of about $0.28\beta$–$0.35\beta$ which could achieve the desirable modification of coating on the premise of without breaking through the maximum stress constraint of the coating.

Table 2 The total pressure of LSPP processes and the obtained LIDT with different overlapping rates and laser energies.

3.4.2 Application of the plasma pressure model to two-scan processing

To perfect and further verify the validity of the equation, a preliminary experiment on the effect of the number of scans on total pressure and post-processing effect was also conducted. In our LSPP experiment, macro-damages of coatings occurred once the number of scans was greater than two even with the lowest laser energy 0.2 J; thus we only tried the two scans in some cases herein. As shown in Figure 7, when the number of scans was increased from one to two, the laser-induced damage resistance of coatings post-processed with an overlapping rate of 30% and laser energy of 0.4 J was further improved, yet was weakened with an overlapping rate of 50% and laser energy of 0.2 J. It further suggested the significance of finding the critical total pressure and verified that the number of scans, laser energy, and overlapping rate will all influence the promotion effect of LSPP through changing the total pressures.

Figure 7 The one-on-one damage probabilities of the 1064 nm HR coatings with or without LSPP under the different numbers of scans (a) at an overlapping rate of 30% and laser energy of 0.4 J and (b) at an overlapping rate of 50% and laser energy of 0.2 J.

The total pressures of the two LSPP processes with the two scans were also calculated using Equation (3) as listed in Table 2. Although the LIDTs were both 15.9 J/cm² in these two cases, it was believed that their corresponding total pressures were different and distributed on the two sides of the critical value. By comparing the LIDTs and total pressures listed in Table 2, we infer that $0.23 \left(1+{\omega}_2^{\prime}\right)\beta$ should be greater than 0.23$\beta$ and less than 0.25$\beta$ whereas $0.29 \left(1+{\omega}_2^{\prime \prime}\right)\beta$ should be greater than 0.35$\beta$ and less than 0.41$\beta$. Thus, the absorption coefficient of the absorbing layer with two scans was found to spread over the range of $0<{\omega}_2^{\prime }<0.09$ and $0.21<{\omega}_2^{\prime \prime }<0.41$. The prediction that ${\omega}_2^{\prime }<{\omega}_2^{\prime \prime }$ indicated that more absorbing layer was consumed with a higher laser energy of 0.4 J in the first scan, even though the total pressure was relatively low.