Open Access
Add to BibSonomy
Abstract
The performance of a mixture-based picosecond laser mirror (MPLM) coating, particularly the picosecond (ps) laser-induced damage threshold (LIDT), is investigated. Two types of 1053 nm ps laser mirror coatings are deposited using electron-beam evaporation: an MPLM coating consists of alternating layers of the HfO2-Al2O3 mixture and SiO2, and a traditional picosecond laser mirror (TPLM) coating consists of alternating layers of HfO2 and SiO2. Comparative studies on the optical, microstructural and mechanical properties, and LIDT are carried out. For an s-polarized 8 ps laser pulse at a wavelength of 1053 nm, the ps-LIDT of the MPLM coating is approximately 1.2 times higher than that of the TPLM coating in both atmosphere and vacuum test environments. Typical damage morphologies and laser-induced temperature simulations by finite element modeling suggest that the enhanced LIDT of the MPLM coating may be attributed to the lower laser-induced temperature rise in the MPLM coating.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Lasers operates in the pulse width of several picosecond (ps) regime is usually used for high energy density related research, such as OMEGA EP [1], NIF ARC [2], and SG-II-UP PW [3]. Mirror coatings are key components in picosecond laser systems, and their ability to deliver high-intensity picosecond laser pulses is limited by the laser-induced damage threshold (LIDT). Many studies have been conducted to examine the laser-induced damage performance of mirror coatings under picosecond laser irradiation from different perspectives, including coating materials, coating designs, deposition methods, and laser pulse widths [4–7]. The test environment is also a concern for researchers, as picosecond laser mirror coatings are usually used in vacuum environments. Compared to atmosphere environments, the LIDT of laser mirror coatings tends to decrease in vacuum environments [8,9]. Previous studies have shown that LIDT degradation in a vacuum environment is associated with a decrease in material thermal conductivity, an increase in laser-induced defects (oxygen vacancy defects), and the accumulation of organic molecular contaminants on the coating surfaces [ [10–12]]. Research on the laser damage mechanism indicates that the damage caused to the mirror under laser irradiation is mainly due to electric (E)-field-induced volume breakdown for pulses shorter than approximately 2.3 ps, and isolated nanoscale defect structures for pulses between 2.3 and 100 ps [6, [13–15]]. Furthermore, according to a worldwide LIDT competition (laser pulse width: 150 ps) for broadband low-dispersion mirrors [16], the mirror with the highest LIDT uses HfO2 and SiO2 as high refractive index (n) and low-n materials, respectively.
In recent years, co-evaporated/co-sputtered mixture coating materials have become a research hotspot due to their tunable n and optical band gap [17–23]. Reported research have shown that coatings exhibit superior performance over pure materials and can improve the spectral performance and LIDT (nanosecond or femtosecond laser pulses) of mirror coatings [20], polarizer coatings [21], and dichroic mirror coatings [22]. Our previous work on monolayer coatings has also demonstrated that HfO2-Al2O3 mixture monolayer coatings exhibit higher LIDTs than pure HfO2 monolayer coatings under picosecond laser irradiation [5]. However, few studies have explored the properties of mixture-based mirror coatings for applications in the picosecond pulse regime.
In this work, a mixture-based picosecond laser mirror (MPLM) coating is deposited by electron-beam evaporation using co-evaporated HfO2-Al2O3 mixture and pure SiO2 as the high-n and low-n materials, respectively. For comparison, a traditional picosecond laser mirror (TPLM) coating consisting of alternating layers of pure HfO2 and SiO2 is prepared. The optical, microstructural, and mechanical properties of the TPLM and MPLM coatings, as well as their LIDT and damage morphology under picosecond laser pulse (8 ps, 1053 nm) irradiation in atmosphere and vacuum environments are investigated.
2. Experimental details
2.1 Design and preparation of coatings
An MPLM coating with a substrate/2L1(ML1)12M4.2L1/air structure is designed to achieve an s-polarized reflectance (Rs) ≥ 99.5% (incidence angle of 48°) at 1053 nm in an atmosphere environment. Here, M and L1 represent the HfO2-Al2O3 mixture and SiO2 layers (dM = 168.25 nm, dL1 = 207.52 nm) with a design n value of ∼ 1.761 and ∼ 1.428, respectively. For comparison, a TPLM coating with a substrate/ 2L2(HL2)10H4.2L2/air structure is designed to achieve a Rs ≥ 99.5% (incidence angle of 53°) at 1053 nm. Here, H and L2 represent the HfO2 and SiO2 layers (dH = 164.87 nm, dL2 = 211.90 nm) with a design n value of ∼1.835 and ∼1.428, respectively. The MPLM and TPLM coatings are deposited on BK7 substrates with a diameter of 50 mm and a thickness of 5 mm using electron-beam co-evaporation. The details of the co-evaporation system are shown in Supplementary Figs. S1. All substrates are cleaned ultrasonically in deionized water before being loaded into the coating chamber. The coating chamber is heated to 473 K and evacuated to a base pressure of 5 × 10−4 Pa prior to deposition, and the coating chamber is maintained at a constant temperature of 473 K throughout the deposition process. The HfO2 and SiO2 layers are deposited by using metallic Hf and SiO2 as starting materials, respectively. HfO2-Al2O3 mixture layer is deposited by dual electron-beam co-evaporation of metallic Hf and Al2O3 [5]. The HfO2 and Al2O3 deposition rates of the HfO2-Al2O3 mixture layer in the MPLM coating are 0.06 and 0.04 nm/s, respectively. The mixture ratio about 60% HfO2 and 40% Al2O3 is chosen because this ratio can provide a suitable coating thickness and a wider reflection bandwidth of the designed MPLM coating. The deposition rate of HfO2 in the TPLM coating is 0.1 nm/s. The deposition rate of SiO2 in both MPLM and TPLM coating is 0.2 nm/s. The oxygen pressures of the SiO2 layer and other layers are 5.0 × 10−3 Pa and 1.8 × 10−2 Pa, respectively.
2.2 Characterization of optical, mechanical properties and microstructure
The transmittance spectra are measured using a spectrometer (Perkin Elmer Lambda 1050, UV/VIS/NIR) in a controlled atmosphere environment (temperature: 23 ± 1.5 °C; relative humidity: 45% ± 5%) and a vacuum environment (∼ 5.4 × 10−4 Pa, achieved using an in-house-developed portable vacuum chamber [24]), respectively. The rest of the tests in this section are conducted in the controlled atmosphere environment described above. The sample surfaces before (substrate) and every several days after the coating deposition are inspected using a 632.8 nm wavelength interferometer (ZYGO Mark IIIGPI). The coating stress is calculated by Stoney’s formula [25]. The structural information of the samples is characterized by an X-ray diffraction (XRD; PANalytical Empyrean). The elemental composition profiles of the samples are determined using an X-ray photoelectron spectroscope (XPS; Thermo Scientific K-Alpha) with a monochromatic Al Kα (1486.6 eV) X-ray source. The spectra are recorded every 20 s of etching with 1 keV Ar+ ions. The surface roughness is evaluated by atomic force microscopy (AFM; Veeco Dimension 3100).
2.3 Characterization of LIDT and damage morphology
The LIDT measurements are performed in 1-on-1 test mode according to the ISO 21254 standard procedure. An s-polarized 1 ω Nd: glass laser (wavelength: 1053 nm, pulse width: 8 ps) is used as the light source. The pulse shape is Gaussian with a spot diameter of 96 µ;m @1/e2, a light non-uniformity (far field laser spot test) of < 10%, and an energy stability (RMS) of 0.96%. The LIDT tests are performed in atmosphere (in a Class 1000 clean room) and vacuum (∼ 5.0 × 10−4 Pa) environments, respectively. According to the spectra measured in different environments, the light incident angle is adjusted so that the center wavelength of the reflectance spectrum under different LIDT measurement environments is located at 1053 nm. Thus, the E-field intensity of the coating-air interface is close to zero in all different measurement environments (see Supplementary Fig. S2). The detailed measurement parameters are listed in Table 1. Prior to LIDT measurement, compressed air is used to blow dust particles away from the sample surface. For each sample, ten sites are irradiated at each energy fluence. Since the angle of incidence differs from 0 rad, the beam area at the coating-air interface is used instead of the beam cross-sectional area as the effective area for LIDT calculations. The LIDT value is determined by linearly extrapolating the damage probability data to a 0% damage probability. Due to the uncertainties caused by the inhomogeneity between samples (± 3%), measurement uncertainty of the laser spot area (± 2.5%), and laser fluence fluctuation during the measurement (± 2.5%), the relative error of the damage probability measurements amounts to ± 9%. The surface and cross-sectional damage morphologies are characterized by a focused ion beam scanning electron microscope (FIB-SEM; Carl Zeiss AURIGA Cross Beam).
Table 1. Detailed measurement parameters for the both coatings.
3. Results and discussions
3.1 Optical properties
The incident angle of the spectral measurement is adjusted such that the center wavelengths for the reflection bands of the both coatings are located at 1053 nm in both atmosphere and vacuum environments, as shown in Fig. 1. The reflectance spectra are calculated from transmittance results ignoring absorption. The spectral blue shift from atmosphere environment to vacuum environment is attributed to the change in the optical thickness of the coating caused by the desorption of water molecules in the porous coating structure [26]. The TPLM and MPLM coatings show a Rs higher than 99.5% at 1053 nm in both atmosphere and vacuum environments, as designed.
Fig. 1. Reflectance spectra (s-polarized light) of the TPLM and MPLM coatings in (a) atmosphere environment, and (b) vacuum environment (pressure: ∼ 5.4 × 10−4 Pa).
3.2 Microstructure and mechanical properties
The elemental percentage profiles from low-n to high-n layers in the TPLM and MPLM coatings are compared in Fig. 2(a). The elemental content ratio of HfO2 to Al2O3 in the HfO2-Al2O3 mixture layer of the MPLM coating is calculated to be ∼1.52:1, which is close to the design ratio. The XRD spectra of the two coatings are shown in Fig. 2(b). Multiple sharp diffraction peaks are observed in the TPLM coating, all the peak positions of the TPLM coating correspond to the monoclinic phase of the HfO2 layer in the multilayer coating according to the reference card PDF#74-1506 [27]. Obvious sharp diffraction peaks are not observed in the XRD pattern of the MPLM coating, indicating the amorphous nature of the coating. The stress-aging behavior of the both coatings are compared in Fig. 2(c). The MPLM coating exhibits a higher compressive stress than the TPLM coating, which means that it can withstand a lower humidity environment. The compressive stress of both coatings shows a tendency to release over time. The surface morphology of the coating is characterized by AFM, as shown in Fig. 2(d). For each sample, an area of 5 × 5 µ;m is sampled. The measured root-mean-square (RMS) roughness values of the TPLM and MPLM coatings are 2.6 nm and 1.4 nm, respectively. The RMS roughness value of the MPLM coating is noticed to be significantly lower than that of the TPLM coating.
Fig. 2. (a) Elemental percentage profiles from the low-n layer to the high-n layer, (b) XRD spectra, (c) stress aging behavior, and (d) surface morphologies of the TPLM and MPLM coatings.
3.3 Picosecond LIDT and damage morphology
The laser-induced damage probabilities tested in atmosphere and vacuum environments are shown in Fig. 3. In the atmosphere environment, the LIDTs of the TPLM and MPLM coatings are 7.3 J/cm2 and 8.9 J/cm2, respectively. In the vacuum environment, the LIDTs of the TPLM and MPLM coatings are 5.7 J/cm2 and 6.6 J/cm2, respectively. Compared with the TPLM coating, the LIDT of MPLM coating increases by a factor of ∼1.22 and ∼1.16 in atmosphere and vacuum environments, respectively.
Fig. 3. Single-pulse damage probability as a function of the input fluence, measured in (a) atmosphere environment, and (b) vacuum environment, respectively.
Typical damage morphologies of the TPLM and MPLM coatings after laser irradiation in an atmosphere environment are shown in Figs. 4(a) and 4(b), respectively. Overall, the damage morphologies for both coatings are similar. After laser irradiation with a fluence slightly higher than LIDT, three typical morphological features are observed, including tiny pits with a size of hundreds of nanometers, sharp pits and crater pits with a size of several micrometers. The observed damage morphologies are isolated, indicating that the laser damage originates from isolated defect structures [6,28]. The difference in damage pit morphology may be related to the geometry, size and location of the defect [6,29]. These damage sites are accompanied by the presence of melted material, indicating a gradual cooling process after energy deposition. As the laser fluence increases, the density of the damage pits increases, and some adjacent pits join together to form larger pits. When the laser fluence is further increased, the delamination type damage is observed. The cross-sectional morphology shows a delamination depth greater than the thickness of the SiO2 overcoat layer, much deeper than the pit/crater damage produced at lower laser fluence, as we will show later in Fig. 5. The detailed delamination depth depends on coating design, laser fluence and measurement environment. For the TPLM coating irradiated with a laser fluence of 9.7 J/cm2 in atmosphere environment, the delamination location is at the interface of layers 3 and 4 [see cross-sectional image in Fig. 4(a)]. Here, the number of layers is counted from the air-to-substrate direction. Surface and cross-sectional morphologies show traces of material melting in the top two layers, and suggest that this type of damage may relate to the thermal stress generated at high temperatures, poor adhesion [30], and the stress mismatch [31,32] between the high-n and low-n layers. When delamination damage occurs, the damage probability of the coating reaches 100%.
Fig. 4. Full-view and cross-section damage morphology evaluated using SEM-FIB for (a) TPLM and (b) MPLM coatings measured in atmosphere environment, (c) TPLM and (d) MPLM coating measured in vacuum environment.
Fig. 5. (a) E-field distribution of TPLM coating and MPLM coating in atmosphere environment. The surface and cross-sectional morphologies of the typical damaged sites irradiated in atmosphere environment: (b–d) TPLM coating and (e–i) MPLM coating.
Typical damage morphologies of the TPLM and MPLM coatings after laser irradiation in a vacuum environment are shown in Figs. 4(c) and 4(d), respectively. When the laser fluence is slightly higher than LIDT, two typical morphological features, isolated tiny pits and sharp pits, are observed. The difference in laser-induced damage morphology under atmosphere and vacuum test environments may be related to different thermal interactions and oxygen vacancy defects during irradiation. In a vacuum environment, while the absorption driven energy deposition does not change, the energy dissipation rate is lower due to the lower thermal conductivity, which results in a higher laser energy deposition in a smaller localized region compared to irradiation under atmosphere [9,10]. In addition, laser irradiated in vacuum environment may lead to more oxygen loss and formation of sub-stoichiometry defects [33,34]. As a result, more tiny pits and sharp pits are observed under near-LIDT laser irradiation. With increasing laser fluence, isolated crater pits and a higher density of pits (include tiny pits, sharp pits and crater pits) are observed, and some adjacent pits are joined together to form larger pits. When the laser fluence is further increased, the TPLM coating exhibits delamination-type damage similar to that observed in atmosphere test environment. The delamination depth of the MPLM coating is shallower and accompanied with more traces of material melting, which is consistent with the traces of material melting observed at the edges of other delamination morphologies.
The detailed damage morphological features of the TPLM and MPLM coatings irradiated in atmosphere and vacuum environments are shown in Figs. 5 and 6, respectively. The cross-sectional images of the laser damage induced by near-LIDT laser fluence are compared with the corresponding E-field distributions. As shown in Figs. 5(b), 5(e), 6(b), and 6(e), the depths of the tiny pits in both coatings are close to the E-field peak position (see pentagram labels in Figs. 5(a) and 6(a)) of the SiO2 overcoat layer, indicating that damage onset is closely related to the E-field distribution. Cross-sectional images of sharp pits (Figs. 5(c), 5(f), 6(c), and 6(f)), and crater pits (Figs. 5(d), 5(g), 5(i), 6(d), and 6(g)) indicate that these types of damage are closely related to the E-field peak, as well as absorptive defects at the interfaces. Microcracks are observed at the damaged sidewall (Fig. 5(h)), and at the interface between the overcoat SiO2 layer and the underlying high-n layer (Figs. 5(c) and 5(f)), suggesting that the damage is related to the overall tensile stress of the coating and thermal stress mismatch between the high-n and low-n layers, which is caused by the considerably high temperature generated in the laser-induced damage process. Overall, most of the pit-type damage are shallower than the delamination-type damage.
Fig. 6. (a) E-field distribution of TPLM coating and MPLM coating in vacuum environment. The surface and cross-section morphologies of the typical damaged sites irradiated in vacuum environment: (b–d) TPLM coating and (e–g) MPLM coating.
3.4 Modeling mechanism of the damage sites
Finite element modeling (FEM) simulations are used to investigate the laser-induced temperature distribution at absorptive defects in the coatings, according to the model described in Ref. [6]. For comparison, the input laser parameters for the TPLM and MPLM coatings are kept the same (laser wavelength: 1053 nm, pulse width: 8 ps, and input fluence: 9 J/cm2). For each coating, three spherical absorptive defects with a diameter of 20 nm are located at the positions of the first, second, and third E-field peaks, respectively. Considering that both the value of the defect absorption coefficient and the size of the absorber change during the laser pulse irradiation. For simplicity, it is assumed that all laser light is absorbed, the defect absorbs thermal power according to its cross-sectional area π$\textrm{R}_{\textrm{defect}}^\textrm{2}$ and distributes the thermal power on its volume (4/3)π$\textrm{R}_{\textrm{defect}}^\textrm{3}$ [6]. The thermophysical parameters used in the simulation are the values of the corresponding bulk materials, and the parameters of the HfO2-Al2O3 mixture layer are calculated from the parameters of HfO2 and Al2O3 according to the mixture ratio (HfO2:Al2O3 = 3:2) [35]. See Table 2 for details [6,36]. The thermal model used shows that HfO2 layer and HfO2-Al2O3 mixture layer have a melting point ∼ 1.1 times higher and a boiling point ∼1.2 times higher. It is worth pointing out that the thermophysical parameters of coating layers are different from those of bulk materials, and different in vacuum and atmospheric environments. The simulation results are qualitative analysis to understand the laser induced damage mechanism.
Table 2. Parameters of the HfO2, SiO2, Al2O3 and HfO2-Al2O3 mixture
Figure 7 shows the simulated temperature distributions with a 10-ns delay resulting from localized thermal absorption. The maximum temperature for absorbing defects in the TPLM coating is approximately 1.41 times higher than that observed in the MPLM coating. According to the temperature boundary conditions in the experiment, when damage occurs, the highest temperature in the material should exceed the boiling point temperature of SiO2 (2503 K). Moreover, the simulation results show that when the 1-on-1 laser pulse action is completed, the temperature of the absorbing defects in TPLM coating first reaches the critical temperature of SiO2 thermal explosion, which leads to the occurrence of damage. The results suggest that the enhanced LIDT of the MPLM coating might be related to the lower laser-induced temperature rise in the MPLM coating.
Fig. 7. Simulated temperature distributions of absorbing defects located at the positions of the first, second and third E-field peaks in the (a) TPLM and (b) MPLM coatings, respectively.
4. Conclusion
In summary, an MPLM coating composed of alternating HfO2-Al2O3 mixtures and SiO2 layers is experimentally compared with a TPLM coating composed consisting of alternating HfO2 and SiO2 layers. Experimental results show that the MPLM coating exhibit a lower surface roughness, a higher compressive stress and a higher LIDT under ps laser irradiation in both atmosphere and vacuum environments, compared to the TPLM coating. The typical damage morphologies suggest that the laser-induced damage of the two coatings is closely related to the E-field distribution, coating defects and coating stress. The FEM simulation results suggest that the enhanced LIDT of the MPLM coating might be attributed to the lower laser-induced temperature rise in the MPLM coating. Overall, the MPLM coating exhibit better ps laser-induced damage resistance compared to the TPLM coating.
Funding
National Natural Science Foundation of China (61975215); Youth Innovation Promotion Association of the Chinese Academy of Sciences.
Acknowledgments
The authors express their appreciation to Longsheng Wang and Yun Cui for their assistance in sample preparation and FIB measurement, respectively.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the corresponding authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
References
1. L. J. Waxer, D. N. Maywar, J. H. Kelly, T. J. Kessler, B. E. Kruschwitz, S. J. Loucks, R. L. McCrory, D. D. Meyerhofer, S. F. B. Morse, C. Stoeckl, and J. D. Zuegel, “High-energy petawatt capability for the OMEGA laser,” Opt. Photonics News 16(7), 30–36 (2005). [CrossRef]
2. J. E. Heebner, R. L. Acree Jr, D. A. Alessi, et al., “Injection laser system for advanced radiographic capability using chirped pulse amplification on the National Ignition Facility,” Appl. Opt. 58(31), 8501–8510 (2019). [CrossRef]
3. L. Ren, P. Shao, D. Zhao, Y. Zhou, Z. Cai, N. Hua, Z. Jiao, L. Xia, Z. Qiao, R. Wu, L. Ji, D. Liu, L. Ju, W. Pan, Q. Li, Q. Ye, M. Sun, J. Zhu, and Z. Lin, “Target alignment in the Shen-Guang II Upgrade laser facility,” High Power Laser Sci. Eng. 6, e10 (2018). [CrossRef]
4. C. Li, Y. Zhao, Y. Cui, Y. Wang, X. Peng, C. Shan, M. Zhu, J. Wang, and J. Shao, “Investigation on picosecond laser-induced damage in HfO2/SiO2 high-reflective coatings,” Opt. Laser Technol. 106, 372–377 (2018). [CrossRef]
5. J. Shi, M. Zhu, W. Du, T. Liu, L. Zhou, Y. Jiang, and J. Shao, “Effect of annealing on the properties of HfO2-Al2O3 mixture coatings for picosecond laser applications,” Appl. Surf. Sci. 579, 152192 (2022). [CrossRef]
6. A. A. Kozlov, J. C. Lambropoulos, J. B. Oliver, B. N. Hoffman, and S. G. Demos, “Mechanisms of picosecond laser-induced damage in common multilayer dielectric coatings,” Sci. Rep. 9(1), 607 (2019). [CrossRef]
7. H. Kiriyama, Y. Miyasaka, A. Kon, M. Nishiuchi, A. Sagisaka, H. Sasao, A. S. Pirozhkov, Y. Fukuda, K. Ogura, K. Kondo, N. P. Dover, and M. Kando, “Enhancement of pre-pulse and picosecond pedestal contrast of the petawatt J-KAREN-P laser,” High Power Laser Sci. Eng. 9, e62 (2021). [CrossRef]
8. R. Diaz, M. Chambonneau, P. Grua, J. L. Rullier, J. Y. Natoli, and L. Lamaignère, “Influence of vacuum on nanosecond laser-induced surface damage morphology in fused silica at 1064 nm,” Appl. Surf. Sci. 362, 290–296 (2016). [CrossRef]
9. X. Ling, S. Liu, and X. Liu, “Different material modifications in laser-induced damage of optical films in air and vacuum environments,” Thin Solid Films 703, 137974 (2020). [CrossRef]
10. X. Ling, Y. Zhao, D. Li, J. Shao, and Z. Fan, “Damage investigations of AR coating under atmospheric and vacuum conditions,” Opt. Laser Technol. 41(7), 857–861 (2009). [CrossRef]
11. B. Ma, J. Han, J. Li, K. Wang, S. Guan, X. Niu, H. Li, J. Zhang, H. Jiao, X. Cheng, and Z. Wan, “Damage characteristics of dual-band high reflectors affected by nodule defects in the femtosecond regime,” Chin. Opt. Lett. 19(8), 081403 (2021). [CrossRef]
12. T. Pu, W. Liu, Y. Wang, X. Pan, L. Chen, and X. Liu, “A novel laser shock post-processing technique on the laser-induced damage resistance of 1ω HfO2/SiO2 multilayer coatings,” High Power Laser Sci. Eng. 9, e19 (2021). [CrossRef]
13. A. A. Kozlov, S. Papernov, J. B. Oliver, A. Rigatti, B. Taylor, B. Charles, and C. Smith, “Study of the picosecond laser damage in HfO2/SiO2 based thin-film coatings in vacuum,” Proc. SPIE 10014, 100141Y (2017). [CrossRef]
14. S. Ly, N. Shen, R. A. Negres, C. W. Carr, D. A. Alessi, J. D. Bude, A. Rigatti, and T. A. Laurence, “The role of defects in laser-induced modifications of silica coatings and fused silica using picosecond pulses at 1053 nm: I. damage morphology,” Opt. Express 25(13), 15161–15178 (2017). [CrossRef]
15. T. A. Laurence, R. A. Negres, S. Ly, N. Shen, C. W. Carr, D. A. Alessi, A. Rigatti, and J. D. Bude, “Role of defects in laser-induced modifications of silica coatings and fused silica using picosecond pulses at 1053 nm: II. Scaling laws and the density of precursors,” Opt. Express 25(13), 15381–15401 (2017). [CrossRef]
16. C. J. Stolz, R. A. Negres, K. Kafka, E. Chowdhury, M. Kirchner, K. Shea, and M. Daly, “150-ps broadband low dispersion mirror thin film damage competition,” Proc. SPIE 9632, 96320C (2015). [CrossRef]
17. H. Xing, M. Zhu, Y. Chai, K. Yi, J. Sun, Y. Cui, and J. Shao, “Improving laser damage resistance of 355 nm high-reflective coatings by co-evaporated interfaces,” Opt. Lett. 41(6), 1253–1256 (2016). [CrossRef]
18. M. Zhu, N. Xu, B. Roshanzadeh, S. T. P. Boyd, W. Rudolph, Y. Chai, and J. Shao, “Nanolaminate-based design for UV laser mirror coatings,” Light: Sci. Appl. 9(1), 20 (2020). [CrossRef]
19. Q. Jin, E. Yiwen, S. Gao, and X. Zhang, “Preference of sub-picosecond laser pulses for terahertz wave generation from liquids,” Adv. Photonics 2(1), 015001 (2020). [CrossRef]
20. T. Willemsen, M. Jupé, M. Gyamfi, S. Schlichting, and D. Ristau, “Enhancement of the damage resistance of ultra-fast optics by novel design approaches,” Opt. Express 25(25), 31948–31959 (2017). [CrossRef]
21. N. Xu, M. Zhu, J. Sun, Y. Chai, K. Yi, Y. Zhao, and J. Shao, “Study on Brewster angle thin film polarizer using hafnia-silica mixture as high-refractive-index material,” Opt. Eng. 57(02), 1 (2018). [CrossRef]
22. T. Zeng, M. Zhu, Y. Chai, J. Li, and J. Shao, “Dichroic laser mirrors with mixture layers and sandwich-like-structure interfaces,” Photonics Res. 9(2), 229–236 (2021). [CrossRef]
23. W. Du, M. Zhu, J. Shi, T. Liu, T. Zeng, J. Sun, K. Yi, and J. Shao, “Plate laser beam splitter with mixture-based quarter-wave coating design,” Opt. Laser Technol. 155, 108399 (2022). [CrossRef]
24. T. Zeng, M. Zhu, Y. Chai, R. Zhang, H. Liu, C. Yin, N. Xu, Y. Zhao, and J. Shao, “Environmental stability investigation on electron-beam deposited coatings with dense capping layer,” Opt. Eng. 57(08), 1 (2018). [CrossRef]
25. G. G. Stoney, “The tension of metallic films deposited by electrolysis,” Proc. R. Soc. Lond. A 82(553), 172–175 (1909). [CrossRef]
26. P. Ma, Y. Pu, W. Zhang, J. Die, M. Zhang, and H. Liu, “Protecting the EBE coatings from vacuum-air-shift by ion assistance or ALD capping layer,” Ceram. Int. 48(2), 2670–2676 (2022). [CrossRef]
27. J. Hu, J. Wang, Y. Wei, Q. Wu, F. Zhang, and Q. Xu, “Effect of film growth thickness on the refractive index and crystallization of HfO2 film,” Ceram. Int. 47(23), 33751–33757 (2021). [CrossRef]
28. M. Chorel, S. Papernov, A. A. Kozlov, B. N. Hoffman, J. B. Oliver, S. G. Demos, T. Lanternier, É. Lavastre, L. Lamaignère, N. Roquin, B. Bousquet, N. Bonod, and J. Néauport, “Influence of absorption-edge properties on subpicosecond intrinsic laser-damage threshold at 1053 nm in hafnia and silica monolayers,” Opt. Express 27(12), 16922–16934 (2019). [CrossRef]
29. X. Ling, X. Chen, and X. Liu, “Revisiting Defect-Induced Light Field Enhancement in Optical Thin Films,” Micromachines 13(6), 911 (2022). [CrossRef]
30. N. Xu, M. Zhu, Y. Chai, B. Roshanzadeh, S. T. P. Boyd, W. Rudolph, Y. Zhao, R. Chen, and J. Shao, “Laser resistance dependence of interface for high-reflective coatings studied by capacitance-voltage and absorption measurement,” Opt. Lett. 43(18), 4538–4541 (2018). [CrossRef]
31. J. Dijon, G. Ravel, and B. Andre, “Thermomechanical model of mirror laser damage at 1.06 µ;m: II. Flat bottom pits formation,” Proc. SPIE 3578, 398–407 (1999). [CrossRef]
32. H. Wang, H. Qi, W. Zhang, J. Sun, Y. Chai, F. Tu, J. Zhao, Z. Yu, B. Wang, and M. Zhu, “Suppression of nano-absorbing precursors and damage mechanism in optical coatings for 3 omega mirrors,” Opt. Lett. 41(6), 1209–1212 (2016). [CrossRef]
33. X. Ling, S. Liua, and X. Liu, “The effect of water vapor on nanosecond laser damage resistance of optical coatings in vacuum,” Optik 164, 654–660 (2018). [CrossRef]
34. X. Ling, Y. Zhao, D. Li, J. Shao, and Z. Fan, “Laser conditioning of high-reflective and anti-reflective coatings in vacuum environments,” Opt. Commun. 283(13), 2728–2731 (2010). [CrossRef]
35. K. A. Hamid, W. H. Azmi, M. F. Nabil, R. Mamat, and K. V. Sharma, “Experimental investigation of thermal conductivity and dynamic viscosity on nanoparticle mixture ratios of TiO2-SiO2 nanofluids,” Int. J. Heat Mass Transf. 116, 1143–1152 (2018). [CrossRef]
36. B. Dongre, J. Carrete, N. Mingo, and G. K. H. Madsen, “Ab initio lattice thermal conductivity of bulk and thin-film alpha-Al2O3,” MRS Commun. 8(3), 1119–1123 (2018). [CrossRef]
