Open Access
Add to BibSonomy
Abstract
Dichroic beam splitters are widely used in multi wavelength laser systems, and their scattering loss affects the signal-to-noise ratio and performance of the system. In this study, we investigate forward and backward scattering induced by nodular defects in a dichroic beam splitter. The seed size, seed position, and geometric constants of nodules exhibited distinct effects on the scattering characteristics. The modeling and simulation provide valuable insights into the relationship between the structural parameters of nodules and their scattering characteristics, offering practical guidance for various high-performance optical multilayer coatings and systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Owing to rapid advancements in technology, lasers are widely used in scientific research, medical treatment, industrial processing, and military applications. To achieve diverse functionalities in these applications, designing complex multi wavelength beam-combining and beam-splitting systems is imperative. Dichroic beam splitters are important components in various optical systems because they can split incident light into reflected and transmitted components. Moreover, they route different wavelengths along different optical paths through reflection and transmission. Consequently, they are widely used in various laser systems with dual-wavelength operation modes, including space light detection and ranging (LiDAR) [1–4], multiphoton and fluorescence microscopy [5–9], laser beam combination and splitting systems [10,11], double-frequency lasers, femtosecond pulsed laser [12–16], and various other laser systems with multi laser sources [17–21].
With the increasing demand for enhancing optical thin-film device performance, optical scattering has been considered as a primary factor that limits their performance. The scattering loss in the optical film results in the generation of stray light in the system, reducing the clarity and contrast of the detector. Additionally, it reduces the energy distribution reaching the detection sensitivity region and makes the signal to be obliterated in stray light [22,23]. Therefore, the analyzing scattering characteristics and identifying the factors that influence scattering are crucial for the effective control of scattering loss in films.
The theory and measurement of multilayer coating scattering has been studied extensively, especially by the Fresnel Institute group, which is a pioneer in the study of multilayer optical scattering [24,25]. C. Amra et al. comprehensively analyzed various factors affecting multilayer optical scattering [26,27]. With the advancement of high-energy deposition techniques, the scattering resulting from bulk inhomogeneity has typically become negligible [28,29]. Nevertheless, the presence of inevitable defects in coatings remains a primary concern because of their significant contribution to scattering losses. It has been established that the measured scattering intensity of the coatings with only a few defects was considerably higher than that caused by roughness [30–32]. Nodular defects are common in multilayer coatings [33,34]. Quantitative analysis has demonstrated that the presence of a single nodule per square millimeter in high-reflection (HR) multilayer coatings can result in scattering losses that are approximately two to three times higher than those attributed to roughness [35].
The scattering characteristics of nodular defects in HR multilayer coatings and their underlying physical mechanisms have previously been investigated and discussed [36]. However, owing to the intricate functionality of dichroic beam splitters, the scattering characteristics induced by defects in them has not been extensively discussed. Therefore, understanding the forward and backward scattering properties of dichroic beam splitters is essential. Moreover, the interaction process between the incident light and nodular structures for the simultaneous suppression of scattering losses in different optical path directions of the system should also be clarified. The structure of a nodule has diverse and uncertain variations, and the effect of structural variants on the scattering characteristics remains unclear. Therefore, the scattering values of different nodular structures should be quantitatively analyzed to summarize the law of scattering characteristics variation with structural parameters.
In this study, we investigate the forward and backward scattering properties of nodular defects in a dichroic beam splitter at operating wavelengths of 1064 and 532 nm. The underlying physical mechanisms responsible for the differences between forward and backward scattering were analyzed using field distributions obtained from finite-difference time-domain (FDTD) simulations. We thoroughly examined the parameters affecting the formation of the nodular structures, quantitatively calculated the scattering characteristics of different structures, and evaluated the structural features that affect the scattering characteristics. Our findings provide valuable insights into the mitigation of forward and backward scattering losses from nodular defects in dichroic beam splitters and multi laser beam systems.
2. Modeling and simulation of nodular defects
The presence of nodular defects induces forward and backward scattering in a dichroic beam splitter, as shown in Fig. 1(a), where θi is the incident angle, θs is the scattering angle, and ΔSΩ is the detector aperture used for measurement. The analysis in this study was conducted under normal incidence; thus, the incident angle θi was zero. Nodular defects usually originate from contamination during substrate preparation and coating processes and manifest as elliptical micrometer-sized domes protruding above the coating surface [33,34]. In this study, we introduced artificial spherical seed structures onto a dielectric substrate and assumed that the modeling of defect-containing multilayers is accomplished using an ion assisted deposition (IAD) coating process. The inset in Fig. 1(a) shows a schematic cross section of the nodular defect structure. We designed a commonly used dichroic beam splitter with high transmittance and high reflectivity at operating wavelengths of 1064 nm and 532 nm, respectively. The dichroic beam splitter consists of alternating stacks of Ta2O5 and SiO2 as high- and low-refractive-index materials, respectively, in multilayer coatings. Figure 1(b) and Fig. 1(c) show the coating design and the theoretical spectral properties of the dichroic beam splitter, respectively.
Fig. 1. (a) Scattering schematic diagram of nodular structure in dichroic beam splitter. (b) Design of physical layer thicknesses in the dichroic beam splitter. (c) Theoretical spectral properties characteristics of dichroic beam splitter.
Angle-resolved scattering (ARS) is defined as the ratio of the intensity of the scattered light received by the detector at different angles to that of the incident light. This parameter provides insights into the scattering intensity properties at different scattering angles and can be expressed as:
3. Forward and backward scattering characteristics of nodules in dichroic beam splitters
In this study, we calculated and analyzed scattering characteristics with respect to the seed size of nodular defects using the homemade FDTD software named Gallop [36]. Previous studies have analyzed the characteristics of the scattering induced by roughness in antireflective and highly reflective coatings [37,38]. These studies have shown that the level of scattering intensity is directly related to the transmittance and reflectance of the coating. The high transmittance of multilayer coatings increases the level of forward scattering, and the high reflectivity increases the level of backscattering. To fully describe the scattering properties, we focused on the total forward scattering (TSf) at the transmitting operating wavelength of 1064 nm and the total backscattering (TSb) at the reflecting operating wavelength of 532 nm for the dichroic beam splitter with nodules.
Figure 2 shows the variations in TSf and TSb with seed sizes at incident wavelengths of 1064 and 532 nm. The forward and backward scattering of the nodular defects exhibited distinctly different characteristics. At 1064 nm, the total forward scattering value increased monotonically with nodule size. This observation aligns with the intuitive understanding of structure-induced scattering properties, in which larger defect structures result in stronger scattering. The variation in the TSf with respect to the seed diameter, which describes the scattering characteristics of nodules, can be summarized by Eq. (3),
where k1 represents the linear parameter indicating the rate of increase in TSf with increasing seed diameter. At 532 nm, as the seed size increased, the total backward scattering value oscillated with the occurrence of maxima and minima, rather than showing a monotonic increase. This behavior is consistent with our previous finding that nodular defects in highly reflective multilayer coatings exhibit anomalous scattering properties [36]. The relationship between the scattering values and seed size contains two components: a linear component that increases with seed size and an oscillatory component that varies with seed size. The variation in TSb with seed diameter, which describes the scattering characteristics of nodules, can be summarized by Eq. (4), where k2 and k3 are the linear and oscillation parameters, respectively. Parameter k2 represents the rate of increase of TSb with increasing seed diameter, and k3 represents the characteristic of TSb oscillation with variations in the seed diameter. We verified that the backscattering of the structure also exhibited oscillation characteristics at a wavelength of 1064 nm, indicating that the oscillation characteristics of nodular backscattering are wavelength-independent. The effect of the wavelength of the incident light on the scattering characteristics is manifested by the difference in the number of backscattering maxima and minima at different wavelengths.Fig. 2. Calculated values of TSf and TSb for a single nodule with different seed diameters in a dichroic beam splitter at incident wavelengths of 1064 nm and 532 nm.
The electric field distribution was calculated to observe the interaction between the incident light and nodular structures. We studied the nodular structures have the maximum and minimum TS values observed in oscillatory backscattering, corresponding to the seed sizes of 0.5, 0.6, 0.8, and 0.9 µm. Figure 3(a) and 3(b) illustrate the electric-field Re(z) distributions of the nodular structures with different seed diameters at incident wavelengths of 1064 and 532 nm, respectively. Different interactions between the incident light and structure were observed owing to the different properties of the multilayer coatings at different operating wavelengths. At an incident wavelength of 1064 nm, the coating exhibited transmissive properties, and almost all the incident light passed through the nodular structure, as shown in Fig. 3(a). In this case, the interaction between the structure and incident light is relatively simple, leading to a monotonically increasing forward scattering value with increasing nodule size. Conversely, at a wavelength of 532 nm, the coating demonstrated reflective properties, and the interaction between the incident light and the nodule dome structure protruding from the coating surface produced a coupling effect, as shown in Fig. 3(b). Some of the incident energy was trapped and formed a guided wave near the top surface, enhancing the electric field in the top region of the structure. The superposed coherent and suppressed scattered waves across the far field were the main reasons for the maxima and minima in the TSb values. The nodular microlens-like focusing effect enhanced the electric-field strength at the center of the nodular structure at both operating wavelengths; however, this effect had a negligible impact on scattering.
Fig. 3. (a,b) Electric field distributions in nodules with different seed diameters in a dichroic beam splitter at an incident wavelength of 1064 nm and 532 nm, respectively. (c,d) ARS curves and corresponding TS values for the dichroic beam splitter with nodules at operating wavelengths of 1064 and 532 nm.
The ARS curves provide insight into the scattering distribution of the nodular structure at different angles in the far field. Figure 3(c) and Fig. 3(d) show the ARS curves of the nodular structure with different seed diameters at 1064 and 532 nm, respectively. Insets show the corresponding TS values. For forward scattering at an incident wavelength of 1064 nm, both the ARS intensity and TS values exhibited monotonic variation with increasing structure size. For backscattering at 532 nm, the ARS curves of different structures exhibited significant differences in the scattering intensity at different reception angles owing to the coupling effect between the nodular structure and incident light. This difference is characterized by the changes in the TS with respect to the seed size as shown in the insert in Fig. 3(c) and Fig. 3(d).
4. Scattering characteristics analysis for different nodular structures
Nodular structures are complex defects, whose formation processes are often affected by various factors other than seed size. The structural properties of nodules can be understood through the mathematical expression of the nodule diameter $D = \sqrt {Cdt} $, where C is a geometric constant, d and t are the seed diameter and depth, respectively [39–44]. Therefore, considering only the effect of the seed size on the nodules limits the comprehensive analysis of the scattering properties of the nodules. In this study, the effects of seed size, seed position, and geometric constants on the scattering properties of nodular structures were considered to comprehensively analyze the scattering patterns of various nodular structures.
The locations and sources of seeds that lead to the formation of nodular defects can be divided into two categories. In one category, the seeds are located on the surface of the substrate. These seeds are mainly contaminants left on the substrate during cleaning before coating or contaminants adsorbed on the substrate during transportation and vacuum pumping. The other type of seeds is located between the multilayers. These seeds are mainly microparticles of different sizes formed by the splashing of evaporation source materials during the coating process or material impurity particles shed in the vacuum chamber of the coater [45–47]. The effect of the seeds located at 1/2 tcoating, 1/3 tcoating, 1/4 tcoating, and the substrate surface on the scattering properties of the nodular structures is discussed in this study. Figure 4(a) shows the nodular structures formed from seeds at different locations. As the distance between the seed position and the substrate increases, fewer layers envelope the seed during the coating process, resulting in smaller nodular structures.
Fig. 4. (a) Schematic of nodular structure variations with respect to the seeds located at 1/2 tcoating, 1/3 tcoating, 1/4 tcoating, and substrate surface. (b) Schematic of the nodular structure with different geometric constants C of 2, 2.5, 4, and 8.
The geometric constant C, known as the aspect ratio, plays a crucial role in determining the size of the nodules relative to that of the seed. The value of C depends on the deposition methods and conditions, indicating the extent to which the growth of the nodule will surpass that of the seed. Different coating methods result in different C values for the nodular structure owing to differences in the geometry of the coater and the mobility of the deposited atoms [41]. The nodules in the coatings prepared through electron beam evaporation (EBE) exhibited relatively large C values, typically ranging from ∼4 to 8. This was attributed to the self-shadowing effect of the seeds and the limited mobility of the evaporated atoms. Nodules in coatings prepared through IAD and ion beam sputtering (IBS) have smaller C values, approximately 2.5 and 2, respectively [42]. Nodular structures with different geometrical constants are shown in Fig. 4(b). Notably, when the seed size is determined, the height of the nodular structure remains fixed. Consequently, larger values of the C result in a larger lateral dimension D of the structure.
The forward and backward scattering properties and corresponding electric field distributions of the nodular structures formed due to seeds located at different positions are shown in Fig. 5. As shown in Fig. 5(a) and 5(c), the calculated TS values indicate that as the seed position shifts higher, the forward and backward scattering values of the nodules decreases. By comparing the variations in TS values with respect to the seed size, as shown in Fig. 5, with those in Fig. 2, it can be concluded that the linear parameters k1 and k2 are affected by the position of the seed at different coating layers. However, the oscillation parameter k3 is not directly related to the seed position. As shown in Fig. 5(b), at a transmission wavelength of 1064 nm, no coupling effect in the structure was observed, and the forward scattering varied monotonically with the seed position. As shown in Fig. 5(d), at a reflected wavelength of 532 nm, the electric field distribution indicated the existence of a coupling effect between the arc-top structure and the incident light for nodular structures at different seeding positions. Because the strength of each electric field had the same order of magnitude, backward scattering exhibited strong oscillatory properties at both high and low seeding positions.
Fig. 5. (a) Forward TS values for the nodular defects with seeds located at 1/2 tcoating, 1/3 tcoating, 1/4 tcoating, and the substrate surface. (b) Electric field distribution of nodules with seeds at different locations at a wavelength of 1064 nm. (c) Backward TS values for the nodular defects with seeds at different locations. (d) The electric field distribution of nodules with seed at different locations at wavelength of 532 nm.
The forward and backward scattering characteristics and corresponding electric field distributions of the nodular structures with different geometrical constants C of 2, 2.5, 4, and 8 are shown in Fig. 6. The scattering loss calculations revealed that the overall intensities of both the forward and backward scattering values increased with increasing C, as shown in Fig. 6(a) and Fig. 6(c). By comparing the variations in TS with the seed size shown in Fig. 6 with those shown in Fig. 2, it can be concluded that both the linear parameters k1 and k2 with the oscillation parameter k3 are affected by the geometric constant of the nodular structure. Most of the incident light passed through the structure at an incident wavelength of 1064 nm, and the change in the C value did not affect the monotonic variation in forward scattering with an increase in the size of the structure, as shown in Fig. 6(b). The coupling effects between the various structures became complicated with an increase in C value at an incident wavelength of 532 nm, as shown in Fig. 6(d). The electric field strength owing to the coupling effect of each structure did not increase significantly with an increase in C value. Consequently, the overall strength of the scattering increases with increasing structure size, but the oscillatory property changes from significant to insignificant.
Fig. 6. (a) Forward TS values for the nodular defects with geometric constant C values of 2, 2.5, 4, and 8. (b) Electric field distribution of nodular structures with different C at the incident wavelength of 1064 nm. (c) Backward TS values for the nodular defects with different C values. (d) Electric field distribution of nodular structures with different C at the incident wavelength of 532 nm.
Through modeling and simulation, we have demonstrated that the variation of seed size, seed position and geometric constants influence the scattering characteristics of nodular defects. Different structural parameters of the nodules impact the interaction between the incident light and the structure, consequently leading to changes in the scattering characteristics. Based on the above analyses, the scattering characteristics caused by different nodular structures in dichroic splitter are summarized, thereby offering effective approaches for controlling scattering properties in practical applications. One of such approaches is to reduce the number of seeds located on the substrate by improving the cleaning process of the substrate to reduce the generation of larger defective structures, which consequently reduces the scattering loss. Another approach is to change the growth structure of nodular defects by adjusting the coating process. Using high-energy coating methods to increase the coating density and control nodular structures with small lateral dimensions can suppresses scattering effects. For example, calculation results show that the scattering value of nodular defects produced using the IAD and IBS coating processes can be reduced by approximately 50% compared to that of nodular defects produced by the EBE coating process. Minimizing the size of the seed contaminants further reduces the scattering loss of the nodules. The effectiveness of these suggestions was verified by the results of specific numerical analysis. It is noteworthy that these analysis results of scattering properties are applicable not only to dichroic beam splitters but also to high-transmittance and high-reflectance coatings.
5. Conclusion
In this study, we quantitatively evaluated the forward and backward scattering induced by nodular defects in a dichroic beam splitter at different operating wavelengths using numerical simulations. Our findings revealed that the forward scattering induced by the nodule in the dichroic beam splitter increases monotonically with increasing structure size, whereas the backscattering exhibits an oscillatory characteristic. Electric field analysis showed that the presence or absence of the coupling effect between the structure and the incident light determines the difference in the forward and backward scattering characteristics of the dichroic beam splitter. In addition, we analyzed the influence of structural parameters on the characteristics of the nodular structures, quantitatively calculated the scattering characteristics corresponding to different nodular structures. Theoretical simulations emphasize the importance of characterizing and controlling the defect structure to regulate the scattering properties induced by nodular defects in optical multilayer coatings. The scattering characteristics of other complex structural defects will be studied in the future to provide a solid foundation for the study of scattering characteristics in optical systems.
Funding
National Key Research and Development Program of China (Grant No.2022YFF0604802); National Natural Science Foundation of China (61925504, 6201101335, 62020106009, 62061136008, 62111530053, 62192770, 62192772, 62205249); Science and Technology Commission of Shanghai Municipality (17JC1400800, 20JC1414600, 21JC1406100); The Special Development Funds for Major Projects of Shanghai Zhangjiang National Independent Innovation Demonstration Zone (Grant No. ZJ2021-ZD-008); Shanghai Municipal Science and Technology Major Project (2021SHZDZX0100); Fundamental Research Funds for the Central Universities.
Acknowledgments
The authors thank Zhanyi Zhang for valuable comments in preparing the publication.
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 authors upon reasonable request.
References
1. D. M. Winker, M. A. Vaughan, A. Omar, et al., “Overview of the CALIPSO mission and CALIOP data processing algorithms,” J. Atmos. Ocean. Tech. 26(11), 2310–2323 (2009). [CrossRef]
2. W. H. Hunt, D. M. Winker, M. A. Vaughan, et al., “CALIPSO lidar description and performance assessment,” J. Atmos. Ocean. Tech. 26(7), 1214–1228 (2009). [CrossRef]
3. X. Sun, J. B. Abshire, J. F. McGarry, et al., “Space lidar developed at the NASA Goddard Space Flight Center—The first 20 years,” IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing 6(3), 1660–1675 (2013). [CrossRef]
4. D. M. Winker, W. H. Hunt, and C. A. Hostetler, “Status and performance of the CALIOP lidar,” Proc. SPIE 5575, 8–15 (2004). [CrossRef]
5. M. J. Sanderson, I. Smith, I. Parker, et al., “Fluorescence microscopy,” Cold Spring Harb. Protoc. 2014(10), pdb.top071795 (2014). [CrossRef]
6. T. A. Klar, S. Jakobs, M. Dyba, et al., “Fluorescence microscopy with diffraction resolution barrier broken by stimulated emission,” Proc. Natl. Acad. Sci. U. S. A. 97(15), 8206–8210 (2000). [CrossRef]
7. L. Gu, Y. Li, S. Zhang, et al., “Molecular resolution imaging by repetitive optical selective exposure,” Nat. Methods 16(11), 1114–1118 (2019). [CrossRef]
8. I. Testa, C. A. Wurm, R. Medda, et al., “Multicolor fluorescence nanoscopy in fixed and living cells by exciting conventional fluorophores with a single wavelength,” Biophys. J. 99(8), 2686–2694 (2010). [CrossRef]
9. M. Lelek, M. T. Gyparaki, G. Beliu, et al., “Single-molecule localization microscopy,” Nat. Rev. Methods Primers 1(1), 39 (2021). [CrossRef]
10. U. Witte, F. Schneider, M. Traub, et al., “kW-class direct diode laser for sheet metal cutting based on DWDM of pump modules by use of ultra-steep dielectric filters,” Opt. Express 24(20), 22917–22929 (2016). [CrossRef]
11. H. Zhu, X. Lin, Y. Zhang, et al., “kW-class fiber-coupled diode laser source based on dense spectral multiplexing of an ultra-narrow channel spacing,” Opt. Express 26(19), 24723–24733 (2018). [CrossRef]
12. R. L. Byer, “Diode laser—Pumped solid-state lasers,” Science 239(4841), 742–747 (1988). [CrossRef]
13. S. S. Sané, S. Bennetts, J. E. Debs, et al., “11 W narrow linewidth laser source at 780 nm for laser cooling and manipulation of rubidium,” Opt. Express 20(8), 8915–8919 (2012). [CrossRef]
14. S. W. Chiow, T. Kovachy, J. M. Hogan, et al., “Generation of 43 W of quasi-continuous 780-nm laser light via high-efficiency, single-pass frequency doubling in periodically poled lithium niobate crystals,” Opt. Lett. 37(18), 3861–3863 (2012). [CrossRef]
15. K. Mizuuchi, A. Morikawa, T. Sugita, et al., “High-power continuous wave green generation by single-pass frequency doubling of a Nd:GdVO4 laser in a periodically poled MgO:LiNbO3 operating at room temperature,” Jpn. J. Appl. Phys. 42(11A), L1296–L1298 (2003). [CrossRef]
16. S. C. Kumar, J. C. Casals, E. S. Bautista, et al., “Yb-fiber-laser-based, 1.8 W average power, picosecond ultraviolet source at 266 nm,” Opt. Lett. 40(10), 2397–2400 (2015). [CrossRef]
17. Y. Deng, J. Bechhoefer, and N. R. Forde, “Brownian motion in a modulated optical trap,” J. Opt. A: Pure Appl. Opt. 9(8), S256–S263 (2007). [CrossRef]
18. H. Lin and J. Cheng, “Computational coherent Raman scattering imaging: breaking physical barriers by fusion of advanced instrumentation and data science,” eLight 3(1), 6 (2023). [CrossRef]
19. A. Minopoli, S. Wagner, E. Erben, et al., “ISO-FLUCS: symmetrization of optofluidic manipulations in quasi-isothermal micro-environments,” eLight 3(1), 16 (2023). [CrossRef]
20. Z. Feng, T. Shi, G. Geng, et al., “Dual-band polarized upconversion photoluminescence enhanced by resonant dielectric metasurfaces,” eLight 3(1), 21 (2023). [CrossRef]
21. F. Getman, M. Makarenko, A. Burguete-Lopez, et al., “Broadband vectorial ultrathin optics with experimental efficiency up to 99% in the visible region via universal approximators,” Light: Sci. Appl. 10(1), 47 (2021). [CrossRef]
22. C. J. Stolz, “The national ignition facility: The world’s largest optical system,” Proc. SPIE 6834, 683402 (2007). [CrossRef]
23. M. B. Moran, R. H. Kuo, and C. D. Marrs, “Scatter intensity mapping of laser-illuminated coating defects,” Appl. Opt. 27(5), 957–962 (1988). [CrossRef]
24. C. Amra, “Light scattering from multilayer optics. I. Tools of investigation,” J. Opt. Soc. Am. A 11(1), 197–210 (1994). [CrossRef]
25. C. Amra, “Light scattering from multilayer optics. II. Application to experiment,” J. Opt. Soc. Am. A 11(1), 211–226 (1994). [CrossRef]
26. S. Maure, G. Albrand, and C. Amra, “Low-level scattering and localized defects,” Appl. Opt. 35(28), 5573–5582 (1996). [CrossRef]
27. M. Lequime, M. Zerrad, C. Deumie, et al., “A goniometric light scattering instrument with high-resolution imaging,” Opt. Commun. 282(7), 1265–1273 (2009). [CrossRef]
28. D. Ristau and T. Gross, “Ion beam sputter coatings for laser technology,” Proc. SPIE 5963, 596313 (2005). [CrossRef]
29. L. Pinard, B. Sassolas, R. Flaminio, et al., “Toward a new generation of low-loss mirrors for the advanced gravitational waves interferometers,” Opt. Lett. 36(8), 1407–1409 (2011). [CrossRef]
30. C. Amra, J. H. Apfel, and E. Pelletier, “Role of interface correlation in light scattering by a multiplayer,” Appl. Opt. 31(16), 3134–3151 (1992). [CrossRef]
31. M. Zerrad, M. Lequime, C. Deumié, et al., “Development of a goniometric light scatter instrument with sample imaging ability,” Proc. SPIE 7102, 710207 (2008). [CrossRef]
32. S. Schröder, M. Trost, M. Garrick, et al., “Origins of light scattering from thin film coatings,” Thin Solid Films 592, 248–255 (2015). [CrossRef]
33. M. Staggs, M. Balooch, M. R. Kozlowski, et al., “In-situ atomic force microscopy of laser-conditioned and laser-damaged HfO2/SiO2 dielectric mirror coatings,” Proc. SPIE 1624, 375–385 (1992). [CrossRef]
34. M. J. Brett, R. N. Tait, S. K. Dew, et al., “Nodular defect growth in thin films,” J. Mater. Sci.: Mater. Electron. 3(1), 64–70 (1992). [CrossRef]
35. L. Zhang, Z. Wei, J. Zhang, et al., “Quantitative assessment and suppression of defect-induced scattering in low-loss mirrors,” Opt. Lett. 43(24), 6025–6028 (2018). [CrossRef]
36. H. Li, Z. Wei, J. Zhang, et al., “Anomalous light scattering from multilayer coatings with nodular defects,” Opt. Express 30(4), 5414–5422 (2022). [CrossRef]
37. A. Hultaker, N. Benkert, S. Gliech, et al., “Characterizing CaF2 for VUV optical components: Roughness, surface scatter, and bulk scatter,” Proc. SPIE 4932, 444–451 (2003). [CrossRef]
38. S. Schröder, S. Gliech, and A. Duparré, “Measurement system to determine the total and angle-resolved light scattering of optical components in the deep-ultraviolet and vacuum-ultraviolet spectral regions,” Appl. Opt. 44(29), 6093–6107 (2005). [CrossRef]
39. M. C. Staggs, M. R. Kozlowski, W. J. Siekhaus, et al., “Correlation of damage threshold and surface geometry of nodular defects on HR coatings as determined by in-situ atomic force microscopy,” Proc. SPIE 1848, 234–242 (1993). [CrossRef]
40. X. Cheng and Z. Wang, “Defect-related properties of optical coatings,” Adv. Opt. Technol. 3(1), 65–90 (2014). [CrossRef]
41. B. Liao, D. J. Smith, and B. Mcintyre, “The formation and development of nodular defects in optical coatings,” NBS Spec. Publ. 746, 305 (1987).
42. J. Zhang, H. Jiao, B. Ma, et al., “Laser-induced damage of nodular defects in dielectric multilayer coatings,” Opt. Eng. 57(12), 1 (2018). [CrossRef]
43. X. Cheng, T. Ding, W. He, et al., “Using engineered nodules to study laser-induced damage in optical thin films with nanosecond pulses,” Proc. SPIE 8190, 819002 (2011). [CrossRef]
44. X. Cheng, J. Zhang, T. Ding, et al., “The effect of an electric field on the thermomechanical damage of nodular defects in dielectric multilayer coatings irradiated by nanosecond laser pulses,” Light: Sci. Appl. 2(6), e80 (2013). [CrossRef]
45. C. J. Stolz, R. J. Tench, M. R. Kozlowski, et al., “Comparison of nodular defect seed geometries from different deposition techniques,” Proc. SPIE 2714, 374–382 (1996). [CrossRef]
46. X. Cheng, Z. Shen, H. Jiao, et al., “Laser damage study of nodules in electron-beam-evaporated HfO2/SiO2 high reflectors,” Appl. Opt. 50(9), C357–C363 (2011). [CrossRef]
47. X. Liu, D. Li, Y. Zhao, et al., “Further investigation of the characteristics of nodular defects,” Appl. Opt. 49(10), 1774–1779 (2010). [CrossRef]
