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Abstract
Diffractive surface patterns with complex textures are generated on metal surfaces by picosecond UV laser ablation using an interference setup. Two diffraction gratings with variable distance and rotation angle provide a huge variety of interference patterns and thus resulting surface topographies. This variety can be further enhanced by selecting or blocking particular beams. A correlation analysis of the complex diffraction patterns generated by reflection of visible laser light at these surface topographies demonstrates that patterns with slightly differing fabrication parameters (variation of 0.5 mm in distance or 1° in rotation) can be clearly distinguished.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The interference of two or more coherent laser beams can be utilized for various kinds of micro- and nanostructuring of materials. Besides interference lithography requiring additional development steps, the direct laser processing by interference patterning as a single step process is very attractive for many applications.
Periodic volume patterns can be generated in the bulk of transparent materials like polymers [1,2]. The pattern consists of a periodic variation of the refractive index as a consequence of the modification of the chemistry or the density of the material. In this case mostly fs-lasers are applied enabling nonlinear absorption in the vicinity of the beam waist (localized intensity peaks).
Besides volumetric fabrication, periodic surface patterns can also be obtained on transparent as well as on absorbing materials like metals. They can be applied for marking, reduction of friction, cell growth engineering, self-cleaning surfaces, field amplification or many other purposes. The surface pattern can consist of a periodic modification of the material near the surface, or a periodic topography obtained by material ablation. However, in the case of materials with high thermal conductivity (e.g. metals), the use of short laser pulses (femtosecond or picosecond) is required to provide high structure resolution by limiting thermal diffusion of the absorbed energy to non-irradiated material [3–6]. For polymers or glass, high resolution is already obtained using nanosecond pulsed irradiation, preferentially at deep UV wavelengths [7,8].
In laser interference techniques, the required coherent beams are generated by reflective or diffractive beam splitters and recombined on or in the sample [9–14]. Segmentation of a beam and recombination of the generated beamlets can also be accomplished by prisms and acute or flat-topped multi-faceted glass pyramids [15,16]. The interference pattern depends on the number of beams, their angles of incidence, their amplitude, phase and polarization [17–21]. To utilize this variability, a number of irradiation schemes have been implemented. The phase of partial beams with respect to other partial beams is shifted by inserting or tilting glass plates in specific beams [22] or by using a set of two diffractive elements with variable spacing [23].
It has been shown that this kind of ablative periodic surface patterning can be utilized for marking or decorating surfaces of glass [24] or metals [25,26] with opalescent labels of high contrast. A technique based on a spatial light modulator (SLM) has been used to inscribe regular ≈1 μm period structures by two-, three- and four-beam interference patterns [27]. However, because of the discretized wavefront manipulation by SLMs, it is not possible to create arbitrary grating periods but only multiples of the SLM pitch size. Even much more critical is the adjustment of multiple beam interference patterns, where the interference planes of adjacent beams should be rotated at small angles. This poses a stringent limitation to the total number of interference patterns that can be realized.
In contrast, the scheme presented in this paper allows easy upscaling and selection of the number of interfering beams and, more importantly, an almost arbitrary adjustment of the angle of the interfering beams. In this way, an incomparably higher number of possible regular diffraction patterns can be realized. This is of significant importance for application e.g. in product traceability and counterfeit protection.
2. Interference pattern generator
The specific interference pattern is defined by the number of overlapping coherent beams and their respective angles and phase relations. To ensure coherent overlapping of all used beams, a projection imaging scheme is appropriate. The basic projection setup is described in [23]: a set of two diffraction gratings positioned in the object plane is imaged onto the sample surface. In the simplest case, for two identical linear gratings positioned in parallel planes with distance D, and with grating lines oriented perpendicular to each other, the path difference between the zero order and the ± first order beams diffracted at the first grating under the angle α when reaching the second grating amounts to
corresponding to a phase difference ofwith the wavelength λ. This phase difference between the particular beam pairs generated at the second grating remains constant throughout the further beam propagation and can be finely tuned by varying the separation of the gratings D. Similar relations are valid for the other diffracted beams.In extension of this configuration we choose two crossed-gratings with variable distance D (Fig. 1). One of the gratings can be rotated with respect to the other by an arbitrary angle.
Fig. 1 Two crossed gratings with variable distance and rotation angle for the generation of phase controlled diffracted beams.
The theoretically expected resulting zero and first order beams generated by this configuration are sketched in Fig. 2. At the first grating, the incoming beam is partially diffracted into eight first order beams and partially transmitted resulting in nine beams shown as red dots. At the second grating, each of these beams is diffracted in the same way resulting in a large number of additional first order beams. The zero order beam is diffracted into eight first order beams shown in green. The eight first order beams generated at grating one are diffracted in the same way, resulting in first order beams shown in light blue.
Fig. 2 Distribution of all first order beams generated at the first grating G1 (red dots) and the second grating G2 (green and blue dots) for six different rotation angles between the gratings. The white ring represents the open aperture of the optical system.
The variety of beam- and phase arrangements is enhanced by the choice of the rotation angle and the selection of interfering beams by blocking specific diffracted partial beams. The white ring shown in Fig. 2 represents the open aperture of the optical system. Arbitrary beams passing through this aperture can be selected for interference. The huge variability of this scheme can be seen in Fig. 2, where only a few beam configurations obtained with two gratings at various angles are shown. Figure 3 shows the same beam patterns recorded with a camera in front of the imaging optics.
Fig. 3 Camera pictures of the beam patterns obtained with the setup of Fig. 1 taken in front of the imaging optics at various rotation angles between the gratings.
With regard to the set-up shown in [23], several improvements have been implemented. To demonstrate the possibility of high duty operation on an industrial scale, a picosecond UV-laser system (Coherent Hyper Rapid 50) is used instead of the laboratory fs-excimer system applied in [23]. The laser wavelength of 355 nm is more appropriate to an industrial environment compared to 248 nm, while still providing sufficient sub-µm optical resolution. The pulse duration of ≤ 10 ps is short enough to ensure limited heat affected zones necessary for transferring optical resolution into topographical resolution even on highly heat conductive metals [3]. For metals, the sub-µm scale structure formation upon irradiation with ultrashort pulses was studied in detail in experiment and theory [6].
To utilize the laser energy most efficiently, fused silica phase masks are used as diffractive optical elements (DOE) for the beam splitting [10]. Such phase masks can be designed to optimally distribute the laser light into desired diffraction orders without significant losses [28]. Furthermore they exhibit far higher damage thresholds compared to otherwise used Cr on quartz masks.
2.1. Optical setup
The optical system used in the experiments is sketched in Fig. 4. The incoming beam ist split into multiple beams by two phase gratings having a structure period of 20 µm (pattern generator). Directly after the second grating the beams pass through a field mask of 14 x 14 mm2 which is imaged onto the sample surface with 14 x demagnification resulting in a strucured area of 1 mm2 and a structural period of 714 nm on the sample surface. Spaciotemporal overlap of all generated and selected beams on the sample surface is guaranteed in case of a quasi aberration free imaging system. The transmission of the complete system amounts to more than 50%. With a surface quality of the optics of λ/10 or better, a very stable adjustment is possible. The key of the setup is the variation of the interference structures by an introduced controlled phase change of partial beams. Thus the imaging optics must not introduce phase deviations due to imperfect optical surfaces or nonlinear diffraction effects. Therefore a specially designed all reflective Schwarzschild objective (SSO) was used. To guarantee well definded phase relations of all beams over the whole image area, both mirrors had a very high surface quality with a peak to valley deviation of less than 25 nm. The optical resolution of the technique is only limited by the numerical aperture of the imaging optics and the applied wavelength. Using UV light at 266 nm, stuctures with a period of less than 400 nm should be possible.
Fig. 4 Optical system for the fabrication of diffractive patterns. One element of the pattern generator as well as the beam selector can be rotated around the optical axis. SSO: Schwarzschild objective. The length of the setup from the pattern generator to the sample amounts to 350 mm, the width is 250 mm.
To achieve direct ablation on metal surfaces, the fluence on the sample surface must be in the range of several 100 mJ/cm2 demanding a single pulse energy is in the range of several mJ if the whole area is to be ablated simultaneously as demonstrated in [23]. This is far above the maximum pulse energy of only several 10 µJ actual solid state short pulse lasers can provide. To achieve the necessary energy density, the input beam was scanned over the aperture mask while at the same time the central point of the scanner was imaged onto the primary mirror of the SSO. With a beam size of approximately 1 mm2 and a pulse energy of 5 µJ on the field mask a maximum fluence of 500 mJ/cm2 could be obtained on the sample surface allowing direct ablation of the selected patterns in metal surfaces. With these parameters and a beam overlap of 10 µm in the image plane, well defined homogenous patterns were obtained on the surface of stainless steel. A processing rate of > 3 mm2/s has been obtained, and rates of > 10 mm2/s should be easily achievable.
2.2. Beam selection
To further increase the number of possible beam configurations and thus the number of distinguishable patterns, a special beam selector was constructed and placed directly behind the imaging optics where all beams are clearly separated. As the beam pattern and the available space behind the imaging optics are very small, a unique mechanical scheme had to be developed. 16 small blades are arranged in a circular pattern as shown in Fig. 5. Each individual blade is connected to a compact solenoid actuator that moves the blade into or out of the path of selected individual beams. In addition to the independent actuation of specific blades, the beam selector is mounted on a rotation axis allowing a precise rotation matched to the desired beam pattern. In this way, partial obstruction of beams can be avoided when the diffraction gratings are rotated. Thus all 16 beams emerging from the circular aperture can be selected individually. Figure 5 shows two examples, where 4 and 12 beams are selected for interference on the sample surface.
Fig. 5 Beam selector: self-centering blades set to select 4 red beams (left). Selector viewed from the solenoid side (right) set to transmit 12 beams.
3. Validation of the pattern generation approach
In order to assess the quality of the holographic markings and the variability of the laser written structures, a series of patterns were generated on stainless steel surfaces that had been polished to an optical grade surface roughness. During the irradiation experiments, both the laser process parameters (pulse energy, pulse overlap, repetition rate) and the configuration of the pattern generator have been varied. An example of such a series of holographic markings is shown in Fig. 6. The strong diffraction properties are documented by the colored appearance of the markings under white light illumination.
The surface structures within the individual marks were investigated by light microscopy, scanning electron microscopy (SEM), and diffraction pattern analysis. The results are illustrated in Fig. 7 for the example of a variation of the number of beams originating from the pattern generator. Using light microscopy (objective 100x/NA 0.9) the basic features of the microstructure can barely be resolved. However, the images can be used to evaluate the homogeneity of the structures within the processed area. Except from occasional low frequency variations, which are due to imperfections in the diffractive phase elements, the marked areas exhibit good uniformity.
Fig. 7 Light microscopy (top row), scanning electron microscopy (middle row) and diffraction pattern (bottom row) images of three holographic marks that were fabricated with different configurations of the pattern generator as shown in Fig. 5: (a) 4 beams, single phase mask; (b) 12 beams, rotation angle 10° between the two phase masks; (c) 12 beams, rotation angle 30°.
The SEM images, taken at an observation angle of 30°, reveal the structure and complexity of the surface topography with a number of fine details. While the structure in Fig. 7 (a), obtained with 4 beams originating from just a single DOE, basically consists of a crossed grating with approximately 1.4 µm period, a complex and versatile topography is obtained when 12 beams from the two DOEs of the pattern generator are employed during fabrication (Figs. 7 (b) and 7 (c)). The pattern and details of the topology correlate with the interference pattern of the irradiation beams and are highly dependent on the rotation angle between the two phase elements. In the example of Fig. 7, increasing the angle from 10° to 30° leads to a totally different pattern.
The bottom row of Fig. 7 depicts the diffraction patterns that are photographically recorded from a screen at a distance of ~100 mm when the marks are illuminated with a collimated beam from a He-Ne laser at 633 nm wavelength under normal incidence. The diffraction pattern that is obtained by irradiating the surface with 4 interfering beams (Fig. 7(a)) basically shows the usual diffraction spots up to first order ( ± (0,1),(1,0)) and (1,1)) as they are expected from a crossed grating in reflection configuration. Along with the surface topography, the diffraction pattern gets more complex and rich in detail when more interfering beams from the pattern generator are used during fabrication. While in Fig. 7(b) the majority of the numerous diffraction spots is still centered on each of the directions of simple first order diffraction, the pronounced pattern in Fig. 7(c) defies simple interpretation and gives an impression on the variability of the diffraction patterns that can be obtained.
A second example is shown in Fig. 8, where each of the marks has been irradiated using 12 beams from the pattern generator. Except for the angle of rotation between the two DOEs varying from 8° to 35°, all other parameters have been kept constant during fabrication. Yet, compared to Figs. 7(b) and 7(c), the pattern generator has also been set to a different phase relation. The diffraction patterns depicted in the bottom row of Fig. 8 were recorded directly by a CCD camera using an appropriate optical setup as described below. The SEM measurements and diffraction images demonstrate that slight changes in the configuration of the pattern generator lead to highly different structures on the irradiated surfaces and thus to strong variations in the resulting diffraction patterns.
Fig. 8 Scanning electron microscopy (top) and diffraction pattern (bottom) images of holographic marks that were fabricated with 12 beams from the pattern generator (see Fig. 5) and varying rotation angle between the phase masks: (a) 8°; (b) 16°; (c) 35°.
4. Pattern recognition
A more detailed evaluation of the surface structures with regard to the application as a holographic security feature requires a quantitative analysis of the diffraction patterns. For this purpose, an optical setup for the reproducible recording of the diffracted light has been built (Fig. 9).
It basically consists of an achromatic Fourier lens in a 2f-configuration to collect and transfer the far-field diffraction pattern to the back focal plane and a subsequent imaging telescope to adjust the size of the diffraction pattern on a CCD sensor where it is recorded. The holographic markings are illuminated with the 405 nm emission from a GaN-laser diode via a beam splitter and beam forming optics providing a collimated illumination beam under normal incidence. The size of the illuminated spot is adjusted to have a diameter of 0.3 mm. A central beam stop prevents the zero order reflection from reaching the detector. The numerical aperture of the initial Fourier lens determines the maximum diffraction angle that can be recorded and is related to the field of view in the diffraction images (see Fig. 8). A numerical aperture of NA = 0.46 in combination with the 405 nm wavelength ensure that the angular field includes the (1,1) diffraction order of the 1.4 µm period crossed grating, which often forms a basic building block of the surface structures.
To determine the amount of changes in the configuration of the pattern generator that are necessary to obtain distinguishable diffraction patterns, the diffraction images are compared by correlation analysis. As a measure for the similarity of two patterns we use the correlation coefficient , i.e. the maximum value of the normalized cross-covariance function [29]
where i1(r) and i2(r) denote the respective image intensities as recorded by the CCD camera with standard deviationsand , respectively. Here, the usual ensemble average is replaced by a spatial average over the field of view. To reduce the influence of high frequency noise, the images are low-pass filtered by convolution with a 5x5 unity kernel prior to the covariance calculation. Since it is usually more efficient, the calculation of the cross-correlation function ái1(r)i2(r+s)ñ is performed in the Fourier domain. According to the Wiener-Khintchine theorem, the cross correlation function can be obtained by an inverse Fourier transform of the image spectra. The correlation coefficient is then determined from the cross-covariance function by a maximum search with sub-pixel accuracy employing Fourier series expansion as the interpolation technique. Note that the algorithm accounts for possible displacements of the diffraction pattern which occur, for example, if the surface of a sample is slightly tilted. Rotations, on the other hand, will yield strong decorrelation. Yet, in the application as a holographic security mark, the orientation of the surface structure is usually well defined (for example it might be embedded in a data matrix code) and rotation might be viewed as an additional degree of freedom.As a first test, diffraction patterns resulting from holographic marks which are fabricated with identical parameters or patterns from different areas within a single mark are compared. In both cases, correlation coefficients in the range = 0.92 - 0.97 are obtained. The deviation from ideal, unity correlation is on the one hand caused by slight statistical variations in the fine details of the surface structure, which can thus be interpreted as speckle noise. On the other hand, correlation coefficients below unity from identically processed marks must also be attributed to deviations from perfect pattern homogeneity, which are caused, for example, by limited homogeneity of the diffraction gratings and possibly by slight variations in laser pulse energy. The contribution of limited homogeneity can be observed from variations in the low spatial frequency regime of the diffraction patterns (cf. Figure 10). Note, however, that due to the employed pattern generation scheme, no pixel structures are present in the holographic marks.
Fig. 10 SEM (top) and diffraction pattern (bottom) images of two holographic marks generated with 4 beams (see Fig. 5). From left to right the pulse energy during fabrication has been increased by a factor of 1.6 with all other parameters kept constant.
Figure 10 shows the example of two surfaces that are fabricated with identical configurations of the pattern generator (4 beams, single DOE) but pulse energy differing by a factor of 1.6. It is well known that the topography of such periodic patterns may change when varying the fluence due to lateral material movement [6]. The slightly more pronounced grating in case of the higher pulse energy produces slightly stronger side maxima. Correlation analysis of the two diffraction patterns yields a value of = 0.91. Since the pulse energy can be controlled with much closer tolerance, Fig. 10 can be considered as an extreme instance of a random pattern variation.
The effect of changing the configuration of the pattern generator on surface variations is illustrated in Figs. 11 and 12. In both cases, 12 beams from two DOEs have been employed for the fabrication of the surface structures. Figure 11 demonstrates the effect of the rotation angle between the two phase masks on the surface structure and the diffraction pattern. Again, all other parameters were kept constant. In the top row the rotation angle has been increased from 2° to 4°, resulting in a correlation value of the respective diffraction patterns of = 0.48.
Fig. 11 Diffraction pattern images from a set of holographic marks where the rotation angle between the phase masks in the pattern generator during fabrication has been increased from 2° to 12° as indicated.
Fig. 12 SEM (top) and diffraction pattern (bottom) images from a series of holographic marks generated with 12 beams (see Fig. 5). From left to right the distance between the phase masks in the pattern generator during fabrication has been increased from 0.3 mm to 1.2 mm as indicated.
Increasing the rotation angle by 2°, now starting from an initial value of 10°, yields decorrelations down to = 0.31 (Fig. 12, bottom). While the respective diffraction patterns look quite similar, they can be clearly distinguished by image processing. As expected, larger rotation angles lead to still stronger decorrelation. E.g., comparison of the patterns corresponding to 4° and 10° in Fig. 11 yield a correlation value of = 0.17. Considering a correlation coefficient of 0.9 as a threshold for the discrimination of two diffraction patterns, the results suggest that a rotation by 1° leads to distinguishable surface patterns.
The effect of phase relation between the irradiating beams during fabrication is depicted in Fig. 12. From left to right the distance between the phase masks has been increased from 0.3 mm to 1.2 mm while keeping the rotation angle constant at 45°. SEM images are included to illustrate the variations in surface structure. In this case, the positions of the individual diffraction orders are basically stationary and the change of the phase relation gives rise to a redistribution of scattered intensity among the individual orders. Increasing the distance between the phase masks from 0.3 mm 0.6 mm yields a decrease in correlation to = 0.90. From 0.6 mm to 1.2 mm, the correlation decreases to = 0.77. These results suggest that a shift by 0.5 mm in the phase mask distance leads to distinguishable surface patterns.
5. Conclusion
A variety of periodic laser ablation patterns can be created by using a pattern generator comprising a combination of diffraction gratings and a beam selector. A pattern generator consisting of two gratings leads to clearly distinguishable patterns when changing the grating distance by 0.5 mm or when rotating of one grating with respect to the other by 1°. This means that thousands of different patterns are possible. This number can be easily increased to billions by using additional gratings, applying a beam selector, or by using a set of marks with different patterns. Using a ps-laser, such marks can be directly placed on metallic surfaces and used for security labelling and product traceability. Further improvements are possible concerning the reduction of the overall size of the apparatus and the increasing of the transmission of the setup and the processing rate.
Funding
Bundesministerium für Wirtschaft und Energie (BMWi) (VP2411801AB9)
References
1. T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, “Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals,” Appl. Phys. Lett. 79(6), 725–727 (2001). [CrossRef]
2. J. Si, Z. Meng, S. Kanehira, J. Qiu, B. Hua, and K. Hirao, “Multiphoton-induced periodic microstructures inside bulk azodye-doped polymers by multibeam laser interference,” Chem. Phys. Lett. 399(1-3), 276–279 (2004). [CrossRef]
3. P. Simon and J. Ihlemann, “Machining of submicron structures on metals and semiconductors by ultrashort UV-laser pulses,” Appl. Phys., A Mater. Sci. Process. 63(5), 505–508 (1996). [CrossRef]
4. K. Paivasaari, J. J. J. Kaakkunen, M. Kuittinen, and T. Jaaskelainen, “Enhanced optical absorptance of metals using interferometric femtosecond ablation,” Opt. Express 15(21), 13838–13843 (2007). [CrossRef] [PubMed]
5. Y. Nakata, Y. Matsuba, and N. Miyanaga, “Sub-micron period metal lattices fabricated by interfering ultraviolet femtosecond laser processing,” Appl. Phys., A Mater. Sci. Process. 122(5), 532 (2016). [CrossRef]
6. D. S. Ivanov, V. P. Lipp, A. Blumenstein, F. Kleinwort, V. P. Veiko, E. Yakovlev, V. Roddatis, M. E. Garcia, B. Rethfeld, J. Ihlemann, and P. Simon, “Experimental and theoretical investigation of periodic nanostructuring of Au with ultrashort UV laser pulses near the damage threshold,” Phys. Rev. Appl. 4(6), 064006 (2015). [CrossRef]
7. P. E. Dyer, R. J. Farley, R. Giedl, and D. M. Karnakis, “Excimer laser ablation of polymers and glasses for grating fabrication,” Appl. Surf. Sci. 96–98, 537–549 (1996). [CrossRef]
8. J. Békési, J. Meinertz, J. Ihlemann, and P. Simon, “Grating Interferometers for Efficient Generation of Large Area Grating Structures via Laser Ablation,” J. Laser Micro Nanoeng. 2(3), 221–224 (2007). [CrossRef]
9. J. Bekesi, J. Meinertz, P. Simon, and J. Ihlemann, “Sub-500-nm patterning of glass by nanosecond KrF excimer laser ablation,” Appl. Phys., A Mater. Sci. Process. 110(1), 17–21 (2013). [CrossRef]
10. J. Ihlemann, J.-H. Klein-Wiele, J. Bekesi, and P. Simon, “UV Ultrafast Laser Processing using Phase Masks,” J. Phys. Conf. Ser. 59, 449–452 (2007). [CrossRef]
11. E. Molotokaitė, M. Gedvilas, G. Račiukaitis, and V. Girdauskas, “Picosecond Laser Beam Interference Ablation of Thin Metal Films on Glass Substrate,” J. Laser Micro Nanoeng. 5(1), 74–79 (2010). [CrossRef]
12. Y. Bourgin, S. Bakkali, Y. Jourlin, S. Tonchev, and O. Parriaux, “Monolithic double-grating phase mask for large-period highly coherent grating printing,” Opt. Lett. 34(24), 3800–3802 (2009). [CrossRef] [PubMed]
13. M. Steger, C. Hartmann, S. Beckemper, J. Holtkamp, and A. Gillner, “Fabrication of Hierarchical Structures by Direct Laser Writing and Multi-Beam-Interference,” J. Laser Micro Nanoeng. 8(3), 210–215 (2013). [CrossRef]
14. A. F. Lasagni, T. Roch, D. Langheinrich, M. Bieda, and A. Wetzig, “Large Area Direct Fabrication of periodic Arrays using Interference Patterning,” Phys. Proc. 12, 214–220 (2011). [CrossRef]
15. L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and three-dimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86(24), 241102 (2005). [CrossRef]
16. M. Lei, B. Yao, and R. A. Rupp, “Structuring by multi-beam interference using symmetric pyramids,” Opt. Express 14(12), 5803–5811 (2006). [CrossRef] [PubMed]
17. Y. Nakata, K. Murakawa, K. Sonoda, K. Momoo, N. Miyanaga, and T. Hiromoto, “Designing of interference pattern in ultra-short pulse laser processing,” Appl. Phys., A Mater. Sci. Process. 112(1), 191–196 (2013). [CrossRef]
18. J. Huang, S. Beckemper, A. Gillner, and K. Wang, “Tunable surface texturing by polarization-controlled three-beam interference,” J. Micromech. Microeng. 20(9), 095004 (2010). [CrossRef]
19. S. Indrisiunas, B. Voisiat, M. Gedvilas, and G. Raciukaitis, “Two complementary ways of thin-metal-film patterning using laser beam interference and direct ablation,” J. Micromech. Microeng. 23(9), 095034 (2013). [CrossRef]
20. X. Jia and L. Dong, “Fabrication of complex micro/nanopatterns on semiconductors by the multi-beam interference of femtosecond laser,” Phys. Proc. 56, 1059–1065 (2014). [CrossRef]
21. D. Wang, Z. Wang, Z. Zhang, Y. Yue, D. Li, and C. Maple, “Effects of polarization on four-beam laser interference lithography,” Appl. Phys. Lett. 102(8), 081903 (2013). [CrossRef]
22. S. Juodkazis, T. Kondo, V. Mizeikis, S. Matsuo, H. Murata, and H. Misawa, “Three-dimensional recording by femtosecond pulses in dielectrics,” Proc. SPIE 4977, 94–108 (2003). [CrossRef]
23. J.-H. Klein-Wiele and P. Simon, “Fabrication of periodic nanostructures by phase-controlled multiple-beam interference,” Appl. Phys. Lett. 83(23), 4707–4709 (2003). [CrossRef]
24. J. Meinertz, T. Fricke-Begemann, and J. Ihlemann, “Micron and sub-micron gratings on glass by UV laser ablation,” Phys. Proc. 41, 701–705 (2013). [CrossRef]
25. J. J. J. Kaakkunen, K. Paivasaari, and P. Vahimaa, “Fabrication of large-area hole arrays using high-efficiency two-grating interference system and femtosecond laser ablation,” Appl. Phys., A Mater. Sci. Process. 103(2), 267–270 (2011). [CrossRef]
26. J. Bekesi, P. Simon, and J. Ihlemann, “Deterministic sub-micron 2D grating structures on steel by UV-fs-laser interference patterning,” Appl. Phys., A Mater. Sci. Process. 114(1), 69–73 (2014). [CrossRef]
27. F. Knorr, A. Uyttendaele, J. Stauch, F. Schechtel, Y. Reg, and M. Zimmermann, “Large-angle programmable direct laser interference patterning with ultrafast laser using spatial light modulator,” Phys. Proc. 83, 1170–1177 (2016). [CrossRef]
28. J. Ihlemann and R. Weichenhain-Schriever, “Laser Based Rapid Fabrication of SiO2-phase Masks for Efficient UV-laser Micromachining,” J. Laser Micro Nanoeng. 4(2), 100–103 (2009). [CrossRef]
29. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed., (McGraw-Hill, 1991).
