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Abstract
It is known that ultrashort laser welding of materials requires an accurate laser beam focusing and positioning onto the samples interface. This puts forward severe challenges for controlling the focus position particularly considering that the tightly focused Gaussian beam has a short, micron-sized Rayleigh range. Here we propose a large-focal-depth welding method to bond materials by using non-diffractive femtosecond laser Bessel beams. A zero-order Bessel beam is produced by an axicon and directly imaged on the interface between silicon and borosilicate glass to write welding lines, ensuring a non-diffractive length in the 500 μm range and micron-sized FWHM diameter. The focal-position tolerant zone for effective welding increases thus many-fold compared to traditional Gaussian beam welding. The shear joining strength of the sample welded by this method could be as high as 16.5 MPa. The Raman spectrum and element distribution analyses within the cross section of welding line reveal that substance mixing has occurred during laser irradiation, which is considered as the main reason for femtosecond laser induced bonding.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultrashort laser welding, with its intrinsic feature of high spatial selectivity, high precision, and zero discharge of hazardous substances has been demonstrated to be a promising technology, capable of meeting the higher demand in advanced joining techniques. It can be applied in various fields, including precision machinery, healthcare, and optoelectronic industries [1–3]. Especially, the ultrafast welding technology can be applied in the welding of transparent-transparent and transparent-nontransparent materials with no need of inserting absorption layers. When a single ultrashort laser beam is tightly focused onto the sample interface, energy absorption occurs intermediated via plasma generation. In the aftermath quasi-isochoric heating happens, increasing locally the temperature. The level of temperature can be equally supported rapidly succeeding pulses at high repetition rates. Furthermore, thermal expansion, diffusion and phase transformation, would subsequently occur within and outside the laser irradiated region [4–7], assisting the local mixing. All these processes are affected by the energy deposition efficiency and by the lifetime of the heated regions, adjustable via laser pulse parameters. Eventually, a strong bonding strength will be formed on sample interface.
Since Tamaki et al. firstly demonstrated the direct welding of silica glass substrates using 1 kHz, 85 fs, 800 nm Gauss laser beam [1], many works have been published on ultrashort laser welding in recent years [2, 8–15]. These reports mainly focus on mechanism exploration, process optimization, and techniques for specific materials welding. For instance, Watanabe et al. firstly demonstrated the feasibility of direct welding of dissimilar materials using 1 kHz femtosecond laser pulses [2]. Miyamoto et al. [16] reported a simulation model, which can determine laser absorption and temperature distribution in transparent materials, and clarify the ultrashort laser welding mechanism. Then Sugioka et al. and Wu et al. [17, 18] proposed a double-pulse ultrafast laser welding method to increase the localized state absorption efficiency, aiming to improve the sample bonding strength. In addition, Cvecek et al. and Chen et al. [10, 12] have recently realized the joining of transparent glass without pre-existing optical contact by using ultrashort laser source with high repetition rate, respectively. Especially, this technology has been used to weld semiconductors and glass, shows potential application in the packaging of integrated photonic devices, micro-optoelectromechanical systems and solar batteries. Non-alkali glass and silicon substrate has been demonstrated to be welded together using femtosecond laser pulses, resulting in a joining strength of 3.74 MPa [3]. Then, the joining strength of silicon-glass was further improved to tens of MPa by using high repetition rate picosecond laser pulses [15], showing obvious superiority to the nanosecond laser welding technology [19].
However, in all these case reports, the welding experiments were conducted by using ultrashort laser Gaussian beam which is known to have a short Rayleigh range. Considering that ultrashort laser welding require the laser focus to be accurately placed onto sample interface, this would pose a noteworthy challenge for controlling focal position and would increase the difficulty for the industrial application of this emerging welding technology.
Bessel beams, which constitute a class of solutions to the Helmholtz equation [20], have been demonstrated to have unique feature of nearly diffraction-free propagation [21] and have been applied in various fields [22–27]. The focused Bessel-Gauss beam could have a long focal depth (non-diffractive depth), which, geometry-dependent, is typically much larger than the Rayleigh range of focused Gaussian beam. Therefore, the employment of an ultrashort Bessel beam could be used to solve the above existing problem and enable ultrashort laser welding to be relatively relaxed about focal position. The Bessel beam can be generated by various methods, involving among others: aperture modulation [21], phases-design by spatial light modulator [28], aberrating lenses [29] and axicon based techniques [30, 31], under a finite energy approximation. The axicon based method is considered to be the most convenient and effective way for high intensity Bessel beam generation.
In this paper, we propose a Bessel beam based ultrashort laser welding method. The manuscript describes the generation and the application of the Bessel welding methods with subsequent mechanical characterization and elemental mapping of the interaction region. An axicon is used in the experiment to convert Gaussian beams into Bessel beams. Then the 4f system is subsequently utilized to demagnify the initial Bessel beams and image it onto the sample interface to writing welding lines. Comparative studies have been conducted to clarify the advantages of using ultrashort laser Bessel beam in a specific laser interaction regime. The welding of silicon-glass with high accuracy is successfully demonstrated by using this ultrashort laser Bessel beam welding method and the underlying processes are discussed based on the analyses of the laser affected regions across the interface.
2. Experiments
The Bessel beam can be conveniently generated by the axicon. However, in order to induce nonlinear absorption in transparent materials, the ultrashort laser beam usually needs to be tightly focused into micron size in diameter. Therefore, a 4f system is needed to further demagnify the initial Bessel beams produced by the axicon, producing an image at the place of interaction. In addition, considering the transparent borosilicate glass has a thickness of 1 mm in the experiment, the demagnified Bessel beam is expected have an appropriate focus depth no more than 1 mm. To obtain an appropriate ultrashort laser Bessel beam, simulation of Bessel beam intensity distribution is conducted in this work. Considering the Kirchhoff-Fresnel integral, the intensity profile of the Bessel beam generated by an axicon can be obtained by using the stationary phase method [32].
The simulated intensity distribution of Bessel beam demagnified by 4F system in borosilicate glass (Schott D263, nm = 1.52) are shown in Figs. 1(b) and 1(c), respectively. The base angle and material refractive index of axicon is 2° and 1.45, respectively. The laser wavelength λ and beam radius w0 are set as 0.8 μm and 3000 μm, respectively. The resulting Bessel beam is calculated to have a half-cone angle of 11.6° in the borosilicate glass utilizing Snell's law taking the demagnification factor (20) and sample refractive index [23, 32]. It could be seen that the Bessel beam has a relatively uniform intensity distribution in the propagation direction, with a large focal depth of 583 μm (FWHM). In the transverse profile of Bessel beam as shown in Figs. 1(c), the central spot and other surrounding rings retain circular symmetry, and the diameter of the central lobe is 0.9 μm (FWHM). The simulated intensity axial and transverse distributions of a focused Gaussian beam, which directly passes through the convex lens are shown in Figs. 1(d) and 1(e). The transverse profile of focused Gaussian beam has no surrounding rings, being significantly different from the Bessel beam. The focal spot diameter of Gaussian beam is 1.69 μm in 1/e2. The calculated Rayleigh range of focused Gaussian beam is 20.9 μm, which is much shorter than the focal depth of Bessel beam. Therefore, it is evident that Bessel beam has significant advantages in extending focal depth for ultrashort laser welding experiments. Considering the large focal depth, it is necessary to appropriately increase the pulse energy for Bessel beam welding to achieve same welding performance of Gaussian beam welding.
Fig. 1 (a) Experimental setup of ultrashort laser welding using Bessel beam; (b) longitudinal and (c) radial intensity distribution of Bessel beam, (d) longitudinal and (e) radial intensity distribution of Gaussian beam.
The experimental setup used for ultrashort laser welding is shown in Fig. 1(a). An amplified Ti:sapphire laser system emitting 800 nm, 140 fs (FWHM), 50 kHz Gaussian laser pulses are used in the experiment. The half wave plate (HWP) combined with a thin film polarizer (TFP) is employed to adjust the pulse energy. The Gaussian beam passing through the mirrors (Mi) and mechanical shutter (S) is transformed into a Bessel beam by an axicon (base angle δ = 2°, refractive index nax = 1.45). A 4f system composed of a convex lens (f1 = 200 mm) and a 20 × objective lens (NA = 0.42, effective focal length f2 = 10 mm) is utilized to demagnify and image the initial Bessel beam onto sample interface through the borosilicate glass. Note that, for Gaussian beam welding, the femtosecond laser beam is directly focused by 20 × objective lens, without passing through the axicon and convex lens. The single crystal silicon and borosilicate glass, with flatness below λ/4, are clamped together and fixed on a computer-controlled XYZ motion stage for precision position adjustment during laser welding process.
The shear joining strength of welded sample is measured by the setup described in our previous work [13]. The optical transmission microscopy (OTM), optical reflection microscopy (ORM) and scanning electron microscopy (SEM) are used to characterize the morphology of the laser-matter interaction region. The Raman spectrometer and energy dispersive X-ray spectroscopy (EDS) are utilized to analyze the chemistry structure and element content within the cross section of welding lines.
3. Results and discussion
3.1 Interface modification by femtosecond laser Bessel beam
The permanent modifications induced on the interface between silicon and borosilicate glass by the femtosecond laser Bessel beam have been carefully studied. The pulse energy and translation speed are fixed at 8.0 μJ and 200 μm/s, respectively. Figure 2 shows the OTM images of cross section of the laser induced modifications varying the focus position. The enlarged view of interface modification characterized by ORM is shown on the right side. It is obvious that a filament-like interaction region visible in white color is induced in the transparent borosilicate glass. The filament width is measured to be about 4 μm, while the filament length is measured to be about 380 μm, shorter than the simulated focal depth of Bessel beam. This may due to the inaccuracy in the setting of imaging distances which affects the Bessel beam elongation. No high-aspect-ratio microhole [23, 32] which has been reported as being induced in fused silica and PMMA is observed, which is mainly due to the difference in the expansion coefficient and the rigidity of the matrix. When the focal position moves towards sample interface, the filament would be stopped in the near surface of silicon which is non-transparent at the wavelength of 800 nm. The absorbed laser energy on sample interface would induce permanent modification in structure and composition in the near-interface region, which is decisive for the welding process. The ORM images present the morphology of melting pool induced by the Bessel beam. As the sample is processed in a condition of optical contact, the induced melting pool could prevent cracks and suppress shrinkage stress in the welding [15]. It could be seen that the shape of melting pool keeps nearly unchanged when varying the focal position (f0, midpoint of focal depth) in the range of + 200 μm to −210 μm. The width and depth of the melting pool are characterized to be about 27 μm and 15 μm, respectively. This is mainly due to the fact that the laser intensity within the focal field (non-diffractive region) keeps quasi constant in a large range. Consequently, the focused Bessel beam would potentially enable the welding process to be relatively relaxed about the focus position controlling.
Fig. 2 The samples welded by femtosecond laser Bessel beam with different focus positions under a fixed pulse energy of 8.0 μJ and speed of 200 μm/s. The left part is the cross section of the sample characterized by OTM, and the right part is the enlarged images characterized by ORM.
To analyze comparatively, the silicon and borosilicate glass were equally welded together using femtosecond laser Gaussian beams. A similar approach has also been studied by other groups [3, 15, 33]. In this case, the pulse energy and translation speed are fixed at an optimized value of 2.0 μJ and 200 μm/s, respectively. It is found that the modifications induced by femtosecond laser Gaussian beam show a different behavior. Figure 3 shows the OTM and ORM images of cross section of laser induced modifications by varying the focus position. The focused Gaussian beam induced a typical short interaction region in the borosilicate glass. The length and width of the damage are measured to be 45 μm and 4 μm, respectively. The ORM images show that the morphology of melting pool changes obviously with varying focal position f0. The depth of melting pool increases rapidly when the focus approaches to sample interface. At the same time the width of the melting pool increases when the focus moves away from sample interface. The similar results are also observed in the picosecond laser welding between glass and glass [12]. This is mainly due to the fact that the focused Gaussian beam has a short Rayleigh length and a large propagation angle. Therefore, the melting pool would only be well developed when the Gaussian beam focus is positioned near enough to sample interface.
Fig. 3 The samples welded by femtosecond laser Gaussian beam with different focus position under a fixed pulse energy of 2.0 μJ and speed of 200 μm/s. The left part is the cross section of the sample characterized by OTM, and the right part is the enlarged images characterized by ORM.
3.2 Direct welding by femtosecond laser Bessel beam
The silicon and the borosilicate glass in optical contact are directly welded together by femtosecond laser Bessel beam and Gaussian beam, respectively using a multiline procedure. The midpoint of focal depth is placed on sample interface. The ORM images of welding lines on sample interface induced by Bessel beam and Gaussian beam are shown in Fig. 4(a) and 4(b), respectively. A sealed region with a size of 9 × 2 mm2 is formed within the optical contacting region. The interval between the centers of adjacent welding lines is 50 μm. The welding velocity is fixed at 200 μm/s. The pulse energy of Gaussian beam is fixed at an optimized value of 2.0 μJ, while the pulse energy of Bessel beam is fixed at 8.0 μJ. The width of welding line induced by Bessel beam is measured to be about 25 μm, which is wider than that of welding line induced by Gaussian beam (15 μm). This mainly because that silicon is non-transparent at the irradiating laser wavelength, the side lobes of Bessel beam imaged on sample interface may induce damage on silicon side and widen the welding line.
Fig. 4 Top view of welding lines induced by femtosecond laser Bessel beam and Gaussian beam at a same welding speed of 200 μm/s: (a) Bessel beam at pulse energy of 8.0 μJ, (b) Gaussian beam at pulse energy of 2.0 μJ.
The shear joining strength of samples welded by femtosecond laser Bessel beam and Gaussian beam varying focal position are measured by the setup described in our previous work [13]. The thrust force (Fc) in a downward direction is applied onto the silicon to separate the sample into two substrates. The shear joining strength (τ) could be calculated by τ = (Fc-Fo)/Sw, where Fo is the optical contact force, Sw is the sealed area. The welding parameters are consistent with those described above. Note that the values of each point in the figures take an average of three measurement results to reduce measurement error.
Figure 5(a) represents the relationship between shear joining strength and focal position in the Bessel-beam welding. The maximum joining strength is measured to be about 16.5 MPa, and it could be further improved by decreasing the interval between adjacent welding lines. This is because the forming bond mainly concentrates in the part of welding line [15]. The shear joining strength keeps a high value of 12.9 MPa to 16.5 MPa, when the midpoint of focal depth varies from −210 μm to + 200 μm. This is mainly due to the fact that the laser intensity of Bessel beam nearly keeps quasi-constant high value in a large range, which enables the femtosecond laser to induce a melting pool on the sample interface and form a strong bond. When the midpoint of laser focus is placed out of the range from −210 μm to + 200 μm, for instance of fo = −230 μm and fo = + 220 μm, the shear joining strength drastically decreases.
Fig. 5 Shear joining strength of samples welded by femtosecond laser (a) Bessel beam and (b) Gaussian beam varying focal position.
Figure 5(b) represents the relationship between shear joining strength and focal position in the Gaussian-beam welding. The maximum of shear joining strength is measured to be about 13.5 MPa, which is less than that in Bessel-beam welding. This is potentially due to the fact that the width of the welding lines induced by Bessel beam is wider than that of Gaussian beam welding in the experiment. Different from Bessel beam welding (tolerant zone, 410 μm), the focal position tolerant zone for Gaussian beam welding is only 75 μm. When the midpoint of laser focus is placed out of the range from −30 μm to + 45 μm, the shear joining strength begins to drastically decrease. This is attributed to the short Rayleigh length of focused Gaussian beam. Therefore, compared with Gaussian beam, the focused Bessel beam has significant advantage in increasing the focal-position tolerant zone.
In order to characterize the joining area, several characterization methods were applied. Raman spectra within the cross section of samples (across the interface) were characterized by a Renishaw Invia Raman spectrometer equipped with a CW laser operating at 532 nm. Measurements reported here were performed at room temperature, with an x50 objective, across the range from 400 to 1500 cm−1. Note that the sample cross section was polished and cleaned ultrasonically before characterization, and the detecting direction is perpendicular to the welding lines, advancing from one material side across the interface exposed by polishing. Figure 6(a) shows the Raman spectrum of borosilicate glass outside the laser irradiated region. It could be seen that the spectrum can be divided into two regions. In the low-frequency region, there is a broad band at 400 to 600 cm−1, with peak at 481 cm−1, which is assigned to the rocking or bending motion of Si-O-Si bonds and Si-O-B bonds of glass network [34, 35]. The high-frequency region is characterized by the strong 920 cm−1 band and two shoulder peaks near 807 cm−1 and 1065 cm−1, respectively. According to the previous work [36–38], the peak at 807 cm−1 is assigned to Q0 silicon tetrahedra that arises due to Si–O–Si linkages, while the peak at 920 cm−1 are potentially due to the vibrational mode of the Q1 unit. The peak at 1065 cm−1 has been assigned to the Q3 vibrational unit. Note that, Qn represents the kinds of silicate units existing in the glass network, n is the number of bridging oxygen. Figure 6(b) shows the Raman spectrum of silicon outside the laser irradiated region. It is apparent that a sharp peak of single crystal silicon locates at 520 cm−1. Figure 6(c) presents the Raman spectrum of the sample (on the glass side) within the cross section of welding lines. The existing of the peak at 520 cm−1, which is the characteristic peak of single crystal silicon [39], indicates that the materials mixing has occurred during the process of materials phase transition. There is no evident change in the high-frequency region, compared with that of borosilicate glass. However, in the low-frequency region, the peak width apparently decreases, combined with peak shifting from 481 cm−1 to 493 cm−1 and intensity enhancement. This potentially due to the laser induced Si ions migration or structural modification.
Fig. 6 Raman Spectrum within the cross section of sample: (a) borosilicate glass side (outside laser irradiated region), (b) silicon side (outside laser irradiated region), (c) borosilicate glass side (within the cross section of melting pool).
The laser-induced materials mixing also could be proved by characterizing the morphology and chemical composition of cross section of welding line. The cross section of welding line is shown in Fig. 7(a), its magnified version is given in the upper right corner. It is evident that the inner gap between borosilicate glass and silicon is well eliminated. The width and depth of the cross section of welding line are 25 μm and 17 μm, respectively. Figure 7(b) presents the element distribution within the cross section of welding line analyzed by EDS. The concentration gradients of Na and Si along the longitudinal direction indicate that material mixing has occurred during laser irradiation, which is consistent with the characterization result by Raman spectrometer. A similar result has also been observed in the previous work on picosecond laser welding between silicon and glass [15]. The mechanism has been extensively discussed in the previous work. When the femtosecond laser Bessel beam is imaged onto the sample interface, the electrons within the focal region will be rapidly heated, and then transfer energies to the lattice. The heated materials will be melted and flow occurs across the interface accompanied by elemental diffusion driven by thermal gradient. Therefore, materials mixing will be induced, a process that will also be strengthened by subsequent laser pulses. Eventually, the inner gap between silicon and borosilicate glass will be eliminated leaving a complete material mixing within the laser induced melting pool.
Fig. 7 (a) Morphology and (b) chemical elements analysis of the cross section of welding line induced by femtosecond laser Bessel beam. The dotted line in white color represents the sample interface before irradiating. The laser beam incident along the X direction. The welding lines were written in the Z direction. The concentration gradients of Na and Si along the longitudinal direction (yellow line) indicate that material mixing has occurred within the laser irradiating region.
4. Conclusion
In summary, in this work we propose a Bessel beam based femtosecond laser welding method. An axicon in a 4f demagnifying optical system is utilized to generate and project the zero-order Bessel beam across the materials interface. The large non-diffractive focal depth of the demagnified Bessel beam in the range of few hundreds of microns is demonstrated to have significant advantages in relaxing the strict requirement on precisely controlling of focal position. The focal-position tolerant zone has increased 5.5-fold by using zero-order Bessel beam, comparing with Gaussian beam welding. The shear joining strength of the sample is measured to be as high as 16.5 MPa. The materials mixing within the irradiated region has been confirmed by means of Raman spectrometry and EDS, being considered as the main reason for the bonding strength.
Funding
National Natural Science Foundation of China (NSFC) (61378019, 61775236).
Acknowledgments
The corresponding author thanks Dr. Chengyun Zhang and Dr. Zhendong Chen in Shaanxi Normal University for Raman spectra and SEM characterization.
References and links
1. T. Tamaki, W. Watanabe, J. Nishii, and K. Itoh, “Welding of transparent materials using femtosecond laser pulses,” Jpn. J. Appl. Phys. 44(22), L687–L689 (2005). [CrossRef]
2. W. Watanabe, S. Onda, T. Tamaki, K. Itoh, and J. Nishii, “Space-selective laser joining of dissimilar transparent materials using femtosecond laser pulses,” Appl. Phys. Lett. 89(2), 1726 (2006). [CrossRef]
3. T. Tamaki, W. Watanabe, and K. Itoh, “Laser micro-welding of transparent materials by a localized heat accumulation effect using a femtosecond fiber laser at 1558 nm,” Opt. Express 14(22), 10460–10468 (2006). [CrossRef] [PubMed]
4. K. Sokolowski-Tinten, J. Bialkowski, A. Cavalleri, D. von der Linde, A. Oparin, J. Meyer-ter-Vehn, and S. I. Anisimov, “Transient States of Matter during Short Pulse Laser Ablation,” Phys. Rev. Lett. 81(1), 224–227 (1998). [CrossRef]
5. S. K. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002). [CrossRef] [PubMed]
6. P. Lorazo, L. J. Lewis, and M. Meunier, “Short-Pulse Laser Ablation of Solids: From Phase Explosion to Fragmentation,” Phys. Rev. Lett. 91(22), 225502 (2003). [CrossRef] [PubMed]
7. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008). [CrossRef]
8. W. Watanabe, S. Onda, T. Tamaki, and K. Itoh, “Direct joining of glass substrates by 1 kHz femtosecond laser pulses,” Appl. Phys. B 87(1), 85–89 (2007). [CrossRef]
9. D. Hélie, M. Bégin, F. Lacroix, and R. Vallée, “Reinforced direct bonding of optical materials by femtosecond laser welding,” Appl. Opt. 51(12), 2098–2106 (2012). [CrossRef] [PubMed]
10. K. Cvecek, R. Odato, S. Dehmel, I. Miyamoto, and M. Schmidt, “Gap bridging in joining of glass using ultra short laser pulses,” Opt. Express 23(5), 5681–5693 (2015). [CrossRef] [PubMed]
11. A. Volpe, F. Di Niso, C. Gaudiuso, A. De Rosa, R. M. Vázquez, A. Ancona, P. M. Lugarà, and R. Osellame, “Welding of PMMA by a femtosecond fiber laser,” Opt. Express 23(4), 4114–4124 (2015). [CrossRef] [PubMed]
12. J. Chen, R. M. Carter, R. R. Thomson, and D. P. Hand, “Avoiding the requirement for pre-existing optical contact during picosecond laser glass-to-glass welding: erratum,” Opt. Express 23(21), 28104–28105 (2015). [CrossRef] [PubMed]
13. G. Zhang, J. Bai, W. Zhao, K. Zhou, and G. Cheng, “Interface modification based ultrashort laser microwelding between SiC and fused silica,” Opt. Express 25(3), 1702–1709 (2017). [CrossRef]
14. K. Sugioka and Y. Cheng, “Ultrafast lasers-reliable tools for advanced materials processing,” Light Sci. Appl. 3(4), e149 (2014). [CrossRef]
15. I. Miyamoto, Y. Okamoto, A. Hansen, J. Vihinen, T. Amberla, and J. Kangastupa, “High speed, high strength microwelding of Si/glass using ps-laser pulses,” Opt. Express 23(3), 3427–3439 (2015). [CrossRef] [PubMed]
16. I. Miyamoto, K. Cvecek, Y. Okamoto, and M. Schmidt, “Internal modification of glass by ultrashort laser pulse and its application to microwelding,” Appl. Phys., A Mater. Sci. Process. 114(1), 187–208 (2014). [CrossRef]
17. K. Sugioka, M. Iida, H. Takai, and K. Micorikawa, “Efficient microwelding of glass substrates by ultrafast laser irradiation using a double-pulse train,” Opt. Lett. 36(14), 2734–2736 (2011). [CrossRef] [PubMed]
18. S. Wu, D. Wu, J. Xu, H. Wang, T. Makimura, K. Sugioka, and K. Midorikawa, “Absorption mechanism of the second pulse in double-pulse femtosecond laser glass microwelding,” Opt. Express 21(20), 24049–24059 (2013). [CrossRef] [PubMed]
19. C. Luo and L. Lin, “The application of nanosecond-pulsed laser welding technology in MEMS packaging with a shadow mask,” Sens. Actuators A Phys. 97, 398–404 (2002). [CrossRef]
20. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4(4), 651–654 (1987). [CrossRef]
21. J. Durnin, J. Miceli Jr, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987). [CrossRef] [PubMed]
22. F. Courvoisier, P. A. Lacourt, M. Jacquot, M. K. Bhuyan, L. Furfaro, and J. M. Dudley, “Material nanoprocessing with nondiffracting femtosecond Bessel beams,” Opt. Lett. 34(20), 3163–3165 (2009). [CrossRef] [PubMed]
23. M. K. Bhuyan, P. K. Velpula, J. P. Colombier, T. Olivier, N. Faure, and R. Stoian, “Single-shot high aspect ratio bulk nanostructuring of fused silica using chirp-controlled ultrafast laser Bessel beams,” Appl. Phys. Lett. 104(2), 219–377 (2014). [CrossRef]
24. A. Marcinkevicious, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel Beams for Microfabrication of Dielectrics by Femtosecond Laser,” Jpn. J. Appl. Phys. 40, 1197 (2001). [CrossRef]
25. M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012). [CrossRef]
26. G. Cheng, A. Rudenko, C. D’Amico, T. E. Itina, J. P. Colombier, and R. Stoian, “Embedded nanogratings in bulk fused silica under non-diffractive Bessel ultrafast laser irradiation,” Appl. Phys. Lett. 110(26), 261901 (2017). [CrossRef]
27. G. Wang, Y. Yu, L. Jiang, X. Li, Q. Xie, and Y. Lu, “Cylindrical shockwave-induced compression mechanism in femtosecond laser Bessel pulse micro-drilling of PMMA,” Appl. Phys. Lett. 110(16), 161907 (2017). [CrossRef]
28. N. Chattrapiban, E. A. Rogers, D. Cofield, W. T. Hill, and R. Roy, “Generation of nondiffracting Bessel beams by use of a spatial light modulator,” Opt. Lett. 28(22), 2183–2185 (2003). [CrossRef] [PubMed]
29. R. M. Herman and T. A. Wiggins, “Production and uses of diffractionless beams,” J. Opt. Soc. Am. A 8(6), 932–942 (1991). [CrossRef]
30. J. H. Mcleod, “The Axicon: A New Type of Optical Element,” J. Opt. Soc. Am. 44(8), 592 (1954). [CrossRef]
31. G. Roy and R. Tremblay, “Influence of the divergence of a laser beam on the axial intensity distribution of an axicon,” Opt. Commun. 34(1), 1–3 (1980). [CrossRef]
32. Q. Xie, X. Li, L. Jiang, B. Xia, X. Yan, W. Zhao, and Y. Lu, “High-aspect-ratio, high-quality microdrilling by electron density control using a femtosecond laser Bessel beam,” Appl. Phys., A Mater. Sci. Process. 122(2), 136 (2016). [CrossRef]
33. A. Horn, I. Mingareev, A. Werth, M. Kachel, and U. Brenk, “Investigations on ultrafast welding of glass–glass and glass–silicon,” Appl. Phys., A Mater. Sci. Process. 93(1), 171–175 (2008). [CrossRef]
34. T. Furukawa and W. B. White, “Raman spectroscopic investigation of sodium borosilicate glass structure,” J. Mater. Sci. 16(10), 2689–2700 (1981). [CrossRef]
35. B. Parkinson, D. Holland, M. E. Smith, C. Larson, J. Doerr, M. Affatigato, S. A. Feller, A. Howes, and C. Scales, “Quantitative measurement of Q 3 species in silicate and borosilicate glasses using Raman spectroscopy,” J. Non-Cryst. Sol. 354, 1936–1942 (2008).
36. W. L. Konijnendijk and J. Stevels, “The structure of borosilicate glasses studied by Raman scattering,” J. Non-Cryst. Sol. 20, 193–224 (1976).
37. J. Tan, S. Zhao, W. Wang, G. Davies, and X. Mo, “The effect of cooling rate on the structure of sodium silicate glass,” Mater. Sci. Eng. B 106(3), 295–299 (2004). [CrossRef]
38. K. Mishchik, C. D’Amico, P. K. Velpula, C. Mauclair, A. Boukenter, Y. Ouerdane, and R. Stoian, “Ultrafast laser induced electronic and structural modification in bulk fused silica,” J. Appl. Phys. 114(13), 133502 (2013). [CrossRef]
39. H. Richter, Z. Wang, and L. Ley, “The one phonon Raman spectrum in microcrystalline silicon,” Solid State Commun. 39(5), 625–629 (1981). [CrossRef]
