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We report on new developments in wavefront and polarization control for ultrashort-pulse laser microprocessing. We use two Spatial Light Modulators in combination to structure the optical fields of a picosecond-pulse laser beam, producing vortex wavefronts and radial or azimuthal polarization states. We also carry out the first demonstration of multiple first-order beams with vortex wavefronts and radial or azimuthal polarization states, produced using Computer Generated Holograms. The beams produced are used to nano-structure a highly polished metal surface. Laser Induced Periodic Surface Structures are observed and used to directly verify the state of polarization in the focal plane and help to characterize the optical properties of the setup.
© 2013 Optical Society of America
1. Introduction
Laser micromachining using ultrashort pulses with temporal pulselengths <10ps minimises thermal diffusion, lowers ablation threseholds and can generate highly reproducible micro- and nano-structures [1–4]. As a result, industrial processes based on femtosecond and picosecond laser pulse durations are becoming increasingly widespread. Manufacturing applications include the very precise drilling of holes for fuel-injection nozzles [4], the dicing of silicon wafers [5], the scribing of thin film solar cells [6] and the fabrication of volume Bragg gratings in transparent bulk materials [7]. Early ultrashort-pulse laser systems suffered from a comparatively low processing speed which slowed down their uptake in industry [3]. This has partly been addressed by the development of higher repetition laser systems from 200kHz to > 1MHz [8]. However as repetition rates increase above 200kHz, the required scan speeds from Galvo systems can be problematic, leading to a high pulse overlap where plasma absorption can produce wavefront distortions [4].
An additional route to increase process efficiency further is to structure the wavefront of the beam by the use of a fixed optic such as an axicon [9] or a Spatial Light Modulator (SLM) [10]. For example, inducing a vortex structure to the beam wavefront (i.e. adding orbital angular momentum to the laser light) produces a ring-shaped focal spot which helps to reduce the recast formation that typically appears after laser pulse ablation [11, 12]. Furthermore, structuring the beam wavefront with a Computer Generated Hologram (CGH) has also been used to produce multiple diffractive beams for high-speed parallel processing applications such as the manufacture of volume Bragg gratings [7] and of three-dimensional micro-patterns [13]. This method can increase throughput by more than an order of magnitude compared with traditional single-beam processing [14–16]. A greater flexibility for micromachining can also be achieved by controlling polarization, which influences laser-material energy coupling [17]. Polarization is known to affect the speed and quality of processes such as drilling [18] and surface structuring [19]. Circularly polarized beams are chosen for some laser processing applications due to their isotropic properties [18]; however, they do not offer the best processing speed [20]. Radially or azimuthally polarized beams were recently demonstrated to improve processing speed and quality [21–23]. Thanks to the latest developments in liquid-crystal SLM, it is now possible to simultaneously control both the wavefront and polarization of laser beams [16, 24–26]. This enables for example producing multiple diffractive beams, where neighbouring beams have mutually orthogonal linear polarization states [16]. However to our knowledge, no previous research has demonstrated the use of two SLMs for laser processing with parallel vortex beams and parallel beams with a radial or azimuthal polarization state.
This paper thus introduces a new technique for ultrashort-pulse laser microprocessing with complete control of the beam wavefront and polarization, using two SLMs in combination. We first give a brief mathematical description of this technique, using simple Jones vector formalism. We then describe how we implemented this experimentally in a picosecond-pulse laser microprocessing system. We detail how we produced a number of structured beams, including a linearly polarized vortex beam, a radially or azimuthally polarized vortex beam and multiple diffractive beams with a vortex wavefront and a radial or azimuthal polarization state. All these structured beams were used to process stainless steel samples. Laser Induced Periodic Surface Structures (LIPSS) were imprinted on the samples and used to visualize the electric field vector (polarization) structures at the focal plane, helping to characterize the optical properties of the setup.
2. Principle of wavefront and polarization control using Spatial Light Modulators
The wavefront and polarization of a laser beam can be fully controlled using two phase-only SLMs and a pair of waveplates. A phase-only SLM is made of a two-dimensional array of liquid-crystal pixels, to induce relative phase delays across the beam wavefronts [24]. In the proposed setup illustrated in Fig. 1, SLM1 is used for structuring the beam wavefronts while SLM2, combined with a pair of waveplates are used for structuring both the beam wavefronts and polarization. This setup, referred to as an “SLM Converter” henceforth, can be represented using Jones vector formalism.
Fig. 1 Schematic of the SLM Converter, which consists of two SLMs and two zero-order waveplates. SLM1 instigates a phase pattern designed to structure the beam wavefronts. After SLM1, the horizontal polarization is tilted to + 45 with a half-waveplate. SLM2 and the quarter-waveplate are used to convert the incident linear polarization into the desired state of polarization. This schematic represents the top view of the setup. For the Jones vector calculation, we define a coordinate system with a horizontal axis (x) and a vertical axis (y).
The Jones matrix representing the SLM Converter is noted henceforth, where x and y are the cross-sectional coordinates along the horizontal and vertical axis respectively. It is defined as:
S1(x, y) and S2(x, y) are the Jones matrices of individual pixels of SLM1 and SLM2 respectively (see Table 1). and are the relative phase delays induced by one pixel at location (x, y), on SLM1 and SLM2 respectively. H is the Jones matrix of a half-waveplate with its fast axis tilted by radians from the horizontal. Q is the Jones matrix of a quarter-waveplate (see Fig. 1). It is noted that the quarter-waveplate has its fast axis tilted by radians from the horizontal and we represent this by using a rotation matrix R in Eq. (1). This effectively changes the reference coordinate system so that the resulting Jones vectors after the quarter-waveplate are expressed in a coordinate system tilted by radians.
Table 1. Jones matrices
When a linearly polarized laser beam represented by the Jones vector is incident on this setup, the resulting vector is . The full derivation gives:
The fourth term means that the resulting Jones vector represents a linear polarization, rotated by an angle relative to the incident (horizontal) Jones vector . The second and third terms mean has a relative phase delay which is set by both and . As both and are independently controllable for each SLM pixel (i.e. at various locations x, y), the proposed SLM Converter enables high-resolution spatial control of the laser beam wavefront and polarization.
3. Experimental details
To demonstrate how the wavefront and polarization of a laser beam can be controlled simultaneously, an SLM Converter is assembled as part of an ultrashort-pulse laser microprocessing system. A schematic of the experimental setup is shown in Fig. 2.
Fig. 2 Schematic showing how the SLM Converter is used to control the wavefront and polarization of a picosecond-pulse laser microprocessing setup. The “polarization test components” are removed when the micro-processing tests are carried out.
3.1 Experimental setup
The laser source is a Coherent Talisker with a pulse width of 10ps, 532nm wavelength, M2 <1.3, average power of 8W, 200kHz maximum repetition rate and a horizontal linear polarization. A beam-expanding telescope (Jenoptic) with magnification is used to reduce the average intensity of the beam incident on the SLMs.
The SLM Converter (Fig. 1) consists of two Hamamatsu X10468-04 LCOS-SLMs (Liquid-Crystal On Silicon Spatial Light Modulators) and a pair of zero-order waveplates. The SLMs are of the phase-only, reflection type and consist of a 16x12mm, 800x600 pixel array of horizontally oriented liquid-crystal phase retarders.
After the SLM Converter, there is 4f optical system (Lens 1 and 2 in Fig. 2) which uses plano-convex lenses (f = 400mm) to re-image the surface of SLM2 (Fig. 1) to the 15mm input aperture of a scanning galvo. The beam is focused with a flat field f-theta lens (f = 250mm). Samples are mounted on a precision 3-axis (x, y, z) motion control system (A3200 Ndrive system, Aerotech) allowing accurate positioning in the focal plane.
3.2 Experimental procedure
To demonstrate the capabilities of the setup, we produce a number of optical field configurations. In each case, the produced beams are analysed at two places: immediately after the SLM Converter and at the focal plane of the microprocessing setup. After the SLM Converter, a polarizing filter and beam profiler (dotted components in Fig. 2) enable to analyse the collimated beams. To analyse the beams at the focal plane however, we use a different method since the high peak-intensity would damage any optics placed in this region. By focusing the beams on the surface of polished stainless steel samples, the focal intensity distribution is imprinted on the sample surface. Moreover, using a fluence near the ablation thresehold of the material leads to the formation of wavelength-sized LIPSS which typically develop orthogonally to the local electric field vectors [27, 28] and provide a direct method of analysing polarization in the focal region [17].
For all these tests, the laser output is attenuated to produce a pulse energy of 3μJ (~0.3J/cm2 at focal plane), and the samples are exposed for a duration of 5ms (~100 pulses at 20kHz pulse repetition rate) whilst the beam remains static with regards to the sample. After laser exposure, the produced focal spots are imaged with an optical microscope.
4. Results and discussion
The SLM Converter can produce individual as well as multiple first-order beams, each with the desired structured optical fields. A number of experimental configurations are demonstrated below.
4.1 Linearly polarized vortex beams
As a first case study, the SLM Converter was configured to produce a linearly polarized beam with a vortex wavefront (carrying an orbital angular momentum of l = 1). This was achieved by adjusting the phase delays at SLM1, where varied from 0 to 2π depending on the coordinates (x, y), producing a 2π pitch vortex wavefront overall, see Fig. 3(a). In this case, SLM2 was configured so that it did not affect incident wavefronts (i.e. all the pixels were set at: ). As a result, the linearly polarized Gaussian beam from the laser source had its wavefront structured into a phase vortex, whilst its polarization remained unchanged (i.e. it remained linear). The resulting beam was analysed after the SLM Converter. As expected, the beam profile, shown in Fig. 3(c), had the typical annular geometry associated with vortex beams [11, 12]. It is noted that the vortex structure at SLM1 had a central singularity where the rapid transverse phase variation induced significant diffraction effects, visible as diffraction rings around the beam in Fig. 3(c). It is also noted that the incident beam from the laser source, Fig. 3(b), had some residual structures which affected the wavefronts produced. These effects might be reduced by adding a spatial filter in the beam path after the SLM Converter.
Fig. 3 (a) Vortex wavefront induced at SLM1. (b) Incident beam profile before SLM1. (c) Resulting beam profile after SLM1. The colour coded scale represents intensity, in arbitrary units.
The setup was used to imprint focal spots on the surface of a stainless steel sample, as detailed in Section 3.2 above. The produced focal spots had a ring-shaped structure (see optical micrographs in Fig. 4), which is consistent with what is expected when focusing a vortex beam with a low NA lens [11]. As expected, LIPSS have formed within the produced laser spots, developing in a direction perpendicular to that of the incident polarization.
Fig. 4 Optical micrographs showing the focal spot produced with ~100 pulses at 3μJ/pulse, with the SLM Converter producing a Gaussian beam (a) and a vortex beam (b). In each case, the LIPSS are perpendicular to the linear polarization, which is indicated with blue arrows.
4.2 Radially and azimuthally polarized vortex beams
To further illustrate the capabilities of the SLM Converter, we show that both the polarization and wavefront structures of the beam can be controlled simultaneously. The SLM Converter was configured to produce radially and azimuthally polarized vortex beams. In this case, we leave on SLM1 while inducing a vortex wavefront with a 4π pitch (i.e. carrying an orbital angular momentum of l = 2) at SLM2. As varied from 0 to 4π depending on the spatial coordinates (see wavefronts in Fig. 5), it produced a radial polarization overall as described in Eq. (2). In this configuration, the resulting beam has a 2π pitch residual phase vortex [26, 29], which is described by the phase term in Eq. (2). This means that the resulting beam is radially polarized, with a vortex wavefront (i.e. it carries orbital angular momentum of l = 1). Furthermore, by adding a constant phase term π to the overall phase vortex at SLM 2, the output polarization can be converted simply from a radial to its orthogonal azimuthal state (Fig. 5).
Fig. 5 Beam profiles produced by a (a) radially or (b) azimuthally polarized collimated beam, after transmission through a polarizing filter with its transmission axis oriented horizontally. The colour coded scale represents intensity in arbitrary units. The vortex wavefronts which are induced at SLM2 are shown in the top-left inlays.
The produced beams were analysed after the SLM Converter. The measured profiles shown in Fig. 5 are consistent with those typically expected from radially and azimuthally polarized beams, in line with [26, 29]. The profiles also reveal fringe structures within the beams. These structures were produced by interference effects at the centre of the vortex patterns induced by the SLMs [29, 30].
To analyse the intensity profiles and polarization structures at the focal plane, focal spots were marked on the surface of stainless steel samples, as detailed in Section 3.2 above. Optical micrographs in Fig. 6 show the resulting focal spots. It can be seen that LIPSS have been produced around the edges, but not in the centre of the focal spots. As expected, the LIPSS produced with radially and azimuthally polarized beams were orthogonal to each other. The collimated radially polarized vortex beam from the SLM Converter produced a focal spot with LIPSS oriented in a radial pattern, see magnified area in Fig. 6(a). As LIPSS are orthogonal to the local electric field [27, 28], this suggests that the focal field was azimuthally polarized. Similarly, the LIPSS in Fig. 6(b) suggest that the collimated azimuthally polarized vortex beam produced a radially polarized focal field.
Fig. 6 Optical micrographs showing the focal spots produced with ~100 pulses at 3μJ/pulse, with the SLM Converter producing a vortex beam (orbital angular momentum l = 1) polarized radially (a) and azimuthally (b). The blue arrows indicate the polarization fields.
In our previous publication [26], we showed that radially or azimuthally polarized vortex beams with a topological charge l = 1, focused with a low NA lens, typically produce a Gaussian profile with an inversion in the dominant state of polarization at the focal plane. The geometry of the focal spots and the structure of the LIPSS in Fig. 6 are consistent with these earlier results in [26].
Radially/azimuthally polarized vortex beams such as those produced with our SLM Converter (Fig. 5) are expected to increase processing efficiency and speed, compared with conventional linearly or circularly polarized beams [22]. It is noted that the SLM Converter can also produce radially/azimuthally polarized beams with a planar wavefront (i.e. without an orbital angular momentum) which typically produce a ring-shaped intensity structure in the focal plane [30–32]. The detail of these experiments will be published elsewhere.
4.3 Diffractive parallel processing with structured beams
Our earlier publications [7, 15] detailed the concept of diffractive parallel processing with linearly polarized Gaussian beams, using a CGH to produce multiple first-order focal spots. Here we show that the SLM Converter enables diffractive parallel processing with spatially structured wavefront and polarization. The same optical field structures as detailed above (i.e. linear, radial and azimuthal polarization with a vortex wavefront) were combined with a CGH to produce multiple focal spots.
As an example, the CGH shown in Fig. 7(a) is designed to produce three first-order focal spots. The vortex wavefront shown in Fig. 7(b) was combined with the CGH and applied to the wavefront at SLM 1 (i.e. each pixel induced the appropriate value of to shape the wavefront). The samples were exposed to the laser beam as detailed in Section 3.2 above. Figure 7(c) shows an optical micrograph of a set of three focal spots imprinted simultaneously on the surface of a sample. The three spots produced had a ring shape and within each spot, LIPSS were oriented perpendicularly to the direction of the linear polarization (not visible in Fig. 7 due to the chosen magnification). The shape and LIPSS structures of each first-order spot are similar to those obtained when focusing a single linearly polarized vortex beam as described in Section 4.1 above, see Fig. 4(b). This confirms that the SLM Converter enables diffractive parallel processing with multiple first-order vortex beams. It is noted that the produced spots showed some distortion in their shape. This was due to the resolution limit of the SLMs, where the pixel size (~20μm) and discrete phase modulation induced some discontinuity in the produced wavefronts which affected the focal intensity distributions.
Fig. 7 (a) CGH induced at SLM1 to produce three first-order focal spots. (b) Vortex wavefront induced at SLM1, in addition to the CGH. (c) Optical micrograph showing the three focal spots produced simultaneously with a vortex beam mode.
Finally, we show that the SLM Converter can generate diffractive parallel beams with a radial or azimuthal state of polarization. As before, a CGH designed to generate three first-order spots in the focal plane was applied to the wavefront at SLM1. SLM2 was used to structure polarization in the same way as in Section 4.2 (Fig. 5). The produced beams were first analyzed with the SPIRICON beam profiler and the resulting profiles are shown in Fig. 8. As expected, diffraction fringes produced by the three first-order beams superimpose on the beam profiles produced by the radial and azimuthal polarization fields.
Fig. 8 Beam profiles produced by a (a) radially or (b) azimuthally polarized beam, after transmission through a polarizing filter with its transmission axis oriented horizontally. The colour coded scale represents intensity, in arbitrary units. Interference fringes from the first-order diffracted beams superimpose on the radial/azimuthal profiles. The vortex wavefronts which are induced at SLM2 are shown in the top-left inlays.
The focusing properties of these beams were investigated by marking focal spots on the surface of stainless steel samples, as detailed in Section 3.2 above. Optical micrographs in Fig. 9 show the resulting focal spots. As expected, the laser exposure had simultaneously produced three first-order spots at the focal plane, see Fig. 9(a). LIPSS were produced around the edge but not in the centre of each focal spot, see Figs. 9(b) and 9(c), in the same way as with the single beams in Section 4.2 above. A detailed microscopic analysis confirmed that the LIPSS geometry within each spot was similar to that produced with the single beams in Section 4.2 (Fig. 6). The LIPSS geometry in Fig. 9 also indicated that an inversion in the dominant state of polarization had occurred at the focal plane compared to that of the collimated beam, in the same way as with the single beams (see Fig. 6). These results are consistent with multiple first-order focal spots with a radially or azimuthally polarized vortex field being produced at the focal plane. However, it is noted that the discrete phase modulation and pixel structure of the SLMs had induced some residual distortion which affected the polarization purity at the focal plane. This can be seen as a slight irregularity in the cylindrical symmetry of the LIPSS within the focal spots, see blue arrows in Figs. 9(b) and 9(c).
Fig. 9 (a) Optical micrograph showing the multiple laser spots marked simultaneously at the focal plane, with ~100 pulses at 3µJ/pulse, when the SLM Converter produced three first-order beams polarized radially. (b) A magnification of one of three focal spots produced with a radially polarized beam. (c) One of three spots produced with an azimuthally polarized beam. The blue arrows indicate the direction of polarization, which is perpendicular to the LIPSS.
5. Conclusions
In this paper we present new developments in ultrashort-pulse laser microprocessing, using a technique which allows simultaneous control of the beam wavefront and polarization. This technique uses two phase-only liquid-crystal SLMs, where the first SLM structures the wavefront and the second SLM structures both the wavefront and polarization of the beam. As a proof of concept, we structured the wavefront and polarization of a picosecond-pulse laser beam and processed the surface of stainless steel samples. The produced beams had a vortex wavefront and various polarization states, including linear, radial and azimuthal. LIPSS are produced within the processed areas and are used as a direct method to verify the state of polarization in the focal plane. For the first time, diffractive parallel processing with a radial or azimuthal polarization and a vortex wavefront has been demonstrated. The advantage of this method is its flexibility, since it does not require any modification of the laser source and it allows the beam wavefront and polarization to be controlled simultaneously. Future work will further refine the technique, looking at how the polarization and wavefront structures can be produced and controlled dynamically for real-time process optimization. Control of wavefront as well as polarization may open up entirely new possibilities for material micro-structuring applications in the area of surface interactions and thin films.
Acknowledgments
The authors gratefully acknowledge the support of the EPSRC as well as the help of Prof. Miles Padgett who provided the SLM control software used in this research, of Jack Bennett at Hamamatsu for the loan of SLMs and of Dr Mary Erlund for her editorial contribution.
References and links
1. R. Le Harzic, D. Breitling, M. Weikert, S. Sommer, C. Föhl, S. Valette, C. Donnet, E. Audouard, and F. Dausinger, “Pulse width and energy influence on laser micromachining of metals in a range of 100 fs to 5 ps,” Appl. Surf. Sci. 249(1-4), 322–331 (2005). [CrossRef]
2. P. S. Banks, M. D. Feit, A. M. Rubenchik, B. C. Stuart, and M. D. Perry, “Material effects in ultra-short pulse laser drilling of metals,” Appl. Phys., A Mater. Sci. Process. 69(7), S377–S380 (1999). [CrossRef]
3. D. Breitling, C. Föhl, F. Dausinger, T. Kononenko, and V. Konov, “Drilling of metals”, in Femtosecond Technology for Technical and Medical Applications, Topics Appl. Phys. 96, 131–156 (Springer-Verlag, 2004).
4. D. Breitling, A. Ruf, and F. Dausinger, “Fundamental aspects in machining of metals with short and ultrashort laser pulses,” Proc. SPIE 5339, 49–63 (2004). [CrossRef]
5. N. Sudani, K. Venkatakrishnan, and B. Tan, “Laser singulation of thin wafer: die strength and surface roughness analysis of 80μm silicon dice,” Opt. Lasers Eng. 47(7-8), 850–854 (2009). [CrossRef]
6. G. Račiukaitis, S. Grubinskas, P. Gecys, and M. Gedvilas, “Selectiveness of laser processing due to energy coupling localization: case of thin film solar cell scribing,” Appl. Phys., A Mater. Sci. Process. 112(1), 93–98 (2013). [CrossRef]
7. D. Liu, Z. Kuang, W. Perrie, P. J. Scully, A. Baum, S. P. Edwardson, E. Fearon, G. Dearden, and K. G. Watkins, “High-speed uniform parallel 3D refractive index micro-structuring of poly(methyl methacrylate) for volume phase gratings,” Appl. Phys. B 101(4), 817–823 (2010). [CrossRef]
8. Y. Bellouard, A. Champion, B. Lenssen, M. Matteucci, A. Schaap, M. Beresna, C. Corbari, M. Gecevicius, P. Kazansky, O. Chappuis, M. Kral, R. Clavel, F. Barrot, J. M. Breguet, Y. Mabillard, S. Bottinelli, M. Hopper, C. Hoenninger, E. Mottay, and J. Lopez, “The Femtoprint Project,” JLMN 7(1), 1–10 (2012). [CrossRef]
9. M. Rioux, R. Tremblay, and P. A. Bélanger, “Linear, annular, and radial focusing with axicons and applications to laser machining,” Appl. Opt. 17(10), 1532–1536 (1978). [CrossRef] [PubMed]
10. N. Sanner, N. Huot, E. Audouard, C. Larat, and J. P. Huignard, “Direct ultrafast laser micro-structuring of materials using programmable beam shaping,” Opt. Lasers Eng. 45(6), 737–741 (2007). [CrossRef]
11. J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express 18(3), 2144–2151 (2010). [CrossRef] [PubMed]
12. M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev. 6(5), 607–621 (2012). [CrossRef]
13. N. J. Jenness, K. D. Wulff, M. S. Johannes, M. J. Padgett, D. G. Cole, and R. L. Clark, “Three-dimensional parallel holographic micropatterning using a spatial light modulator,” Opt. Express 16(20), 15942–15948 (2008). [CrossRef] [PubMed]
14. Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, “Variable holographic femtosecond laser processing by use of a spatial light modulator,” Appl. Phys. Lett. 87(3), 031101 (2005). [CrossRef]
15. Z. Kuang, W. Perrie, D. Liu, S. Edwardson, J. Cheng, G. Dearden, and K. Watkins, “Diffractive multi-beam surface micro-processing using 10 ps laser pulses,” Appl. Surf. Sci. 255(22), 9040–9044 (2009). [CrossRef]
16. S. Hasegawa and Y. Hayasaki, “Polarization distribution control of parallel femtosecond pulses with spatial light modulators,” Opt. Express 21(11), 12987–12995 (2013). [CrossRef] [PubMed]
17. O. J. Allegre, W. Perrie, K. Bauchert, D. Liu, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Real-time control of polarisation in ultra-short-pulse laser micro-machining,” Appl. Phys., A Mater. Sci. Process. 107(2), 445–454 (2012). [CrossRef]
18. S. Nolte, C. Momma, G. Kamlage, A. Ostendorf, C. Fallnich, F. Von Alvensleben, and H. Welling, “Polarization effects in ultrashort-pulse laser drilling,” Appl. Phys., A Mater. Sci. Process. 68(5), 563–567 (1999). [CrossRef]
19. K. Venkatakrishnan, B. Tan, P. Stanley, and N. R. Sivakumar, “The effect of polarization on ultrashort pulsed laser ablation of thin metal films,” J. Appl. Phys. 92(3), 1604–1607 (2002). [CrossRef]
20. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D Appl. Phys. 32(13), 1455–1461 (1999). [CrossRef]
21. R. Weber, A. Michalowski, M. Abdou-Ahmed, V. Onuseit, V. Rominger, M. Kraus, and T. Graf, “Effects of radial and tangential polarization in laser material processing,” Phys. Procedia 12, 21–30 (2011). [CrossRef]
22. M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process. 86(3), 329–334 (2007). [CrossRef]
23. K. Venkatakrishnan and B. Tan, “Interconnect microvia drilling with a radially polarized laser beam,” J. Micromech. Microeng. 16(12), 2603–2607 (2006). [CrossRef]
24. M. R. Beversluis, L. Novotny, and S. J. Stranick, “Programmable vector point-spread function engineering,” Opt. Express 14(7), 2650–2656 (2006). [CrossRef] [PubMed]
25. J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, and X. Li, “Generation and analysis of both in-phase and out-phase radially polarized femtosecond-pulse beam,” Opt. Eng. 52(2), 024201 (2013). [CrossRef]
26. O. J. Allegre, W. Perrie, S. P. Edwardson, G. Dearden, and K. G. Watkins, “Laser microprocessing of steel with radially and azimuthally polarized femtosecond vortex pulses,” J. Opt. 14(8), 085601 (2012). [CrossRef]
27. Z. Guosheng, P. M. Fauchet, and A. E. Siegman, “Growth of spontaneous periodic surface structures on solids during laser illumination,” Phys. Rev. B 26(10), 5366–5381 (1982). [CrossRef]
28. Q. Z. Zhao, S. Malzer, and L. J. Wang, “Formation of subwavelength periodic structures on tungsten induced by ultrashort laser pulses,” Opt. Lett. 32(13), 1932–1934 (2007). [CrossRef] [PubMed]
29. M. Beresna, M. Gecevicius, P. G. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011). [CrossRef]
30. U. Klug, J. F. Dusing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006, 759006-8 (2010). [CrossRef]
31. K. Lou, S. X. Qian, X. L. Wang, Y. Li, B. Gu, C. Tu, and H. T. Wang, “Two-dimensional microstructures induced by femtosecond vector light fields on silicon,” Opt. Express 20(1), 120–127 (2012). [CrossRef] [PubMed]
32. G. Wu, Q. Lou, J. Zhou, J. Dong, and Y. Wei, “Focal shift in focused radially polarized ultrashort pulsed laser beams,” Appl. Opt. 46(25), 6251–6255 (2007). [CrossRef] [PubMed]
