Abstract

A linear to radial and/or azimuthal polarization converter (LRAC) has been inserted into the beam delivery of a micromachining station equipped with a picosecond laser system. Percussion drilling and helical drilling in steel have been performed using radially as well as azimuthally polarized infrared radiation at 1030 nm. The presented machining results are discussed on the basis of numerical simulations of the polarization-dependent beam propagation inside the fabricated capillaries.

© 2010 OSA

1. Introduction

It is generally accepted that the use of ultrashort laser pulses enables the fabrication of high-precision microholes in metals without post processing, due to the minimization of thermal effects such as melt generation and recast formation [14]. High contour accuracy and machining quality however, are achieved not only by a mere reduction of the pulse duration, but on the basis of adequate processing technology combined with a proper adjustment of a wide range of process and laser parameters. A decisive factor concerning the borehole geometry is the polarization of the laser beam. Ultrashort pulsed laser sources generally emit linearly polarized radiation. A linearly polarized laser beam however, is known to have different absorptivities depending on the cutting direction. Hence, in high-aspect-ratio microdrilling, processing with stationary linear polarization results in linear elongation and distortion of the borehole outlet cross-section [2].

Basically there are two ways in which round borehole geometries can be obtained, and typical circularity tolerances in the order of a few percent of the hole diameter can be met: either utilizing axially symmetric polarization states or rotating linear polarization. The most common approach for the production of circular microholes in steel is to employ a helical drilling process together with circularly polarized radiation [3]. Chang et al. [5] have shown that also random-polarized radiation enables the fabrication of round borehole geometries. The use of rotating linear polarization with parallel orientation with respect to the plane of incidence can be beneficial in terms of roundness and wall smoothness at percussion drilling [2] and helical drilling [4] in steel.

In the last decades, a new kind of polarization states, i.e. radial and azimuthal, have attracted great interest for many applications such as data storage, particle trapping [6] or high-resolution microscopy [7]. This is due to their specific and unique properties. At high-power regimes, it has been reported that using radially or azimuthally polarized beams permits to avoid thermally induced birefringence and bi-focusing in a transversally pumped Nd:YAG rod laser [8]. In material processing Niziev et al. [9] theoretically predicted that up to two times higher overall cutting efficiency of metals using a CO2 laser beams can be reached with radial polarization in comparison to conventional circular polarization. In nanosecond [10] and millisecond regimes [11], drilling experiments with radial and azimuthal polarization have also been reported to be advantageous depending on the material and on the process parameters.

To perform the above described experiments many extra- and intra-cavity approaches for the generation of such laser beams have been investigated and reported in the literature in the past few years [1218]. The extra-cavity techniques are mainly based on interferometric setups [12,13] or by using segmented phase plates [1416] which convert beams with linear or circular polarization into radial or azimuthal polarization. Several intra-cavity optical elements, e.g. conical Brewster windows or resonant grating mirrors [17,18], have also demonstrated an efficient generation of radially and or azimuthally polarized laser beams in different types of laser systems.

In the present paper we report on the first experimental results on microdrilling in steel using picosecond pulsed, radially and azimuthally polarized laser radiation. We have studied the influence of the polarization state on ablation velocity, hole morphology and machining quality at microdrilling in X5CrNi18-10 austenitic steel (EN steel number 1.4301). Fundamental research concerning the drilling rate has been carried out on the basis of percussion drilling. Moreover, cylindrical and negative conical microholes with a diameter in the range of 100 µm have been fabricated in 0.5 mm and 1 mm sheets, utilizing a helical drilling process without core.

2. Experimental setup

The technique we used for the polarization shaping of the beam is based on a linear to radial/azimuthal polarization converter (LRAC) composed of eight half-wave (at a laser wavelength of λ = 1030 nm) plate segments [16] with specific and well defined fast axis orientation. A linearly polarized beam incident to the LRAC will therefore experience a local polarization rotation in the radial or the azimuthal direction depending on the orientation of the main axis of our device. In order to verify the proper behavior of our LRAC, the latter was introduced in the beam path of a 6 mm beam diameter, linearly polarized, single transverse mode (measured M 2 < 1.04) Yb:YAG thin-disk laser setup. A photograph of the LRAC is shown in the inset of Fig. 1 depicting a schematic of the polarization conversion principle. The power transmission through our LRA polarization converter was measured to be as high as 99%.

 

Fig. 1 Linear to radial/azimuthal polarization conversion (LRAC) principle based on a segmented half-wave plates.

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The polarization analysis of the generated beams was performed by using a rotating polarizer coupled to a CCD camera. The recorded intensity distributions with and without the polarizer are given in Fig. 2 for the beam with radial (top row) and with azimuthal (bottom row) polarization. The analysis of the beam was done at a distance of a few tens of centimeters after the LRAC. A beam cleaning system composed of a telescope and a pinhole was inserted in the beam path in front of the CCD camera. Using our 2D polarimeter system the radial and azimuthal polarization purity was measured to be higher than 96%.

 

Fig. 2 Recorded intensity distributions of the radially and azimuthally polarized beams without and with analyzer at different orientations.

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During the experiments the LRAC described above was inserted into the beam delivery of a micromachining station equipped with an experimental picosecond laser system described in details in reference [19]. The setup is based on a master oscillator power amplifier configuration using a commercial mode-locked fiber oscillator in combination with a regenerative Yb:YAG thin-disk amplifier. At the fundamental wavelength of 1030 nm, the laser system generates pulses with a duration of 6 ps at repetition rates of up to 206 kHz and an average output power of up to 40 W. Using a commercially available camera-based beam propagation analyzer (Spiricon M2-200), the M 2 of the linearly polarized beam incident on the LRAC was measured to be 1.3. This fundamental Gaussian beam was transformed to radially and azimuthally polarized (0,1)* Laguerre-Gaussian beams with M 2 close to 2.5.

Helical drilling was performed employing a fully automated helical drilling optics (HDO). The radially and azimuthally polarized beams were focused with an aberration-reduced 4-lens focusing system (f = 100 mm), which produced a focal diameter of 45 ± 3 µm according the second moment definition. All experiments were carried out under helium atmosphere (He 4.6), delivered by a conical single-hole nozzle which was installed coaxially with the laser beam. The inlet and outlet diameters of the fabricated microholes were measured by means of an optical microscope. In addition, scanning electron microscope (SEM) images of inlets, outlets and transverse sections of the holes were recorded to inspect their overall geometry and to obtain information on machining quality.

3. Percussion drilling experiments

The influence of the polarization type on the drilling rate at percussion drilling was investigated by fabricating holes in 980 µm sheets with pulse numbers between 104 and 106, and by subsequently determining the hole-depth. The repetition rate was 103 kHz, and the pulse energy was set to 50 µJ, yielding a focal energy density of 3.1 J/cm2. For the calculation of the energy density, we assumed a circular spot with a uniform intensity distribution. The peak energy density (power density) of the (0,1)* ring mode was 4.6 J/cm2 (7.7∙1011 W/cm2). The focal position was set to −100 µm. The pulse number was adjusted with an accuracy of < 500 pulses, using a mechanical shutter. The hole depth was measured on the basis of transverse sections via an optical microscope. In order to securely detect the maximum depth even for tiny capillary tips, the sections were gradually polished in steps of 5 µm, while the capillary depth was recorded after each polishing step. Consequently an accuracy of 20 µm can be assumed for the depth measurements.

Figure 3 shows the results of the percussion drilling experiments. In the depicted plots of the capillary depth, the solid lines (radial polarization) and the dashed lines (azimuthal polarization) are logarithmic fits of the experimental data. Differentiation of the fitting functions with respect to the pulse number leads to the instantaneous drilling rate curves. The displayed characteristics are consistent with the behavior generally observed in percussion drilling for ms to fs pulse durations [1]. For both polarization states, the highest drilling rate (> 10−2 µm/pulse) is obtained at the beginning of the drilling process. A strong decrease to ~10−3 µm/pulse occurs during the first 2∙105 pulses, followed by a steady decline of the drilling rate to little more than 10−4 µm/pulse, until eventually the penetration of the full sample thickness is completed.

 

Fig. 3 Capillary depth and instantaneous drilling rate versus number of pulses for percussion drilling in CrNi steel with radially (■) and azimuthally (□) polarized radiation. λ = 1030 nm, f p = 103 kHz, Q p = 50 µJ, z f = −100 µm.

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However, the behavior of the two axially symmetric polarization states differs depending on capillary depth. While a similar depth progress can be observed down to a depth of 600 µm (7∙104 pulses), the azimuthally polarized beam advances into the workpiece considerably faster than the radially polarized beam beyond 600 µm. As a consequence, the full sample thickness of 980 µm is penetrated only after ~106 pulses with radial polarization, but already after ~5∙105 pulses with azimuthal polarization. This corresponds to a reduction of the machining time by a factor of two. Although the maximum drilling depth could not be recorded in this work, it is a relevant value that should be considered in further investigations. Using radially and azimuthally polarized beams at percussion drilling in steel with pulse durations in the range of a few hundred µs, we also obtained higher drilling rates for azimuthal polarization [11,20]. Moreover we showed that the boreholes manufactured with azimuthally polarized radiation exhibit smaller diameters, sharper tips and higher aspect ratios. Similar geometrical characteristics were determined for the capillaries fabricated in the present work.

4. Helical drilling experiments

The helical drilling experiments were carried out with the same laser, focusing and material parameters as the percussion drilling experiments. However, in order to minimize deterioration of the inlet quality due to laser-induced ionization of the gas atmosphere inside the capillary, a linear energy ramp starting from 3 µJ was applied over the first 10 s of the drilling process. The rotation frequency of the HDO, the drilling diameter and the beam inclination angle were kept constant over all experiments. Since the average laser power was only 5.15 W, a total machining time of 120 s was needed to complete the desired hole geometry [21].

Figure 4 shows transverse sections of two microholes fabricated with radially (left) and azimuthally (right) polarized radiation. Despite the low pulse energy, the energy ramp and the helium shielding, a widened, funnel-shaped inlet is produced at both polarization states. Accordingly, the capillaries narrow to a waist located about 200 µm below the workpiece surface. The average diameter of the waist is 75 µm for radial compared to 65 µm for azimuthal polarization.

 

Fig. 4 Transverse sections of microholes in 1 mm CrNi steel, drilled with radially (left) and azimuthally (right) polarized radiation. The depicted diameters are each mean values averaged from the major and minor axes of the cross-section. λ = 1030 nm, f p = 103 kHz, Q p = 50 µJ, z f = −100 µm, t D = 120 s, helical drilling.

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Below the waist, the borehole drilled with radial polarization is barrel-shaped with the maximum diameter located at ~700 µm below the sample surface. This morphology can be explained by a high absorptivity of the radially polarized radiation, caused by parallel polarized incidence to the walls over the entire borehole circumference and a large angle of incidence. The high absorptivity, in turn, results in extensive energy transfer to the workpiece in the sheet center and a lack of energy in the outlet zone, the latter resulting in an increasing reduction of the borehole cross-section. This assumption is confirmed by the SEM image of the outlet depicted in Fig. 5 (bottom left), which shows that the outlet orifice has an oval cross-section and a polygonal contour. These indications are typical for insufficient widening due to low energy density.

 

Fig. 5 Inlets and outlets of microholes in 1 mm CrNi steel, drilled with radially (left) and azimuthally (right) polarized radiation. d av denotes the mean diameter averaged from the major diameter d max and the minor diameter d min. λ = 1030 nm, f p = 103 kHz, Q p = 50 µJ, z f = −100 µm, t D = 120 s, helical drilling.

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On the other hand, using azimuthal polarization, a slender capillary with straight walls and a regular conical shape, corresponding to the beam inclination angle of 3°, is produced. Furthermore, as can be seen from Fig. 5 (bottom right), the outlet roundness could be enhanced substantially. Since the absorptivity of the azimuthally polarized radiation is comparably low at the side walls, less energy is absorbed in the upper region of the capillary, leaving a bigger fraction of the pulse energy available in the outlet zone.

The differences in hole morphology become evident also in the temporal evolution of the capillary. At the beginning of the drilling process, the borehole proceeds into the workpiece in the form of a pointed capillary [22], whereas a particularly fine tip is created at drilling with azimuthal polarization. The breakthrough is reached after ~10 s for both polarization states. Subsequently, for radial polarization, the capillary strongly expands in the sheet center. At drilling with azimuthal polarization, though, only negligible diameter growth is recorded in the inlet zone and the sheet center, while steady widening takes place in the outlet region. Reduced radial expansion and higher aspect ratios have also been observed at helical drilling with azimuthal polarization in 0.5 mm sheets.

Figure 5 compares SEM images of the borehole inlets and outlets, thus enabling a detailed analysis of quality aspects. For both polarization states, the depicted inlets have an acceptable roundness. They are free of visible melt deposits and debris on the workpiece surface. Nevertheless, the inlet quality shows significant drawbacks. The edge of the borehole is damaged by nicks, which are assumed to be caused by a halo surrounding the actual doughnut-shaped (0,1)* mode. The halo is mainly due to the discrete number of segments of the LRAC. It can be suppressed by spatial filtering. As already discussed above, there is a striking difference in the roundness of the outlet orifices. Apart from geometrical criteria, sharp edges and smooth hole walls are shown for both polarization states. Altogether, no significant difference can be stated in terms of machining quality between the boreholes fabricated with radial and azimuthal polarization. This means that, at helical drilling without core in the ps regime, a comparable quality is achieved at parallel and perpendicular incidence of the radiation to the hole walls.

5. Simulation of the polarization-dependent absorption

In order to estimate the influence which the dependence of absorption on polarization exerts on the drilling process, raytracing calculations have been carried out employing a self-implemented algorithm. This algorithm approximates the caustic of the incoming laser beam using bended rays until the first impact onto the material. The subsequent propagation including multiple reflections uses straight rays. The number of multiple reflections was limited to 40. The z-axis was chosen as the incident propagation direction of the central ray of a bundle containing a total of 2x106 rays. The local distances ri(z) of a ray i to the optical axis was defined by

ri(z)=kiw(z)=kiw01+(zzf)2z02,
where z 0 is the Rayleigh length, z f the coordinate of the focal plane and w 0 the waist radius. The factor ki denotes the distance of a calculated ray from the central ray in relation to the beam radius. The intensity distribution of the Laguerre-Gaussian (0,1)* mode used for the calculation was defined by
I(xi2+yi2)=I(ri)=16ri2πw(z)4e4ri2w(z)2.
This definition implies a second-moment-based beam radius w(z) and a total power of 1. Both coordinates xi and yi were randomly distributed inside a circle with ri < rmax according to the uniform distribution. The polarization direction was chosen radially or azimuthally for the incident rays, and the absorbed intensity was calculated with the Fresnel equations for absorbing materials.

For the simulation, a rotationally symmetric capillary with a depth of 400 µm was approximated from the transverse section of a blind hole formed with 4.1∙104 pulses using a percussion drilling process with radial polarization, as described in Sec. 3. The dependence of the borehole radius on the z coordinate was described by a polynomial

R(z)=j=06ajzj.
The corresponding coefficients are a0 = 29.37, a1 = −0.47, a2 = 6.73∙10−3, a3 = −5.36∙10−5, a4 = 2.12∙10−7, a5 = −3.95∙10−10 and a6 = 2.79∙10−13. The capillary surface was modeled for the depth range 0 ≤ z ≤ 400 and discretized into 120 x 200 triangles. Furthermore a small aperture of 1.5 µm diameter was left open at the tip of the capillary in order to extract the transmitted power. For the index of refraction at 1030 nm the value n = 2.59 + i4.87 was used for steel. The results of the simulation are shown in Fig. 6 . The calculated absorption of the capillary was 98.8% for radial and 91.1% for azimuthal polarization. Accordingly the transmission through the 1.5 µm hole at the tip was 1% and 8.5%.

 

Fig. 6 Comparison of the absorbed intensity at the hole walls for azimuthal and radial polarization. The diagram shows the absorbed intensity relative to the peak intensity of the incident ring mode at focal level. For the calculations the focal plane was located at −100 µm.

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It can be seen from Fig. 6 that more intensity is absorbed in the upper region of the capillary and at the bottleneck located at the sheet center for radial compared to azimuthal polarization. In contrast significant absorption is observed at the tip of the borehole for the azimuthally polarized beam, thus predicting narrower and deeper boreholes. Moreover, it was found that, for the considered capillary, the highest power absorption occurs at the first reflection for radial polarization whereas for azimuthal polarization the highest absorption takes place at the fifth reflection. This is in good agreement with the experimental results given in Figs. 3 and 7 .

 

Fig. 7 Geometry of blind holes in 1 mm CrNi steel, formed with 105 laser pulses using a percussion drilling process with radially (left) and azimuthally (right) polarized radiation. A deeper and narrower capillary is obtained for azimuthal polarization. λ = 1030 nm, f p = 103 kHz, Q p = 50 µJ, z f = −100 µm.

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6. Conclusion

High-precision microholes have been fabricated in austenitic steel sheets using picosecond pulsed, radially and azimuthally polarized infrared laser radiation. The linear to radial and/or azimuthal polarization conversion was accomplished using a converter composed of eight half-wave plate segments.

At percussion drilling, the full penetration of 1 mm sheets could be completed two times faster using azimuthal compared to radial polarization. At helical drilling, pronounced radial widening and barrelling were observed for radial polarization, whereas slender capillaries with straight walls and a negative conical shape were obtained with azimuthal polarization. Unlike the borehole morphology, the machining quality turned out to be comparable at both polarization states. These findings indicate that the use of radial polarization is suitable rather for the fabrication of boreholes with relatively large diameters in thin sheets (s ≤ 500 µm), while azimuthal polarization can be recommended for the generation of high aspect ratios in thick sheets (s ≥ 1 mm) or extraordinarily small diameters (d ≤ 50 µm).

A comparative numerical ray tracing simulation of multiple reflections at the borehole walls has been carried out for both polarization states. The obtained results show an enhanced absorption in the upper part of the capillary and at bottlenecks for radial polarization, whereas azimuthal polarization enables a more efficient energy transport into the tip of the hole. This results in narrower and deeper holes. Altogether the simulation was in good agreement with the experimental observation.

As a next step, a general evaluation of potential benefits of radial or azimuthal polarization for microdrilling with ultrashort laser pulses should be performed by comparing with circular polarization, which is typically used in picosecond microdrilling applications today.

Acknowledgements

This research was supported by the Baden-Württemberg Stiftung within the project RaPoS, the Deutsche Forschungsgemeinschaft (DFG) under contract GR3172/7-1 and the German Federal Ministry for Education and Research (BMBF) under contract 13N8583. The authors would like to thank their associate Johannes Früchtenicht for maintaining the laser system.

References and links

1. D. Breitling, C. Föhl, F. Dausinger, T. Kononenko, and V. Konov, in Femtosecond Technology for Technical and Medical Applications, F. Dausinger, F. Lichtner and H. Lubatschowski, eds. (Springer, Berlin, 2004).

2. H. Tönshoff, C. Momma, A. Ostendorf, S. Nolte, and G. Kamlage, “Microdrilling of metals with ultrashort laser pulses,” J. Laser Appl. 12(1), 23–27 (2000). [CrossRef]  

3. A. Ancona, F. Röser, K. Rademaker, J. Limpert, S. Nolte, and A. Tünnermann, “High speed laser drilling of metals using a high repetition rate, high average power ultrafast fiber CPA system,” Opt. Express 16(12), 8958–8968 (2008). [CrossRef]   [PubMed]  

4. C. Föhl and F. Dausinger, “High precision deep drilling with ultrashort pulses,” Proc. SPIE 5063, 346–351 (2003). [CrossRef]  

5. J. Chang, B. Warner, E. Dragon, and M. Martinez, “Precision micromachining with pulsed green lasers,” J. Laser Appl. 10(6), 285–291 (1998). [CrossRef]  

6. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004). [CrossRef]   [PubMed]  

7. V. P. Kalosha and I. Golub, “Toward the subdiffraction focusing limit of optical superresolution,” Opt. Lett. 32(24), 3540–3542 (2007). [CrossRef]   [PubMed]  

8. I. Moshe, S. Jackel, and A. Meir, “Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects,” Opt. Lett. 28(10), 807–809 (2003). [CrossRef]   [PubMed]  

9. 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]  

10. 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]  

11. T. Moser, M. Abdou Ahmed, M. Schäfer, A. Voss, M. Vogel, and T. Graf, “Exploiting radial polarization in material processing,” presented at the Stuttgart Laser Technology Forum, Stuttgart, Germany, 4–6 March 2008.

12. S. C. Tidwell, G. H. Kim, and W. D. Kimura, “Efficient radially polarized laser beam generation with a double interferometer,” Appl. Opt. 32(27), 5222–5229 (1993). [CrossRef]   [PubMed]  

13. K. C. Toussaint Jr, S. Park, J. E. Jureller, and N. F. Scherer, “Generation of optical vector beams with a diffractive optical element interferometer,” Opt. Lett. 30(21), 2846–2848 (2005). [CrossRef]   [PubMed]  

14. S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005). [CrossRef]  

15. W. J. Lai, B. C. Lim, P. B. Phua, K. S. Tiaw, H. H. Teo, and M. H. Hong, “Generation of radially polarized beam with a segmented spiral varying retarder,” Opt. Express 16(20), 15694–15699 (2008). [CrossRef]   [PubMed]  

16. M. Abdou-Ahmed, M. Vogel, V. Onuseit, A. Voss, R. Weber, and T. Graf, “Radially polarized thin-disk laser with 1-kW power,” invited talk, presented at the International Laser Physics Workshop, Barcelona, Spain, 13–17 July 2009.

17. M. A. Ahmed, J. Schulz, A. Voss, O. Parriaux, J. C. Pommier, and T. Graf, “Radially polarized 3 kW beam from a CO2 laser with an intracavity resonant grating mirror,” Opt. Lett. 32(13), 1824–1826 (2007). [CrossRef]   [PubMed]  

18. T. Moser, J. Balmer, D. Delbeke, P. Muys, S. Verstuyft, and R. Baets, “Intracavity generation of radially polarized CO2 laser beams based on a simple binary dielectric diffraction grating,” Appl. Opt. 45(33), 8517–8522 (2006). [CrossRef]   [PubMed]  

19. C. Stolzenburg, and A. Giesen, “Picosecond Regenerative Yb:YAG Thin Disk Amplifier at 200 kHz Repetition Rate and 62 W Output Power,” in Advanced Solid-State Photonics, Technical Digest (CD) (Optical Society of America, 2007), paper MA6.

20. M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008). [CrossRef]  

21. M. Kraus, S. Collmer, S. Sommer, and F. Dausinger, “Microdrilling in steel with frequency-doubled ultrashort pulsed laser radiation,” J. Laser Micro/Nanoengineering 3(3), 129–134 (2008). [CrossRef]  

22. A. Michalowski, D. Walter, F. Dausinger, and T. Graf, “Melt dynamics and hole formation during drilling with ultrashort pulses,” J. Laser Micro/Nanoengineering 3(3), 211–215 (2008). [CrossRef]  

References

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  1. D. Breitling, C. Föhl, F. Dausinger, T. Kononenko, and V. Konov, in Femtosecond Technology for Technical and Medical Applications, F. Dausinger, F. Lichtner and H. Lubatschowski, eds. (Springer, Berlin, 2004).
  2. H. Tönshoff, C. Momma, A. Ostendorf, S. Nolte, and G. Kamlage, “Microdrilling of metals with ultrashort laser pulses,” J. Laser Appl. 12(1), 23–27 (2000).
    [Crossref]
  3. A. Ancona, F. Röser, K. Rademaker, J. Limpert, S. Nolte, and A. Tünnermann, “High speed laser drilling of metals using a high repetition rate, high average power ultrafast fiber CPA system,” Opt. Express 16(12), 8958–8968 (2008).
    [Crossref] [PubMed]
  4. C. Föhl and F. Dausinger, “High precision deep drilling with ultrashort pulses,” Proc. SPIE 5063, 346–351 (2003).
    [Crossref]
  5. J. Chang, B. Warner, E. Dragon, and M. Martinez, “Precision micromachining with pulsed green lasers,” J. Laser Appl. 10(6), 285–291 (1998).
    [Crossref]
  6. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
    [Crossref] [PubMed]
  7. V. P. Kalosha and I. Golub, “Toward the subdiffraction focusing limit of optical superresolution,” Opt. Lett. 32(24), 3540–3542 (2007).
    [Crossref] [PubMed]
  8. I. Moshe, S. Jackel, and A. Meir, “Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects,” Opt. Lett. 28(10), 807–809 (2003).
    [Crossref] [PubMed]
  9. 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]
  10. 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]
  11. T. Moser, M. Abdou Ahmed, M. Schäfer, A. Voss, M. Vogel, and T. Graf, “Exploiting radial polarization in material processing,” presented at the Stuttgart Laser Technology Forum, Stuttgart, Germany, 4–6 March 2008.
  12. S. C. Tidwell, G. H. Kim, and W. D. Kimura, “Efficient radially polarized laser beam generation with a double interferometer,” Appl. Opt. 32(27), 5222–5229 (1993).
    [Crossref] [PubMed]
  13. K. C. Toussaint, S. Park, J. E. Jureller, and N. F. Scherer, “Generation of optical vector beams with a diffractive optical element interferometer,” Opt. Lett. 30(21), 2846–2848 (2005).
    [Crossref] [PubMed]
  14. S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
    [Crossref]
  15. W. J. Lai, B. C. Lim, P. B. Phua, K. S. Tiaw, H. H. Teo, and M. H. Hong, “Generation of radially polarized beam with a segmented spiral varying retarder,” Opt. Express 16(20), 15694–15699 (2008).
    [Crossref] [PubMed]
  16. M. Abdou-Ahmed, M. Vogel, V. Onuseit, A. Voss, R. Weber, and T. Graf, “Radially polarized thin-disk laser with 1-kW power,” invited talk, presented at the International Laser Physics Workshop, Barcelona, Spain, 13–17 July 2009.
  17. M. A. Ahmed, J. Schulz, A. Voss, O. Parriaux, J. C. Pommier, and T. Graf, “Radially polarized 3 kW beam from a CO2 laser with an intracavity resonant grating mirror,” Opt. Lett. 32(13), 1824–1826 (2007).
    [Crossref] [PubMed]
  18. T. Moser, J. Balmer, D. Delbeke, P. Muys, S. Verstuyft, and R. Baets, “Intracavity generation of radially polarized CO2 laser beams based on a simple binary dielectric diffraction grating,” Appl. Opt. 45(33), 8517–8522 (2006).
    [Crossref] [PubMed]
  19. C. Stolzenburg, and A. Giesen, “Picosecond Regenerative Yb:YAG Thin Disk Amplifier at 200 kHz Repetition Rate and 62 W Output Power,” in Advanced Solid-State Photonics, Technical Digest (CD) (Optical Society of America, 2007), paper MA6.
  20. M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
    [Crossref]
  21. M. Kraus, S. Collmer, S. Sommer, and F. Dausinger, “Microdrilling in steel with frequency-doubled ultrashort pulsed laser radiation,” J. Laser Micro/Nanoengineering 3(3), 129–134 (2008).
    [Crossref]
  22. A. Michalowski, D. Walter, F. Dausinger, and T. Graf, “Melt dynamics and hole formation during drilling with ultrashort pulses,” J. Laser Micro/Nanoengineering 3(3), 211–215 (2008).
    [Crossref]

2008 (5)

A. Ancona, F. Röser, K. Rademaker, J. Limpert, S. Nolte, and A. Tünnermann, “High speed laser drilling of metals using a high repetition rate, high average power ultrafast fiber CPA system,” Opt. Express 16(12), 8958–8968 (2008).
[Crossref] [PubMed]

W. J. Lai, B. C. Lim, P. B. Phua, K. S. Tiaw, H. H. Teo, and M. H. Hong, “Generation of radially polarized beam with a segmented spiral varying retarder,” Opt. Express 16(20), 15694–15699 (2008).
[Crossref] [PubMed]

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

M. Kraus, S. Collmer, S. Sommer, and F. Dausinger, “Microdrilling in steel with frequency-doubled ultrashort pulsed laser radiation,” J. Laser Micro/Nanoengineering 3(3), 129–134 (2008).
[Crossref]

A. Michalowski, D. Walter, F. Dausinger, and T. Graf, “Melt dynamics and hole formation during drilling with ultrashort pulses,” J. Laser Micro/Nanoengineering 3(3), 211–215 (2008).
[Crossref]

2007 (3)

2006 (1)

2005 (2)

K. C. Toussaint, S. Park, J. E. Jureller, and N. F. Scherer, “Generation of optical vector beams with a diffractive optical element interferometer,” Opt. Lett. 30(21), 2846–2848 (2005).
[Crossref] [PubMed]

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[Crossref]

2004 (1)

2003 (2)

2000 (1)

H. Tönshoff, C. Momma, A. Ostendorf, S. Nolte, and G. Kamlage, “Microdrilling of metals with ultrashort laser pulses,” J. Laser Appl. 12(1), 23–27 (2000).
[Crossref]

1999 (1)

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]

1998 (1)

J. Chang, B. Warner, E. Dragon, and M. Martinez, “Precision micromachining with pulsed green lasers,” J. Laser Appl. 10(6), 285–291 (1998).
[Crossref]

1993 (1)

Abdou Ahmed, M.

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

Ahmed, M. A.

Ancona, A.

Austerschulte, A.

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

Baets, R.

Balmer, J.

Chang, J.

J. Chang, B. Warner, E. Dragon, and M. Martinez, “Precision micromachining with pulsed green lasers,” J. Laser Appl. 10(6), 285–291 (1998).
[Crossref]

Collmer, S.

M. Kraus, S. Collmer, S. Sommer, and F. Dausinger, “Microdrilling in steel with frequency-doubled ultrashort pulsed laser radiation,” J. Laser Micro/Nanoengineering 3(3), 129–134 (2008).
[Crossref]

Dausinger, F.

M. Kraus, S. Collmer, S. Sommer, and F. Dausinger, “Microdrilling in steel with frequency-doubled ultrashort pulsed laser radiation,” J. Laser Micro/Nanoengineering 3(3), 129–134 (2008).
[Crossref]

A. Michalowski, D. Walter, F. Dausinger, and T. Graf, “Melt dynamics and hole formation during drilling with ultrashort pulses,” J. Laser Micro/Nanoengineering 3(3), 211–215 (2008).
[Crossref]

C. Föhl and F. Dausinger, “High precision deep drilling with ultrashort pulses,” Proc. SPIE 5063, 346–351 (2003).
[Crossref]

Delbeke, D.

Dorn, R.

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[Crossref]

Dragon, E.

J. Chang, B. Warner, E. Dragon, and M. Martinez, “Precision micromachining with pulsed green lasers,” J. Laser Appl. 10(6), 285–291 (1998).
[Crossref]

Feurer, T.

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]

Föhl, C.

C. Föhl and F. Dausinger, “High precision deep drilling with ultrashort pulses,” Proc. SPIE 5063, 346–351 (2003).
[Crossref]

Golub, I.

Graf, T.

A. Michalowski, D. Walter, F. Dausinger, and T. Graf, “Melt dynamics and hole formation during drilling with ultrashort pulses,” J. Laser Micro/Nanoengineering 3(3), 211–215 (2008).
[Crossref]

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

M. A. Ahmed, J. Schulz, A. Voss, O. Parriaux, J. C. Pommier, and T. Graf, “Radially polarized 3 kW beam from a CO2 laser with an intracavity resonant grating mirror,” Opt. Lett. 32(13), 1824–1826 (2007).
[Crossref] [PubMed]

Hong, M. H.

Jackel, S.

Jureller, J. E.

Kalosha, V. P.

Kamlage, G.

H. Tönshoff, C. Momma, A. Ostendorf, S. Nolte, and G. Kamlage, “Microdrilling of metals with ultrashort laser pulses,” J. Laser Appl. 12(1), 23–27 (2000).
[Crossref]

Kim, G. H.

Kimura, W. D.

Kraus, M.

M. Kraus, S. Collmer, S. Sommer, and F. Dausinger, “Microdrilling in steel with frequency-doubled ultrashort pulsed laser radiation,” J. Laser Micro/Nanoengineering 3(3), 129–134 (2008).
[Crossref]

Lai, W. J.

Leuchs, G.

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[Crossref]

Lim, B. C.

Limpert, J.

Martinez, M.

J. Chang, B. Warner, E. Dragon, and M. Martinez, “Precision micromachining with pulsed green lasers,” J. Laser Appl. 10(6), 285–291 (1998).
[Crossref]

Meier, M.

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]

Meir, A.

Metsch, V.

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

Michalowski, A.

A. Michalowski, D. Walter, F. Dausinger, and T. Graf, “Melt dynamics and hole formation during drilling with ultrashort pulses,” J. Laser Micro/Nanoengineering 3(3), 211–215 (2008).
[Crossref]

Momma, C.

H. Tönshoff, C. Momma, A. Ostendorf, S. Nolte, and G. Kamlage, “Microdrilling of metals with ultrashort laser pulses,” J. Laser Appl. 12(1), 23–27 (2000).
[Crossref]

Moser, T.

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

T. Moser, J. Balmer, D. Delbeke, P. Muys, S. Verstuyft, and R. Baets, “Intracavity generation of radially polarized CO2 laser beams based on a simple binary dielectric diffraction grating,” Appl. Opt. 45(33), 8517–8522 (2006).
[Crossref] [PubMed]

Moshe, I.

Muys, P.

Nesterov, A. V.

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]

Niziev, V. G.

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]

Nolte, S.

Ostendorf, A.

H. Tönshoff, C. Momma, A. Ostendorf, S. Nolte, and G. Kamlage, “Microdrilling of metals with ultrashort laser pulses,” J. Laser Appl. 12(1), 23–27 (2000).
[Crossref]

Park, S.

Parriaux, O.

Phua, P. B.

Pommier, J. C.

Quabis, S.

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[Crossref]

Rademaker, K.

Romano, V.

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]

Röser, F.

Scherer, N. F.

Schulz, J.

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

M. A. Ahmed, J. Schulz, A. Voss, O. Parriaux, J. C. Pommier, and T. Graf, “Radially polarized 3 kW beam from a CO2 laser with an intracavity resonant grating mirror,” Opt. Lett. 32(13), 1824–1826 (2007).
[Crossref] [PubMed]

Sommer, S.

M. Kraus, S. Collmer, S. Sommer, and F. Dausinger, “Microdrilling in steel with frequency-doubled ultrashort pulsed laser radiation,” J. Laser Micro/Nanoengineering 3(3), 129–134 (2008).
[Crossref]

Teo, H. H.

Tiaw, K. S.

Tidwell, S. C.

Tönshoff, H.

H. Tönshoff, C. Momma, A. Ostendorf, S. Nolte, and G. Kamlage, “Microdrilling of metals with ultrashort laser pulses,” J. Laser Appl. 12(1), 23–27 (2000).
[Crossref]

Toussaint, K. C.

Tünnermann, A.

Verstuyft, S.

Vogel, M.

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

Voß, A.

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

Voss, A.

Walter, D.

A. Michalowski, D. Walter, F. Dausinger, and T. Graf, “Melt dynamics and hole formation during drilling with ultrashort pulses,” J. Laser Micro/Nanoengineering 3(3), 211–215 (2008).
[Crossref]

Warner, B.

J. Chang, B. Warner, E. Dragon, and M. Martinez, “Precision micromachining with pulsed green lasers,” J. Laser Appl. 10(6), 285–291 (1998).
[Crossref]

Zhan, Q.

Appl. Opt. (2)

Appl. Phys. B (1)

S. Quabis, R. Dorn, and G. Leuchs, “Generation of a radially polarized doughnut mode of high quality,” Appl. Phys. B 81(5), 597–600 (2005).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (1)

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]

J. Laser Appl. (2)

J. Chang, B. Warner, E. Dragon, and M. Martinez, “Precision micromachining with pulsed green lasers,” J. Laser Appl. 10(6), 285–291 (1998).
[Crossref]

H. Tönshoff, C. Momma, A. Ostendorf, S. Nolte, and G. Kamlage, “Microdrilling of metals with ultrashort laser pulses,” J. Laser Appl. 12(1), 23–27 (2000).
[Crossref]

J. Laser Micro/Nanoengineering (2)

M. Kraus, S. Collmer, S. Sommer, and F. Dausinger, “Microdrilling in steel with frequency-doubled ultrashort pulsed laser radiation,” J. Laser Micro/Nanoengineering 3(3), 129–134 (2008).
[Crossref]

A. Michalowski, D. Walter, F. Dausinger, and T. Graf, “Melt dynamics and hole formation during drilling with ultrashort pulses,” J. Laser Micro/Nanoengineering 3(3), 211–215 (2008).
[Crossref]

J. Phys. D Appl. Phys. (1)

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]

Opt. Express (3)

Opt. Lett. (4)

Proc. SPIE (2)

M. Abdou Ahmed, A. Voß, M. Vogel, A. Austerschulte, J. Schulz, V. Metsch, T. Moser, and T. Graf, “Radially polarized high-power lasers,” Proc. SPIE 7131, 71311I (2008).
[Crossref]

C. Föhl and F. Dausinger, “High precision deep drilling with ultrashort pulses,” Proc. SPIE 5063, 346–351 (2003).
[Crossref]

Other (4)

D. Breitling, C. Föhl, F. Dausinger, T. Kononenko, and V. Konov, in Femtosecond Technology for Technical and Medical Applications, F. Dausinger, F. Lichtner and H. Lubatschowski, eds. (Springer, Berlin, 2004).

T. Moser, M. Abdou Ahmed, M. Schäfer, A. Voss, M. Vogel, and T. Graf, “Exploiting radial polarization in material processing,” presented at the Stuttgart Laser Technology Forum, Stuttgart, Germany, 4–6 March 2008.

M. Abdou-Ahmed, M. Vogel, V. Onuseit, A. Voss, R. Weber, and T. Graf, “Radially polarized thin-disk laser with 1-kW power,” invited talk, presented at the International Laser Physics Workshop, Barcelona, Spain, 13–17 July 2009.

C. Stolzenburg, and A. Giesen, “Picosecond Regenerative Yb:YAG Thin Disk Amplifier at 200 kHz Repetition Rate and 62 W Output Power,” in Advanced Solid-State Photonics, Technical Digest (CD) (Optical Society of America, 2007), paper MA6.

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Figures (7)

Fig. 1
Fig. 1

Linear to radial/azimuthal polarization conversion (LRAC) principle based on a segmented half-wave plates.

Fig. 2
Fig. 2

Recorded intensity distributions of the radially and azimuthally polarized beams without and with analyzer at different orientations.

Fig. 3
Fig. 3

Capillary depth and instantaneous drilling rate versus number of pulses for percussion drilling in CrNi steel with radially (■) and azimuthally (□) polarized radiation. λ = 1030 nm, f p = 103 kHz, Q p = 50 µJ, z f = −100 µm.

Fig. 4
Fig. 4

Transverse sections of microholes in 1 mm CrNi steel, drilled with radially (left) and azimuthally (right) polarized radiation. The depicted diameters are each mean values averaged from the major and minor axes of the cross-section. λ = 1030 nm, f p = 103 kHz, Q p = 50 µJ, z f = −100 µm, t D = 120 s, helical drilling.

Fig. 5
Fig. 5

Inlets and outlets of microholes in 1 mm CrNi steel, drilled with radially (left) and azimuthally (right) polarized radiation. d av denotes the mean diameter averaged from the major diameter d max and the minor diameter d min. λ = 1030 nm, f p = 103 kHz, Q p = 50 µJ, z f = −100 µm, t D = 120 s, helical drilling.

Fig. 6
Fig. 6

Comparison of the absorbed intensity at the hole walls for azimuthal and radial polarization. The diagram shows the absorbed intensity relative to the peak intensity of the incident ring mode at focal level. For the calculations the focal plane was located at −100 µm.

Fig. 7
Fig. 7

Geometry of blind holes in 1 mm CrNi steel, formed with 105 laser pulses using a percussion drilling process with radially (left) and azimuthally (right) polarized radiation. A deeper and narrower capillary is obtained for azimuthal polarization. λ = 1030 nm, f p = 103 kHz, Q p = 50 µJ, z f = −100 µm.

Equations (3)

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r i ( z ) = k i w ( z ) = k i w 0 1 + ( z z f ) 2 z 0 2 ,
I ( x i 2 + y i 2 ) = I ( r i ) = 16 r i 2 π w ( z ) 4 e 4 r i 2 w ( z ) 2 .
R ( z ) = j = 0 6 a j z j .

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