Abstract

Precise tailoring of optical vector beams is demonstrated, shaping their focal electric fields and used to create complex laser micro-patterning on a metal surface. A Spatial Light Modulator (SLM) and a micro-structured S-waveplate were integrated with a picosecond laser system and employed to structure the vector fields into radial and azimuthal polarizations with and without a vortex phase wavefront as well as superposition states. Imprinting Laser Induced Periodic Surface Structures (LIPSS) elucidates the detailed vector fields around the focal region. In addition to clear azimuthal and radial plasmon surface structures, unique, variable logarithmic spiral micro-structures with a pitch Λ ∼1μm, not observed previously, were imprinted on the surface, confirming unambiguously the complex 2D focal electric fields. We show clearly also how the Orbital Angular Momentum(OAM) associated with a helical wavefront induces rotation of vector fields along the optic axis of a focusing lens and confirmed by the observed surface micro-structures.

© 2015 Optical Society of America

1. Introduction

Laser beams with a space-variant electric field orientation and amplitude are referred to as vector beams [1] and have great potential for furthering theoretical understanding of light waves and light-material interactions. Radial and azimuthal polarization states are extreme examples of these vector states and can be produced with specific laser cavity designs [2], a Spatial Light Modulator (SLM) [3] or nano-structured waveplates [4]. Pure radial and azimuthal polarizations have a Laguerre Gaussian (LG) ring intensity distribution with a polarization singularity at the centre while pure vortex beams with any given polarization have a LG intensity distribution with a phase singularity. The use of vector beams has resulted in advances in applications such as microscopy [5], optical trapping [6] and ultra-relativistic electron acceleration [7]. With tight focusing at high numerical aperture NA ∼1, a z-component of electric field, along the optic axis has been observed, contrary to expectations from Maxwell’s equations [811]. This additional component can be combined in a 3D vector field to produce an optical field equivalent of a Mobius strip [12], recently demonstrated [13]. This z-component is negligible when focusing with low NA optics, hence 2D vector fields result in a fixed plane, orthogonal to the beam k-vector. A recent study on femtosecond laser induced LIPSS structuring on Silicon using optical vortex beams by K K Anoop et al [14] created with a liquid crystal q-plate showed a developing radial micro-structure, highlighting the multi-pulse feedback mechanism responsible for plasmon structuring while the central zero intensity singularity expected of a Laguerre Gaussian (LG) ring intensity mode was decorated with nano-particles. As Silicon is a particularly difficult material to micro-structure, even with femtosecond pulses [15,16], these results are all the more impressive. In addition, K. Lou et al [17], using femtosecond laser vector fields, generated 2D near wavelength micro-structures on a thin copper film on fused silica substrate. Here, an SLM was combined with an interferometric technique to add a spiral phase and variable phase shift φ0 which controlled the detailed vector fields and hence plasmon structuring. Previously, Yang et al [3], using two Spatial Light Modulators demonstrated the ability to dynamically modulate radial and azimuthal polarization states in real time along with linearly polarized LG intensity profiles with a 532nm wavelength picosecond laser, synchronized to the motion control system. The resulting low frequency surface plasmon micro-structure LIPSS and patterns with ∼0.5 μm pitch confirmed the purity of the desired 2D vector fields for surface patterning.

In this paper, we demonstrate complex 2D vector fields, generated by combining a phase only SLM and nano-structured S-waveplate with a NIR picosecond laser source to machine surface micro-patterns via plasmon structuring which highlights the orthogonal local electric field structure [18, 19]. OAM was then added with a helical phase applied to the SLM. As the near field beam intensity profiles are Laguerre Gaussian due to the phase/polarization singularities, detailed polarization analysis of vector beams with and without OAM are analyzed around the focal point of a lens by translating a detector consisting of a polarizer and CCD camera. This clarifies the effect of a vortex phase on the propagating vector fields which induces a clear rotation of the vector field around the lens focal plane and further supported by the observed Plasmon structuring.

Also, by altering linear polarization direction incident on the S-waveplate, complex surface patterning was extended to a new level, creating remarkable logarithmic spiral LIPSS which result from the field generated by a superposition of radial and azimuthal polarizations. Logarithmic spirals (first described by Descartes and admired by Bernoulli) often appear in nature, for example, the spiral arms of galaxies [20], the cloud formations observed from space in a cyclone and spiral patterns in shells. These natural spirals can be described by the polar equation r(ϕ)=aekϕwhere a and k are arbitrary constants and ϕ is the angle measured from the x-axis.

While vector fields (more complex than shown here) have been clearly impressed on low power Gaussian beams with 633nm [21] and 532nm [22] sources, the application to high power picosecond laser surface plasmon structuring has been more limited and thus of great interest in the search for precise surface patterning with a high degree of complexity.

2. Experimental details

The experimental setup is shown in Fig. 1. A seeded ultrafast laser Regenerative amplifier (High-Q IC-355-800, Photonic Solutions) has a 10ps temporal pulse width, 1064nm wavelength, M2 <1.3, 50kHz repetition rate and horizontal linear polarization output. The laser beam is expanded with a x3 telescope (CVI) to a diameter of 8mm, passes through an attenuator and beam vector fields structured using a reflective phase only SLM (Hamamatsu X10468-03) and a uncoated fused silica S-waveplate (Altechna). With the SLM used as a mirror (fixed phase), radial and azimuthal states were created by rotating the S-waveplate axis to θ = 0 and ± 90° respectively while superposition vector fields could be generated when the waveplate was set in the range −90° < θ < + 90°. OAM was added by applying a spiral phase (topological charge m = 1, phase eimϕ) Computer Generated Hologram (CGH) to the SLM. A 4-f system (Lens 1 and 2 in Fig. 1, f1 = f2 = 300mm) re-images the resulting beam vector fields into the 10mm input aperture of a scanning galvo (Nutfield) and focused with a flat field f-theta lens (f = 100mm). Polished stainless steel samples, mounted on a precision 5-axis (x, y, z, A, U) motion control system (A3200 Npaq system, Aerotech) were carefully positioned at the Fourier plane of the lens.

 

Fig. 1 Experimental set up. The linearly polarized laser output is expanded x3, then passes through an attenuator (λ/2 plate and Glan-laser polarizer with transmission axis horizontal), reflected from the SLM then directed to the S-waveplate. A 4f system re-images the complex field after reflection from SLM to the Galvo input aperture for surface micro-structuring while the introduction of a flip mirror re-directs the focused beam instead to the polarization analyzer (45° B/S) and Spiricon camera.

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Also, by having a 45° flip mirror, the transmitted radiation through lens L1 (f = 300mm) was re-directed to the Spiricon camera (model SP620U) via a wedged fused silica beam splitter (45° AOI) which acted as a polarization analyzer since the first surface was close to the Brewster angle. The reflected beam is therefore vertically polarized. Translation of the camera along the optic axis near the focal plane of lens L1 allowed spatial polarization analysis along the z-axis. This allowed measurement of the vector fields confirming the effect (or otherwise) of OAM on both polarization and intensity, prior to surface micro-structuring with the f-theta lens.

2.1 Optical configurations

Henceforth, vector beams with a radial, and azimuthal, or an intermediate tilted polarization are referred to as RP, (θ = 0°), AP (θ = 90°), and IP, (θ = + 45°), beams respectively. Additionally, radially, azimuthally and intermediately polarized beams with an orbital angular momentum are referred to as RPOAM, APOAM and IPOAM respectively.

3. Results and discussion

3.1 Polarization analysis

Figure 2 shows the measured intensity profiles when translating the polarization analyzer/camera in the vicinity of the lens focal plane and reveals a clear distinction between the vector beams with and without orbital angular momentum. These far field RP, AP and IP beams produced with the S-waveplate and polarizer have a distinct double-lobe intensity profile [Fig. 2(a)-2(c)] which rotates with the angle θ and is invariant as it propagates along the optic axis of the focusing lens apart from the obvious scale factor, proportional to the distance away from the focal plane. On the other hand, all the beams with orbital angular momentum have a twisted profile with non-zero intensity at the centre [Fig. 2(d)-2(f)], which varies significantly along the optic axis. These results highlight the complexity of the focal electric fields and the remarkable effect of the presence of a vortex phase on the vector beams which leads to rotation of the vector fields around the focal plane and inversion of the spiral direction, which was quite unexpected. At the focal plane, the profile has an approximately elliptical shape with spiral arms, indicated in the middle row [Z = 0, Fig. 2(d)-2(f)] with the long axis of the ellipse dependent on the incident polarization [i.e. horizontal or vertical when the incident beam is radially or azimuthally polarized respectively, see Fig. 2(d) and 2(e) respectively]. A clockwise rotation of the waveplate also caused a clockwise rotation of the ellipse axis, whereas the central peak intensity remains unchanged, which implies a hybrid polarization state.

 

Fig. 2 Reflected intensity distributions measured when polarization analyzer was translated near lens through focal plane, (a) RP (θ = 0°), (b) AP (θ = 90°), (c) IP (θ = + 45°), (d) RPAOM, (e) APAOM, (f) IPOAM. Note the rotation of the vector fields with addition of OAM and the non-zero intensity at the centre.

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For further clarity, Fig. 3 shows the measured reflected intensity profiles measured up to d = ± 40mm from the lens Fourier plane and stacked in an isometric view. Thus, we are observing the profiles along the optic axis over distances much greater than the Rayleigh length.

 

Fig. 3 More detailed polarization analysis along optic axis within ± 40mm of the far field, with (a) RP, (b) AP, (c) IP, (d) RPOAM, (e) APOAM and (f) IPOAM. The beams without OAM have stationary vector fields with z, but the vector fields with OAM show a non-zero intensity on axis and vector field rotation due to the spiral phase.

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The field distribution of the spiral phase mode Laguerre Gaussian LG(0,1)* can be described by [23]:

E(r,ϕ)=E0ρeρ/2e±iϕ
where r and φ are the cylindrical coordinates (where ρ=2r2/w2, w is the spot size of the Gaussian beam) and helicity depending on the ± sign. Hence, intensity distribution given by I(r,ϕ)=E*E=I0ρeρ, a ring intensity with zero intensity (phase singularity) in the middle, plotted in Fig. 4(a). In the case of a radially polarized beam with the same intensity distribution passing through a polarizer, the observed double lobe intensity pattern in Fig. 2 can be understood simply. Following Machavariani [23], the LG(0,1)* spiral phase mode can be represented by a superposition of two orthogonal degenerate LG modes;

 

Fig. 4 (a) LG(0,1)* radial polarized intensity distribution 2D, (b) 2D double lobe intensity distribution calculated from Eq. (6) when a radially polarized beam is reflected from a linear polariser (transmission axis horizontal), (c) 3D intensity representation of (b).

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Ex(r,ϕ)=E0ρeρ/2cos(ϕ)
Ey(r,ϕ)=E0ρeρ/2sin(ϕ)

Radial polarization can thus be represented by radially oriented field vectors, given at each point in the field given by:

E(r,ϕ)=E0ρeρ/2cosϕex+E0ρeρ/2sinϕey
where ex and ey are the unit vectors in the x and y directions. Passing this beam through a linear polarizer with the transmission axis in the x-direction yields an electric field given by:
E(r,ϕ)=E0ρeρ/2cosϕexex(exey=0)
and hence transmitted intensity distribution,
I(r,ϕ)=E*E=I0ρeρcos2ϕ
while the reflected intensity (relevant here) must have the angular termcos2ϕ in Eq. (6) replaced with sin2ϕ. This resulting 2D intensity distribution is plotted in Fig. 4(b) and compares very favorably with that observed in Fig. 2(a).

3.2 Surface processing

To elucidate vector fields further, surface laser plasmon structuring was carried out on polished stainless steel samples placed in the focal region of the f-theta lens (Fig. 1). Near threshold ablation on the metal results in the growth of microscopic Laser Induced Periodic Surface Structures (LIPSS) within the ablation spots. The finesse of these low frequency periodic micro-structures with period Λ ∼λ initially improves with exposure and develops orthogonally to the local electric field vectors [18, 24, 25]. This enables the analysis the vector field landscape unambiguously in the focal region complementing the polarization measurements. By translating the surface above and below the focal plane while observing the LIPSS after laser exposure, the resulting plasmon patterns confirmed the local vector field distributions. With the laser operating at 5kHz frequency, the fluence focused at the sample surface was attenuated to F ~0.4J/cm2 per pulse and exposure set to N = 50 pulses/spot. After laser exposure, the ablation spots were imaged with an SEM microscope.

Figure 5 shows SEM images of LIPSS patterns on the ablation spots structured with AP and RP beams, from Z = + 0.5mm above the focal plane, at the focal plane, Z = 0, and Z = −0.5 mm below the focal plane. The LIPPS, which have an annular structure with zero intensity at centre, are very clear, maintaining their orientation, thus stationary, independent of focus position. Radial polarization produces circular LIPSS and azimuthal polarization produces radial LIPSS, entirely consistent with polarization analysis in Fig. 2. These patterns also confirm the polarization purity to be excellent.

 

Fig. 5 SEM images of stationary LIPSS patterns structured with RP and AP beams when substrate translated through the focal plane (a) RP 0.5mm above focal plane, (b) at the focal lane and (c) 0.5mm below the focal plane, (d) AP 0.5mm above focal plane, (e) at the focal plane and (f) 0.5mm below the focal plane.

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Figure 6 shows the ablation spots produced round the focal plane when the RPOAM and APOAM beams had a helical phase added with topological charge m = 1. Photons thus carry a z-component of angular momentumLz= per photon due to the vortex wavefront. The SEM images now confirm that there is no singularity thus showing ablation at centre consistent with a Gaussian-like intensity profile already observed in the polarization measurements, [Fig. 2(d) and 2(e)]. There may however be some distortions induced due to steps in the vortex phase-map applied to the SLM. From Fig. 6, clear spiral LIPSS are produced just outside the central region but LIPSS finesse reduces at the centre of the focal spots, which one might expect to be due to overexposure. However, when significantly reducing fluence per spot, it remained difficult to produce clear LIPSS in the centre of the laser focal spots, consistent with the centre being circularly polarized [23]. Furthermore, the incident RPOAM beam produced a focal spot with LIPSS oriented in a radial pattern confirming that the focal field was azimuthally polarized in these regions, and vice versa with azimuthal, consistent with our previous study [26]. The addition of OAM thus appears to transform the incident RPOAM beam to its orthogonal state, APOAM at the focal plane and vice versa. The spiral direction (right handed above) also reverses to left handed below the focal plane, in accord with the spiral flip observed on the polarization analysis.

 

Fig. 6 LIPSS formation with the RPOAM and APOAM beams when substrate translated through the focal plane (a) RPOAM 0.5mm above focal plane, (b) at the focal lane and (c) 0.5mm below the focal plane, (d) APOAM 0.5mm above focal plane, (e) at the focal plane and (f) 0.5mm below the focal plane. The spiral structures reverse direction above and below the Fourier plane consistent with polarization observations.

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These important experimental results demonstrate the variability of the focal fields along the optic axis due to the addition of orbital angular momentum. However, the properties of LIPSS with circular (or random) polarization cannot be analyzed in this way. A Jones vector analysis (not shown here) confirmed that the beam polarization on axis at the Fourier plane is indeed circular, and consistent with that predicted by Macharavani et al [23] explaining the reduced finesse of LIPSS. Cardano et al [20] previously investigated experimentally the effect of spin to OAM conversion with a q-plate and measured the detailed spatial vector fields (via Stokes parameters) near the focal plane of a lens within one Rayleigh range. Their results showed a clear vector field rotation as observed here by both polarization analysis and surface micro-structures.

With OAM removed while rotating the S-waveplate to intermediate angles, −90° < θ < 90°, a series of unique, remarkable spiral Plasmon micro-patterns resulted at the lens focal plane, Fig. 7. By rotating the S-waveplate axis (angle θ) relative to the incident linear polarization, it was possible to generate plane wave radial (θ = 0°) and azimuthal (θ = ± 90°) polarizations and a series of highly interesting spirals at intermediate angles. Orthogonal polarization states have a δθ = 90° hence Fig. 7(a) and 7(e), 7(b) and 7(f), 7(c) and 7(g), 7(d) and 7(h) correspond to orthogonal polarization states. We believe that these are the first observations of such micro-structured spirals created by multi-pulse exposure with spiral vector fields.

 

Fig. 7 SEM images of spiral plasmons from superposition states generated by altering S-waveplate axis θ (a) −67.5°, (b) −45°, (c) −22.5°, (d) 0° (radial), (e) + 22.5°, (f) + 45°, (g) + 67.5° and (h) + 90° (azimuthal).

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The spiral geometry has been analyzed for θ = 22.5° and 45° and found to fit closely the logarithmic spiral function, r(ϕ)=aekϕwhere a = 0.57 (with r in μm) and k = 0.414 and 1.0 respectively. The constant k determines the spiral winding and thus k=tanθ. The fits to these spirals are very satisfying and shown in Fig. 8(a) and 8(b). For example, the average deviation in the θ = 45° fit, |δ(ϕ)|=|ϕfitϕexp| was found to be |δ(ϕ)|=0.093±0.091 radian or 5.3° ± 5.2°, a satisfactory outcome. The fit to θ = 22.5° looks even better. All the spirals are logarithmic - where the spiral separations along a given axis increase with rotation. At any given point in the field, the tangent to the curve and a radial line from the centre has a fixed angle.

 

Fig. 8 Detail of SEM images at (a) θ = 22.5° and (b) θ = 45° with the fits to logarithmic spirals where a = 0.57 and k = 0.414 and 1.0 respectively, (c) a simple geometric superposition of radial and azimuthal field components (with equal amplitude) at θ = 45°, generating a spiral electrical field distribution whose field direction is orthogonal to the plasmon spirals at every location in (b).

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We conjecture that the spiral micro-structures result from a superposition of the radial and azimuthal vector field components. Such logarithmic spiral electric fields, due to superpositions of radial and azimuthal polarizations were previously predicted by F.Gori in 2001 [27]. Figure 8(c) also supports this idea which shows the vector field in a geometrical model (when θ = 45°) when summing radial and azimuthal field components with equal amplitude at each location in the vector field.

5. Conclusions

Complex 2D laser vector fields were generated by combining a phase only SLM and nano-structured S-waveplate with NIR picosecond laser pulses and used to machine highly complex surface micro-patterns. A detailed polarization analysis of vector beams with and without OAM was accomplished by translating a polarizer and CCD camera through the far field of a lens, radial and azimuthal polarization states (and superpositions states) without OAM maintain a stationary electric field distribution along the propagation axis and LG intensity with a polarization singularity and intensity distribution scaling with distance from the focal plane. On the other hand, the effect of adding a helical phase applied to the SLM results in clear rotation of the vector fields with spiral direction inverting above and below the focal plane and a quasi-Gaussian intensity distribution with circular polarization at the beam centre. Experimental results based on surface plasmon LIPSS confirm these observations.

In addition, remarkable, complex logarithmic spiral Plasmon micro-structures were produced on steel substrates when rotating the S-waveplate axis relative to the incident linear polarization without OAM. These are the first observations of such micro-structures due to spiral electric field distributions, although theoretically predicted [27]. By drawing normals to the spiral structures, the local orthogonal laser electric fields can be determined. Alternatively, the magnetic field vectors associated with the radiation fields are parallel to the spiral LIPSS.

Applications of these complex spiral structures and field distributions are envisaged. For example, polymer moulds of these 40μm diameter spirals, although having ~1μm pitch (and which have smaller nano-structures within) might well affect cell interactions on surfaces if the pitch of these LIPSS could be reduced with shorter wavelengths, which could be expected. The spots inscribed with different vector states also represent a form of information encoding. If one dynamically rotates incident linear polarization (possible with the SLM) while synchronizing motion on a substrate [3], pre-determined patterns could be created at will. In the case of utrahigh intensity femtosecond pulses with these spiral electrical fields, particle acceleration might be advanced. It is interesting to note that by starting with patterned dielectric arrays of SiN nano-pillars in a Vogel spiral, near field coupling of the incident radiation along the spiral arms was recently experimentally demonstrated and theoretically predicted [28].

Acknowledgments

The authors gratefully acknowledge Prof. Miles Padgett who provided the SLM control software used in this research.

References and links

1. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1 (2009). [CrossRef]  

2. A. Tovar, “Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams,” J. Opt. Soc. Am. A 15(10), 2705 (1998). [CrossRef]  

3. Y. Jin, O. J. Allegre, W. Perrie, K. Abrams, J. Ouyang, E. Fearon, S. P. Edwardson, and G. Dearden, “Dynamic modulation of spatially structured polarization fields for real-time control of ultrafast laser-material interactions,” Opt. Express 21(21), 25333–25343 (2013). [CrossRef]   [PubMed]  

4. M. Beresna, M. Gecevičius, P. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011). [CrossRef]  

5. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001). [CrossRef]   [PubMed]  

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

7. C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74(S1), s83–s88 (2002). [CrossRef]  

8. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003). [CrossRef]   [PubMed]  

9. Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002). [CrossRef]   [PubMed]  

10. C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing Local Field Structure of Focused Ultrashort Pulses,” Phys. Rev. Lett. 106(12), 123901 (2011). [CrossRef]   [PubMed]  

11. C. Hnatovsky, V. G. Shvedov, and W. Krolikowski, “The role of light-induced nanostructures in femtosecond laser micromachining with vector and scalar pulses,” Opt. Express 21(10), 12651–12656 (2013). [CrossRef]   [PubMed]  

12. I. Freund, “Optical Möbius strips, twisted ribbons, and the index theorem,” Opt. Lett. 36(23), 4506–4508 (2011). [CrossRef]   [PubMed]  

13. T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015). [CrossRef]   [PubMed]  

14. K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014). [CrossRef]  

15. J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon–modification thresholds and morphology,” Appl. Phys., A Mater. Sci. Process. 74(1), 19–25 (2002). [CrossRef]  

16. 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]  

17. K. Lou, S. Qian, Z. Ren, X. Wang, Y. Li, C. Tu, and H. Wang, “Self-formed two-dimensional near-wavelength microstructures on copper induced by multipulse femtosecond vector optical fields,” J. Opt. Soc. Am. B 29(9), 2282 (2012). [CrossRef]  

18. Z. Guosheng, P. Fauchet, and A. Siegman, “Growth of spontaneous periodic surface structures on solids during laser illumination,” Phys. Rev. B 26(10), 5366–5381 (1982). [CrossRef]  

19. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of Laser-Induced Near-Subwavelength Ripples: Interference between Surface Plasmons and Incident Laser,” ACS Nano 3(12), 4062–4070 (2009). [CrossRef]   [PubMed]  

20. H. Ringermacher and L. Mead, “A new formula describing the scaffold structure of spiral galaxies,” Mon. Not. R. Astron. Soc. 397(1), 164–171 (2009). [CrossRef]  

21. F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013). [CrossRef]   [PubMed]  

22. X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007). [CrossRef]   [PubMed]  

23. G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1) LG beam,” Opt. Commun. 271(1), 190–196 (2007). [CrossRef]  

24. 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]  

25. U. Klug, J. Düsing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006 (2010). [CrossRef]  

26. O. J. Allegre, Y. Jin, W. Perrie, J. Ouyang, E. Fearon, S. P. Edwardson, and G. Dearden, “Complete wavefront and polarization control for ultrashort-pulse laser microprocessing,” Opt. Express 21(18), 21198–21207 (2013). [CrossRef]   [PubMed]  

27. F. Gori, “Polarization basis for vortex beams,” J. Opt. Soc. Am. A 18(7), 1612–1617 (2001). [CrossRef]   [PubMed]  

28. F. Intonti, N. Caselli, N. Lawrence, J. Trevino, D. Wiersma, and L. Dal Negro, “Near-field distribution and propagation of scattering resonances in Vogel spiral arrays of dielectric nanopillars,” New J. Phys. 15(8), 085023 (2013). [CrossRef]  

References

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  1. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1 (2009).
    [Crossref]
  2. A. Tovar, “Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams,” J. Opt. Soc. Am. A 15(10), 2705 (1998).
    [Crossref]
  3. Y. Jin, O. J. Allegre, W. Perrie, K. Abrams, J. Ouyang, E. Fearon, S. P. Edwardson, and G. Dearden, “Dynamic modulation of spatially structured polarization fields for real-time control of ultrafast laser-material interactions,” Opt. Express 21(21), 25333–25343 (2013).
    [Crossref] [PubMed]
  4. M. Beresna, M. Gecevičius, P. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
    [Crossref]
  5. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
    [Crossref] [PubMed]
  6. Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express 12(15), 3377–3382 (2004).
    [Crossref] [PubMed]
  7. C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74(S1), s83–s88 (2002).
    [Crossref]
  8. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
    [Crossref] [PubMed]
  9. Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
    [Crossref] [PubMed]
  10. C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing Local Field Structure of Focused Ultrashort Pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
    [Crossref] [PubMed]
  11. C. Hnatovsky, V. G. Shvedov, and W. Krolikowski, “The role of light-induced nanostructures in femtosecond laser micromachining with vector and scalar pulses,” Opt. Express 21(10), 12651–12656 (2013).
    [Crossref] [PubMed]
  12. I. Freund, “Optical Möbius strips, twisted ribbons, and the index theorem,” Opt. Lett. 36(23), 4506–4508 (2011).
    [Crossref] [PubMed]
  13. T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
    [Crossref] [PubMed]
  14. K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
    [Crossref]
  15. J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon–modification thresholds and morphology,” Appl. Phys., A Mater. Sci. Process. 74(1), 19–25 (2002).
    [Crossref]
  16. 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]
  17. K. Lou, S. Qian, Z. Ren, X. Wang, Y. Li, C. Tu, and H. Wang, “Self-formed two-dimensional near-wavelength microstructures on copper induced by multipulse femtosecond vector optical fields,” J. Opt. Soc. Am. B 29(9), 2282 (2012).
    [Crossref]
  18. Z. Guosheng, P. Fauchet, and A. Siegman, “Growth of spontaneous periodic surface structures on solids during laser illumination,” Phys. Rev. B 26(10), 5366–5381 (1982).
    [Crossref]
  19. M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of Laser-Induced Near-Subwavelength Ripples: Interference between Surface Plasmons and Incident Laser,” ACS Nano 3(12), 4062–4070 (2009).
    [Crossref] [PubMed]
  20. H. Ringermacher and L. Mead, “A new formula describing the scaffold structure of spiral galaxies,” Mon. Not. R. Astron. Soc. 397(1), 164–171 (2009).
    [Crossref]
  21. F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013).
    [Crossref] [PubMed]
  22. X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
    [Crossref] [PubMed]
  23. G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1) LG beam,” Opt. Commun. 271(1), 190–196 (2007).
    [Crossref]
  24. 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]
  25. U. Klug, J. Düsing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006 (2010).
    [Crossref]
  26. O. J. Allegre, Y. Jin, W. Perrie, J. Ouyang, E. Fearon, S. P. Edwardson, and G. Dearden, “Complete wavefront and polarization control for ultrashort-pulse laser microprocessing,” Opt. Express 21(18), 21198–21207 (2013).
    [Crossref] [PubMed]
  27. F. Gori, “Polarization basis for vortex beams,” J. Opt. Soc. Am. A 18(7), 1612–1617 (2001).
    [Crossref] [PubMed]
  28. F. Intonti, N. Caselli, N. Lawrence, J. Trevino, D. Wiersma, and L. Dal Negro, “Near-field distribution and propagation of scattering resonances in Vogel spiral arrays of dielectric nanopillars,” New J. Phys. 15(8), 085023 (2013).
    [Crossref]

2015 (1)

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

2014 (1)

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

2013 (5)

2012 (2)

2011 (3)

I. Freund, “Optical Möbius strips, twisted ribbons, and the index theorem,” Opt. Lett. 36(23), 4506–4508 (2011).
[Crossref] [PubMed]

M. Beresna, M. Gecevičius, P. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing Local Field Structure of Focused Ultrashort Pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

2010 (1)

U. Klug, J. Düsing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006 (2010).
[Crossref]

2009 (3)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1 (2009).
[Crossref]

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of Laser-Induced Near-Subwavelength Ripples: Interference between Surface Plasmons and Incident Laser,” ACS Nano 3(12), 4062–4070 (2009).
[Crossref] [PubMed]

H. Ringermacher and L. Mead, “A new formula describing the scaffold structure of spiral galaxies,” Mon. Not. R. Astron. Soc. 397(1), 164–171 (2009).
[Crossref]

2007 (3)

2004 (1)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

2002 (3)

Q. Zhan and J. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002).
[Crossref] [PubMed]

C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74(S1), s83–s88 (2002).
[Crossref]

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon–modification thresholds and morphology,” Appl. Phys., A Mater. Sci. Process. 74(1), 19–25 (2002).
[Crossref]

2001 (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

F. Gori, “Polarization basis for vortex beams,” J. Opt. Soc. Am. A 18(7), 1612–1617 (2001).
[Crossref] [PubMed]

1998 (1)

1982 (1)

Z. Guosheng, P. Fauchet, and A. Siegman, “Growth of spontaneous periodic surface structures on solids during laser illumination,” Phys. Rev. B 26(10), 5366–5381 (1982).
[Crossref]

Abrams, K.

Allegre, O. J.

Amoruso, S.

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

Anoop, K.

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

Banzer, P.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Baudach, S.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon–modification thresholds and morphology,” Appl. Phys., A Mater. Sci. Process. 74(1), 19–25 (2002).
[Crossref]

Bauer, T.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Beresna, M.

M. Beresna, M. Gecevičius, P. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Bonse, J.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon–modification thresholds and morphology,” Appl. Phys., A Mater. Sci. Process. 74(1), 19–25 (2002).
[Crossref]

Boyd, R. W.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Bruzzese, R.

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

Cardano, F.

Caselli, N.

F. Intonti, N. Caselli, N. Lawrence, J. Trevino, D. Wiersma, and L. Dal Negro, “Near-field distribution and propagation of scattering resonances in Vogel spiral arrays of dielectric nanopillars,” New J. Phys. 15(8), 085023 (2013).
[Crossref]

Cheng, Y.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of Laser-Induced Near-Subwavelength Ripples: Interference between Surface Plasmons and Incident Laser,” ACS Nano 3(12), 4062–4070 (2009).
[Crossref] [PubMed]

Dal Negro, L.

F. Intonti, N. Caselli, N. Lawrence, J. Trevino, D. Wiersma, and L. Dal Negro, “Near-field distribution and propagation of scattering resonances in Vogel spiral arrays of dielectric nanopillars,” New J. Phys. 15(8), 085023 (2013).
[Crossref]

de Lisio, C.

Dearden, G.

Ding, J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Düsing, J.

U. Klug, J. Düsing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006 (2010).
[Crossref]

Edwardson, S. P.

Fauchet, P.

Z. Guosheng, P. Fauchet, and A. Siegman, “Growth of spontaneous periodic surface structures on solids during laser illumination,” Phys. Rev. B 26(10), 5366–5381 (1982).
[Crossref]

Fearon, E.

Fittipaldi, R.

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

Freund, I.

Gecevicius, M.

M. Beresna, M. Gecevičius, P. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

Gertus, T.

M. Beresna, M. Gecevičius, P. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

Gori, F.

Gu, B.

Guo, C. S.

Guosheng, Z.

Z. Guosheng, P. Fauchet, and A. Siegman, “Growth of spontaneous periodic surface structures on solids during laser illumination,” Phys. Rev. B 26(10), 5366–5381 (1982).
[Crossref]

Hnatovsky, C.

C. Hnatovsky, V. G. Shvedov, and W. Krolikowski, “The role of light-induced nanostructures in femtosecond laser micromachining with vector and scalar pulses,” Opt. Express 21(10), 12651–12656 (2013).
[Crossref] [PubMed]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing Local Field Structure of Focused Ultrashort Pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

Huang, M.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of Laser-Induced Near-Subwavelength Ripples: Interference between Surface Plasmons and Incident Laser,” ACS Nano 3(12), 4062–4070 (2009).
[Crossref] [PubMed]

Intonti, F.

F. Intonti, N. Caselli, N. Lawrence, J. Trevino, D. Wiersma, and L. Dal Negro, “Near-field distribution and propagation of scattering resonances in Vogel spiral arrays of dielectric nanopillars,” New J. Phys. 15(8), 085023 (2013).
[Crossref]

Jackel, S.

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1) LG beam,” Opt. Commun. 271(1), 190–196 (2007).
[Crossref]

Jin, Y.

Karimi, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013).
[Crossref] [PubMed]

Kautek, W.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon–modification thresholds and morphology,” Appl. Phys., A Mater. Sci. Process. 74(1), 19–25 (2002).
[Crossref]

Kazansky, P.

M. Beresna, M. Gecevičius, P. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

Kling, R.

U. Klug, J. Düsing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006 (2010).
[Crossref]

Klug, U.

U. Klug, J. Düsing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006 (2010).
[Crossref]

Krolikowski, W.

C. Hnatovsky, V. G. Shvedov, and W. Krolikowski, “The role of light-induced nanostructures in femtosecond laser micromachining with vector and scalar pulses,” Opt. Express 21(10), 12651–12656 (2013).
[Crossref] [PubMed]

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing Local Field Structure of Focused Ultrashort Pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

Krüger, J.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon–modification thresholds and morphology,” Appl. Phys., A Mater. Sci. Process. 74(1), 19–25 (2002).
[Crossref]

Lawrence, N.

F. Intonti, N. Caselli, N. Lawrence, J. Trevino, D. Wiersma, and L. Dal Negro, “Near-field distribution and propagation of scattering resonances in Vogel spiral arrays of dielectric nanopillars,” New J. Phys. 15(8), 085023 (2013).
[Crossref]

Leger, J.

Lenzner, M.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon–modification thresholds and morphology,” Appl. Phys., A Mater. Sci. Process. 74(1), 19–25 (2002).
[Crossref]

Leuchs, G.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Li, Y.

Lou, K.

Lumer, Y.

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1) LG beam,” Opt. Commun. 271(1), 190–196 (2007).
[Crossref]

Machavariani, G.

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1) LG beam,” Opt. Commun. 271(1), 190–196 (2007).
[Crossref]

Malzer, S.

Marrucci, L.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013).
[Crossref] [PubMed]

Mead, L.

H. Ringermacher and L. Mead, “A new formula describing the scaffold structure of spiral galaxies,” Mon. Not. R. Astron. Soc. 397(1), 164–171 (2009).
[Crossref]

Moshe, I.

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1) LG beam,” Opt. Commun. 271(1), 190–196 (2007).
[Crossref]

Ni, W. J.

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Orlov, S.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Ouyang, J.

Paparo, D.

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

Perrie, W.

Piché, M.

C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74(S1), s83–s88 (2002).
[Crossref]

Qian, S.

Qian, S. X.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91(23), 233901 (2003).
[Crossref] [PubMed]

Ren, Z.

Ringermacher, H.

H. Ringermacher and L. Mead, “A new formula describing the scaffold structure of spiral galaxies,” Mon. Not. R. Astron. Soc. 397(1), 164–171 (2009).
[Crossref]

Rode, A.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing Local Field Structure of Focused Ultrashort Pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

Rubano, A.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

Santamato, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

F. Cardano, E. Karimi, L. Marrucci, C. de Lisio, and E. Santamato, “Generation and dynamics of optical beams with polarization singularities,” Opt. Express 21(7), 8815–8820 (2013).
[Crossref] [PubMed]

Sato, T.

U. Klug, J. Düsing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006 (2010).
[Crossref]

Shvedov, V.

C. Hnatovsky, V. Shvedov, W. Krolikowski, and A. Rode, “Revealing Local Field Structure of Focused Ultrashort Pulses,” Phys. Rev. Lett. 106(12), 123901 (2011).
[Crossref] [PubMed]

Shvedov, V. G.

Siegman, A.

Z. Guosheng, P. Fauchet, and A. Siegman, “Growth of spontaneous periodic surface structures on solids during laser illumination,” Phys. Rev. B 26(10), 5366–5381 (1982).
[Crossref]

Tovar, A.

Trevino, J.

F. Intonti, N. Caselli, N. Lawrence, J. Trevino, D. Wiersma, and L. Dal Negro, “Near-field distribution and propagation of scattering resonances in Vogel spiral arrays of dielectric nanopillars,” New J. Phys. 15(8), 085023 (2013).
[Crossref]

Tu, C.

Varin, C.

C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B 74(S1), s83–s88 (2002).
[Crossref]

Vecchione, A.

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

Wang, H.

Wang, H. T.

Wang, L. J.

Wang, X.

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
[Crossref]

K. Lou, S. Qian, Z. Ren, X. Wang, Y. Li, C. Tu, and H. Wang, “Self-formed two-dimensional near-wavelength microstructures on copper induced by multipulse femtosecond vector optical fields,” J. Opt. Soc. Am. B 29(9), 2282 (2012).
[Crossref]

Wang, X. L.

Washio, K.

U. Klug, J. Düsing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006 (2010).
[Crossref]

Wiersma, D.

F. Intonti, N. Caselli, N. Lawrence, J. Trevino, D. Wiersma, and L. Dal Negro, “Near-field distribution and propagation of scattering resonances in Vogel spiral arrays of dielectric nanopillars,” New J. Phys. 15(8), 085023 (2013).
[Crossref]

Xu, N.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of Laser-Induced Near-Subwavelength Ripples: Interference between Surface Plasmons and Incident Laser,” ACS Nano 3(12), 4062–4070 (2009).
[Crossref] [PubMed]

Xu, Z.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of Laser-Induced Near-Subwavelength Ripples: Interference between Surface Plasmons and Incident Laser,” ACS Nano 3(12), 4062–4070 (2009).
[Crossref] [PubMed]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86(23), 5251–5254 (2001).
[Crossref] [PubMed]

Zhan, Q.

Zhao, F.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of Laser-Induced Near-Subwavelength Ripples: Interference between Surface Plasmons and Incident Laser,” ACS Nano 3(12), 4062–4070 (2009).
[Crossref] [PubMed]

Zhao, Q. Z.

ACS Nano (1)

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of Laser-Induced Near-Subwavelength Ripples: Interference between Surface Plasmons and Incident Laser,” ACS Nano 3(12), 4062–4070 (2009).
[Crossref] [PubMed]

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Appl. Phys. B (1)

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M. Beresna, M. Gecevičius, P. Kazansky, and T. Gertus, “Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass,” Appl. Phys. Lett. 98(20), 201101 (2011).
[Crossref]

K. Anoop, A. Rubano, R. Fittipaldi, X. Wang, D. Paparo, A. Vecchione, L. Marrucci, R. Bruzzese, and S. Amoruso, “Femtosecond laser surface structuring of silicon using optical vortex beams generated by a q-plate,” Appl. Phys. Lett. 104(24), 241604 (2014).
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Appl. Phys., A Mater. Sci. Process. (1)

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon–modification thresholds and morphology,” Appl. Phys., A Mater. Sci. Process. 74(1), 19–25 (2002).
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Opt. Commun. (1)

G. Machavariani, Y. Lumer, I. Moshe, and S. Jackel, “Effect of the spiral phase element on the radial-polarization (0,1) LG beam,” Opt. Commun. 271(1), 190–196 (2007).
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U. Klug, J. Düsing, T. Sato, K. Washio, and R. Kling, “Polarization converted laser beams for micromachining applications,” Proc. SPIE 7590, 759006 (2010).
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Science (1)

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 Experimental set up. The linearly polarized laser output is expanded x3, then passes through an attenuator (λ/2 plate and Glan-laser polarizer with transmission axis horizontal), reflected from the SLM then directed to the S-waveplate. A 4f system re-images the complex field after reflection from SLM to the Galvo input aperture for surface micro-structuring while the introduction of a flip mirror re-directs the focused beam instead to the polarization analyzer (45° B/S) and Spiricon camera.
Fig. 2
Fig. 2 Reflected intensity distributions measured when polarization analyzer was translated near lens through focal plane, (a) RP (θ = 0°), (b) AP (θ = 90°), (c) IP (θ = + 45°), (d) RPAOM, (e) APAOM, (f) IPOAM. Note the rotation of the vector fields with addition of OAM and the non-zero intensity at the centre.
Fig. 3
Fig. 3 More detailed polarization analysis along optic axis within ± 40mm of the far field, with (a) RP, (b) AP, (c) IP, (d) RPOAM, (e) APOAM and (f) IPOAM. The beams without OAM have stationary vector fields with z, but the vector fields with OAM show a non-zero intensity on axis and vector field rotation due to the spiral phase.
Fig. 4
Fig. 4 (a) LG(0,1)* radial polarized intensity distribution 2D, (b) 2D double lobe intensity distribution calculated from Eq. (6) when a radially polarized beam is reflected from a linear polariser (transmission axis horizontal), (c) 3D intensity representation of (b).
Fig. 5
Fig. 5 SEM images of stationary LIPSS patterns structured with RP and AP beams when substrate translated through the focal plane (a) RP 0.5mm above focal plane, (b) at the focal lane and (c) 0.5mm below the focal plane, (d) AP 0.5mm above focal plane, (e) at the focal plane and (f) 0.5mm below the focal plane.
Fig. 6
Fig. 6 LIPSS formation with the RPOAM and APOAM beams when substrate translated through the focal plane (a) RPOAM 0.5mm above focal plane, (b) at the focal lane and (c) 0.5mm below the focal plane, (d) APOAM 0.5mm above focal plane, (e) at the focal plane and (f) 0.5mm below the focal plane. The spiral structures reverse direction above and below the Fourier plane consistent with polarization observations.
Fig. 7
Fig. 7 SEM images of spiral plasmons from superposition states generated by altering S-waveplate axis θ (a) −67.5°, (b) −45°, (c) −22.5°, (d) 0° (radial), (e) + 22.5°, (f) + 45°, (g) + 67.5° and (h) + 90° (azimuthal).
Fig. 8
Fig. 8 Detail of SEM images at (a) θ = 22.5° and (b) θ = 45° with the fits to logarithmic spirals where a = 0.57 and k = 0.414 and 1.0 respectively, (c) a simple geometric superposition of radial and azimuthal field components (with equal amplitude) at θ = 45°, generating a spiral electrical field distribution whose field direction is orthogonal to the plasmon spirals at every location in (b).

Equations (6)

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E(r,ϕ)= E 0 ρ e ρ/2 e ±iϕ
E x (r,ϕ)= E 0 ρ e ρ/2 cos(ϕ)
E y (r,ϕ)= E 0 ρ e ρ/2 sin(ϕ)
E(r,ϕ)= E 0 ρ e ρ/2 cosϕ e x + E 0 ρ e ρ/2 sinϕ e y
E(r,ϕ)= E 0 ρ e ρ/2 cosϕ e x e x ( e x e y =0)
I(r,ϕ)= E * E= I 0 ρ e ρ cos 2 ϕ

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