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
Laser beams with a space-variant electric field orientation and amplitude are referred to as vector beams  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 , a Spatial Light Modulator (SLM)  or nano-structured waveplates . 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 , optical trapping  and ultra-relativistic electron acceleration . 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 [8–11]. This additional component can be combined in a 3D vector field to produce an optical field equivalent of a Mobius strip , recently demonstrated . 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  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 , 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 , 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 , the cloud formations observed from space in a cyclone and spiral patterns in shells. These natural spirals can be described by the polar equation where 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  and 532nm  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.
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.
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.
The field distribution of the spiral phase mode Laguerre Gaussian LG(0,1)* can be described by :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 , the LG(0,1)* spiral phase mode can be represented by a superposition of two orthogonal degenerate LG modes;
Radial polarization can thus be represented by radially oriented field vectors, given at each point in the field given by:Eq. (6) replaced with . 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.
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 momentum 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 . 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 . 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.
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  explaining the reduced finesse of LIPSS. Cardano et al  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.
The spiral geometry has been analyzed for θ = 22.5° and 45° and found to fit closely the logarithmic spiral function, where a = 0.57 (with r in μm) and k = 0.414 and 1.0 respectively. The constant k determines the spiral winding and thus . 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, was found to be 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.
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 . 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.
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 . 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 , 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 .
The authors gratefully acknowledge Prof. Miles Padgett who provided the SLM control software used in this research.
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