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Femtosecond vector vortex laser ablation in tungsten: chiral nano-micro texturing and structuring

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Abstract

We demonstrate laser-induced periodic surface structure (LIPSS) formation on tungsten with femtosecond vector vortex laser ablation for the first time, and investigate the properties of vector vortex LIPSS by contrasting its properties with Gaussian beam irradiation, and provide some demonstrations of complex microstructuring. The annular intensity profile of vector vortex beams allows LIPSS formation over wider energy range than Gaussian beams. Also, we demonstrate 2 and 3-dimensional chiral texturing and structuring by femtosecond vector vortex laser ablation. Vector vortex beam laser processing, which enables the fabrication of controllable complex structures, will open the door to innovative applications of tungsten.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Tungsten is an industrially important material because of its excellent physical properties such as high melting point, toughness, wear resistance, and heat resistance. The high heat resistance of tungsten and its compounds make them promising for the divertors in experimental nuclear fusion reactors [14]. In recent years, tungsten has also attracted attention as a promising substrate material for light-absorption applications such as photocatalysis and energy devices [5]. Surface micromachining or texturing are important methods to dramatically improve these properties of tungsten. Recently, it was also discovered that submicron periodic structuring of tungsten (period: 200–1000 nm, structure size: 100–1000 nm) on nano-to-micro scales enables the fabrication of tungsten periodic absorbers to enhance solar-thermal energy harvesting [68]. Microstructuring the tungsten surface improves its physico-chemical and mechanical properties: for example, it can be expected to enhance the efficiency of bonding with other metals and improve device characteristics. In addition, nanometer to micrometer scale surface texturing increases the surface area of various tungsten compounds (tungsten sulfides and oxides) that are attracting attention as environmentally friendly catalysts, and can be expected to improve the efficiency of catalytic decomposition. Therefore, there is a need for a technique that can produce surface structures that are stable over large areas and that can create a variety of patterns.

Tungsten is extremely difficult to process mechanically. Laser processing is an important method for patterning tungsten, and elucidating its laser processing characteristics is an important issue. In our group, we have used a nanosecond Q-switched Nd:YAG laser system to study the ablation properties of pure W and W-Re alloys as materials for use in the field of fusion science [9]. In femtosecond laser processing, laser-induced periodic surface structure (LIPSS) [1013] which is created by irradiation with linearly polarized ultrashort laser pulses, have been widely investigated as possible means of producing surfaces with desirable properties. The LIPSS process allows patterning of the surface of various materials, including metals such as tungsten [1416], semiconductors [1720], and glass [21,22], to fabricate one-dimensional (1D) periodic structures at the sub-wavelength scale depending on the direction of laser polarization. Employing a laser beam with nonuniform polarization breaks through the limitations of 1D LIPSS formation. In particular, the “vector vortex beam” allows controllable nonuniform spatial polarization of the beam profile, such as radially and azimuthally polarized beams; thus, it has allowed the fabrication of surface structures with unconventional 2-dimensional (2D) periodic nano-patterns [2326]. However, most previous studies on LIPSS fabrication by vector vortex beams have only paid attention to complex 2D structuring on the surface of a planar target substrate. Furthermore, the femtosecond laser ablation properties of vector vortex beams used for LIPSS formation have rarely been investigated, in contrast with the conventional Gaussian beam profile, despite the significant differences in their intensity profiles.

In this study, we investigate the processing characteristics of LIPSS formed on tungsten using a femtosecond vector vortex beam and propose a simple microstructure formation method. This is the first report of tungsten LIPSS processing using femtosecond optical vortex beams. We investigated the energy characteristics of femtosecond vector vortex beam processing of tungsten in detail by contrasting it with Gaussian beam irradiation. Further, we demonstrated the fabrication of unprecedented micro topological structures due to the spatial distribution of polarization and the ring intensity profile of the optical vortex beam. The obtained findings will open the door to innovative applications of tungsten.

2. Materials and methods

In this study, we employed a tungsten substrate with <99.95% purity (20 × 20 × 5 mm, Nippon Tungsten Co.) as the target for irradiation. The surface of the substrate was mechanically polished with abrasive paper (P200 to P2500, PRESI Co.) to a uniform mirror surface. Using a confocal laser scanning microscope with wavelength of 404 nm, the tungsten surface roughness was measured as less than 200 nm, which is the depth accuracy of the objective lens. This means that the machined surface is essentially uniform.

Figure 1 shows the experimental optical setup for femtosecond vector vortex LIPSS, using a mode-locked femtosecond laser with a regenerative amplifier with fundamental wavelength: 1040 nm, pulse duration: 430 fs, and repetition frequency: 500 kHz (Spirit 1040-4, Spectra-Physics Ink.). Its output was converted to 520 nm by second harmonic generation with a BBO crystal. The attenuator consisted of a polarized light splitter (PBS) and half-wave plate (HWP), which was used to control the pulse energy and transmit the uniform linearly polarized light component. Its output was converted to a vector vortex beam by a vortex retarder plate composed of a zero-order half-wave plate. By adjusting the angle of the fast axis of the vortex retarder with respect to the polarization direction δ, it was possible to generate a radially polarized mode (δ=0), an azimuthally polarized mode (δ=π/2), and their superposition [27]: a spirally polarized mode (0<δ <π/2). In this paper, the electric field of the spirally polarized mode ${E_{\textrm{Spiral}}}$ is expressed by the following equation using the mixing ratio θ, with radially polarization and azimuthal polarization as the fundamental modes.

$$\boldsymbol{E}{(\boldsymbol{r} )_{\textrm{Spiral}}} = {\boldsymbol{E}_{\textrm{Radial}}}(\boldsymbol{r} )\textrm{cos}\theta + {\boldsymbol{E}_{\textrm{Azimuth}}}(\boldsymbol{r} )\textrm{sin}\theta $$

 figure: Fig. 1.

Fig. 1. (a) Schematic diagram of experimental setup for vector vortex LIPSS. (b) Image obtained with middle polarization mode. It can be described by the superposition of the radial and azimuthal beams.

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Here, ${E_{\textrm{Radial}}}$, ${E_{\textrm{Azimuth}}}$ represent the spatial distribution of the electric field amplitude for radial polarization and azimuthal polarization, respectively. The mixing ratio θ is equivalent to the rotation angle of the vortex retarder plate δ. The generated vector vortex beam was focused on the surface of the tungsten substrate by a spherical lens with a focal length of 150 mm, and the generated spot size was estimated to be ∼35 µm (radially or azimuthally polarized beam). Here, the beam size was estimated from the size of a focal spot produced by a lens with f = 750 mm and scaling of the measured value of the back aperture. The beam spot size was defined as the diameter of the area with 1/e2 times the peak intensity. Also, the Gaussian beam used for comparison could be generated by simply removing the vortex retarder plate. The focused spot diameter of the Gaussian beam with the same optical system was estimated to be 24 µm, which is smaller than that of the vector vortex beam. The dose energy was controlled by changing the irradiation pulse number with a mechanical optical shutter.

In this paper, the fluence is defined as the average pulse fluence obtained by dividing the pulse energy by the beam cross-sectional area using the beam size determined above. Using the fluence makes it possible to discuss laser processing in a unified manner using Gaussian beams and polarized beams, which have different beam spot sizes. However, it should be noted that the peak energy is different for the annular beam and the Gaussian beam even at the same fluence.

The fabricated structures were observed by field-emission scanning electron microscopy (FE-SEM; JSM-7100F, JEOL Co.) after ultrasonic washing in acetone for 5 min.

3. Results and discussion

3.1 Laser-induced periodic surface structures by vector vortex beam

Both Gaussian and vector vortex beam irradiation could fabricate LIPSS on the tungsten surface under certain laser irradiation conditions. Figure 2 shows a typical LIPSS pattern formed on tungsten surfaces by irradiation with a Gaussian beam, and azimuthally and radially polarized beams. The pulse number N was fixed at 25000 for all cases, while the laser fluence $F$ was 0.108 J·cm−2 (radially and azimuthally polarized beam) or 0.0863 J·cm−2 (Gaussian).

 figure: Fig. 2.

Fig. 2. Typical FE-SEM images of fabricated surface structures created by irradiation with (a) Gaussian beam, (b) azimuthally polarized beam, and (c) radially polarized beam. The periodic structures were formed in the direction perpendicular to the linear polarization direction in each case.

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Using Gaussian beam irradiation, periodic submicron structures with a period of ∼400 nm were formed in the direction perpendicular to the laser polarization in the circular laser-irradiated area, same as previously reported [14,28]. In the center of the beam, with the highest intensity, the tungsten surface was removed by ablation and the surface was no longer flat. A very complex LIPSS was formed inside the holes generated by such laser ablation, and no longer maintained a uniform periodic structure on the surface [29].

By contrast, the azimuthal and radial beams produced a circularly symmetrical ordered surface pattern with a period of ∼400 nm, which is the same as that created by the Gaussian beam, perpendicular to the polarization direction. It is noteworthy that the tungsten maintained a smooth planar surface without excavation by ablation even though the average fluence was higher than that of the Gaussian beam. Furthermore, in contrast to the Gaussian beam, the center of the beam spot has zero intensity, and particles are transported from the surrounding areas and deposited as debris. At first glance, the debris in the center appears to be arranged periodically with a spacing of ∼1 µm. However, the debris formation phenomenon was a result of the aggregation of small particles such as atoms or atomic clusters on the substrate surface [30,31] and did not depend on the polarization state. Thus, this periodic structure is completely different from the LIPSS phenomenon, which depends on the polarization state.

3.2 Fundamental properties of vector vortex beam processing

It is important to compare the conditions for LIPSS formation by Gaussian and vector vortex beams. LIPSS formation was strongly dependent on the irradiation fluence: At low fluence, the tungsten surface roughening occurred without LIPSS formation. Conversely, at high fluence, the surface of metal was removed to create a hole, destroying the orderliness of the LIPSS. Therefore, in this paper, we define the term “critical range”, which indicates the fluence range where LIPSS formation occurs without drilling of the surface. Fluences within the “critical range” allow stable LIPSS formation with a uniform period on flat material surfaces. Figure 3(a) shows the dependence of the LIPSS period ${\mathrm{\Lambda }_{\textrm{LIPSS}}}$ on the laser fluence. ${\mathrm{\Lambda }_{\textrm{LIPSS}}}$ was measured for LIPSS formed on flat surfaces that were not excavated by laser ablation (The periods could be determined even if the irradiation fluence exceeded the drilling threshold). For the same number of pulses, the period decreased linearly as the irradiation fluence increased. For both Gaussian beams and vector vortex beams, LIPSS was always fabricated perpendicular to the polarization direction in the fluence range measured here and had a period comparable to the wavelength, which is similar to the case for low-spatial-frequency LIPSS (LSFL). It is worth mentioning that in the higher fluence range, there is the possibility of transitioning to high-spatial-frequency LIPSS (HSFL) with a period well below half a wavelength parallel to the polarization direction [15]. Consequently, the critical range for tungsten LIPSS formation for vector vortex beam and Gaussian beam irradiation can be estimated. For azimuthally or radially polarized beam irradiation, the fluence critical ranges for LIPSS fabrication were calculated to be ΔF = 0.11 J·cm−2 (0.043–0.15 J·cm−2: red area in the graph) in either case. Surprisingly, this value was 250% larger than that of a Gaussian beam: ΔF = 0.043 J·cm−2 (0.043–0.086 J·cm−2: blue area in the graph). The vector vortex beam has an annular intensity distribution in which the peak intensity is spatially averaged, so it has only about 50% of the peak energy of a Gaussian beam with the same beam diameter and pulse energy. This result shows that vector vortex LIPSS formation can be a robust structuring technology even with energy fluctuations.

 figure: Fig. 3.

Fig. 3. (a) Dependence of LIPSS period on laser fluence with N = 25000. The red and blue areas show the critical range for LIPSS formation on flat surfaces without excavation by laser ablation. (b) Dependence of LIPSS period on laser fluence with pulse number N (laser fluence 0.86 Jµcm−2). (c) Dependence of ablation depth D on laser fluence with N = 25000. The curves are fits using the equation for laser ablation efficiency, $D = \xi \textrm{ln}({F/{F_{\textrm{th}}}} )$.

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Figure 3(b) shows the dependence of the LIPSS period on the number of pulses. The period decreased from 400 nm to a minimum of 180 nm as the number of pulses increased, regardless of the polarization distribution, but after that, when N > 2.5 × 106, it began to increase to about 200 nm. Since both the laser fluence and pulse number show similar trends (Fig. 3(a,b)), it is possible that the cumulative energy is a factor that determines the LIPSS period. These results, including the fluence dependence of the period in Fig. 3(a), are very similar to those for LIPSS formation by a grating-assisted surface plasmon polariton excitation mechanism, which includes a partial transformation of the incident femtosecond laser radiation into surface electromagnetic waves [17]. Periodic structure formation in tungsten that could be analogized by a plasmon-coupling-like theory has been previously reported [17]. According to this theory, the LIPSS period in tungsten is expressed by the following formula, similar to plasmon coupling theory [14].

$${\Lambda _{\textrm{LIPSS}}} = \frac{\lambda }{{\sqrt {\left( {\frac{\varepsilon }{{\varepsilon + 1}}} \right) \pm \sin \theta } }}$$

Here, λ and ε represent the incident light wavelength and the real part of the permittivity for tungsten, respectively. The complex permittivity for tungsten is characterized by the refractive index n = 1.751 and the optical extinction coefficient κ=4.98 [32]. Thus, the LIPSS period is calculated to be 415 nm. This value is on the order of the experimental value ${\varLambda _{\textrm{LIPSS}}}$∼300 nm, but this is a high estimate. In this experiment, the number of pulses was at least 25,000. The decrease in period with increasing number of laser pulses in LSFL formation can be explained by grating-assisted surface plasmon-laser coupling. The LIPSS on the surface formed by irradiation with the first few pulses forces the resonance wavelength of the SPP to undergo a red-shift due to interference between SPP enhanced by the periodic nanostructure on the metal surface and the incident waves. This phenomenon leads to a decrease in the LIPSS period during multi-pulse irradiation [33,34]. Incidentally, hydrodynamic effects such as nonlinear convection may also be important for the formation of fine periodic structures [13,33]. However, since relatively few hot spots would be generated on tungsten, it is unlikely that a hydrodynamic mechanism is involved in the LIPSS formation mechanism.

We also investigated ablation-induced perforation, an effect that inhibits uniform LIPSS formation. As representative circular beams, we compare the ablation ratio of the azimuthally polarized beam and the Gaussian beam in Fig. 3(c). The ablation depth per 2.5 × 104 pulses was evaluated from $D = \xi \textrm{ln}({F/{F_{\textrm{th}}}} )$. [35] Here, $D$, $\xi $, and ${F_{th}}$ indicate the ablation depth, optical penetration depth and ablation-threshold fluence, respectively. The values of ${F_{\textrm{th}}}$ were calculated to be 0.12 J·cm−2 for the annular beam and 0.032 J·cm−2 for the Gaussian beam. Therefore, the ablation threshold for the annular beam is about 3.8 times higher than that for the Gaussian beam.

In conclusion, although a vector vortex beam with a nonuniform polarization distribution does not cause a difference in the principles of LIPSS formation, the vector vortex laser allows LIPSS formation over a wider energy range. Thus, vector vortex LIPSS would improve uniformity in large-area surface processing that requires a long scanning time.

3.2 Demonstration of texturing and structuring of tungsten surface

Finally, we demonstrate an advanced microstructuring method based on femtosecond vector vortex laser processing of tungsten. Cylindrically symmetric spatial polarization and an annular intensity profile can be achieved by a vector vortex beam to produce complex chiral nanoscale-to-microscale structures in a simple method. For example, by introducing a mixed mode of radially polarized and azimuthally polarized light, yielding spiral polarization, a helical surface structure can be systematically produced at any desired angle. Figure 4(a) shows the machined surface structure obtained with a spirally polarized beam with a radial-to-azimuthal mixing ratio of θ = ±π/4. The irradiation fluence is 0.02 J·cm−2 and the pulse number is 25000.

 figure: Fig. 4.

Fig. 4. Fabricated chiral surface structures employing vector vortex beam superposition mode characterized by mixture ratio θ (-π/2 ∼ π/3). This method can fabricate arbitrary helical surface patterns.

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Even with such a complex polarization distribution, a periodic structure on the order of the wavelength is formed in a direction orthogonal to the polarization direction at every position; that is, a spiral texture with chirality opposite to the helicity of the polarization distribution is formed. By reversing the spiral direction of the polarized light, both left-handed (θ=-π/4) and right-handed (θ=π/4) spiral textures can be created. Furthermore, by finely adjusting the mixing ratio between the radial beam and the azimuthal beam to θπ/6, π/3, we were able to easily generate a spiral texture with a flexible curvature that reflects each polarization state. The chiral helical surface structures with arbitrary helical curvature properties generated by this method open up potential applications such as chiral metamaterials.

When the irradiation fluence is increased, surface material is removed by ablation. In contrast, in the vector vortex beam, the material in the central non-diffractive dark spot is relatively unaffected by processing. This opens up the possibility of novel 3-dimensional (3D) chiral microstructuring, such as chiral nano-needle fabrication [36] shown in previous work.

Figure 5 illustrates a structure generated by a vector vortex beam with θπ/4 under irradiation conditions of 0.17 J·cm−2 and N = 5 × 105. Even under tight beam focus, a spiral-shaped LIPSS reflecting the polarization state was formed, indicating that the polarization dependence of LIPSS formation was maintained. Also, with increasing number of irradiation pulses, the period decreased to >200 nm. Furthermore, in addition to LIPSS formation on a flat surface, the high-density vector vortex beam with a central dark spot also caused micrometer-scale structuring by particle deposition in the center and ring-shaped material removal by laser ablation. When we measured the 3D structure using a laser microscope, we found that the singular point region of the optical vortex beam formed a hemisphere with a diameter of approximately 10 µm. In this way, we succeeded in extending the fabrication of a helical structure with arbitrary curvature to a 3D structure by using the vector vortex beam.

 figure: Fig. 5.

Fig. 5. Demonstration of 3D advanced structuring utilizing vector vortex beams. (a) Chiral micro-helical structure that combines hemispherical structure formation created by annular intensity distribution and helical LIPSS texturing by spiral polarization mode (left: θ=-π/4, right: θ=π/4). The diameter of the hemispherical structure was measured as >10 µm by 3D measurement using a laser microscope. (b) Topological structuring based on phenomena occurring within dark spot of vector vortex beam. The distorted circular intensity distribution could produce a spiral structure with a size of about 10 µm and a chiral overhand knot structure with a finely textured surface was fabricated. Also, chiral texturing is possible for this structure. (c) The experimental intensity profile and stokes parameter of vector vortex beam (θ=-π/3, -π/4) focused by the spherical lens f = 50 mm.

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Finally, we mention the possibility of forming complex 3D topological structures that go beyond texturing by vector vortex beam irradiation, as shown in Fig. 5(b). Irradiation by a spiral polarized beam under enhanced light convergence, utilizing an f = 50 mm lens, θ = -π/3, pulse fluence: 0.775 J·cm−2, N = 25000 pulses produced a micrometer-scale logarithmic spiral structure. However, irradiation with θ = -π/4, pulse fluence: 1.55 J·cm−2, pulse number N = 2.5 × 106 produced a micrometer-scale left overhand knot-shape structure. Interestingly, at higher pulse fluence, the chirality of the overhand knot structure reversed to a right overhand knot.

Figure 5(c) shows the intensity and Stokes parameters S1, S2, and S3 profiles at the focal plane of the vector vortex beam with θ = 3/π and π/4, the conditions under which the 3D topological structure was generated. Here, there indicate the difference of the power between horizontal and vertical linear polarized components (S1), between +π/4 and −π/4 linearly polarized components (S2), and between right and left circularly polarized components (S3), respectively. The polarization state of each beam was measured using a polarizer. The beam diameter was measured to be 13 µm. Although there is some distortion due to the experimental conditions, both the profile of intensity and Stokes parameter ware almost uniform, and we could not observe any optical structure that would induce the topological structure formation in (b).

However, it is noteworthy that the intensity of the central polarization singularity exhibited clearly non-zero, especially in the S1 component. This result probably indicates the longitudinal electromagnetic field induced by the focused beam. It should be mentioned here that the longitudinal electromagnetic field could form a 3D topological polarization structure in a tight-focused vector vortex beam. It has been mentioned that a tight-focused beam with a topological polarization structure, such as a lemon beam generates a 3D topological polarization structure called an “optical polarization Möbius strip” caused by a longitudinal electromagnetic field with orbital angular momentum [37,38], and this is very similar to the overhand knot structure in Fig. 5(b). In this experiment, only a weak longitudinal electric field could exist due to the relaxed focus condition of approximately numerical aperture; NA 0.22, but this could trigger topological structuring such as an overhand knot structure. Furthermore, in vector vortex beams, there are several factors that could cause chiral topological structuring, such as Gouy phase shift [39] due to defocusing and spin-orbit angular momentum conversion [40] by the structured surfaces. However, it is difficult to explain the phenomenon of overhand knot structure inversion at this point, and further detailed research will be needed to clarify the mechanism. Regardless, femtosecond vector vortex laser processing under tight-focus conditions provides us with an attractive for the new generation's topological structure material processing.

In conclusion, this investigation underscores the transformative potential of vector vortex beams in the generation of complex structures within hard materials. The observed helical, chiral, and 3D configurations hold promise for novel material fabrication techniques. The interplay of optical manipulation and structural engineering provides fertile ground for diverse scientific and industrial applications.

4. Conclusion

We demonstrated LIPSS formation in tungsten employing femtosecond vector vortex beams for the first time, investigated the basic properties of vector vortex LIPSS by contrasting it with Gaussian beam irradiation, and provided some demonstrations.

Femtosecond vector vortex beam irradiation couldn't cause crucial differences in the principles of LIPSS formation. However, the annular intensity profile of the vector vortex beam allows stable LIPSS formation over a wider energy range because the ablation threshold, which is a factor that inhibits planar LIPSS formation, is higher than that with a Gaussian beam. This allows the stable large-area processing that requires long scanning. By using a linearly polarized phase vortex beam [41] with a similar intensity distribution, due to the helical structure of the phase distribution rather than polarization distribution, it may become possible to stabilize the texturing of periodic structures during large-area scanning. Therefore, femtosecond optical vortex LIPSS is effective for improving the quality of divertors for fusion reactors employing tungsten due to effects such as increased bonding strength as a result of increased anchoring effects.

As a more advanced and unique application, we also demonstrated 2D and 3D chiral texturing and structuring by femtosecond vector vortex laser ablation. Such controllable spiral texturing and 3D topological structuring are phenomena unique to an optical vortex with a central singularity point, opening the development of thermal and optical metasurfaces (e.g., optical vortex beam generation of plasmonic devices for optical orbital angular momentum fast communication [42]) and new functional surfaces. In conclusion, femtosecond vector vortex beams exhibit the potential to generate complex tungsten structures.

Funding

Japan Society for the Promotion of Science (23K19204); National Institute for Fusion Science (JII1001, KIIH001, KIIH002, KIIH007, MIS012); New Energy and Industrial Technology Development Organization; Amada Foundation (AF-2023220-B3).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic diagram of experimental setup for vector vortex LIPSS. (b) Image obtained with middle polarization mode. It can be described by the superposition of the radial and azimuthal beams.
Fig. 2.
Fig. 2. Typical FE-SEM images of fabricated surface structures created by irradiation with (a) Gaussian beam, (b) azimuthally polarized beam, and (c) radially polarized beam. The periodic structures were formed in the direction perpendicular to the linear polarization direction in each case.
Fig. 3.
Fig. 3. (a) Dependence of LIPSS period on laser fluence with N = 25000. The red and blue areas show the critical range for LIPSS formation on flat surfaces without excavation by laser ablation. (b) Dependence of LIPSS period on laser fluence with pulse number N (laser fluence 0.86 Jµcm−2). (c) Dependence of ablation depth D on laser fluence with N = 25000. The curves are fits using the equation for laser ablation efficiency, $D = \xi \textrm{ln}({F/{F_{\textrm{th}}}} )$.
Fig. 4.
Fig. 4. Fabricated chiral surface structures employing vector vortex beam superposition mode characterized by mixture ratio θ (-π/2 ∼ π/3). This method can fabricate arbitrary helical surface patterns.
Fig. 5.
Fig. 5. Demonstration of 3D advanced structuring utilizing vector vortex beams. (a) Chiral micro-helical structure that combines hemispherical structure formation created by annular intensity distribution and helical LIPSS texturing by spiral polarization mode (left: θ=-π/4, right: θ=π/4). The diameter of the hemispherical structure was measured as >10 µm by 3D measurement using a laser microscope. (b) Topological structuring based on phenomena occurring within dark spot of vector vortex beam. The distorted circular intensity distribution could produce a spiral structure with a size of about 10 µm and a chiral overhand knot structure with a finely textured surface was fabricated. Also, chiral texturing is possible for this structure. (c) The experimental intensity profile and stokes parameter of vector vortex beam (θ=-π/3, -π/4) focused by the spherical lens f = 50 mm.

Equations (2)

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E ( r ) Spiral = E Radial ( r ) cos θ + E Azimuth ( r ) sin θ
Λ LIPSS = λ ( ε ε + 1 ) ± sin θ
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