We report on the fabrication of an axicon by applying a two-step manufacturing process including a 1030 nm femtosecond and a 10.6 µm CO2 laser. First, the pre-defined axicon geometry is generated by high-precision femtosecond layer-by-layer ablation. In order to meet high surface quality requirements, inevitable stipulated for optical use, the surface of the thus structured axicon is smoothened by a subsequent CO2 laser polishing process. The finalized axicon fulfills optical quality as the surface roughness Ra is significantly reduced from 0.56 µm to 34 nm. For the evaluation of the optical quality, the axicon is placed in a measurement setup including the femtosecond laser. Comparison between the calculated Bessel beam for an ideal axicon and the quasi-Bessel beam generated and measured by the fabricated axicon reveals excellent agreement, verifying our precise manufacturing method.
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Bessel beams, are the propagation-invariant solutions of the Helmholtz equation, theoretically first described by Durnin et al.  in 1987. Ideal non-diffractive Bessel beams are of infinite transverse extent, carry infinite energy, and thus cannot be generated experimentally [2, 3]. Approximations to the ideal Bessel beams can be found for a finite spatial range, firstly shown by Durnin et al.  in 1987 by the use of an annular slit in the back focal plane of a lens. Another effective method is the use of axicons, transferring the incident intensity distribution of a Gaussian beam in a so-called quasi-Bessel beam. Figure 1 shows an axicon with an apex angle α and the range z max in which the quasi-Bessel beam exists for a Gaussian beam having a radius of ω0. The intensity distribution behind an ideal axicon is calculated by Eq. (1) .
Here, P describes the power of the incident Gaussian beam, k = 2π/λ the angular wavenumber with λ being the wavelength, Θ the polar angle (see Fig. 1) and J0 the zeroth-order Bessel function of first kind. The polar angle Θ depends on the apex angle, the refractive index n of the axicon and n0 of the surrounding medium and can be calculated using Eq. (2).
Based on their intensity distribution, quasi-Bessel beams provide several advantages over conventional Gaussian beams for laser micromachining processes. Xie et al.  used an axicon for femtosecond micro-hole drilling in PMMA with different pulse numbers while the single pulse drilling revealed the best quality. The micro-holes have a diameter of 1.5 µm – 2.4 µm while the aspect ratio is up to 330. Bhuyan et al.  fabricated single-shot nanovoids in fused silica with quasi-Bessel beams having different pulse durations of 60 fs – 5.2 ps. While the nanovoids reveal diameters between 200 nm and 400 nm, the aspect ratio exceeds 1000. Furthermore, femtosecond single-shot voids are also fabricated by Mitra et al.  in borosilicate glass revealing an aspect ratio of 1200. Another application of quasi-Bessel beams has been shown by different authors using the generation of holes/voids for cleaving of glasses and crystals with femtosecond lasers [7, 8]. In this context, Dudutis et al.  presented the control of the crack propagation within the bulk modification of soda-lime glass for a 300 ps laser system, with respect to glass cutting applications. Applying quasi-Bessel beams for generating high-aspect ratio structures via two-photon polymerization has been demonstrated by Li et al. . Ježek et al.  also used a polymerization process to generate photopolymerized fibers having a diameter of 2 µm and a length exceeding 1.5 cm with continuous-wave quasi-Bessel beams. Furthermore, Zhang et al.  used femtosecond quasi-Bessel beams for the welding of silicon and borosilicate glass.
In this paper, we report on the fabrication of a small-sized axicon in fused silica for the generation of a quasi-Bessel beam, by combining a high-precision femtosecond laser ablation process with a subsequent CO2 laser polishing step. In a recent publication, we presented this two-step process chain and demonstrated their applicability by generating a cylindrical lens . Compared to conventional fabrication method (grinding and polishing), this laser based manufacturing process reveal significant advantages e.g. offering a higher degree of freedom in optical design, presenting a wear-free fabrication method and being applicable for rapid prototyping and thus time- and cost-efficient.
Femtosecond or CO2 laser based fabrication of optical components have been shown by different authors in literature. Guo et al.  generated microlenses with a femtosecond laser induced two-photon polymerization process. The fabrication of cylindrical and hemispherical lenses was reported by Cheng et al.  applying photosensitive glass in a four step process chain. Here, an initial femtosecond laser step generates the curved surfaces in the photosensitive material. Zheng et al.  fabricated embedded micro-ball lenses inside PMMA by focusing a femtosecond laser inside the substrate while Pan et al.  and Tsai et al.  applied different fabrication methods including femtosecond laser processing and wet etching for optics fabrication. Choi et al.  and Delgado et al.  produced micro optics whereas an ultrashort pulsed laser forms the geometrical preforms that are subsequently transformed into the desired optical component geometry. In both approaches [19, 20], the required curvatures are introduced to the preforms by a CO2 laser reshaping process, which is accompanied by a surface polishing. Contrary to Choi et al., Delgodo et al. used an etching step between the two laser processes to remove debris from the samples. Another combination of femtosecond and CO2 laser has been described by Heidrich et al.  using the later one to generate and polish the optical components in a two-step process and, finally, employ an ultrashort pulsed laser in a third step to correct minor form deviations. Serhatlioglu et al.  also used a CO2 laser for the polishing of femtosecond generated structures. Therefore, microwells and microfluidic channels are fabricated in fused silica by a HF acid assisted femtosecond laser microfabrication technique. The subsequent CO2 laser step leads to a lower surface roughness and higher optical imaging quality.
Contrary to these all laser based fabrication methods, our manufacturing process has the possibility for rapid prototyping even for 3D optical components with complex free-form surfaces in glass, overcoming limitations of the other methods, e.g. offering a higher degree of freedom in generation of complex freeform surfaces, leading to a lower surface roughness, offering a higher contour accuracy or reducing the required process steps. After the fabrication of cylindrical surfaces, here we demonstrate the high-quality fabrication of an axicon and highlight the excellent agreement between the experimentally generated intensity profile of the quasi-Bessel beam by the fabricated axicon and theoretical calculations for an ideal axicon.
We employed a Yb:KGW ultrashort pulsed laser (Pharos, Light Conversion) for a precise layer-by-layer ablation process and a CO2 laser (Infinity, Iradion) for a subsequent polishing step. The ultrashort pulsed laser is used to ablate a pre-defined geometry in glass and is specified by its wavelength of 1030 nm and a pulse duration of 230 fs (FWHM) at a repetition rate of 50 kHz in our experiments. The laser is equipped to a micromachining system (MM200-USP, Optec) with a galvo scanner (RTA AR800 2G+, Newson) and an f-Θ-lens having a focal length of 100 mm, mounted on a motorized z-stage (PRO165, Aerotech), resulting in a focal beam diameter of 33 µm (1/e2). The focal beam diameter measurement as well as the later axicon characterization is done with a high-resolution CCD camera having a pixel size of 1.67 µm (UI-1490SE-M-GL, IDS). An external attenuator is used to adjust the pulse energy of the laser. The CO2 laser system is specified by a wavelength of 10.6 µm, an maximum output power of 77 W and a beam diameter of 5 mm (1/e2) as being measured with a beam profiler (FocusMonitor, Primes) at the processing station, which is used without focussing optic in the polishing process. Due to its wide-ranging usage for optical components, polished fused silica samples (GVB solutions in glass) are used in our experiments. The samples have a round surface with a diameter of 14 mm. To analyze the generated 3D structures in detail, a laser scanning microscope (VK-X210, Keyence) is used.
3.1. Ultrashort pulsed laser ablation
As previously reported, the ultrashort pulsed laser is used to ablate a defined geometry i.e. an axicon in a precise layer-by-layer ablation process by scanning the laser spot over the sample. The applied pulse distance (PD), both in x- and y-direction, as well as the fluence mainly influence this ablation process. To ensure a homogeneous energy input over the scanned area, a theoretical approach is used to determine the necessary pulse distance. Equation (5) describes the accumulated fluence Φacc on the fused silica specimen, while Φ0 is the single pulse peak fluence, i and j are integer numbers, xi and yi are the relative central positions of the ith and jth pulse, and ω0 is the radius of the applied laser spot .
Figure 2 shows 3D calculations and 2D cross-sections of the accumulated fluences for 10×10 pulses with different pulse distances i.e. 18, 16, 14 and 12 µm. The beam radius is set to 16.5 µm, as in our experiments while Φ0 = 1.0 J/cm2 is exemplarilly chosen. Apparently, for decreasing pulse distances, the maximum accumulated fluence increases due to the greater pulse overlap. For a pulse distance of 18 µm, the peaks of the individual laser pulses are clearly visible and disappear for smaller values of PD. At 12 µm PD, we found a homogeneous fluence distribution, while Φacc reaches a relative level of ≈3 J/cm2 and a radial pulse overlap (overlap of diameters) of 64%. Therefore, we choose this PD as optimum overlapping parameter for a homogenous laser ablation process, leading to a scanning speed of 600 mm/s for our 50 kHz laser system.
To get acquainted with the fluence dependent femtosecond laser ablation process, we perform a parameter study varying the applied laser fluence. Hatches consisting of parallel lines, having a line distance of 12 µm, as determined before, as well as the scanning speed of 600 mm/s are ablated while 10 layers are scanned to perform a more accurate evaluation of the ablated step height. After each ablated layer, the hatch is rotated by 100°, corresponding to the later used scan strategy of the 3D axicon fabrication to ensure a more homogeneous ablation process. Please note the polished fused silica surface is roughened before the ablation experiment to guarantee a comparable surface morphology and thus a comparable absorption behaviour of the laser pulses. For this roughening, a fluence of 3.00 J/cm2 and a pulse distance of 6 µm are used, determined by a previous roughening experiment. We found the ablated depth increases with increasing fluence in a linear behaviour within the applied fluence range from 1.91 J/cm2 to 3.77 J/cm2. To ensure a precise layer-by-layer ablation process, we choose a step height of 1 µm per layer, corresponding to a fluence of 2.34 J/cm2.
The precise femtosecond ablation process is demonstrated by the ablation of a small-sized sharp-tip axicon. Therefore, we designed the axicon to have a base radius of 1 mm and an apex angle of 170°. Again, the surface of the silica sample is roughened before the 3D geometry is ablated by the layer-by-layer ablation process with the parameters and scanning strategy defined before while the focus is readjusted after each layer with the motorized z-stage. Figure 3(a) shows the 3D geometry of the axicon after the ablation process.
Obviously, the axicon has a sharp tip and the apex angle is measured to be 170° (Fig. 3(b)) being in excellent agreement with the designed geometry, confirming our high-precision ablation step. The roughness Ra of the ablated axicon is about 0.56 µm, measured within 5 lines of 2 mm length across the axicon. Consequently, a following polishing step is mandatory for optical usage.
3.2. CO2 laser polishing
The high-precision layer-by-layer ablation process offers the possibility for small-sized 3D geometry production. In order to achieve optical quality, a second post-processing step is required. A CO2 laser is used to polish the afore fabricated fused silica axicon because of the high absorption of about 80% for fused silica and having a temperature dependent penetration depth of about 4 – 34 µm [24,25]. Therefore, CO2 laser irradiation leads to heating up of a thin fused silica surface layer and a viscosity reduction resulting in a smoothening of the surface due to surface tension of melted glass . Weingarten et al.  and Hildebrand et al.  showed that a defocused laser spot can successfully be used for CO2 laser polishing of glass. Therefore, we decide to use the CO2 laser without focusing optic and thus employing a beam diameter of 5 mm (1/e2). For an efficient polishing process, we used the maximum power of 77 W of the CO2 laser to heat up the axicon surface. As a result, we varied the scanning speed of the laser and found a speed of 9.2 mm/s which is accompanied by a modulation of the laser with 0.36 kHz as preferential setup. The scanning strategy is chosen to be a round hatch having a diameter of 16 mm consisting of parallel lines with a line distance of 25.4 µm. This hatch is scanned 4 times with a 90° rotation after each repetition while the silica sample is placed in a metallic holder.
Figure 3(b) compares cross-sections of a polished and an unpolished axicon. Apparently, an inevitable tip-rounding of the axicon comes with the polishing process. Furthermore, we found a significant reduction of the surface roughness Ra from initially 0.56 µm to 34 nm. Figure 4(a) shows the enlarged area of the polished axicon tip including a circle having a radius R of 1.1 mm. This radius represents the rounding of the axicon tip after the polishing process. The error map in Fig. 4(b) shows the difference in height between an ideal and the experimentally fabrication axicon. Smaller deviations are apparent over the entire axicon surface while the largest is at the axicon tip having a deviation of −3.5 µm. Again, we highlight the high contour accuracy after the polishing step and the surface roughness being reduced to optical quality ≪ λ/10 for the applied femtosecond laser (λ = 1030 nm).
3.3. Axicon characterization
To assess the functionality of the finished optical component, the ultrashort pulsed laser system, employed for the 3D laser ablation process, is used in a modified setup. Figure 5(a) shows the optical system used for the axicon evaluation. As the raw beam diameter is too large for the small-sized axicon, an asymmetric 4f-setup consisting of two plano-convex lenses, L1 and L2, having a focal length of f1 = 200 mm and f2 = 50 mm are used, respectively. The resulting beam diameter at the axicon is measured with the CCD camera to be 0.98 mm (1/e2). An optical microscopy setup consisting of a 10× infinity corrected objective (NA = 0.25, Olympus), a plano-convex lens (L3), having a focal length of f3 = 100 mm and the high-resolution CCD camera is used for monitoring the quasi-Bessel beam behind the axicon tip. This microscopy setup is required to display the intensity profile of the quasi-Bessel beam near the axicon tip as well as to magnify the small quasi-Bessel beam for a better representation. The magnification of the optical microscopy setup can be calculated with f3/fobjective = 100 mm / 18 mm = 5.56. In addition, for evaluation of the beam profile in propagation direction, the optical microscopy setup is mounted on a motorized stage (BP1M2-300, Thorlabs). Thus, the quasi-Bessel beam propagating behind the axicon tip is demonstrated precisely at each z-position.
Figure 5(b) shows the intensity distribution at 2 mm steps behind the axicon tip. At a distance of 2 mm, the quasi-Bessel beam starts to form, a behaviour described by Brzobohatý et al.  for a round-tip axicon. The quasi-Bessel beam remains to a distance up to over 16 mm, confirming the calculated range zmax = 12.4 mm (Eq. (3)). The intensity distribution is typically, having a sharp peak in the centre surrounded by several radial distributed intensity rings. This intensity profile, excluding the distance directly behind the axicon tip, is experimentally be confirmed within the range of zmax.
Comparison between calculated and measured intensity distributions at a distance of 8 mm behind the axicon is shown in Fig. 6. The calculated intensity profile and the radius of the quasi-Bessel beam are calculated with Eqs. (1) and (4), respectively. The radius of the Bessel beam is described by the distance of the peak intensity in the centre to the first minimum and is calculated to be 10 µm for our axicon. We highlight the excellent agreement of both, the height and the distance between the radially distributed peaks.
We have demonstrated the fabrication of a small-sized axicon in fused silica by a two-step process chain. A femtosecond laser is used for a high-precision layer-by-layer ablation process, generating the predefined 3D structure, followed by a CO2 laser polishing step, making the rough surface applicable for optical usage. In this contribution, the surface roughness of the axicon is reduced from 0.56 µm after the ablation process to 34 nm after the polishing step. The error map shows a maximum deviation of −3.5 µm at the tip of the axicon, resulting in a tip radius of 1.1 mm. The functionality of the optical component is demonstrated by imaging the intensity profile of the quasi-Bessel beam behind the axicon tip with a high-resolution CCD camera. We found excellent agreement between calculated and experimentally taken intensity profiles, highlighting the high quality of the manufactured optical component.
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