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Abstract
We report on the fabrication and evaluation of a sharp tip negative axicon paving the way for applications in high-power ultrashort pulsed laser systems. The negative axicon is manufactured by applying a two-step all laser-based process chain consisting of ultrashort pulsed laser ablation and CO2 laser polishing finishing the component in less than 5 minutes. The finalized negative axicon reveals a surface roughness of 18 nm, fulfilling optical quality. Two measurement setups, including the ultrashort pulsed laser itself, are used to evaluate the formation of Bessel beams in detail. By applying a focusing lens behind the negative axicon, well-developed Bessel beams are generated while their lengths depend on the distance between the negative axicon and the lens. Furthermore, the diameter of the Bessel beams increase strongly with the propagation distance. By adding a second focusing lens, Bessel beams are generated at its focal position, being almost invariant of its position. Hence, the typical Bessel beam intensity distribution is observed over an entire moving range of this second lens of 300 mm. While these Bessel beams show superior quality in terms of sharp peaks with homogeneous concentric rings, only minor deviations in intensity and diameter are observed over the moving range.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Bessel beams are the propagation-invariant solutions of the Helmholtz equation, theoretically first described by Durnin et al. in 1987 [1]. Ideal non-diffractive Bessel beams are of infinite transverse extent, carry infinite energy, and thus cannot be generated experimentally [2,3]. Approximations of the ideal Bessel beams can be found for a finite spatial range, firstly shown by Durnin et al. [4] by the use of an annular slit in the back focal plane of a lens. Afterwards, several other alternatives including spatial light modulators (SLM) [5–7], holograms or hologram in combination with axicon [8–10], tunable acoustic gradient lens [11], meta-axicons [12–14] or axicons [2,15,16] have been demonstrated for the generation of different types of Bessel beams. However, the simplest and most common way to generate Bessel beams is the usage of axicons, cone-shaped optical components, which were firstly described by McLeod in 1954 [17]. These elements are able to transfer an initial Gaussian beam into a Bessel beam having a significantly increased focal length as compared to the Gaussian beam [3]. Applications of axicons have been shown in the fields of, e.g., laser material processing [15,16,18,19], optical tweezers [20,21], optical imaging [22] or non-linear optics such as second-harmonic generation [23]. In particular, in the field of laser micro material processing using ultrashort pulsed lasers, their potential is demonstrated for applications such as drilling/void generation [3,15,19], dicing [24,25], polymerization [26] and welding [27].
Positive axicons with an apex angle $\Theta$ transfer an initial Gaussian beam having a radius of $\omega _0$ into a Bessel beam within the Bessel region $z_{max}$ (Fig. 1(a)). For laser material processing, the generated Bessel region is commonly imaged onto the specimen to be processed by a lens setup consisting of two lenses or a lens and microscope objective [3,15,16,27]. However, the Bessel region having a significantly increased peak intensity as compared to the initial Gaussian beam, is still present directly behind the axicon tip. For ultrashort pulsed lasers, it is well-known that high pulse intensities will cause effects like the generation of plasma and filamentation in air [28–30] which should be avoided to ensure efficient and controllable machining processes. A possibility to overcome the generation of Bessel beams with additional focal region is the usage of negative axicons, splitting the incoming Gaussian beam instead of superimposing. Figure 1(b) shows the propagation of a Gaussian beam by a negative axicon into a ring shaped beam profile which can be focused afterwards for the generation of a Bessel beam. Compared to positive axicons, no additional Bessel region behind the optical element exists.
While commercial axicons are created from bulk glass materials by time-consuming mechanical grinding and polishing steps, this method is not appropriate for negative axicons exhibiting a sharp tip. Therefore, we report for the first time on the fabrication of a negative axicon with an all laser-based processing method. Compared to conventional axicon fabrication (grinding and polishing), our process can be applied also for negative axicon geometries even for well-developed tips. Here, a combination of an ultrashort pulsed and a CO$_2$ laser is used. Especially the ultrashort pulsed laser is well-known for its excellent machining quality due to an efficient energy deposition and minimized heat-affected zone [31–33]. Its short pulse durations and thus high intensity laser pulses allow the excitation of electrons from the valence into the conduction band by multi-photon absorption and avalanche ionization processes which subsequently transfer their energy to the lattice and causing material modification or ablation even in dielectric materials such as glasses or polymers [34–37]. In literature, different ultrashort pulsed laser-based fabrication techniques for optical elements such as, e.g., multi-photon polymerization [38–40], laser ablation and wet etching [41–43] or exposure of photosensitive glass [44] have been demonstrated. Furthermore, combinations of both, ultrashort pulsed and CO$_2$ lasers have been applied for the manufacturing of glass optics. Choi et al. [45] fabricated spherical and cylindrical lens arrays in fused silica while Delgado et al. [46] fabricated lens arrays in soda-lime glass. Both utilized the ultrashort pulsed laser to ablate the material, forming micro-structures at the surface. Afterwards, a CO$_2$ laser with its high absorption rate of up to 80% in fused silica [47] is applied to reshape this micro-structures, forming the final lens geometries. This surface reshaping is accompanied by a surface polishing due to the surface tension of the molten glass. Contrary to these processes, we used the ultrashort pulsed laser for a precise layer-wise ablation, forming the designed geometry of the negative axicon. In a second process, the CO$_2$ laser is used to reduce the previously introduced surface roughness while a reshaping of the initially ultrashort pulsed laser generated geometry should be minimized.
2. Experimental
2.1 Fabrication of negative axicons
A negative axicon is fabricated out of fused silica within a two-step all laser-based manufacturing process. Firstly, a Yb:KGW ultrashort pulsed laser (Pharos, Light Conversion) having a wavelength of 1030 nm, a pulse duration of 230 fs (FWHM - full width at half maximum) and a repetition rate of 50 kHz is used to ablate the negative axicon preform. The laser is equipped to a micromachining system including a galvanometer scanner (RTA AR800 2G+, Newson) with an f-$\Theta$-lens having a focal length of 100 mm resulting in a focal diameter of 33 µm (1/e$^2$), measured with a high-resolution camera (UI-1490SE-M-GL, IDS). The negative axicon geometry is created by a layer-wise removal of the silica substrate in steps of 1 µm in height for a high contour accuracy. Within each layer, contour adapted hatches consisting of parallel lines are scanned by the laser. Therefore, a pulse distance of 12 µm in both, scanning direction and perpendicular thereto is chosen resulting in a scanning speed of 600 mm/s and a line distance of 12 µm. A fluence of 2.37 J/cm$^2$ is applied to remove exactly 1 µm substrate within each layer, while after each layer, the focal position of the laser is adjusted by a motorized z-stage (PRO165, Aerotech) and the hatch orientation is rotated by 100$^\circ$. Please note, the glass substrate was initially roughened with adapted laser parameters due to changes in morphology and absorption behaviour, ensuring a constant ablation process. Secondly, a CO$_2$ laser (Infinity, Iradion) having a wavelength of 10.6 µm is used to polish the previously generated preform. The CO$_2$ laser is scanned across the sample by a flying optic having a focal length of 63.5 mm. A defocus of 20 mm is applied resulting in a spot diameter on the sample surface of 1.5 mm (1/e$^2$). Round hatches (Ø = 16 mm) consisting of parallel lines having a line distance of 25.4 µm are scanned twice. Both scans are executed with a laser power of 73 W at sample surface allowing a high scanning speed. The first pass is used to polish the sample, while the second pass removes smaller debris remaining at the surface. For both passes, different scanning speeds are chosen, 146 mm/s for the first and 178 mm/s for the second pass, respectively. It should be noted that the scanning speed within the first pass is a compromise between the degree of surface polishing and the resulting contour accuracy. A similar process chain for the manufacturing of single optical elements such as cylindrical lenses [48], axicons [49] and axicon arrays [50] has been demonstrated previously. Due to its wide-ranging use for optical components, polished fused silica (GVB solutions in glass) is used in our experiments. The specimen have a diameter of 14 mm and a thickness of 2 mm.
The negative axicon is designed to have a base radius of 1 mm and a negative apex angle of 170$^\circ$. Figure 2(a) shows a 3D laser scanning microscope (VK-X210, Keyence) image of the finalized optic, illustrating the negative axicon. Figure 2(b) exemplifies a cross section over the tip. The contour (blue line) indicates smaller rounding on the base and the tip of the axicon which are introduced by the CO$_2$ laser polishing process. However, the designed apex angle of 170$^\circ$ is fabricated exactly, indicated by the dashed lines. The surface roughness R$_a$ of the finalized negative axicon is about 18 nm, revealing optical quality (R$_a$ $<$ $\lambda$/20) for the 1030 nm ultrashort pulsed laser while the tip rounding was measured to have a radius of about 0.7 mm. Beside the overall good contour accuracy, the laser processing time was under 5 min, 1 min for the ultrashort pulsed laser ablation and 3.4 min for the polishing. Both, the high contour accuracy, as well as the fast processing time highlight the high-precision ultra fast fabrication process.
Fig. 2. Laser scanning microscope image of (a) 3D contour and (b) cross section over the tip of the fabricated negative axicon.
3. Results and discussion
3.1 Evaluation of negative axicon with a single focussing lens
To assess the functionality of the fabricated negative axicon, the ultrashort pulsed laser system that had already been employed for the 3D laser ablation process, is now used in a modified setup (Fig. 3) having a beam diameter of 1 mm (1/e$^2$) at the negative axicon. To investigate the generated Bessel beams in its lateral extent as well as in propagation direction, a high-resolution camera (UI-1490SE-M-GL, IDS) is mounted on a motorized stage (BP1M2-300, Thorlabs) having a maximum travel range of 300 mm (z = 0 mm to z = 300 mm). Please note, an offset between the negative axicon and the camera is applied, resulting in a distance between these two components of 182 mm (z = 0 mm) to 482 mm (z = 300 mm), demonstrated by the orange label z$_{actual}$ in Fig. 3. The formed ring profile behind the negative axicon is focused by a single plano-convex lens L1 having a focal length of 50 mm. The position of L1 is set at three different distances d behind the negative axicon, namely 62 mm, 60 mm and 58 mm which are chosen to generate Bessel beams being within the travel range of the motorized stage. The beam propagation illustrated in Fig. 3 is based on calculations using geometrical optics for different distances d. In the overlapping area of the ring, Bessel beams are formed. Obviously, the calculations reveal a larger Bessel region for smaller distances between the negative axicon and L1 due to the flatter angle of the focused beam (Fig. 3(a)) as compared to larger distances (Fig. 3(b)).
Fig. 3. Schematics of the optical setup used for the negative axicon evaluation. A plano-convex lens L1 having a focal length of 50 mm is used to focus the formed ring profile for (a) smaller distance d and (b) larger distance d between the negative axicon and L1. The illustrated beam propagation is calculated by geometrical optics. Please note, for better comprehension the dimensions of this drawing do not scale to the actual proportions. Inserted z-labels indicate the travel range of the motorized axis (distance between negative axicon and camera is thus 182 mm - 482 mm).
The experimental results are shown in Fig. 4 for different distances d between the negative axicon and L1 while the camera, mounted on the motorized stage, is moved in steps of 1 mm to precisely trace the propagation behaviour of the focused beam. Slices along the propagation direction as well as its maximum intensities and beam diameters are shown. Obviously, Bessel beams are formed within the evaluated range whereby two points are particularly noticeable. Firstly, the region in which the Bessel beams are formed increase with decreasing distance d and, secondly, the Bessel beams diverge strongly with continuous propagation. Both observations can easily be described with calculations of the beam propagation by geometrical optics as shown in Fig. 3. L1 focuses the ring profile into a Bessel beam, while an increased distance between the negative axicon and the lens causes a sharper focus of the formed ring, resulting in a smaller Bessel region. Furthermore, the inner parts of the ring are less refracted than the outer ones resulting in an intermediate focus of the ring as well as unsymmetrical overlapping Bessel beams. The maximum intensities on the right side of Fig. 4 show a similar distribution for the different setups. The intensities strongly increase before they flatten out slower with increasing propagation distance, a behaviour similar to Bessel beams generated by positive axicons [2,22,51]. Furthermore, the deviations within the intensities (peaks, valleys or saddle points) are similar for the different setups. The Bessel regions are measured to be 80 mm (FWHM), 100 mm (FWHM) and 131 mm (FWHM) for 62 mm, 60 mm and 58 mm, respectively. The irregularities of the intensity profiles in propagation direction are a typical behaviour also observed for non-ideal positive axicons and can be explained by the round tip of the axicons [2,16,52,53]. The according diameters of the beams are calculated by fit functions. Please note, beam diameters are calculated only at z-positions, in which the intensity has a maximum which is 20x larger than the sensitivity of the applied camera, otherwise it is set to 0 µm. The diameter increase with the propagation of the laser from 16.1 µm (FWHM) to 75.8 µm (FWHM) for 62 mm, from 17.7 µm (FWHM) to 81.9 µm (FWHM) for 60 mm and from 19.4 µm (FWHM) to 95.5 µm (FWHM) for 58 mm, respectively.
Fig. 4. Properties of the formed Bessel beams along the propagation axis of the laser for three different distances between the negative axicon and L1 (a) 62 mm, (b) 60 mm and (c) 58 mm. The left parts of the pictures show the intensity distributions while the right parts show the maximum intensities (blue lines) and the beam diameters (red lines) along the z-axis. Color of each setup has been normalized for a better visibility.
Lateral intensity distributions of the formed Bessel beams are shown in Fig. 5 at steps of 60 mm for the three different distance between the negative axicon and L1. Obviously, Bessel beams are clearly visible having a sharp peak in the middle surrounded by concentric rings. While for d = 62 mm (Fig. 5(a)), Bessel beams are visible only at z = 60 mm and 120 mm, some features are still visible at 180 mm for d = 60 mm and even at 240 mm for d = 58 mm. However, the cross sections (white lines) show homogeneous intensity distributions while the Bessel beam diameter increase with propagation of the laser beam. This setup demonstrates that negative axicons in combination with a single focal lens can generate Bessel beams while their propagation length can be modified by the distance between the two optical elements.
Fig. 5. Lateral intensity distributions and cross sections (white lines) of the formed Bessel beams behind the focusing lens L1, taken at different axis positions from 0 mm to 300 mm in steps of 60 mm for different distances between the negative axicon and L1 (a) 62 mm, (b) 60 mm and (c) 58 mm. Color of each setup has been normalized for a better visibility.
3.2 Evaluation of negative axicon with additional lens
To demonstrate a more application-oriented purpose, a second plano-convex lens is added to the previous setup. This second lens has a focal length of f$_2$ = 100 mm and is mounted between L1 and the camera, having its focal position fixed on the camera. Furthermore, L2 is also mounted on the motorized stage to simultaneously move the camera and L2, consistently warrant imaging of its focal position. This setup may represent a typical galvanometer configuration using a motorized axis for laser micromachining in which it is important to know the exact intensity distribution of the laser beam in the focal position at different z-positions. Please note, the distance in the experimental study between the negative axicon and L1 is adjusted (otherwise, no Bessel beam is generated at the focal position of L2). The applied setup is schematically shown in Fig. 6 for two different axis positions (same distance d). Moving the motorized stage and thus, L2 and the camera, the calculated beam propagation reveal Bessel beams, imaged on the camera for the different axis positions.
Fig. 6. Schematics of the optical setup used for the negative axicon evaluation. Two plano-convex lenses L1 and L2 having focal lengths of 50 mm and 100 mm are used to image the formed Bessel beam onto the camera for (a) a smaller z-value and (b) a larger z-value. Please note, for better comprehension the dimensions of this drawing do not scale to the actual proportions. Inserted z-labels indicate the travel range of the motorized axis (distance between negative axicon and camera is thus 182 mm - 482 mm).
The experimental results are shown in Fig. 7 and Fig. 8, again for different distances d between the negative axicon and L1, namely 48 mm, 46 mm and 44 mm. Slices along the z-axis (in the focal plane of L2) show a homogeneous intensity distribution along the entire range of 300 mm being almost invariant of the position of L2. It is found that for decreasing distances d, more features around the intense core are visible, representing the concentric rings around the Bessel beam peaks. The maximum intensities on the right side indicate a slightly increasing intensity of about 13% over the entire travel range for all configurations (calculated by linear regression). Regarding the Bessel beam diameters, a decrease from 23.4 µm (FWHM) to 21.8 µm (FWHM) for d = 48 mm, 20.5 µm (FWHM) to 19.1 µm (FWHM) for d = 46 mm and 20.0 µm (FWHM) to 18.6 µm (FWHM) for d = 44 mm is observed.
Fig. 7. Properties of the formed Bessel beams in the focal plane of L2 along the propagation axis of the laser for the three different distances between the negative axicon and L1 (a) 48 mm, (b) 46 mm and (c) 44 mm. The left parts of the pictures show slices of the intensity distributions while the right parts show the maximum intensities (blue lines) and the beam diameters (red lines) along the z-axis. Color of each setup has been normalized for a better visibility.
Fig. 8. Lateral intensity distributions and cross sections (white lines) of the formed Bessel beams in the focal plane of L2 taken at different axis positions from 0 mm to 300 mm in steps of 60 mm for different distances between the negative axicon and L1 (a) 48 mm, (b) 46 mm and (c) 44 mm. Color of each setup has been normalized for a better visibility.
The lateral intensity distributions of these Bessel beams are shown in Fig. 8 again for different distances d. Well-defined Bessel beams without significant variations within their intensity distributions are found over the entire range of 300 mm. For d = 48 mm, the Bessel beams start to form, as being indicated by the peak surrounded by a few rings. As discussed before, the number of rings increases with decreasing distance d. The white lines show the corresponding cross sections of the intensities. Again, the high quality of the Bessel beams is confirmed by the cross sections showing a similar intensity distribution on both sides of the peak. Furthermore, by changing the distance between the negative axicon and the following lens, the intensity profile in the focal plane of L2 can be precisely adjusted according to potential application needs. Compendiously, these results demonstrate a simple optical setup for the generation of excellent Bessel beams being independent of the position of the second lens, making them particularly interesting for laser micromachining processes at different z-levels with a constant intensity distribution.
3.3 Discussion
Fig. 9. Lateral intensity distributions at the position of L2 at different axis positions for d = 48 mm. Color of each image has been normalized for a better visibility.
The formation of Bessel beams by a laser micromachined negative axicon made of fused silica has been demonstrated. A first setup including a single plano-convex lens generates strongly diverge Bessel beams, while their formation length can be defined by the distance between the negative axicon and the lens. By inserting a second plano-convex lens, the experimental results show that Bessel beams can be formed in the focal position of this lens, being invariant of its position. This setup enables the possibility for different Bessel beam applications such as micromachining or optical imaging at different z-positions having an almost constant beam intensity distribution. Especially in the field of ultrashort pulsed laser micromachining, galvanometer scanners in combination with f-$\Theta$-lenses are usually used for guiding and focussing the laser beam [54–56]. Again, the main advantage is the variable position of the second lens (e.g. galvanometer scanner with an f-$\Theta$-lens) while keeping the position of the negative axicon unchanged. However, some drawbacks have to be discussed. Figure 9(a) shows the lateral intensity distributions on the position of L2 for d = 48 mm used in the experiments. At an axis position of 30 mm, a sharp ring can be found on L2 which is also indicated by geometrical calculations shown in Fig. 3 and Fig. 6. At larger distances, the ring vanishes while several concentric rings are formed. At positions 210 mm and 270 mm, the formation of Bessel beams on L2 can be seen. These measurements show, that the beam profiles at the position of L2 varies strongly with Bessel beams found for larger propagation distances. As the previous experiments show, all these intensity profiles (on L2) i.e. well-defined ring, concentric rings or even Bessel beams in the middle form a similar intensity distribution in the focal plane of L2. For high-power applications, the range in which the position of L2 can be altered is thus limited by the intensity at the position of L2 to avoid damage. In most applications such as micromachining, a moving range of the second lens of 300 mm is clearly outside the scope while some millimetres will be sufficient enough in which the generate ring-shaped intensity distribution does not change significantly. However, using a lens behind a negative axicon will cause an intermediate focused ring due to the stronger refraction of the outer parts of the beam compared to the inner ones as shown in Fig. 10(a). To overcome this drawback, the first lens L1 can be replaced by a positive axicon having the same apex angle as the negative axicon. Figure 10(b) shows the generation of a propagation invariant ring profile behind the positive axicon which can be further focused by a lens resulting in the generation of a very small Bessel region. Compared to the optical setups including both, negative and positive axicons, the configuration shown in our experimental study is kept much simpler due to the usage of common optics (plano-convex lenses instead of positive axicon) which are not as cost-intensive as axicons. However, the general usage of negative axicons enable the possibility for high-power laser systems without the risk of plasma generation or filamentation in air due to the absence of an additional Bessel region directly behind the axicon tip (see Fig. 1).
Fig. 10. Schematics of the optical setup including a negative axicon and (a) two-plano convex lenses or (b) a positive axicon and one plano-convex lens. The enlargement show the focused or invariant ring.
4. Conclusion
We have demonstrated the fabrication of a negative axicon in fused silica by an all laser-based two-step process chain. Firstly, an ultrashort pulsed laser is used for high-precision layer-by-layer ablation, generating the predefined 3D structure. Secondly, a CO$_2$ laser polishing step is introduced, reducing the surface roughness of the element for optical usage. In this contribution, a negative axicon is fabricated in under 5 minutes revealing a surface roughness of 18 nm (< $\lambda$/20). The functionality of the optical component is demonstrated by focussing the intensity profile behind the negative axicon onto a camera, mounted on a motorized stage. Therefore, two different setups including a single plano-convex and a combination of two plano-convex lenses are chosen. For the single lens configuration, Bessel beams are found, having a finite propagation region which can be increased by decreasing the distance between the negative axcion and the following lens. Here, the diameter of the Bessel beams increase strongly with increasing propagation region. Applying an additional plano-convex lens mounted in front of the camera on the motorized axis shows excellent Bessel beams at its focal plane being almost invariant of its position. The generated beams show a small increase of their intensity by about 13% over the entire lens moving range of 300 mm while their diameters slightly decrease. This demonstrates the enormous potential of negative axicons for high-power ultrashort pulsed laser applications such as micromachining without an additional focal region in air.
Disclosures
The authors declare no conflicts of interest.
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