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The extended focal depth of Bessel beams is a very attracting property for glass cutting applications. However, Bessel beam generation with a non-ideal conical lens induces beam pattern distortions. We present our novel results on bulk modifications of soda-lime glass using a non-ideal axicon-generated Bessel beam. Modelling of the Bessel beam pattern and experimental measurements indicated ellipticity of the central core diameter. That resulted in the formation of cracks in a transverse direction inside the bulk of glass. Furthermore, we demonstrate the possibility to control the transverse crack propagation direction, which is crucial in the case of glass cutting applications.
© 2016 Optical Society of America
1. Introduction
Unique optical and mechanical properties of glass make it one of the most important engineering materials. Glass is used for a number of applications in the field of architecture, medicine, optics, packaging of electronic components, solar panels, and so on. Despite the fact that conventional glass processing techniques, including wheel cutters and diamond tools, may offer low costs and high processing speed, they are limited due to the incapability of performing complex cuts, poor surface quality and the need for post-processing. Various laser tools are thought to give the best alternative [1].
Usually, the laser beam can be focused to a tiny spot on the glass surface, and the material can be removed by multiple laser beam scans via direct laser ablation. Such method is effective for ablating shallow trenches and cutting or drilling complex geometries in thin glasses. However, when the channel becomes deeper, the ejection of ablated material becomes more complicated, and debris accumulation takes place. Laser beam interaction with ablation products and plasma, accumulation of debris, heat and stresses significantly reduce the processing quality, achievable aspect ratio and throughput [2]. These drawbacks can be suppressed by initiating the cutting process from the rear side of a sample when ablated material is ejected through the formed channel in the opposite direction [3–5]. Therefore, the incident radiation is not scattered, and the laser fluence can be kept constant. However, even using nanosecond pulses, which generate microcracks in the glass, and material is ejected in the form of large particles, such method still suffers from the lack of processing speed in the case of high volume cutting applications [6].
The most energy-efficient and material-efficient method for cutting simple contours is a generation of micro-cracks and material modifications in the bulk of glass. The material is weakened locally, and then sheets can be separated by applying thermal or mechanical load. Such method gives a clean cut and almost zero kerf width with no post-processing needed. However, laser-induced cracks have to be generated along the entire depth of the glass sheet. Therefore multiple scans of the tightly focused beam are required. On the other hand, elongated modification along the whole glass thickness can also be applied by using laser filamentation, dual spot optics or Bessel beams [7–10].
The extended focal depth, a small central core radius, and self-reconstruction after an obstruction of Bessel beams are very attracting properties for laser micromachining. Bessel-like beams were successfully applied for glass cutting applications [7,10], intra-volume modifications [11,12] and the formation of micro and nano channels in transparent materials [13]. Even drilling of non-transparent materials, such as thin stainless steel [14] and copper foils [15], silicon [16], thin molybdenum film ablation [17] was demonstrated using such beams. However, employment of Bessel beams for non-transparent materials processing is still questionable because of the absorption of the side lobes, which act as an energy reservoir for the central core.
The approximation of Bessel beams can be obtained over a finite area using amplitude or phase modulation of the incident beam. Such beams are generated by the illumination of the annular slit in the back focal plane of a lens [18], variously shaped axicons or microaxicon-like elements [19], holograms, spatial light modulators, tunable acoustic gradient lenses or using other techniques [20].
Axicons are one of the most convenient tools for the Bessel beam generation. However, it is also well known, that manufactured conical lenses do not fully match the shape of the ideal conical surface. Usually, two main manufacturing errors are discussed in the literature - lens-like oblate tip [21–23] and elliptical shape of the axicon cross-section [24]. Both manufacturing errors distort the generated Bessel beam shape, although these effects are not fully investigated in the case of glass bulk modification. Spatial filtering can be used to correct the imperfections of the Bessel beams. However, power loss due to filtering may be crucial in the case of laser cutting applications.
In this paper, we report our novel results on intra-volume modification of glass using an axicon-generated Bessel beam. We have investigated the shape of a conical lens and its effect on the intensity distribution of the generated beam. Furthermore, we show intra-volume glass modification results using Bessel beams distorted by manufacturing error of the axicon and its effect on the elongated modification shape and crack propagation in the glass.
2. Experimental
Experiments were carried out using the fundamental frequency of the diode-pumped solid-state picosecond laser Atlantic HE (from Ekspla). The laser operated at 1064 nm wavelength and delivered 300 ps pulses at 1 kHz repetition rate. Maximum output power of 2.5 W was attenuated by a pair of a half-wave plate and a polarizer. Samples were mounted on the XY positioning stage (ALS25020, from Aerotech). A stage with a stepper motor (8MT167-100, from Standa) was used to adjust the sample position in the Z-axis.
A conical lens with an apex angle of 170 deg (AX255-C, from Thorlabs) was used to transform the incident Gaussian beam into the Bessel beam. The length of non-diffractive propagation of such beam depends on the half-angle of a cone θ0 and the incident beam radius ω0 and can be estimated using the following equation:
During the experiments, the Gaussian beam diameter at 1/e2 intensity level was varied from 3 mm to 4.5 mm using a beam expander. The central core radius was evaluated using the following equation:
where k is a wave vector.We used a 4F optical system to reduce the central core diameter and increase a peak intensity in it as depicted in Fig. 1. Such demagnifying telescope consisted of two positive lenses with the focal length ratio f1 / f2, which determined the reduction factor of the central core diameter. The Bessel zone length was suppressed by a factor of (f1 / f2)2 after passing through the telescope.
Fig. 1 The generation scheme of the Bessel beam using a conical lens and the demagnifying 4F optical system.
One can notice that such optical setup allows generation of a beam with a small central core radius and any preferred focal depth by simple adjustments of the incident beam radius and a demagnification factor. However, the problem of finite apertures of optical elements and the finite amount of energy still exists.
The generated beam profile was investigated by imaging the intensity pattern on the CCD camera using an aspheric lens with the focal length of 8 mm. The magnification factor depended on the distance between the imaging lens and CCD camera and was varied from 15 to 35 times. The shape of a conical lens was investigated using a stylus profiler (HOMMEL-ETAMIC nanoscan 855, from Jenoptik, the vertical resolution of 1.2 nm, tip size 500 µm).
Soda-lime glass sheets with the thickness of 4 mm were laser-treated. Intra-volume modifications were evaluated by scanning separated lines in the volume of glass at various vertical positions. Then, samples were cleaved perpendicularly to the scanning direction, polished and the axial length of modifications was measured using an optical microscope.
3. Modelling
The intensity distribution behind the conical lens was calculated using MATLAB software. Simulation of the laser beam propagation was based on the scalar diffraction theory and two-dimensional fast Fourier transform (FFT) algorithm. The Fresnel approximation was taken into account [25,26]. The field distribution in the observation plane U2 (x, y) was calculated by applying the Fourier convolution theorem to the diffraction integral:
where U1 (x, y) defines the field distribution in the source plane, fX and fY are spatial frequencies, and H is the Fresnel transfer function through the free space:where is the optical wavelength, is the wavenumber, z is the distance between the parallel source and observation planes. If the waist of an incident Gaussian beam with the radius of ω0 lies in the same plane as an axicon, the field in the source plane can be stated as:where U0 denotes the on-axis amplitude of the field, n is the refractive index of the axicon, d(x, y) represents the axicon profile, which was measured by a stylus profilometer and approximated by a polynomial with coefficients a0...a30.where and . Such expression gave an elliptical cross-section of the axicon with a steeper slope in the Y direction. The ellipticity parameter depended on the transverse distance to the optical axis:Coefficients B, t, were obtained from geometrical analysis of the axicon shape.In the case of the sharp tip axicon with an apex angle of 170°, the profile function can be stated as:
When the field distribution is known, the intensity distribution in the observation plane can be evaluated as:
4. Results
4.1 Axicon geometry evaluation
A conical lens with an apex angle of 170 deg was used to transform the incident Gaussian beam into the Bessel beam. Unfortunately, manufactured axicons do not fully match the shape of the ideal conical surface. Usually, two main manufacturing errors are discussed in the literature - lens-like oblate tip [21–23] and elliptical shape of the axicon cross-section [24]. Both manufacturing errors distort the generated Bessel beam shape. Therefore it is necessary to validate the axicon geometrical properties. In order to measure the conical lens tip geometry, stylus profilometry was applied. The measurement results are presented in the Fig. 2. As expected, the axicon tip was rounded.
Fig. 2 Measurement of the axicon geometry. (a) The red area represents the profile of the investigated axicon surface in X direction, while black curve represents the axicon profile deviation error from the ideal conical surface. (b) The axicon cross-section ellipticity versus axicon radius is represented by the black curve, while red area represents the axicon profile.
The largest deviation error of ~50 µm from the ideal conical surface was detected at the center of the oblate tip. However, measurements in the Fig. 2(a) show that the error tends to decrease while moving towards the outer edge of the axicon. Furthermore, the axicon cross-section exhibited an elliptical shape. In this paper, the major axis of the ellipse was referred as the X axis and the smaller one as the Y axis. The ellipticity of the axicon versus axicon radius is displayed in the Fig. 2(b) (1.0 corresponds to circular shape). The largest ellipticity was observed near the oblate tip surface with a maximum value of 1.021. When moving away from the axicon center, the ellipticity tended to decrease. Typical input beam radius was in the range of 1.5 mm and 2.25 mm, therefore at these axicon radiuses, the ellipticity exceeded 1.011 and 1.008, respectively.
4.2 Axicon-generated beam intensity distribution
The axicon-generated beam was characterized and modeled straight after the conical lens. Typical intensity distribution of such beam in the XZ plane is shown in the Fig. 3(a). The image was obtained by measurement of the beam patterns with a CCD camera in the XY plane at various Z positions. Afterwards, the image cross-sections in the X direction at various Z positions were stacked together. The Fig. 3(a) shows Bessel beam pattern distortions, which are inevitably modulated by a non-ideal shape of the conical lens. The generated beam is clearly shifted 12 mm further from the axicon, while intensity modulation along the beam propagation direction is observed as well. Numerical calculations of the Bessel beam pattern distribution in the XZ plane is presented in Fig. 3(b). In this case, non-ideal axicon profile, approximated from the axicon geometry measurements was used in the simulation (oblate tip axicon with variable shape ellipticity). The calculated Bessel beam profile cross-section in the XZ plane was in good agreement with experimentally observed, indicating distortions caused by the oblate axicon tip. This phenomenon was investigated in detail by Brzobohaty et al. [21]. They stated, that the beam shift is observed due to the partial focusing of the wave by the axicon round tip. Furthermore, new wave refracted by the round tip propagates behind the axicon and interferes with the Bessel beam resulting in axial modulation. This effect is illustrated in the Fig. 3(c).
Fig. 3 (a) The beam intensity distribution in the XZ plane, generated by the oblate tip axicon with variable shape ellipticity. (b) Simulation of the Bessel beam distribution in the XZ plane. (c) Axial modulation of the axicon-generated beam distribution. The axicon placement is at the top of the image at Z position equal to 0.
An interesting transformation of the central core was observed along the Z axis. Figure 4 illustrates simulation and experimental results on the Bessel beam profile evolution versus distance. The simulation depicted in the Fig. 4(a) reveals, that an elliptical sharp tip axicon generates the intensity pattern with several maxima. These effects become more pronounced as the beam propagation distance increases. Such behavior was discussed more deeply in [24]. The same effect was noticed when axicon was obliquely illuminated, and it was attributed to astigmatic aberrations [27]. Despite the elliptical axicon shape, the central core profile was symmetrical in X and Y directions as seen in Fig. 4(b). In the case of oblate tip axicon, both simulated and experimental beam profile measurements were applied and are shown in Fig. 4(a) and Fig. 4(b). The beam central core diameter was higher close to the axicon tip and was extremely reduced at longer propagation distances. A beam more detached from the tip in the propagation direction was generated by the part of the axicon, which was comparable to the ideal cone shape. As a result, the diameter of the central core was reduced. Furthermore, the central core ellipticity was observed both in experimental measurements and simulation results. The ellipticity was evaluated as the ratio of major to minor axis length.
Fig. 4 (a) Simulated and experimentally measured Bessel beam patterns versus the distance. Simulations were performed for oblate and sharp tip axicon with variable cross-section ellipticity. (b) Beam central core diameter dependence on the beam propagation distance.
The generated central core was elliptical at 12-18 mm from the axicon tip and its ellipticity decreased with the increase of the beam propagation distance as seen in the Fig. 4(b). Typical central core ellipticity of 1.04-1.09 was measured from the CCD images in this case. The simulation showed very similar ellipticity ratios as well. This phenomenon can be explained as a result of aberrations of the non-ideal part of the axicon. In fact, an ideal conical lens is sensitive only to the even order aberrations, such as astigmatic aberrations, which cause symmetrical spreading of the intensity pattern to the X and Y directions [27]. On the contrary, spreading, caused by asymmetric spherical tip surface, is nonsymmetrical and the spot is lengthened in one direction. Therefore, we can divide our axicon into two parts, which contributes differently to the generation of a beam: an asymmetric lens-like oblate tip and a frustum of a cone.
4.3 Intra-volume modification of glass
In order to make modifications in the glass, the demagnifying 4F optical system was used to decrease the Bessel beam core diameter and increase the peak intensity. When waves pass from a low refractive index media (air) to media with the high one (glass), the Bessel zone length (Zmax) is extended approximately by a factor of the glass refractive index n. However, the central core radius remains the same, because the wavelength in the glass is also shortened by its refractive index. In the case of high laser peak powers, the Bessel beam reshaping can occur due to self-focusing and nonlinear losses [28]. However, these effects are more pronounced at the intensity levels above 1012 W/cm2 [28,29]. In our case, such intensities were reached only in the Bessel beam central core. For this, the probability of the Bessel beam reshaping was minimal. The axial length of the modification lines, as a function of the pulse energy, is shown in Fig. 5(a). Linear axial length dependence on the laser pulse energy in a logarithmic scale was observed. The modification length was as long as several millimeters and depended on the 4F optical configuration and the incident Gaussian beam diameter. The maximum length of modifications was obtained using the f1 / f2 = 7.5 optical system, which allowed us to generate cracks of 2.5 mm in axial direction. A cross-section of glass with such modifications is given in Fig. 5(b). Also, we have demonstrated the possibility to change the position of modifications by moving the positioning stage in the vertical direction.
Fig. 5 (a) Crack formation length versus laser pulse energy. (b) A cross-section of glass modifications at various depths, f1 / f2 = 7.5, 2ω0 = 4.5 mm, 2 mJ, 1 kHz, 2.5 mm/s.
Further investigations were carried out using the f1 / f2 = 6.5 optical system with 3 mm diameter of the incident Gaussian beam. Single-shot intra-volume void examination in the transverse direction is depicted in the Fig. 6. The cracks spreading in the transverse direction were several times longer than the transverse width of the laser-induced modifications itself. Furthermore, transverse cracks tended to spread and align with one dominant direction on the XY plane, which was parallel to the long axis of the beam elliptical intensity pattern. Such behavior of glass could be attributed to the nonsymmetrical laser-induced stress distribution in the material, which pushes cracks to propagate only in one direction. Linear transverse cracks length dependence on the laser pulse energy in the logarithmic scale was observed.
Furthermore, we studied the transverse crack propagation along the Z direction. The non-diffractive Bessel beam propagation length was approximately 1 mm in this case. We performed series of single-shot voids in the bulk of glass by varying a Z position of the Bessel beam as seen in Fig. 7(c). When we shifted the Bessel beam towards the back-surface, the bulk cracks started to appear on the glass surface. By applying this technique, we could track the transverse cracks propagation along the Z direction. The results are shown in the Fig. 7.
Fig. 7 (a) Transverse crack formation on the back-surface of the glass. (b) Transverse crack length and Bessel beam ellipticity at the back-surface of glass in respect to beam Z position. Laser pulse energy 2 mJ. (c) Illustration of the experimental scheme.
The Z position of 0 mm indicates that the back-surface of glass was modified with a top of the Bessel beam pattern. While Z positions 0.2-0.9 mm indicate, that the Bessel beam pattern penetrates inside the glass. At the Z position 0-0.2 mm, no transverse crack formation was observed. Although, beam pattern ellipticity at the glass back-surface was the highest with maximum experimentally measured value of 1.18. When the Bessel beam started to penetrate inside the glass further up to 0.6 mm, cracks began to form. However, Bessel beam ellipticity tended to decrease to 1.02. From this point, crack formation completely stopped. Such behavior could be attributed to the on-axis beam intensity drop as well as the Bessel beam ellipticity reduction. Furthermore, the depth of the transverse crack can reach up to 40% of total Bessel beam propagation length. Finally, we demonstrate the possibility to control the transverse crack orientation by rotating the axicon around the beam propagation axis. For this, the Bessel beam pattern was focused inside the glass. For better observations, cracks were generated with the top-part of the Bessel beam on the back-surface of glass. The results are shown in the Fig. 8. The orientation of cracks linearly depended on the axicon axial position. Also, insignificant transverse crack length variation was observed. The average crack length was 169 µm with a standard deviation of 12 µm. This final result is crucial in the case of the glass cutting applications. The control of the crack propagation direction gives a possibility to form a uniform cutting path in such way, that cracks are always aligned parallel to the scanning direction. Therefore, the cutting speed can be optimized, especially in the case of the elliptically shaped cutting paths.
Fig. 8 (a) The change of cracks orientation when the axicon is rotated around the beam propagation axis. (b) The dependence of the laser-induced cracks orientation and length on the axicon axial position. Laser pulse energy was 2 mJ.
5. Summary
We investigated pattern distribution of the non-ideal axicon-generated Bessel beam and its effects on the glass bulk modification. At first, the axicon geometrical characterization was performed in order to define the optical element geometry. We found that the axicon surface deviated from the ideal conical surface. Furthermore, the largest deviation error of ~50 µm was observed at the center of the axicon, which was attributed to the axicon round tip geometry. Furthermore, the axicon cross-section exhibited elliptical shape with largest ellipticity value of 1.021 near the oblate tip surface. Even such small deviations from ideal geometrical properties distorted the generated Bessel beam pattern which was confirmed by theoretical simulation and experimental measurements. The Bessel beam was clearly shifted 12 mm further from the axicon, while intensity modulation along the beam propagation direction was observed as well. The elliptical axicon generated the intensity pattern, which was gradually transformed into several maxima as the beam propagation distance increased. The ellipticity of the central core diameter was observed as well. Such behavior was attributed to the asymmetric oblate tip, which acted as an elliptical focusing lens.
Further, we investigated glass bulk modification with the Bessel beam pattern. The longest axial modification length of 2.5 mm was observed which depended on the laser pulse energy. Single-shot intra-volume void examination revealed that cracks are spreading in the transverse direction as well. Such behavior was attributed to the elliptical shape of the central core diameter. Furthermore, the depth of the transverse crack reached up to 40% of total modification depth.
Finally, we demonstrated the possibility to control the transverse crack orientation in the bulk of soda-lime glass by rotating the axicon around the beam propagation axis. This is crucial in the case of the glass cutting applications. The control of the crack propagation direction gives a possibility to form a uniform cutting path in such way, that cracks are always aligned parallel to the scanning direction. The extended single-shot damage plane in the laser scanning direction using glass cracks can additionally weaken the glass material along the cutting direction. Therefore, cutting speed and efficiency can be enlarged keeping stable glass sheet mechanical separation process. Also, it becomes possible to control the cut channel fracture orientation even for elliptical geometries.
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