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Abstract
The control of laser-induced microcracks in the volume of transparent materials is essential for scribing processes. In this paper, we investigate the effect of various amplitude and single-level phase masks on both transverse and axial intensity distribution of the conventional axicon-generated Bessel beams. Furthermore, we demonstrate the volumetric crack control induced by an asymmetrical central core with an appropriately selected intensity level to avoid the influence of peripheral intensity maxima. Proper alignment of cracks and intra-distance between the modifications results in the reduced separation stress of the scribed samples. Furthermore, the additional amplitude modulation of the incident Gaussian beam is introduced to flatten the axial intensity distribution of the axicon-generated Bessel beam.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Laser-based intra-volume modification and subsequent separation remain as one of the most efficient glass cutting methods. Thanks to the development of advanced laser and optical systems redistributing the laser pulse energy along a line, rather than focused to an ellipsoid, scribing of glasses with the thickness of tens of millimeters is possible [1–3]. However, if we assume that the separation stress of the scribed material remains constant [4], the cleaving force scales as a square of its thickness. Therefore, the application of Bessel-like laser beams having a long non-diffractive zone together with the asymmetrical intensity distribution in the transverse plane for the induction of asymmetrical modifications aiming to facilitate glass cutting has been a hot topic for the past few years, gathering many scientific and industrial groups [4–9].
The symmetrical intensity distribution is inevitably broken when non-ideal conical lenses having an oblate tip and an elliptical cross-section are used for Bessel beam generation [5]. The resulting intensity pattern leads to the induction of the directional intra-volume cracks, which enhance glass cleaving during the separation stage [10,11]. Furthermore, asymmetry and induced cracks could be controlled by tilting the axicon [12,13]. Although these techniques are simple and easy to implement, the resulting intensity patterns are quite complex and dependent on the beam propagation distance and the actual geometry of an axicon. Therefore, they may be unattractive for applications, where maintaining the same shape of the transverse intensity pattern is crucial. Alternatively, optical schemes, where the axicon-generated beam spatial spectrum or the conical wavefront, imprinted in the incident Gaussian beam, is additionally modulated azimuthally, can be used. For instance, in the field of optical light-sheet microscopy, Fahrbach et al. [14] introduced sectioned Bessel beams, of which opposite sections of the angular spectrum is removed. A similar approach, using rectangular-shaped opaque filters, was implemented by Meyer et al. [15] to induce elliptical nanochannels in a glass. Jenne et al. [4,16] demonstrated the induction of directional transverse cracks for glass scribing using modulated Bessel beams, generated either by a spatial light modulator (SLM) or the static diffractive optical element. However, although SLMs are a flexible tool for the generation of arbitrary intensity patterns, aberration-correction for chamfer fabrication [8,17] and curved edge cutting [18], they are expensive, demonstrate low efficiency and are limited for low-power applications due to the low damage threshold [4]. Alternatively, Baltrukonis et al. [9] have demonstrated the controllability of cracks using vector Bessel beams, generated using an S-wave plate, a polarizer and a standard axicon. However, the generation of double voids is a drawback of this polarization-based method.
The axial intensity distribution of the generated beam is important as well since different intensity levels trigger various processes, or side lobes may play an important role in material modification. The flattened Bessel beams can be obtained using the annular slit and apertured lens-based methods [19,20], plane wave-illuminated holographic [21,22] and refractive [23] logarithmic axicons, specially-designed diffractive optical elements [24]. Arbitrary shaping of the axial intensity distribution was demonstrated using SLMs [25–29]. In laser micromachining, the typical Bessel beam generation setup comprises an axicon illuminated with a Gaussian beam. Herein, the on-axis intensity distribution of the generated Bessel beam can be flattened by the amplitude modulation of the incident Gaussian beam with an annular aperture [30,31]. The axial intensity distribution could also be controlled by amplitude filters with tailored transmission [32].
In this context, we present an investigation of simple optical configurations utilizing standard axicon-generated beams. Their spatial spectra are modulated using hourglass- and triangle-shaped amplitude masks made from stainless steel and hourglass-shaped phase masks with a single level, imprinted in fused silica via direct femtosecond laser writing technique. Different masks were compared in terms of the central core ellipticity and intensity. Additionally, the on-axis intensity distribution was flattened using opaque masks for the modulation of the incident Gaussian beam. Generated laser intensity distributions were applied for glass processing, inducing directional transverse cracks, enhancing glass cleaving. Results were discussed in the framework of linear elastic fracture mechanics.
2. Methods
2.1 Experimental setup
Glass processing experiments were carried out using the 1064 nm-wavelength picosecond laser Atlantic (Ekspla) with a pulse duration of ∼10 ps (at FWHM), maximum pulse energy of 300 µJ and pulse repetition rate of 200 kHz.
Figure 1(a) shows the numerically modelled intensity distributions, calculated at indicated positions in the schematic experimental setup with raytracing, shown in Fig. 1(b). Herein, the beam propagation direction is from left to right. The diameter of the incident Gaussian beam at 1/e2 intensity level was equal to 4.8 mm. The masks in front of the axicon were used to flatten the axial intensity distribution of the generated Bessel beam [31]. To obtain the annular intensity distribution without supports, the inner mask IM with a diameter of 1 mm was fabricated by milling (roughening) a circular blind hole in fused silica. The diameter of the outer iris aperture OA was 4.5 mm. The axicon AX255-C (Thorlabs) with the shape of the positive conical lens with the nominal apex angle of 170 deg (the base angle of 5 deg) was used to generate the symmetrical Bessel beam.
Fig. 1. (a) Numerically modelled transverse intensity distributions at indicated positions of (b) experimental setup for modulation of the axicon-generated Bessel beam for glass processing. The laser beam propagates from left to right. (c) Optical microscope images of the hourglass and triangle-shaped amplitude masks and an hourglass-shaped phase mask used for filtering of spatial frequencies in the Fourier plane of the first 4F system. Images are taken in the transmission regime; the rightmost image is obtained by crossed polarized illumination. Scale bars are 0.5 mm-length.
The first 4F optical system consisting of +100 mm-focal-length lenses L1 and L2 was used for filtering of spatial frequencies of the generated Bessel beam to introduce asymmetry in the transverse plane (XY). Masks were placed in the Fourier plane of the first lens L1, which carries out the Fourier transform of the Bessel beam, which spectrum of spatial frequencies should be a ring of infinitely small width in an ideal case. The second lens, L2, carries out the inverse Fourier transform.
Two different designs of amplitude masks were investigated, shown in Fig. 1(c). Hourglass-shaped masks (H-amp) were used to remove the opposite sections with an angle β from the spectrum of spatial frequencies, while triangle-shaped masks (T-amp) were used to remove only one section. Amplitude masks were cut from the stainless-steel foil with a thickness of 40 µm-200 µm using a picosecond laser Atlantic (Ekspla).
Hourglass-shaped phase masks were fabricated by the femtosecond laser direct writing (FLDW) technology inducing a positive refractive index change of Δn∼9.4 × 10−4 in the bulk of fused silica substrate. The laser source was femtosecond laser Pharos (Light Conversion) operating at 515 nm wavelength and ∼300 fs pulse duration (at FWHM). Phase masks were formed by stacking multiple layers along the beam propagation direction to get a required phase delay of the designed element, which was either π/2 or π. For this, 12 or 23 layers were required, resulting in the overall height of the modified zone equal to 300 µm and 600 µm, respectively. Analysis of the axial intensity distribution level indicated that the beam shaping efficiency using a phase mask was over 85%, including losses due to reflections (∼7%). Thus, the efficiency could be improved by antireflective coatings.
It should be noted that angular masks (especially amplitude) are easily implemented in different optical setups with the ring-like intensity distribution of the different extensions in the XY plane. Furthermore, they are less dependent on the strict positioning along Z-axis and could also be applied for the angular modulation of the beams with the broadened spatial spectrum, for instance, due to low-frequency components generated by the oblate axicon tip [13,33].
Alternatively, masks for the transverse intensity distribution modulation may be placed directly in front of the axicon. However, in the case of phase masks, the quality of the generated beam was deteriorated due to irregularities of induced modifications, especially at the center and boundary of a modified region. As a result, the generated transverse intensity distribution depended on the beam propagation distance and differed significantly compared to modelled patterns. Furthermore, the additional axial intensity modulations were observed as well. On the contrary, edges of written masks make less impact when the ring-like intensity distribution with the diameter in the centimeter scale is modulated in the Fourier plane of the 4F optical system.
The generated and modulated Bessel-like beam was imaged on the Beamage-4M (Gentec) CMOS camera using the 8 mm-focal length aspheric lens.
The demagnifying telescopic system consisted of a positive lens L3 with a focal length of 75 mm and an objective lens L4 with a focal length of 10 mm. The demagnification factor was equal to M = 7.5. In the general case, the first 4F system may be used to demagnify the beam as well. Then, the overall demagnification factor would be M = M1 × M2. The demagnified beam was applied for glass processing. Samples were translated in the XY plane using the linear positioning stages ALS25020 (Aerotech). Sample position along the vertical axis Z was adjusted using the stepper motor-driven positioning table 8MVT120-25 (Standa).
2.2 Modelling of the laser beam intensity distribution
The laser intensity distribution at a given propagation distance was modelled by solving the Rayleigh–Sommerfeld diffraction integral in a convolution formulation, using the two-dimensional fast Fourier transform and propagation transfer functions [34]. Formulae could be found in a more comprehensive form in Ref. [5]. Axicons converting the incident Gaussian beam to the Bessel beam were treated as rotationally symmetrical conical elements having a sharp tip. To investigate the transverse intensity distribution, simulations were carried out by modulating the spectra of spatial frequencies of the generated Bessel beam by using the hourglass-shaped amplitude and phase masks and triangle amplitude masks.
In order to simulate the Bessel beam propagation through the demagnifying system, lenses L3 and L4 were treated as phase masks [33]. Since the intensity pattern was demagnified, the Fresnel two-step propagation approach was applied to increase the transverse resolution [34]. The incident Gaussian beam was modulated to flatten the axial intensity distribution.
2.3 Sample characterization
The induced modifications in soda-lime glass plates were characterized using the optical microscope Eclipse LV100NDA (Nikon).
76 × 26 mm2 soda-lime glass plates with a thickness of 1 mm were used for glass scribing and cleaving experiments. Modified samples were cleaved using the four-point bending setup, placing the induced modifications parallel to supports in the middle of the tensioned zone as shown in Fig. 2(a). The force to separate a sample was measured using the digital dynamometer FMI-S30A5 (Alluris) with an additional lever to extend the measuring range. The separation stress was calculated according to [35]:
where F is the load force at a moment of sample cleaving, L and l are outer and inner support spans, equal to 60 mm and 16 mm, respectively. b and t are sample width and thickness, respectively. The typical loading rate was 0.37 MPa/s unless otherwise stated. At least 5 samples were cleaved for each configuration to calculate mean values of the separation stress, given in Fig. 9, wherein error bars represent the standard deviation.Fig. 2. (a) Four-point bending setup to cleave modified glass plates. (b) The illustration of multiple colinear cracks with the half-length a with the intra-distance W (pitch) under tensile stress σ.
The side-wall roughness of samples was measured along the laser beam scanning direction using the optical profiler S neox (Sensofar). Roughness was separated from waviness by applying the sampling and evaluation lengths given in the ISO 4288:1996 [36].
2.4 Simulation of the separation stress
Laser-induced cracks and other flaws are stress concentrators, which lead to the reduced strength of the modified specimen. Glass cleaving is achieved when the stress intensity factor is equal or over the critical factor of KIC = ∼0.75 MPa m1/2 for soda-lime glass [37]. However, cracks may grow subcritically as well when the stress intensity factor KI is larger than the threshold Kth, which was taken to be equal to 0.2 MPa m1/2 for soda-lime glass [37]. Crack propagation was numerically simulated according to [38]:
where ai is the initial half-width of a crack, v0 = 6 mm/s and n = 16 in ambient air [37]. The time step interval dt was 0.1 ms. For a single crack with a half-width of a under tensile stress σ, the stress intensity factor could be estimated as:However, the stress intensity factor amplifies for multiple colinear cracks [Fig. 2(b)]:
where W is the intra-distance between modifications (or pitch) [39]. The load σ, initial crack length ai and, consequently, the stress intensity factor are time dependent.3. Results and discussion
3.1 Modulated intensity patterns
The simulated transverse intensity distributions in the XY plane of modulated Bessel beams using hourglass and triangle-shaped amplitude masks with different angles are shown in Fig. 3. Intensity distributions were investigated at a half-length distance of the non-diffracting zone behind the axicon with an apex angle of 170 deg without demagnification and axial modulation. The diameter of the incident Gaussian beam at 1/e2 level was 2 mm. The estimation of the full width at half maximum (FWHM) of the central core in the XY plane and intensity of the central core and side lobes is illustrated in Fig. 4(a)-(c). The central core width dependence on the filter angle is presented in Fig. 4(d). The central core extension, using both amplitude masks, increases along the spectrum blocking direction (Y-axis) with increased filter angle.
Fig. 3. The simulated intensity distribution in the XY plane using (a) hourglass and (b) triangle-shaped amplitude masks with different angles. Scale bars are 50 µm-length.
Fig. 4. (a-c) Evaluation of the relative maximum and side-lobe intensity and transverse extension along the X and Y axes. (d) The full width at half maximum (FWHM) of the central core of simulated intensity distributions in the XY plane using hourglass (H-amp) and triangle-shaped (T-amp) amplitude and hourglass-shaped phase masks with different angles. The FWHM was measured along the X-axis (dotted lines) and Y-axis (solid lines). Bessel beam is generated with an ideal axicon with a base angle of 5 deg. (e) The ellipticity of the central core is obtained by dividing the width along the Y-axis by the width along the X-axis. For the hourglass mask, the dashed line shows analytically estimated ellipticity according to Fahrbach et al. [14]. (f) Side-lobe intensity to the maximum intensity ratio.
Furthermore, the core width is suppressed along the perpendicular direction (X-axis) using the hourglass amplitude mask (T-amp), discrepant to results of Fahrbach et al. [14], where the highest beam confinement along both directions was for the symmetrical Bessel beam. The central core diameter of the non-modulated Bessel beam, measuring between minima, is equal to dB = 0.765λ/sin θB, where θB is the half-angle of the Bessel beam. For large angles of a filter, the intensity pattern can be treated as a result of interference of two plane waves, which periodicity could be calculated as d = 0.5λ/sin θB. Therefore, the suppression of the beam along an axis perpendicular to a blocking aperture is expected.
In the case of the triangle mask (T-amp), the core width reaches its minimum value at ∼100 deg and then starts to increase. However, the central core ellipticity, which was evaluated as a ratio of FWHMs along the Y and X axes, increases using both masks [Fig. 4(e)]. For the hourglass mask, the dashed line shows analytically estimated ellipticity cot((π-β)/4) as a ratio of the beam extension along Y and X axes, derived by Fahrbach et al. [14], where β is the angle of a filter in radians. The discrepancy with numerical simulations occurred due to the width evaluation at different intensity levels. We validated that the analytical formula may be used when the central core width is measured between intensity minima.
The side effect is the increase of the intensity of side maxima, as seen in [Fig. 4(f)], which was evaluated as a ratio of the side-lobe intensity along the X direction through the minor ellipse axis and maximum intensity of the particular case [Fig. 4 (b)]. For comparison, the intensity of the side lobe of the symmetrical Bessel beam is 16% of the maximum intensity value.
The simulated intensity distributions in the XY plane using hourglass phase masks with different delays (π/4, π/2, 3π/4, π) and angles are shown in Fig. 5. The π/4 phase mask does little influence on the intensity pattern. Using the π/2 phase mask, the maximum ellipticity is achieved at 50 deg and then starts to decrease up to 90 deg, when the symmetrical distribution along X and Y axes are generated. Interesting patterns are generated using 3π/4 and π phase masks when the side-lobe intensity becomes larger than the central core intensity.
Fig. 5. The simulated intensity distribution in the XY plane using hourglass-shaped phase masks with different delays and angles. The scale bar is 50 µm-length.
For comparison of different Bessel beam modulation techniques, the relative side-lobe intensity and maximum intensity was plotted versus central core ellipticity as a figure of merit [ Fig. 6]. Intensity distributions with the side-lobe intensity larger than that of the central core were removed from data analysis. In the low ellipticity range, different mask configurations give comparable results, which is also visible comparing intensity patterns in the XY plane, shown in Fig. 3 and Fig. 5. However, the relative intensity of side lobes is larger using phase masks [Fig. 6(a)]. Furthermore, the maximum intensity decreases when Bessel beams are modulated, compared to the non-modulated beam [Fig. 6(b)]. At the same ellipticity value, the highest maximum intensity with the lowest side lobe intensity is obtained using triangle masks. However, the contrast reduction and increase of the side-lobe intensity near the vertices of the elliptical core is observed for larger filter angles (an example is indicated by a red arrow for 270 deg T-amp mask in Fig. 3(b)).
Fig. 6. (a) Side-lobe intensity to the maximum intensity ratio versus central core ellipticity of simulated intensity distributions in the XY plane using hourglass (H-amp) and triangle-shaped (T-amp) amplitude and hourglass-shaped phase masks with different delays. (b) The maximum intensity of the simulated beam versus central core ellipticity.
3.2 Experimentally generated intensity patterns
Experimental investigation of modulated Bessel beams was carried out using the optical scheme, shown in Fig. 1(a). Generated intensity patterns were imaged after passing through the demagnifying optical system. To obtain a more uniform axial intensity distribution of the generated Bessel beam, the incident Gaussian beam in front of the axicon was blocked by the inner mask and the outer aperture, similarly to the method in Ref. [31]. In simulations and experiments, the diameter of the incident Gaussian beam was 4.8 mm.
The numerically simulated on-axis intensity distributions are shown in the upper graph in Fig. 7(a). Simulations reveal that the slowly changing on-axis intensity distribution of the non-modulated Bessel-Gaussian beam can be flattened using masks, which are placed in front of the axicon as schematically shown in Fig. 1(b). Furthermore, the intensity gradient was increased as well, as it was demonstrated by Stsepuro et al. [31]. However, the oscillatory behaviour could be observed close to propagation distances with large intensity gradients [Fig. 7(a)]. This is attributed to the knife-edge diffraction effects by circular apertures [19,40]. Oscillations could be potentially reduced by the softened aperture edges with smoothened transmission change [41,42] or cardioid-shaped apertures [32,43]. We also note that the resulting axial intensity distribution depends on the distance between a mask, an aperture and an axicon since we used separate elements. However, in simulations, it was assumed that elements line in the same plane.
Fig. 7. (a) Simulated (upper) and experimentally measured (bottom) on-axis intensity distributions of modulated Bessel beams, using amplitude masks. Intensity patterns were captured behind the demagnifying optical system. (b) The experimentally measured central core at FWHM over the beam propagation distance along X (black curve) and Y (red curve) axes. (c) The experimentally captured intensity patterns in the XY plane at given propagation distances (0.8–1.2 mm). The filter angle of the hourglass-shaped amplitude mask (H-amp) was 25 deg. The filter angle of the triangle-shaped amplitude mask (T-amp) was 90 deg. The scale bar is 5 µm-length.
Experimental measurements of the on-axis intensity distribution are shown in the bottom graph in Fig. 7(a). The measured non-diffractive length was larger compared to simulations. For example, the length at FWHM was equal to 1.1 mm and 0.8 mm of non-modulated and flattened beams (compared to 0.9 mm and 0.7 mm according to simulations). That was enough for processing 1 mm-thick glass, considering the multiplication of the non-diffractive zone length by a factor of the material refractive index. In general, the non-diffractive length of the Bessel beam could be adjusted by the variation of the radii of the incident Gaussian beam and annular apertures.
The on-axis intensity distribution of the Bessel beam, which was modulated using a 25 deg hourglass-like amplitude filter, resembled the shape of the flattened beam. Other masks showed the same trend, just with different intensity levels.
The experimentally measured central core extension (at FWHM) along X and Y directions is shown in Fig. 7(b). For the non-modulated beam, the oblate axicon tip leads to an increased central core width at short propagation distances [5,33] and asymmetrical width variations at longer distances, which could be caused by the non-symmetrical incident Gaussian beam [44]. However, beam flattening reduces these variations. When a mask is introduced, the beam becomes asymmetrical over the entire propagation distance (bottom graph). The experimentally captured intensity distributions in the XY plane at different propagation distances are shown in Fig. 7(c), indicating that the shape of the intensity distribution remains constant over 0.8 mm-distance.
The next section shows that the induction of transverse cracks is intensity-dependent. Therefore, flattening operation helped to maintain the similar maximum axial intensity level in the bulk of glass and close to its surfaces. It is essential to induce large and controllable transverse cracks close to the tensioned surface, which encaunters the highest stress during the separation stage. Furthermore, this technology could be applied for other applications, such as precise material modification, which depends on the intensity level [45,46]. The steeper intensity gradients could reduce the longitudinal length of unfavourable modifications triggered by the lower light intensity.
3.3 Glass processing
Modulated Bessel beams were applied for single-shot glass processing using 10 ps pulses at the wavelength of 1064 nm. Symmetrical Bessel beam with only flattened on-axis distribution results in the chaotic orientation of induced cracks, which are not aligned in a single plane and which orientation varies along the Z-axis, corresponding to our previous results [12]. The top and in-volume view of single-shot modifications, induced using modulated beams, is shown in Fig. 8. The pulse energy was measured in front of a sample. Intensity distributions with a well-defined elliptical central core got using 25 deg hourglass and 90 deg triangle-like amplitude masks and 60 deg π/2-delay phase masks induced single cracks with enhanced orientation. The half-length a of single-shot cracks [Fig. 8(a)], measured in the transverse plane (XY), was equal to 5–6 µm. To demonstrate the controllability of cracks, a mask was rotated around its axis to align the major axis of the central core either along the Y direction (0 deg orientation) or along the X direction (90 deg orientation).
Fig. 8. Top and in-volume view of single-shot modifications in the XY plane, induced using asymmetrical Bessel beams, modulated by the (a) 25 deg hourglass and (b) 90 deg triangle-shaped amplitude masks, (c, d) hourglass-shaped phase masks at given pulse energies. Scale bars are 10 µm-length.
It is of prime importance to use the appropriate pulse energy since at high-intensity levels, the deterioration of cracks is observed, i.e. at 117 µJ pulse energy using a 90 deg-orientated H-amp mask [Fig. 8(a)] or 95 µJ pulse energy using T-amp mask at both configurations [Fig. 8(b)]. At high-intensity levels, side lobes start to contribute to the induction of cracks. In the case of the 25 deg H-amp mask, the cracks induction started at ∼60 µJ. Therefore, we would expect induction of cracks solely by side lobes at ∼160 µJ, since their intensity is lower by a factor of 2.7 comparing to the maximum intensity. However, although there is no permanent damage, the thermal contribution to the evolution of cracks by side lobes may be expected even at lower energy. Furthermore, ablation with side lobes of the top surface, which has a lower damage threshold, was observed as well (for example, the leftmost image in Fig. 8(a)).
The half-length of the directional transverse cracks obtained with the 90 deg T-amp mask was lower (a = 3.5 µm) compared to the 25 deg H-amp and 60 deg π/2 phase masks. Interestingly, the central core ellipticity (experimental value of 1.38) was larger for the 90 deg T-amp mask compared to generated using 25 deg H-amp and 60 deg π/2 phase masks (1.17 and 1.13, respectively). The 60 deg T-amp mask with the generated central core ellipticity of 1.24 induced a similar crack length as using the 90 deg T-amp mask. However, when the filter angle of the T-amp mask was reduced to 30 deg, cracks became uncontrollable due to a too low ellipticity value of 1.09.
Notably, the length of induced cracks was larger than the central core extension (∼2 µm at FWHM). Thus, the elliptical intensity distribution only provides an initial elliptical damage site where crack propagation originates. That can explain why patterns of various asymmetries could induce cracks with comparable lengths. However, the final crack length depends on many phenomena (e.g. induced shockwaves [47], contribution by side lobe maxima). Therefore, the detailed modelling of the laser-material interaction, combined with the pump-probe experiments, is needed to understand these processes better.
Intensity distributions with double maxima in the XY plane, i.e. obtained by the 60 deg phase masks with a delay of π [Fig. 8(d)], resulted in a double crack generation, which originated at these maxima. However, even in this case, the dominant cracks orientation direction was along the Y-axis, along which the major axis of the individual asymmetrical maximum is orientated.
Modulated Bessel beams were applied for 1 mm-thick soda-lime glass intra-volume scribing and subsequent separation using the 4-point bending setup [Fig. 2 (a)] at a load rate of 0.37 MPa/s. Laser pulse repetition rate was 8 kHz. 25 deg hourglass-shaped amplitude and 60 deg π/2 phase masks, giving a single maximum, which induces a single crack, were further investigated since double crack configuration will result in the decrease of the stress intensity factor [39] due to the shielding effect [48] when two parallel cracked planes are created.
The dependence of the tensile stress to separate modified glass sheets on the pitch using the 25 deg hourglass amplitude mask (H-amp) is shown in Fig. 9(a). Dots denote the experimental mean value of at least 5 cleaved samples with a standard deviation shown as an error bar. When the major axis of the elliptical central core is orientated perpendicularly to the scanning direction, the separation stress is high (34 MPa) even at a low pitch of 1 µm at 71 µJ pulse energy. Furthermore, cracks spread into the bulk of the material, as seen in the leftmost optical microscope image in Fig. 9(c), which reduce the flexural strength of fabricated parts [49]. However, the separation stress is significantly reduced when cracks are aligned parallel to the scanning direction (open dots in Fig. 9(a)). The minimal value was equal to 11 MPa (6 µm-pitch). Furthermore, the separation stress was reduced for perpendicular scanning directions, Y and X (circles and squares), when cracks were aligned along the scanning direction by rotating a mask.
Fig. 9. (a) Dependence of separation stress of volumetrically scribed samples on the pitch. Dots represent experimental data when transverse cracks are orientated perpendicularly (solid red circles) and parallel (open dots) to the cutting direction. Solid lines show simulation results for modified sheets with multiple colinear cracks with the corresponding half-length a of 4.4 µm (□), 5 µm (○) and 6.1 µm (∇). Open squares and circles represent data at perpendicular scanning directions when cracks were aligned parallel to the scanning direction by rotating a mask. (b) Dependence of the separation stress on the ratio of the pitch to the full crack length. (c) Optical microscope images of scribed samples at a different pitch. The scale bar is 10 µm-length. Transverse cracks were orientated perpendicular (W=3 µm) and parallel (W=2–9 µm). (d) Dependence of the separation stress on the load rate. (e) Topographies (1 mm × 5.7 mm) of laser-scribed (the beam propagation direction is from left to right) and cleaved samples. (f) Average roughness dependence on the pitch. The mean value of 5 samples was calculated. Lines are for eye-guiding only.
Furthermore, the working window of the pitch was increased up to 10 µm, which was comparable to the entire length of single-shot cracks. The average roughness Ra of a cleavage plane was 0.5–0.6 µm in this range [Fig. 9(f)], while for a 90 deg configuration, the steep increase of roughness with an increase of pitch was observed. Quality deterioration of the cleaved surfaces is clearly seen in topographies, shown in Fig. 9(e). Furthermore, when cracks were orientated parallel to the cutting direction, the working window could be further increased by inducing longer cracks at 94 µJ pulse energy (a = 6.1 µm).
The comparable minimal stress of 11 MPa was achieved by the 60 deg π/2 phase mask as well (6 µm-pitch, 124 µJ). Surface roughness was comparable to scribing using the H-amp mask [Fig. 9(f)].
The simulated separation stress of modified sheets with multiple colinear cracks with the half-length a of 4.4–6.1 µm, corresponding to experimentally measured values for separated cracks, are shown as solid lines in Fig. 9(a). In simulations, the subcritical crack growth during loading was taken into account, as well as the amplification of the stress intensity factor due to tightly spaced colinear cracks. The subcritical crack growth was confirmed by additional experiments when samples, modified using the 60 deg π/2 phase mask (8 µm-pitch, 124 µJ), were cleaved at different load rates (0.37–31 MPa/s) in ambient air under normal conditions. The separation stress increased with increasing load rate, as shown in Fig. 9(d). The trend was confirmed by modelling data taking fictitious parameters (8 µm-pitch, a = 3.935 µm) to obtain comparable values. Therefore, it is essential to provide all experimental conditions, including load history, to properly compare the cleaving results demonstrated by different authors.
Experimental and simulation results are replotted in Fig. 9(b) as a separation stress dependence on the ratio of the pitch to the full crack length. The crack length was measured at a high pitch when modifications became separated. As a result of the stress intensity factor amplification, the stress is significantly reduced when the pitch is comparable to the double half-length of cracks. However, the predicted separation stress reduction going virtually to zero when an infinitely small gap between cracks are created is unattainable experimentally. Experimentally induced cracks still have length, orientation variation from damage site to site and over Z direction.
When the pitch is slightly lower than the full crack length, adjacent cracks start to overlap. However, they do not necessarily make a single plane, as shown in Fig. 9(c) at 8 µm and 9 µm-pitch. When the pitch is further reduced, the processing regime changes from single-shot to multiple-shot, where previous modifications affect the new ones [10,16], since the temporal separation between pulses (0.13 ms) is by far larger compared to the development time of cracks in the nanosecond scale [47]. Cracks enhance the optical field intensity [50], leading to a larger amount of deposited energy and non-controlled spreading of cracks into the bulk of a sample (Fig. 9(c) at 2 µm-pitch), facilitated by material weakening due to pre-existing cracks [51]. Furthermore, cracks may perturb the propagation of the incoming laser beam, leading to discontinuous modifications along the Z-axis. Consequently, due to the disruption of cracked planes, the increase of the separation stress is observed at a low pitch, especially when W/2a < 0.5.
A steep separation stress increase is observed when the pitch is higher than the full length of transverse cracks (W/2a > 1). According to modelling results, when the pitch is larger than the full crack length of 10 µm by only 1 µm, the separation stress increases to 37 MPa. The increase also depends on the half-length of cracks since the stress intensity factor scales as a root of a crack half-length. Therefore, the optimal working window (W/2a) is between ∼0.5–1, shown as dashed lines in Fig. 9(b). The comparable trend of the separation stress dependence on the pitch was also observed for samples, which were scribed using the 300 ps mJ-level pulses and elliptical Bessel beam due to the oblate axicon tip and its elliptical cross-section [10] and tilted axicon configurations [13]. However, the minimum mean separation stress value was lower than picosecond laser processing and equaled 4 MPa [10].
4. Summary and conclusions
Hourglass and triangle-shaped amplitude and hourglass-shaped single-level phase masks were applied to modulate the spatial spectrum of axicon-generated optical Bessel beams to obtain the quasi-constant asymmetrical transversal intensity distribution over the beam non-diffractive propagation distance. For a more flatter axial intensity distribution, the incident Gaussian beam distribution in front of the axicon was modulated by opaque masks.
A notable drawback of the transverse intensity modulation using hourglass-shaped amplitude and phase masks is the relative increase of the side-lobe intensity with an increase of the central core ellipticity. However, we demonstrate that this effect could be suppressed using the novel triangle-shaped amplitude masks, giving the opportunity to exploit highly elliptical transverse patterns for various practical applications, such as laser-induced intra-volume modification, cutting, surface patterning, etc.
The elliptical central core, obtained by different means, allows to induce and control the directional cracks in the volume of glass in a controllable manner when appropriate pulse energy (intensity) is selected to avoid the perturbations driven by side maxima. Although different modulation techniques give a comparable result, the easier-to-implement amplitude modulation is more appealing to the mass industry from the technological point of view. However, phase modulation allows generating more atypical patterns, such as having double maxima.
The maximum achievable half-length of directional transverse cracks was equal to 5–6 µm using single-shot picosecond pulses. In the scribing experiments, the minimum tensile stress required to separate a 1 mm-thick soda-lime glass sample was equal to 11 MPa, when intra-distance between parallelly aligned transverse cracks was lower than the full crack length. The measured average surface roughness was independent of the pitch and equaled to 0.5–0.6 µm. A theoretical prediction of the flexural stress going virtually to zero because of the stress intensity factor amplification due to multiple colinear cracks, spaced by an infinitely small gap, was unachieved experimentally since cracks have size and shape spot-to-spot variation. Also, previous modifications may affect the newly generated ones, especially in the overlapping zone. Furthermore, we demonstrate that the subcritical growth of laser-induced cracks should be considered in glass cleaving experiments since the separation stress increases with an increase in the applied load rate.
Funding
Lietuvos Mokslo Taryba (01.2.2-LMT-K-718-01-0003).
Acknowledgments
This project has received funding from European Regional Development Fund (project No 01.2.2-LMT-K-718-01-0003) under a grant agreement with the Research Council of Lithuania (LMTLT).
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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