Aberration-controlled Bessel beam processing of glass

Juozas Dudutis; Rokas Stonys; Gediminas Račiukaitis; Paulius Gečys

doi:10.1364/OE.26.003627

1. Introduction

Glass dicing is a hot topic for industrial applications. Such method gives a clean cut and almost zero kerf width with no post-processing needed. The material is weakened locally, and then sheets can be separated by applying thermal or mechanical load. However, laser-induced cracks have to be generated along the entire depth of the glass sheet. Therefore, elongated modifications along the whole glass thickness are desirable for maximum processing performance. The elongated modifications in transparent materials can be generated by using laser filamentation, dual spot optics or Bessel beams [1–4].

In 1987, Durnin reported the theoretical existence of non-diffracting waves [5]. Such beams are generated by the illumination of the annular slit in the back focal plane of a lens [6], variously shaped axicons or microaxicon-like elements [7], holograms, spatial light modulators, tunable acoustic gradient lenses or using other techniques [8]. 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. Two main manufacturing errors are discussed in the literature - a lens-like oblate tip [9–11] and elliptical axicon cross-section [12]. Both manufacturing errors distort the generated Bessel beam shape. Severe axial oscillations of the optical intensity occur due to the interference between the quasi-Bessel beam, formed by the off-axis part of the axicon, and the wave refracted by the round tip of the axicon [9]. In the presence of the elliptical manufacturing error the Bessel central spot can spread into checkerboard-like intensity [12].

In our previous research we also found, that elliptical cross-section of the oblate-tip axicon can induce central core ellipticity, which was the cause of transverse crack propagation in the bulk of glass [13]. The direction of generated transverse cracks depended on the axicon rotation around its optical axis. It implies that this effect is caused by the axicon geometrical properties and is not related to the incident beam. Such effects are favorable in the case of glass dicing applications. The transverse cracks can enhance the glass cutting process when cracks are aligned parallel to the scanning direction. Recently, the Courvoisier group used a rectangular aperture to deliberately induce ellipticity of the axicon-generated Bessel beam for particular applications [14,15]. Also, the polarization-controlled crack propagation was investigated for sapphire [16]. Mishchik et al. [17] showed that the transverse cracks generation may be improved by burst-mode processing. Therefore, it is really important to control Bessel beam ellipticity. However, in many applications the symmetric Bessel beam is desirable - for example drilling [18,19] or modifying materials [20], since in this case the laser energy is better concentrated in central core and longer modification tracks could be obtained. Spatial filtering can be used to correct the oblate tip induced imperfections of the Bessel beams. It is well known, that the focused Bessel beam will result in a ring-like structure formation in the lens focal plane [21]. However, the part of the wave refracted by the round axicon tip will be focused close to the lens optical axis. Consequently, it is possible to filter these waves by applying a round disc aperture in the lens focal plane. Of course it is a very effective method, however laser beam power loss is inevitable. The Bessel beam provides the elongated focal depth, therefore laser energy is spread in the volume of transparent material. Therefore, describing the Bessel beam intensity in transparent materials we have to take in mind the laser energy per volume (J/cm³), rather than energy per area (J/cm², classical surface case). For this, high laser pulse energies are needed for elongated Bessel beam modifications and additional power losses by filtering can introduce serious challenges.

In this paper we demonstrated, to our knowledge, for the first time, the aberration compensation of the oblate-tip axicon with elliptical cross-section, and studied in details the generated beam symmetry and on-axis intensity. We introduced additional axicon tilt operation perpendicular to its optical axis. Oblique axicon illumination was well studied in the past [22,23]. However, the authors studied the sharp-tip axicon generated beam. It was found that additional aberrations are introduced during axicon tilt operation, which influence the generated beam pattern. However, we report that additional astigmatic aberrations can be used to compensate Bessel beam distortions induced by the oblate-tip elliptical axicon. We present theoretical calculations of the tilted axicon-generated Bessel beam propagation together with experimental analysis. Also, we present results of the Bessel beam compensation (axicon tilt) effects on the laser-induced intra-volume crack propagation in glass.

2. Experimental

Experiments were carried out using the fundamental harmonic (1064 nm) of the DPSS laser Atlantic HE (from Ekspla), which delivered 2 mJ pulses with 300 ps duration at 1 kHz repetition rate. Laser power was attenuated by a pair of a half wave plate and a Brewster-angle polarizer. The incident Gaussian beam with a radius of ω₀ = 1.5-1.7 mm at 1/e² intensity level was transformed to the Bessel-like beam using the commercially available axicon with an apex angle of 170 degrees (AX255-C, from Thorlabs). The axicon profile was investigated by a stylus profiler with a 0.5 mm-radius tip (HOMMEL-ETAMIC nanoscan 855, from Jenoptik). The detailed axicon description is presented in the references [13,24]. The main findings were that the axicon had an oblate tip with the maximum shape deviation of 50 µm from an ideal cone at the center. Axicon profile measurements are presented in the Fig. 1(a). Also, the axicon cross-section, which was parallel to the axicon base, was elliptical. The ratio of major to minor axis length was used to define the axicon ellipticity parameter ellip, which value decreased with an increase of the transverse distance to the optical axis:

e l l i p (x, y) = B \exp (\frac{\sqrt{x^{2} + y^{2}}}{t}) + e l l i p_{0} .

where B, t and ellip₀ are coefficients of the fitted function. The maximum ellipticity was 1.021 close to the tip and dropped below 1.011 at 1.5 mm distance to the axis.

Fig. 1 In (a) the axicon profile and cross-section ellipticity versus transverse distance to the optical axis. In (b, c) axicon rotation around its axis and tilt operation. In (d) the optical demagnification system.

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During experiments the axicon holder was rotated around the optical axis of a conical lens and Y axis of the coordinate system. These positions are attributed to the axial position β and tilt angle α. When the axial position is set to 0 deg, the major axis of an elliptical cross-section is orientated along the X axis. The axicon rotation procedure is described in Fig. 1(b) and (c).

The intensity pattern of the generated Bessel beam behind the conical lens was imaged on the CCD camera (WindCamD UCD12, from DataRay Inc.) by the aspheric lens with the focal length of 8 mm. The magnification factor was set to 16. Obtained cross-sections of the intensity distribution in the XY plane were approximated by the square of the zero-order Bessel function of the first kind:

I (r) \propto J_{0}^{2} (2.4048 r / r_{0}) .

The central core ellipticity was evaluated as the ratio of major to minor axis length. Initially, the Bessel beam central core diameter was 55 µm at 12.5 mm distance from the tip and decreased with an increase of the propagation distance to 21 µm at 42.5 mm. The demagnifying 4F optical system, which consisted of two positive lenses f₁ and f₂, was used to reduce the central core diameter and to increase its intensity. After passing through such optical system, the Bessel beam core diameter and Bessel zone length was reduced by the factor of f₁ / f₂ = 6.5 and (f₁ / f₂)² = 42.25, respectively. However, the non-diffractive length in transparent material is elongated by the factor of its refractive index, which is 1.51 for soda-lime glass. The scheme of optical demagnification system is presented in the Fig. 1(d).

1 mm-thick soda-lime glass sheets were laser-treated. Samples were mounted on the XY linear stages ALS25020 (from Aerotech). The vertical position was adjusted by the positioning stage 8MT167-100 (from Standa). To evaluate the laser-induced intra-volume modifications, 1 mm-thick glass sheets were initially scribed and broken to 4 mm-width stripes, which sidewalls were mechanically polished. Then samples were processed through the polished surface and side-viewed using the optical microscope Nikon (Eclipse LV100). This technique is favorable for measuring the axial length of laser-induced modifications and to determine how the transverse cracks length changes over the vertical direction. There were four sets of experiments: the laser beam was scanned in X and Y directions while the axicon axial position was set to 0 deg and 90 deg and the holder was rotated around Y axis to adjust the tilt angle.

3. Modelling

The MATLAB software was used to simulate the non-ideal Bessel beam. The intensity pattern at the distance z from the axicon tip was calculated using two-dimensional Fast Fourier Transform, taking the Fresnel approximation into account [25], which is legitimate for a low base-angle axicon. If the incident Gaussian beam waist lies in plane with an axicon, the optical field behind the conical lens can be defined as:

U_{1} (x, y) = U_{0} \exp (- \frac{x^{2} + y^{2}}{ω_{0}^{2}} + i k (n - 1) d (x, y)),

where U₀ is the on-axis intensity and d(x,y) denotes the axicon profile function of the non-tilted axicon, obtained from the stylus profilometry. We have approximated the profile function by a polynomial with a polar coordinate d(x,y) = d(r), where

r = \sqrt{x^{2} + {(e l l i p (x, y) \times y)}^{2}}

and

e l l i p > 1

. Then the field in the observation plane can be calculated as following:

U_{2} (x, y) = ℑ^{- 1} {ℑ (U_{1} (x, y)) H (f_{X}^{2} + f_{Y}^{2})},

where f_x and f_y denotes the spatial frequencies and H is the Fresnel transfer function through the free space:

H (f_{X}, f_{Y}) = e^{j k z} \exp [- j π λ z | (f_{X}^{2} + f_{Y}^{2})],

where λ is the optical wavelength and k = 2π/λ is the wavenumber. However, it is not a straightforward task to find the profile function of the tilted axicon d_tilted(x,y). Herein we implemented the coordinate transformation, which rotated the Cartesian coordinate system by α degree around Y axis, which is perpendicular to the optical axis. In this case the point coordinates (x,y,z) after tilting can be calculated as:

\begin{array}{l} z^{'} = z \cos α - x \sin α, \\ x^{'} = z \sin α + x \cos α, \\ y^{'} = y . \end{array}

To use the equidistant sampling in the XY plane, we can approximately calculate the

Δ x

value so that

x^{'} = (x + Δ x, d (x + Δ x)) = x

:

\begin{array}{l} (d (x, y) + \frac{\partial d (x, y)}{\partial x} Δ x) \sin α + (x + Δ x) \cos α = x, \\ Δ x = \frac{x (1 - \cos α) - d (x, y) \sin α}{\frac{\partial d (x, y)}{\partial x} \sin α + \cos α} \approx \frac{x (1 - \cos α) - d (x, y) \sin α}{\cos α} . \end{array}

Then the surface function of the tilted conical lens is:

d'_{t i l t e d} (x, y) = d (x + Δ x, y) \cos α - (x + Δ x) \sin α .

However, the axicon has a base, which is also rotated and the thickness function finally becomes:

d_{t i l t e d} (x, y) = {d^{'}}_{t i l t e d} (x, y) + x \tan α = d (x + Δ x, y) \cos α - (x + Δ x) \sin α + x \tan α .

The rotation of an axicon around its axis by β degree can be introduced by the additional coordinate transformation:

\begin{array}{l} x^{'} = x \cos β - x \sin β, \\ y' = x \sin β - y \cos β . \end{array}

And the thickness function of the tilted and rotated axicon becomes

d_{t i l t e d} (x^{'}, y^{'})

.

4. Results

4.1 Tilted axicon-generated beam intensity distribution

Comprehensive investigation of the non-tilted axicon beam distribution was made in our previous studies [13,24]. The ideal axicon generates a beam, which on-axis intensity smoothly varies from the tip of an axicon and reaches its peak value at z_max/2. The Bessel zone length, calculated as z_max = ω₀cosθ₀/sinθ₀, depends on the half-angle of a cone and on the radius of the incident Gaussian beam. The central core radius has the propagation invariant shape and can be calculated as ρ₀ = 2.4048/(ksinθ₀). However, this is no longer valid for an oblate-tip axicon where the axicon tip can be approximated as a spherical lens. In this case the generated beam is shifted towards the propagation direction and the on-axis intensity distribution is modulated due to the interference of light with wavevectors of different angles with respect to the optical axis. The central core radius decreases with an increase of the beam propagation distance due to the fact that further parts of the beam in the Z direction are generated by such parts of an axicon, which have higher base angles. Experimental measurement of such Bessel beam distribution in the XZ plane is illustrated in Fig. 2(a). Finally, propagating Bessel beam starts to form the checkerboard-like intensity distribution due to axicon ellipticity. Such behavior is experimentally observed in Fig. 2(c). In the case of the sharp-tip axicon, the spreading is slightly asymmetrical and equals to the axicon cross-section ellipticity [23]. However, a lens-like oblate-tip generates a beam, which asymmetry is much more pronounced. According to experimental measurement in Fig. 2(b) ellipticity decreases with an increase of the propagation distance. More details of such Bessel beam behavior can be found in the reference [13].

Fig. 2 Non-tilted axicon-generated Bessel beam distribution behind the conical lens. In (a) the beam intensity distribution in the XZ plane, generated by the oblate tip axicon with variable cross-section ellipticity. (b) Bessel beam central core ellipticity. In (c) Bessel beam distribution in the XY plane at Z distance equal to 18 mm and 26 mm. The axicon placement is at the top of the image at Z position equal to 0.

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Beam aberrations, caused by the cross-section ellipticity, is similar to ones, originated from the oblique illumination, and is attributed to astigmatic aberrations. The only difference is that the transverse beam distribution is slightly squeezed in one direction in the case of the elliptical sharp-tip axicon. A. Thaning et al. [23] predicted and experimentally confirmed that the elliptical-axicon-generated beam aberrations may be compensated by adjusting the axicon tilt angle. Hence, the Bessel-like distribution in the XY plane may be obtained. The compensation angle α satisfies the condition ellip = 1/cosα.

Experimental measurements and theoretical simulations of the intensity distribution generated by the oblate-tip elliptical axicon are presented in the Fig. 3 and Fig. 4. The axicon was tilted to the maximum angle of 24 deg to change the amount of the introduced aberrations. Measurements of the beam ellipticity were applied at 17 mm and 30 mm distances from the axicon tip. The former distance refers to the maximum on-axis intensity. The later one was chosen as a reference part of the beam, generated by such part of the axicon, which geometry is close to the frustum of the cone. When axicon is rotated around the axis, which lies in plane with the major axis of the ellipse-shaped axicon cross-section, the total amount of aberrations is increased. To emphasize this, the tilt angle has a minus sign. When axicon is rotated around the axis, which is perpendicular to the major axis of the ellipse-shaped axicon cross-section, the total amount of aberrations is decreased, until the compensation angle is reached. When this angle is passed, the oblique illumination induced aberrations overcome the elliptical cross-section induced aberrations and the generated beam is lengthened in the perpendicular direction with respect to the previous distribution.

Fig. 3 Tilted axicon-generated Bessel beam distribution measurement behind the conical lens. In (a) simulated and experimentally measured Bessel beam patterns versus axicon tilt angle. (b) The beam ellipticity in the XY plane versus axicon tilt angle.

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Fig. 4 In (a) Bessel beam core ellipticity versus distance Z for 0 and 10 deg tilt. (c) On-axis intensity of the Bessel beam generated with 0 and 10 deg tilted axicon. The axicon placement is on the left of the image at Z position equal to 0. The measurements were performed behind the conical lens.

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Theoretical and experimental analysis of the Bessel beam pattern evolution versus axicon tilt angle is presented in the Fig. 3(a). When axicon tilt angle equals to 0 deg, the asymmetrical Bessel-like beam is generated at 17 mm distance from the axicon tip. The central core maintains its shape and does not show splitting yet. While propagating further up to 30 mm, the beam starts to spread into a checkerboard-like structure. However, the beam symmetry is increased at such distance. When aberration compensation is introduced (tilt angle of 10 deg, axial position β = 0 deg), the Bessel-like beam behavior is obtained for the observed propagation distance. The Fig. 3(b) shows the Bessel beam central core ellipticity versus axicon tilt angle. The compensation angle was 10.5 deg and 9 deg to obtain the symmetric beam distribution at 17 mm and 30 mm distances, respectively. The difference comes from the fact that the investigated axicon has the variable ellipticity and the further parts of the beam in the Z direction is generated by less elliptical part of the axicon. If we take a thin tube of the incident beam, hitting the axicon at some distance from the optical axis, we can calculate the refraction angle by Snell's law and the distance in the propagation direction, at which waves intersect and the Bessel beam pattern is generated due to light interference. By this we can attribute the axicon cross-section ellipticity to the generated pattern in the particular Z position. Calculated from such rough geometrical assumptions, the cross-section ellipticity, responsible for the generated beam at 17 mm and 30 mm distances, is 1.0185 and 1.0133, respectively. Hence the compensation angle, obtained by satisfying condition (tilt angle α = cos⁻¹(1/ellip)), proposed by A. Thaning et al. [23], is equal to 10.9 deg and 9.3 deg and fits our experimental and numerical simulation results fairly well. Therefore, we have proved that the compensation angle can be evaluated by simple equation even for oblate-tip elliptical axicons. Furthermore, for axicons with the fixed cross-section ellipticity we could expect a single compensation angle for the entire propagation distance. The increase of astigmatic aberrations (tilt angles from 0 to −24 deg, axial position β = 90 deg) results in further asymmetry enhancement and checkerboard-like pattern formation.

The central core ellipticity for non-tilted and 10 deg-tilted axicon (axial position β = 0 deg) is presented in Fig. 4(a). It is obvious, that the upper part of the beam in the Z direction is not compensated enough, while the further part is overcompensated. As previously mentioned, this phenomena occurs due to variable axicon cross-section ellipticity. Axial Bessel beam intensity measurements are presented in the Fig. 4(b). The Bessel zone length is increased and the central core does not show splitting in the investigated propagation distance when 10 deg axicon tilt is applied. Overall, axicon tilting to improve the generated Bessel beam distribution is a very attractive technique.

We showed that Bessel beam central core ellipticity can be reduced simultaneously increasing the Bessel zone length. Further, the central core splitting to checkerboard-like distribution is significantly reduced for higher propagation distances. On the other hand, the high-ellipticity part of the beam, closer to the axicon tip, may be removed by additional spatial filtering in the Fourier plane of the 4F demagnifying system [9]. Therefore, the axicon-generated Bessel beam distribution can be tuned to follow the theoretical pattern.

4.2 Processing of glass with aberration-controlled Bessel beam

To evaluate the laser-induced intra-volume modification formation behavior, the single-shot laser processing of glass stripes was performed. Then side-view observations in XZ and YZ planes were realized. The axicon rotation was applied to compensate the Bessel beam distortions (tilt angles from 0 to 24 deg, axial position β = 0 deg) and further increase the astigmatic aberrations (tilt angles from 0 to −24 deg, axial position β = 90 deg). The Bessel beam core diameter and Bessel zone length were reduced using the 4F optical system with demagnification factor of 6.5 and the laser pulse energy was set to 1.6 mJ. After passing through the 4F system the Bessel beam core diameter was in the range of 8.5-3.2 µm.

The Fig. 5 shows results on the single-shot modification side-view examination in respect to the Bessel beam propagation direction. The crack formation in both XZ and YZ planes together with longitudinal modification length versus axicon tilt angle for aberration compensation are presented in Fig. 6(a) and (b). When axicon tilt angle equaled to 0 deg and the axial position was 0 deg, the transverse cracks propagated in the dominant XZ plane, which was parallel to the major axis of the elliptical intensity pattern. The cracks spreading in the transverse direction was several times longer than the transverse width of the laser-induced modifications itself. The maximum transverse crack width was in the range of 150 µm. This behavior was attributed to the nonsymmetrical Bessel beam core distribution in our previous research [13,24].

Fig. 5 Side view of the Bessel beam induced single-shot modifications in glass at XZ and YZ observation planes for different axicon tilt angles. Beam propagation direction from left to right.

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Fig. 6 Laser-induced modification behavior versus axicon tilt angle. In (a) Top view of the axicon rotation procedure. (b) Laser-induced modification behavior when rotation axis is perpendicular to the major axis of the ellipse-shaped axicon cross-section. In (c) Top view of the axicon rotation procedure. (d) Laser-induced modification behavior when rotation axis is parallel to the major axis of the ellipse-shaped axicon cross-section.

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The transverse cracks were produced mainly in the XZ plane, when the axicon tilt angle was in the range of 0 to 10 deg. The maximum cracks widths were similar until tilt angles of 2-4 deg and then started to decrease. When the axicon was tilted to the angle of 10 deg, the additional aberrations compensated the axicon shape imperfections and the generated Bessel beam core ellipticity was reduced to minimum. It was confirmed by the fact that the dominant transverse crack propagation direction was no longer stable. The cracks tended to spread in both XZ and YZ planes, while the transverse crack widths were 116 µm and 140 µm, respectively. This corresponds well with Bessel beam profile measurements, where we obtained the minimal Bessel beam core ellipticity together with the increased on-axis length. The transverse cracks could be avoided using lower pulse energy or shorter pulse duration to reduce thermal effects. Such regime could be applied for applications where highly symmetric beams with long non-diffractive distance and energy concentrated in the central core are required, for instance, microchannels formation [19,26] or material refractive index modification [20].

Further tilting the axicon resulted in overcompensation of oblate-tip elliptical axicon-induced aberrations and cracks started to spread mainly in the YZ plane. The last result implies that transverse glass cracks can be also induced and controlled by axicon tilt, independently of the oblate-tip axicon cross-section ellipticity. The elliptical cross-section induced aberrations is of the same nature as ones, caused by oblique illumination. It means that directional cracks, which are favorable for glass cutting enhancement, when cracks are aligned parallel with the beam scanning direction, may be induced even by a circular axicon, deliberately tilted to some angle.

Side-view images of the YZ plane in Fig. 5 for 24 deg axicon tilt even showed the formation of several modification tracks. This is an expected result, since at such axicon tilt angles the Bessel beam core starts to form checkerboard-like structures.

Attempts to further increase the axicon astigmatic aberrations are presented in the Fig. 6(c) and (d). In this case, the axicon was tilted from 0 deg to −24 deg, while the axial position was 90 deg. In such regime the dominant crack propagation direction lied in the YZ plane. However, with an increase of the axicon tilt angle, both the transverse crack width and longitudinal modification length were reduced. The Bessel beam core transformation into checkerboard-like distribution is the main cause of such behavior, since the energy in the central core is redistributed to surrounding maxima. Such effects are clearly visible in the Fig. 3 and Fig. 5, since several modification tracks can be observed. Overall, the results of aberration-controlled glass processing indicates that there is an optimal condition for laser-induced transverse cracks generation, when the maximum cracks width together with the large longitudinal modification length may be achieved. Simple axicon tilt operation, reducing or increasing the aberrations, could improve glass cutting process.

5. Summary

We investigated the aberration-controlled Bessel beam distribution and possible applications for glass intra-volume modifications. Our previous studies showed, that a non-ideal axicon generates a beam pattern, which asymmetry is mainly defined by its oblate tip with an elliptical cross-section. While propagating further from the axicon tip, the Bessel beam central core pattern spreads into checkerboard-like structure lowering the on-axis core intensity. Such beam can generate transverse cracks, which dominant propagation direction can be linked to the Bessel beam asymmetry. Laser-induced modifications can be applied for fast glass cutting when transverse cracks are aligned parallel to the scanning direction. Even though the oblate tip is very common for axicons, the cross-section ellipticity may be insufficient or too large for particular application. Also, many applications require a symmetric Bessel beam distributions. Spatial filtering can be used for such tasks. However, additional power losses by filtering can induce serious challenges. Therefore, it is important to control axicon shape-induced aberrations.

In this paper we presented a simple technique for imperfect axicon-generated Bessel beam pattern reconstruction by inducing additional aberrations caused by axicon tilting. The axicon tilt operation was applied for two cases. One included the rotation of the axicon around the axis, which is perpendicular to the major axis of the ellipse-shaped axicon cross-section. The second one was realized by tilting the axicon around the parallel axis. In the first case, while tilting the axicon from 0 to 10 deg, the additional aberrations helped to compensate the imperfect axicon-generated Bessel beam distortions. The angle of 10 deg was found to be optimal, where the Bessel beam central core ellipticity was reduced to minimum, and the on-axis intensity was increased as well. Glass intra-volume modifications with such aberration-compensated beam also showed good agreement. At this tilt angle, no defined crack propagation direction was obtained, as well as the longitudinal modification length was increased compared to processing without aberration correction. When the 10 deg tilt angle was passed, dominant transverse crack direction was rotated by 90 deg. From this point oblique illumination-induced aberrations overcompensated elliptical cross-section-induced aberrations. It implies that transverse cracks can be induced independently of the axicon ellipticity.

In the second case of the axicon tilt operation, we tilted the axicon around the axis, parallel to the major axis of the ellipse-shaped axicon cross-section. The additional aberrations further increased the Bessel beam distortions. The ellipticity of the Bessel beam central core was further increased compared to 0 deg tilt. Glass intra-volume modifications experiments showed that the dominant crack propagation direction was in the YZ plane. However, despite that asymmetry of the generated Bessel beam was increased for higher tilt angles, the crack width together with longitudinal modification length were reduced. Most likely, the formation of the checkerboard–like structure was responsible for Bessel beam central core intensity reduction. For this, the laser energy was spread in higher volume reducing destructive laser-glass interaction zone.

Overall we can conclude, that aberration-controlled Bessel beam generation by tilting the axicon is a very attractive technique. No matter on the experiment needs for symmetric or asymmetric Bessel beams, it is possible both to induce asymmetry as well as to tune up the system for symmetric beam pattern generation.

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Aberration-controlled Bessel beam processing of glass

Abstract

1. Introduction

2. Experimental

3. Modelling

4. Results

4.1 Tilted axicon-generated beam intensity distribution

4.2 Processing of glass with aberration-controlled Bessel beam

5. Summary

References and links

Cited By

Figures (6)

Equations (10)

Optics Express