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Abstract
We introduce the optical vortex beam into simultaneous spatial and temporal focusing (SSTF) technique, and theoretically and experimentally demonstrate the local control of peak intensity distribution at the focus of a simultaneous spatiotemporally focused optical vortex (SSTF OV) beam. To avoid nonlinear self-focusing in the conventional focusing scheme, a spatiotemporally focused femtosecond laser vortex beam was employed to achieve doughnut-shaped ablation and high aspect ratio (∼28) microchannels on the back surface of 3 mm thick soda-lime glass and fused silica substrates.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In recent decades, optical vortices have been widely used in micromanipulation [1–4], free-space communication [5–7] and micro/nanofabrication [8–19]. As one of the key applications, microfabrication using femtosecond vortex beam has attracted much attention for its unique characteristics on helical phase wavefronts and ‘doughnut’-shaped intensity distributions [11–19]. However, the use of optics vortex in femtosecond laser micro/nanofabrication is limited. Most research about optics vortex micromachining is the ablation on the front surface in tightly focusing scheme [11–17], or fabricated in thin polymer [18,19]. The researches on femtosecond vortex micromachining inside the thick bulk or on the back surface of transparent dielectrics are fewer [20], this is mainly because the resolution of optics vortex along axis direction is low, resulting in no ablation in low laser energy and self-focusing effect in high laser energy with conventional focusing optical vortex (CF OV) scheme, which are not benefit for micromachining.
As one of laser beam shaping techniques, simultaneous spatiotemporal focusing (SSTF) technique has provided a new focusing dimension in femtosecond laser micromachining, which makes it prominent in the control of focal spot size and shape, and has been used to effectively avoid nonlinear effects, such as self-focusing and filamentation [21–31]. The working mechanism of SSTF has been described in detail elsewhere [25,27]. Briefly, in the SSTF scheme, the incident femtosecond pulses firstly pass through a pair of gratings, separating the different frequency components from each other in space, and then be focused by the objective lens. After the objective lens, different spectral components overlapped spatially and temporally only at the geometric focus of the focusing lens, which restores the shortest pulse duration to generate the highest peak intensity only at the focus. The pulse durations extended before and after the geometric focus, which effectively reduce the peak intensity and in turn suppress the intensity clamping caused by the nonlinear self-focusing. When SSTF technique is applied to vortex beams, SSTF OV can provide new manipulating dimensions for both SSTF technique and optical vortex, such as pulse width, spatial dispersion and topological charge, which will be useful for light manipulation and femtosecond laser micromachining. However, there are few researches on SSTF OV micromachining, only Cheng et al. combined beam shaping with SSTF to produce doughnut-shaped ablation marks on the back surface of 150 µm thick borosilicate glass plates [20]. So far, the theoretical analysis of intensity distribution of SSTF OV beam has not been studied, and it is still a challenge to fabricated inside the thick bulk or on the back surface of thick transparent dielectrics with femtosecond vortex beam.
In this work, we introduced the optical vortex beam into SSTF technique, theoretically and experimentally demonstrated the characterization of intensity distribution of a simultaneous spatiotemporally focused optical vortex (SSTF OV) beam. We show the ability of doughnut-shaped ablation on the back surface of 3 mm thick soda-lime glass and fused silica glass substrates with SSTF OV scheme, which is unable to achieve with CF OV scheme. Our demonstration also represents a novel and better laser ablation technique for drilling high-throughput and high aspect ratio microchannels using SSTF OV pulses.
2. Experimental setup
Figure 1 shows the schematic of experimental setup for fs-laser fabrication system using spatiotemporal focusing optics vortex pulses. The laser source is an amplified Ti: Sapphire femtosecond laser system (Solstice Ace, Spectra-Physics) with center wavelength of 800 nm and pulse duration of ∼60 fs at 1 kHz repetition rate. The spectral bandwidth is ∼30 nm and maximum pulse energy is ∼5 mJ.
Fig. 1. Schematic illustration of the experimental setup. VF: variable neutral density filter. L1, L2: lenses of different focal lengths which are described in the main text. QP: quarter plate. VR: vortex plate. G1-2: diffraction gratings. OL: objective lens. SA: sample. The configuration of XYZ axes is indicated in the inset.
The laser beam has a nearly perfect Gaussian beam shape with a ∼10 mm diameter. A telescope system consisting of a convex lens L1 (f = 300 mm) and a concave lens L2 (f = −100 mm) was used to reduce the beam width to ∼3 mm (1/e2) for implementing the SSTF scheme. In order to generate the vortex beam, the reduced gaussian beam with p-polarization passes through a quarter-wave plate, and then enters a vortex plate (VRx-800, LBTEK, topological charge m = 6) to generate a vortex beam with the positive topological charge. After the vortex plate, the spatial intensity distribution of the beam presents a central region of zero intensity due to undefined phase on the beam axis. The vortex beam was then directed through the single-pass grating compressor, consisting of two σ = 1200 grooves/mm gratings (Thorlabs). The angle of incidence of the beam on both gratings is 40° and the distance between the gratings is 220 mm. The single pass grating compressor in SSTF scheme have two main purposes. On the one hand, grating compressor introduces spatial dispersion, the distance was adjusted to be 220 mm to make sure that all the spatially dispersed frequency components can fill the pupil of the objective lens (∼10 mm). On the other hand, grating compressor introduces temporal dispersion, Group Delay Dispersion (GDD) introduced by the grating pair in this experiment was -3.37 × 105 fs2, in order to pre-compensate the GDD induced by all optics including variable neutral density filter, lenses, objective lens, grating pair and so on, the input pulse in the amplifier is positively pre-chirped to obtain the shortest pulse at the focus of objective lens. After being dispersed by the grating pair, the laser beam was measured to be ∼10 mm (1/e2) along the x-axis and ∼3 mm (1/e2) along the y-axis. The spatially dispersed femtosecond laser vortex pulses were then focused into the glass sample using an objective lens (Olympus, 10 ×, NA =0.3) with a working distance of 3 mm.
The samples used in the experiment are soda-lime glass and fused silica glass, which are cut into 10 mm × 10 mm × 3mm coupons with the all six sides polished. The samples can be arbitrarily translated three dimensionally by a PC-controlled XYZ stage with a resolution of 1 µm. The machining process is monitored by a charge-coupled device (CCD) camera.
3. Theoretical analysis
Theoretically, simulation of the intensity distribution at the focus with spatiotemporally focused femtosecond laser vortex beam can be achieved using Fresnel diffraction theory [28,32]. We assume that the temporal chirp of incident pulse is pre-compensated. The normalized light field of a spatially dispersed pulse E1 at the entrance aperture of objective lens can be expressed as
Fig. 2. Experimental measured (a)(b) and numerically calculated (c)(d) laser intensity distributions before and after the single-pass grating compressor. The measured intensity variation of the fluence along the Y direction (e)(f) and along the X direction (g). Scale bar is 3 mm.
It is obvious that in the SSTF OV scheme, the incident femtosecond vortex beam before the single-pass grating compressor shows a doughnut-shaped intensity distribution, as shown in Fig. 2(a). Figure 2(e) shows the corresponding intensity variation of the fluence along the diameter the vortex beam. It can be seen that the center intensity of the femtosecond vortex beam is zero as expected, which shows the characteristics of vortex beam clearly. After passing through the pair of gratings, different frequency components are separated from each other in the X direction, the intensity distribution appears to be elliptical, as shown in Fig. 2(b). It shows that the intensity variation of the fluence along the X direction is of Gaussian distribution as shown in Fig. 2(g). The intensity variation along the Y direction shows the characteristics of vortex beam, as shown in Fig. 2(f). It should be noted that the center intensity of the spatially dispersed femtosecond vortex beam is not zero, the reason is that different frequency components are spatially separated and partially overlapped in the X direction. Figure 2(c) and Fig. 2(d) show the numerically calculated results, which are in agreement with the experimental measured results as shown in Fig. 2(a) and Fig. 2(b), respectively.
After passing through the objective lens, the field can be calculated using the slow varying envelope approximation, which can be written as
The intensity distribution in the time domain can thus be obtained by performing an inverse Fourier transform of E3
Numerically calculated and experimental measured spatial intensity distributions of a SSTF OV beam in X-Y planes at the focus of objective lens are shown in Fig. 3. Figure 3(a) shows the simulated intensity distributions at the focus of objective lens, which is characterized by an annular spatial profile. The intensity distributions show doughnut-shaped in the X–Y plane. Figure 3(b) shows the experimental measured intensity distributions of SSTF OV beam in X-Y plan at the focus of objective lens, which was captured by a 4f optical imaging system consisting of the objective lens (10x, 0.3 NA), convex lens (f = 200 mm) and CCD camera, the focus is near the surface of silica glass. It can be seen that the intensity distribution at the focus of objective lens shows a doughnut-shaped intensity distribution with an external diameter of 24 µm, which means that different spectral vortex components overlap at the focus of objective lens. Figure 3(c) shows the simulated and experimental intensity variation of the fluence along the diameter, the intensity line profiles of theoretical analysis and experiment with topological charge m = 6 are well matched.
Fig. 3. Numerically simulated (a) and experimental (b) measured intensity distributions of a SSTF OV beam in X-Y planes at the focus of objective lens. Simulation (black) and experimental (red) intensity variation(c) of the fluence along the diameter. Scale bar is 30 µm.
To compare the intensity distribution along the propagation axis with the CF OV scheme and SSTF OV scheme, we calculated and experimental measured the intensity distributions on the XZ- and YZ-planes for the same parameters, the results are shown in Fig. 4. In the CF OV scheme, the peak intensity distribution of femtosecond vortex pulses near the focus can be calculated using Eq. (1) by assuming that α=0 and ω=ω0. Figure 4(a) shows the calculated intensity distributions with the CF OV scheme, it can be seen that the intensity distributions on the XZ- and YZ-planes are same, which approximates a hyperbola at the axial cross section. But in the SSTF OV scheme, the angular chirp rate α play an important role in the control of intensity distribution at the focus of objective lens. Figure 4(b) and 4(c) show the calculated intensity distributions on the XZ- and YZ-planes with the SSTF OV scheme, respectively. It should be noted that the intensity distributions along the propagation axis are significantly smaller than that in the CF scheme, the axial sizes are ∼100 µm with CF scheme and ∼50 µm with SSTF OV scheme. The volume of focus with SSTF OV scheme is smaller than that with CF OV scheme at the same energy, which means that the higher energy density of focus can be achieved with SSTV OV scheme. The reason for this phenomenon is that in the SSTF OV scheme, different spectral vortex components overlapped spatially and temporally only at the geometric focus of the focusing lens, which restores the shortest pulse duration to generate the highest peak intensity only at the focus. But outside the focus, the pulse durations extend and peak intensity decrease rapidly. The calculated results suggest that compared with the CF OV scheme, SSTF OV scheme can concentrate the electromagnetic energy into smaller regions along the propagation axis.
Fig. 4. Numerically calculated intensity distributions along the propagation axis near the focus with the CF OV scheme (a) and SSTF OV scheme in XZ(b)-and YZ(c) planes, respectively. Images of axial intensity distributions in silica glass captured by CCD camera with the CF OV scheme (d, e) and SSTF OV scheme in XZ(f)-and YZ(g) planes, the pulse energies are (d) 20 µJ, (e, f, g) 30 µJ. Scale bar is 30 µm.
In order to verify whether the axial intensity distribution near the focus can be effectively shortened in the experiment, we simply compared the axial intensity distribution in silica glass with CF OV scheme and SSTF OV scheme. The experiment was carried out by focusing the femtosecond laser vortex beam near the back surface of a 3 mm thick silica glass with CF OV scheme and SSTF OV scheme for the same parameters, the pulse energy was 30 µJ and the effective NA was 0.11, the laser pulse energy was measured after the grating pair. In the CF OV scheme, the pulse compressor in laser source was adjusted to deliver the transform-limited pulses, and the grating pair used in the SSTF OV scheme was replaced with a pair of mirrors. Figure 4(d)-(f) show the images of axial intensity distributions in silica glass captured by CCD camera with the CF OV scheme (d, e) and SSTF OV scheme in XZ(f)-and YZ(g) planes. It can be seen that in the CF OV scheme, a bright light filament is clearly visible in silica glass when the pulse energy was 20 µJ, the length of the filament is ∼175 µm, as shown in Fig. 4(d). When the pulse energy increased to 30 µJ, the filament caused by the balance between nonlinear self-focusing and plasma defocusing generated with the CF OV scheme was quite long along the propagation axis, the length of the filament is ∼510 µm, as shown in Fig. 4(e). On the contrary, in the SSTF OV scheme, the formation of filament is suppressed and plasma is well localized at focal region at the same pulse energy of 30 µJ, the length of the filament is ∼90 µm, as shown in Fig. 4(f)-(g). It can be seen that the length of the filament generated by CF OV pulse is nearly six times as long as that with SSTF OV scheme when the energies are all 30 µJ, which indicates that SSTF OV scheme can suppress nonlinear self-focusing effect and effectively shorten axial intensity distribution.
In general, the calculated and experimental results show that a better confinement of pulse energy along the propagation direction can be achieved with the SSTF OV scheme than the CF OV scheme. This is mainly because the spatial chirp introduced by grating pairs in the SSTF OV scheme. It should be pointed out that the spatial chirp is related to the distance between the gratings pair and the incident angle into the grating, so the intensity distributions along the propagation axis of focused femtosecond vortex beam can be controlled by adjusting the distance between the gratings pair and the incident angle into the grating, which provide a new manipulating dimension for optical vortex.
4. Results and discussions
To compare the capability of fabrication on the back surface of glasses underwent the two focusing schemes, we focused femtosecond laser vortex pulses on the back surface of soda-lime glass substrate in both schemes. The machining parameters remain the same, including pulse energy, the effective NA and the number of laser pulses N. In the experiment, the number of pulses was controlled by an electromechanical shutter and the measurement of the ablation features was carried out using a transilluminated optical microscope (Leica DM2700M).
In the experiment, we found that under the same machining parameters as in SSTF OV scheme, there was no any visible mark on the back surface of 1 mm thick soda-lime glass substrate in the CF OV scheme, even the energy was increased to be 50 µJ with the number of pulses N = 2000. The reason for this is that the filament generated in the CF OV scheme hamper the precise energy deposition and material ablation. For this reason, the ablation results with CF OV scheme are not given here. Figure 5(a) presents the optical micrograph of the ablation feature on the back surface of 1 mm thick soda-lime glass substrate after irradiation with N = 50 SSTF OV pulses, the laser energy E = 26 µJ. It is noteworthy that ablation of material performed using a fixed number of laser vortex pulses is highly reproducible. It can be seen that the inner parts are almost untouched after the ablation process due to the doughnut-shaped intensity distributions. The ablation results show the characteristics of vortex beam clearly. Figure 5(b) is the corresponding magnified optical micrograph of Fig. 5(a). From Fig. 5(b) one can see that the inner diameter of the ablated area Din = 12.5 µm, and the external diameter Dex = 24.5 µm. The shape and size of the ablation area shown in Fig. 5(b) also agree with the theoretical predictions before.
Fig. 5. Optical micrographs of the ablation feature on the back surface of 1 mm (a) and 3 mm (c) thick soda-lime glass substrate with SSTF OV scheme. (b) and (d) are the magnified optical micrographs of (a) and (c), respectively. Scale bar is 20 µm.
In order to investigate the influence of thickness on ablation, we focused femtosecond vortex pulse on the back surface of 3 mm thick soda-lime glass substrates in both schemes, the parameters are same as that in Fig. 5(a). The maximum ablation thickness is limited by the working distances of objective lens. It is not surprising that there is no any mark on the back surface of 3 mm thick glass substrate in the CF OV scheme. Figure 5(c) shows the optical micrograph of doughnut-shaped ablation on the back surface of 3 mm thick soda-lime glass substrate with SSTF OV scheme, Fig. 5(d) is the corresponding magnified optical micrograph of Fig. 5(c). As compared with Fig. 5(a), the shape and size of ablation area are almost unchanged in Fig. 5(c). The ablation results clearly suggested that energy of laser pulse transmitted to the back surface of glass substrates decays with increasing thickness.
In additon, we also studied femtosecond laser vortex ablation on the back surface of 3 mm thick fused silica glass substrate. Compared with soda-lime glass, the pulse-energy threshold for the formation of an ablation mark on the back surface of the fused silica glass is larger. In the experiment, the pulse number N = 50 and laser energy E = 32 uJ. Figure 6(a) shows the optical micrograph of doughnut-shaped ablation on the back surface of 3 mm thick fused silica glass substrate with SSTF OV scheme, and Fig. 6(b) is the corresponding magnified optical micrograph of Fig. 6(a). The results clearly suggest that the shape and size fabricated on the back surface of fused silica glass is similar to those on soda-lime glass substrate shown in Fig. 5, which demonstrates the universality of the SSTF OV for materials processing.
Fig. 6. Optical micrographs of the ablation feature on the back surface of 3 mm thick fused silica glass substrate with SSTF OV scheme. (b) is the magnified optical micrograph of (a). Scale bar is 20 µm.
To examine the capability of fabrication on the back surface of fused silica glass with SSTF OV scheme, we performed the experiments of writing line and square, the scanning directions are indicated by red arrows, and the writing speed was set to be 20 µm/s. Figure 7(a) shows the optical micrograph of line written on the back surface of 3 mm thick fused silica glass substrate with SSTF OV scheme, the length of the line is 300 µm, it can be observed clearly that when the line is written from left to right, the ring-shaped machining area overlaps and the line looks like to be solid, but at the end of line, the ring shaped machining area still exists. The ablation profile of overlapped area shows that the ablation structure is high in the middle and low on both sides, as shown in the chart, which shows the characteristics of vortex beam. Figure 7(b) shows the optical micrograph of square consisting of four lines written in different directions, the ablation effects are almost the same in different directions, but it should be noted that the line written from left to right is different from the line in the opposite direction. From the ablation profile in the chart, we can see that the average depth of line ablated from left to right is ∼18 µm, and the average depth of line ablated from right to left is ∼12 µm, which means that the ablated line written from left to right is deeper than that in opposite direction. This phenomenon can be explained by nonreciprocal writing caused by pulse front tilt (PFT) with SSTF scheme in Ref. [26].
Fig. 7. Optical micrographs of line (a) and square (b) written on the back surface of 3 mm thick fused silica glass substrate with SSTF OV scheme. The scanning directions are indicated by red arrows, scale bar is 20 µm.
To investigate the influence of number of pulses N on ablation, we measured the variation of the internal and external diameters with different number of pulses N on the back surface of 3 mm thickness fused silica glass, the pulse energy was set to be 32 µJ. The number of laser pulses N ranging from 50 to 180 was controlled by an electromechanical shutter. The results are summarized in Fig. 8(a). It is obvious that the external diameters increase with the number of pulses N, eventually tending to level off at high number of pulses. But the internal diameters reduced with N, eventually approaches zero at high number of pulses. When N increases to 180, the external diameter Dex was measured to be 29.4 µm, and the internal diameter Din = 3.2 µm. This trend is related to both the progressive reduction of the fluence threshold for ablation associated to the accumulation effects described by incubation behavior in Ref. [17,33].
Fig. 8. Variation of the internal diameter (Din, black data points) and external diameter (Dex, red data points) as a function of the number of pulses N with the SSTF OV scheme, optical micrograph (b) and the corresponding SEM image (c) of ablation with the number of pulses N = 200. Pulse energy E = 32 µJ. Scale bar is 30 µm.
Figure 8(b) shows the optical micrograph of ablation feature on the back surface of 3 mm thickness fused silica glass with the number of pulses N = 200 at 32 µJ, the doughnut-shaped ablation feature seems to disappear, the external diameter Dex was measured to be 29.5 µm. Figure 8(c) shows the corresponding SEM image of ablation feature in Fig. 8(b). It is obvious that a deep ablation crater has formed under high fluence vortex pulses, this condition typically corresponds to the progressive formation of a deep ablation crater, which can be advantageous for femtosecond laser drilling processing.
To experimentally demonstrated the capability of efficient drilling in thick glass with SSTF vortex pulses, we drilled microchannels from the back surface of 3 mm thick fused silica glass at different writing speed. At the beginning of the experiment, vortex beam was focused at the back surface of 3 mm thickness silica glass which was in direct contact with purified water. It should be noted that purified water played an important role in microchannels drilling because the inflow water would disperse ablated material and debris, which benefit the elongation of microchannels. The glass substrate was translated in the downward direction at a constant speed using the motorized micro-stage. The writing speed was fixed at 5 µm/s and the pulse energy was set to be 32 µJ. The measurements of the fabricated microchannels were also carried out using a transilluminated optical microscope (Leica DM2700M).
Before drilling microchannels, we firstly ablated the back surface of silica glass with the number of pulses N = 200 to observe the ablation features. Figure 9(a) shows the optical micrograph of the ablation craters along the propagation axis near the back surface of 3 mm thick fused silica glass with SSTF OV scheme, it can be seen that there are obvious ablation craters near the back surface of silica glass, and the depth of craters along the propagation axis is ∼ 50 µm, which is conducive to material removal along axis direction and has potential in drilling from the back surface of transparent substrates. Figure 9(c) is the corresponding cross sectional profiles of Fig. 9(a). The shape of the cross sectional profiles of craters is nearly round with a diameter of ∼29.5 µm. It should be noted that the characteristics of ablation profiles near the tip are consistent with the intensity distribution of SSTF OV scheme. Figure 9(b) shows the optical micrograph of the drilled microchannels at different writing speed ranging from 5 µm/s to 20 µm/s, the pulse energy was set to be 32 µJ. Figure 9(d) is the corresponding cross sectional profiles. It can be seen that the fabricated microchannels have smooth edge and there are no signatures of microcracks formed in the microchannels. The cross sectional profiles of microchannels were nearly round-shaped, the diameters of drilled channels were mesured to be 29.5 µm, 29.3 µm, 29.2 µm, 29.0 µm, the lengths of the microchannels were measured to be 823 µm, 762 µm, 733 µm and 720 µm respectively, the maximum aspect ratio of microchannels achieved in our experiment is ∼28. The length of the fabricated microchannel has a limitation because more and more debris generated at the irradiated region will gather together as the length of the microchannel increased, which interrupt the subsequent microchannel fabrication.
Fig. 9. Optical micrographs of craters (a) ablated with the number of pulses N = 200 and microchannels (b) drilled from the back surface of a 3 mm thick silica glass at different speed with SSTF OV scheme. Writing speed in (b) (from left to right): 5 µm/s, 10 µm/s, 15 µm/s and 20 µm/s, laser pulse energy: 32 µJ. (c) and (d) are corresponding cross sectional profiles of (a) and (b), respectively, scale bar is 50 µm.
It should be noted that with CF OV scheme, microchannel can hardly drilled on the back surface of 3 mm thick glass substrate for the same machining parameters. Compared with CF OV scheme, SSTF OV scheme can generate higher aspect ratios microchannels from the back surface of transparent dielectrics, particularly for low NA focal lenses.
5. Conclusion
To conclude, we have theoretically and experimentally demonstrated that a better confinement of intensity distribution along the propagation direction can be achieved with the SSTF OV scheme than the CF OV scheme, and shown the potential of using the SSTF scheme for doughnut-shaped ablation and high aspect ratio drilling on the back surface of 3 mm thick soda-lime glass and fused silica, which is impossible to achieve with CF OV scheme. It is flexible to tune the intensity distributions along the propagation direction by controlling the spatial chirp of the incident pulse at the back aperture of the lens, which provide a new manipulating dimension for optical vortex. SSTF OV can provide new manipulating dimensions for both SSTF technique and optical vortex, such as pulse width, spatial dispersion and topological charge, which will be useful for light manipulation and femtosecond laser micromachining. We expect that the technique can be used for fabrication of high throughput and high-aspect-ratio microchannels in other transparent materials such as polymers and crystals.
Funding
National Natural Science Foundation of China (11874243, 11974218, 12004221, 12104266, 12104268, 12192254, 91750201); Postdoctoral Innovation Talents Support Program of Shandong Province (SDBX2019005); National Key Research and Development Program of China (2019YFA0705000); Innovation Group of Jinan (2018GXRC010); Local Science and Technology Development Project of the Central Government (YDZX20203700001766); Natural Science Foundation of Shandong Province (ZR2021ZD02).
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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