## Abstract

Massively parallel femtosecond laser processing with more than 1000 beams was demonstrated. Parallel beams were generated by a computer-generated hologram (CGH) displayed on a spatial light modulator (SLM). The key to this technique is to optimize the CGH in the laser processing system using a scheme called in-system optimization. It was analytically demonstrated that the number of beams is determined by the horizontal number of pixels in the SLM *N*_{SLM} that is imaged at the pupil plane of an objective lens and a distance parameter *p*_{d} obtained by dividing the distance between adjacent beams by the diffraction-limited beam diameter. A performance limitation of parallel laser processing in our system was estimated at *N*_{SLM} of 250 and *p*_{d} of 7.0. Based on these parameters, the maximum number of beams in a hexagonal close-packed structure was calculated to be 1189 by using an analytical equation.

© 2016 Optical Society of America

## 1. Introduction

Femtosecond laser processing is a promising tool for fabricating novel and useful structures on the surfaces of and inside materials. An enormous number of pulse irradiation points will be required for fabricating actual structures with millimeter to centimeter scale, and therefore, the throughput of femtosecond laser processing must be improved for practical adoption of this technique. One promising method to improve throughput is parallel pulse generation based on a computer-generated hologram (CGH) displayed on a spatial light modulator (SLM), a technique called holographic femtosecond laser processing [1]. The method has also been applied to shaped beam fabrication [2] and single-shot three-dimensional (3D) fabrication [3]. The holographic method has the following advantages:

- • Improved throughput of laser processing with beam splitting and beam shaping.
- • Improved light use efficiency. A typical pulse energy irradiated from a femtosecond Ti:sapphire regenerative amplifier is the order of 1 mJ, and the pulse energy required to perform an ablation of glass is several 10 nJ. To bridge the gap between these energies, the parallel processing method is very useful.
- • Variable patterning by using an SLM to perform reconfigurable beam shaping, which enables novel laser processing schemes. In addition, coordinated control of scanning devices, such as galvanometer scanners and motor- and piezo-driven stages, is very important for industrial laser processing [4,5].
- • 3D processing. Control of the axial profiles of the beams in addition to their lateral profiles allows 3D structures to be formed inside transparent materials [3,6,7]. For instance, the fabrication of high-aspect-ratio nanochannels in glass using single-shot femtosecond Bessel beams generated by a diffractive axicon lens has been demonstrated [8].
- • Instantaneous processing. There are many difficulties in processing at the proper position when a target moves and deforms. Laser processing requires feedback control implemented with a beam-position detection system and a beam steering system. The parallelism reduces the number of required position and shape measurements.
- • Correction of the optical system. Typically, spherical aberrations originating from a refractive index mismatch between the immersion medium of an objective lens and a target transparent material can be corrected using a CGH [9,10]. Spatial non-uniformity of the modulation properties and spatial frequency properties of an SLM was corrected by calculating a suitable CGH [11,12]. This is also effective for compensating unknown static imperfections in an optical system; that is, in-system optimization was performed to correct them [13–15].
- • Adaptive correction of the optical system. A CGH can be adaptively optimized to compensate for dynamic unpredictable mechanical movements and air disturbances.

Due to these advantages, holographic manipulation of femtosecond laser pulses has been used in a number of applications, such as two-photon microscopy [16], two-photon polymerization [17–21], optical waveguide fabrication [22–24], fabrication of volume optical devices [25,26], and cell transfection [27]. It has also been applied to surface nano-structuring [28], which is a useful application of the femtosecond laser processing [29–32]. However, all of these studies were merely for basic scientific research or proof-of-principle demonstrations; therefore, for more-practical industrial applications, the processing throughput needs to be drastically improved.

A high throughput can be achieved by improving the laser source and beam steering system. In holographic laser processing, which is one method of beam steering, it is important to increase the number of parallel beams. However, it may be very difficult to realize a high-degree of parallelism because of undefined imperfections in holographic laser processing systems. Therefore, there have been no studies that estimated the theoretical and experimental limitations of holographic laser processing.

In this paper, we describe the challenges faced in realizing massively-parallel femtosecond laser processing. Analytical estimations give the maximum number of parallel beams. We found that the maximum number of beams is determined by the number of pixels in the SLM at the pupil plane of an objective lens and a distance parameter that is obtained by dividing the distance between adjacent beams by the diffraction-limited beam diameter. We also present experimental results of massively-parallel femtosecond laser processing with more than 1000 beams.

## 2. Analysis of the number of parallel beams

#### 2.1 Processing throughput of parallel laser processing

The processing throughput *T*_{P} (*s*^{−1}) is defined by the number of fabricated points per unit time. If a fixed CGH is used, the processing throughput, *T*_{P}, is expressed as

*f*

_{rep},

*N*

_{parallel}, and

*N*

_{pulse}are the repetition rate of the laser, the number of parallel beams generated by the CGH, and the number of pulse shots required to fabricate a desired structure, respectively. Moreover, in actual laser processing, laser pulses are delivered using scanning devices, such as beam scanner and mechanical movement stages, to perform large-area processing.

If a variable CGH displayed on an SLM is used to fabricate a different structure for each pulse repetition, the processing throughput depends on the refresh frequency of the SLM, *f*_{SLM}, and the processing throughput in Eq. (1) is given by replacing *f*_{rep} with *f*_{SLM}. Hence a larger *N*_{parallel} is required to perform a higher throughput because *f*_{SLM} < *f*_{rep} at present.

#### 2.2 Number of parallel beams

In principle, *N*_{parallel} is simply given by the total number of pixels in the SLM; in practice however, it is given by the size of the focused beams, which is determined by the diffraction of light and the spatial frequency response of the SLM. The distance between two adjacent diffraction spots *D*_{spot} is given by

*d*

_{Airy}= ~0.5λ/

*NA*is the full width at half maximum (FWHM) of the Airy disk diameter in the diffraction beam, λ is the wavelength,

*NA*is the numerical aperture of the objective lens,

*F*

_{OL}is the focal length of the objective lens,

*W*

_{pupil}is the diameter of the pupil of the objective lens, and

*p*

_{d}is a distance parameter. According to our previous work [33], the minimum

*p*

_{d}was estimated to be 2.80, and

*p*

_{d}depended on the size of focused beam, including its side lobe.

On the Fourier reconstruction plane of the CGH, the diffraction beams are arranged in a circular area with a radius *R* defined as the distance from the optical axis. Using the paraxial approximation, *R* is expressed as

*ν*is the spatial frequency of the CGH on the SLM that generates a diffraction beam, and

*M*is the magnification of the optical system. When the aperture of the SLM is imaged on the pupil of the objective lens for effective use of the pixels of the SLM and to achieve a diffraction-limited focal spot diameter of the objective lens, that is,

*M*=

*W*

_{pupil}/

*W*

_{SLM}, where

*W*

_{SLM}is the side length (shorter) of the aperture of the SLM, the maximum radius

*R*

_{SLM}depends on the horizontal number of pixels in the SLM imaged on the pupil of the objective lens,

*N*

_{SLM}, as follows

*ν*

_{SLM}is the maximum spatial frequency that the SLM is capable of.

The spatial frequency response of an ordinary SLM decreases with increasing *ν*. Therefore, *ν* should be limited to an appropriate value *ν*_{a} (<*ν*_{SLM}), and the circular area in which the diffraction beams are arranged is also limited to the radius *R*_{a} ( = *α R*_{SLM}, 0 < *α* ≤ 1). Here, *N*_{parallel} is determined by the number of beams arranged on the radius, that is, the ratio of *R*_{a} to *D*_{spot}. This is denoted as *n*, and by rearranging Eqs. (2) and (4) we have

*n*is proportional to

*N*

_{SLM}(the horizontal number of pixels in the SLM) and

*α*(which is related to the spatial frequency response of the SLM) and is inversely proportional to

*p*

_{d}(the distance parameter that depends on the diffraction of the beam).

#### 2.3 Two-dimensional hexagonal close-packed structure

If the diffraction beams are arranged in a two-dimensional hexagonal close-packed structure as shown in Fig. 1, *N*_{parallel} is larger than in the case of a hexagon inscribed in a circle with a radius of *R*_{a} and smaller than in the case of a hexagon that circumscribes a circle, that is to say,

Figure 2 shows how *N*_{parallel} depends on *p*_{d} and *αN*_{SLM}. The filled circles indicate the computer simulation results (*p*_{d} = 4.1, 6.2, 8.2, 10.3), and the open circles indicate the results of the experiments (*p*_{d} = 6.2, 6.7, 7.2, 7.7, 10.3) described in detail later. The solid curves are obtained from fitting the following equation

*C*

_{1}= 3.20 and

*C*

_{2}= 3.55. These coefficients were 3 <

*C*

_{1}< 2$\sqrt{3}$ and 3 <

*C*

_{2}< 4, from Eq. (6). We found that

*N*

_{parallel}was well characterized with the quadratic function of

*n*shown in Eq. (5). For example, 1,000, 3,000, and 10,000 beams will be achieved by

*αN*

_{SLM}of 203, 355, and 653, respectively, with

*p*

_{d}= 6.2. It is noted that naturally the maximum

*N*

_{parallel}is also given by dividing the total pulse energy of the light source by the pulse energy required to process the target material.

## 3. In-system optimization of CGH

Even if a CGH is optimized to have a diffraction efficiency of more than 99% and a uniformity of more than 99% in a computer, the reconstruction of the CGH in an actual optical system degrades due to imperfections of the optical system, including the aberrations of lenses, the imperfect laser beam profile, the spatial frequency response and spatial non-uniform modulation of the SLM, and slight misalignments. The degradation becomes more apparent as the degree of parallelism increases. In order to perform massively parallel laser processing, the CGH should be optimized in the actual laser processing system used, because it is difficult to perfectly reproduce the imperfections in a computer. This so-called in-system optimization automatically cancels out imperfections. In our previous research, we adopted the optimal-rotation-angle (ORA) algorithm for optimizing a CGH [34], and a modified version of that algorithm was applied in the present work to parallel laser processing. The algorithm is described as follows.

The relationship between the amplitude *a*_{h} and phase *ϕ*_{h}^{(i)} at a pixel *h* on the CGH plane, and the complex amplitude *U*_{r}^{(i)} at a pixel *r* on the reconstruction plane in the *i*-th iterative process is described as,

*ϕ*

_{hr}is the phase contribution from the light propagation from

*h*on the CGH plane to

*r*on the reconstruction plane, and

*w*

_{r}

^{(i)}is a weight coefficient to control the diffraction light intensity at

*r*. In order to maximize the sum of the diffraction light intensities, Σ

_{r}|

*U*

_{r}

^{(i)}|

^{2}, the phase variation Δ

*ϕ*

_{h}

^{(i)}added to

*ϕ*

_{h}

^{(i)}at

*h*is calculated using the following equations:

*ϕ*

_{r}is the phase at pixel

*r*on the reconstruction plane. The phase of the CGH,

*ϕ*

_{h}

^{(i)}, is then updated with the calculated Δ

*ϕ*

_{h}

^{(i)}:Furthermore, in order to control the light intensity at pixel

*r*on the reconstruction plane,

*w*

_{r}

^{(i)}is also updated based on the diffraction light intensity estimated by the optical reconstruction in the actual setup using the following equation:

*I*

_{r}

^{(i)}= |

*U*

_{r}

^{(i)}|

^{2}is the optical light intensity at

*r*in the

*i*-th iterative process,

*I*

_{r}

^{d}is the desired light intensity, and

*α*

_{ORA}is a constant. The phase variation Δ

*ϕ*

_{h}

^{(i)}and the weight coefficient

*w*

_{r}

^{(i)}are optimized by the above iterative process from Eqs. (9)-(11) until

*I*

_{r}

^{(i)}is nearly equal to

*I*

_{r}

^{d}.

## 4. Experimental setup

Figure 3 shows the holographic femtosecond laser processing system, which is mainly composed of an amplified femtosecond laser system (Coherent, Micra and Legend Elite), a liquid-crystal on silicon SLM (LCOS-SLM; Hamamatsu, X10468-02, effective region:16 × 12 mm, pixel number:800 × 600), imaging and focusing optics, and a personal computer (PC; Intel Core i5 3.20 GHz, 2 GB RAM). The femtosecond pulse had a center wavelength of 800 nm, a spectral width of 8 nm FWHM, a pulse width of 110 fs, and a repetition frequency of 1 kHz, and was fed to a CGH displayed on the LCOS-SLM through a prism mirror (PM). The spectrum width was set to prevent a pulse dispersion. The reconstruction was divided by a beam sampler (BS) and was captured by a cooled charge coupled device (CCD) image sensor (BITRAN, BU-50LN). The PC evaluated the uniformity of the reconstructed images and recalculated the CGH using the modified ORA method. The reconstruction was optimized until sufficiently uniform intensity was obtained, and was directed to the optics, containing a 60 × objective lens (OL) with NA = 0.85 (Edmund Optics, *f* = 3.09 mm) through a λ/4 wave plate (QWP) in order to adjust the polarization to a circular one because the shape of focused spot slightly depends on the polarization of the light in the case of high NA [35]. The number of pulse shots was controlled by a mechanical shutter (SH; NM Laser Products, LS055). The processing was observed with an observation system including a halogen lamp (HL), a dichroic mirror (DM), an infrared (IR) cut filter, and a complementary metal oxide semiconductor (CMOS) image sensor (Lumenara, Lu125M), which is used for the alignment of the laser processing system. The sample was super white crown glass (Schott, B270). The irradiation pulse energy at the SLM plane, *E*_{SLM}, and the average energy of each spot on the sample plane, *E*_{sample}, were obtained as follows. First, the ratio *E*^{R}_{SLM} between the energy at the SLM plane and the energy split off by the BS arranged in front of SLM was estimated. In addition, the ratio *E*^{R}_{sample} between the energy at the sample plane and the energy split off by the BS was also measured. The total irradiation pulse energy on the SLM plane and the sample plane were continuously monitored using a power meter, as the product of the energy split off by the BS and these ratios. As a result, *E*_{sample} is equal to the total irradiation energy divided by the number of diffraction spots. In our system, *E*^{R}_{SLM} and *E*^{R}_{sample} were 77.0 and 13.6, respectively. In one combination, the parameters *p*_{d} and *αN*_{SLM} were set to 7.70 and 252 pixel, respectively. Therefore, the number of parallel beams *N*_{parallel} was estimated to be 1005 by using Eq. (7). The structure fabricated by laser processing was observed in detail using an optical microscope (OLYMPUS, LEXT OLS4000) after the experiment.

## 5. Experimental results

Figure 4(a) shows an optical reconstruction of a CGH optimized only in a computer, which is the conventional method, and its intensity profile on the line indicated by the gray arrow. The number of parallel beams *N*_{parallel} was 1005 (*p*_{d} = 7.70 and *αN*_{SLM} = 252). The CGH optimization with 100 iterations required about 124 minutes in the case of a CGH with 800 × 600 pixels. The central spot in the reconstruction was the non-diffracted 0-th order light. Several methods to cancel the 0-th order light have been reported [9,36]. These methods are useful, however, a computational cost of CGH design and a complexity of the optical setup increases. Therefore, the 0-th order remained in the reconstruction. The uniformity *U*, defined as the ratio of the maximum and the minimum peak intensities in the reconstruction, was 0.32. The average (*AVG*) and the standard deviation (*SD*) of the peak intensities were 116 and 27, respectively. The intensity *I* was measured as an 8-bit signal for the captured image obtained by the cooled CCD image sensor. The actual quality of the reconstruction was low, although the reconstruction in the computer had *U* > 0.99. In particular, the peak intensities in the high-spatial-frequency region were obviously low, as a result of the spatial frequency response of the SLM. Figure 4(b) shows the optical reconstruction optimized only in the computer and its intensity profile, in the case where the spatial frequency response of the SLM in the computational reconstruction was taken into account [12]. The optical reconstruction was also degraded to *U* = 0.46, *AVG* = 176, and *SD* = 23, due to unknown properties of the optical system, although the beams arranged in a high-spatial-frequency area were improved. The reconstruction in the computer was also degraded to *U* = 0.81 (see the solid curve in Fig. 4(d)) because of mutual interference between the side lobes and high-order diffraction peaks. Figure 4(c) shows the optical reconstruction of the CGH optimized using the in-system optimization. *U* was improved to 0.84 (see the filled circles in Fig. 4(d)). This value was comparable to the computational reconstruction in which the spatial frequency response of the SLM was taken into account, with *AVG* = 131 and *SD* = 4. In particular, the intensities in the high-frequency region were significantly enhanced. Figure 4(d) shows the change of *U* with increasing number of iterations in the CGH optimization process. The solid line indicates the optimization process in the computer with the spatial frequency response of the SLM taken into account, shown in Fig. 4(b). The filled circles indicate the process with the in-system optimization, shown in Fig. 4(c). They showed almost the same performance. This means that the in-system optimization reached the limit of the optical system performance. This is the first demonstration of CGH optimization for multiple beams with a high degree of parallelism with high uniformity.

Figure 5 shows massively parallel femtosecond laser processing of a glass surface. The parallel beams shown in Fig. 4 were used. Figure 5(a) shows optical microscope images of the structure processed by the reconstruction shown in Fig. 4(a). The processing was performed with five pulse shots with gradually increasing average pulse energy *E*_{sample}. In the images, the gray and white circles indicate positions with and without a pit fabricated by the pulse irradiation. In the inset of the figure, *N*_{pit} indicates the number of fabricated pits. Mainly the center part of the reconstruction was processed, despite the increase of *E*_{sample}. Figure 5(b) shows optical microscope images of the structure processed by the reconstruction shown in Fig. 4(b). The processing was discretely performed in the reconstruction with the increase of the *E*_{sample} because the intensity distribution became more uniform. Figure 5(c) shows optical microscope images of the structure processed by the reconstruction shown in Fig. 4(c). The two images arranged right the figure are magnified optical microscope images showing the results without and with the in-system optimization when *E*_{sample} was set to 50 and 49 nJ, respectively. Improved quality in the fabricated structure was experimentally demonstrated. Figure 5(d) shows *N*_{pit} versus *E*_{sample} without (dashed and dot lines) and with (solid line) the in-system optimization, corresponding to Figs. 4(a), 4(b) and 4(c), respectively. In the results without the optimization, *R*_{E} = 0.16 and 0.24, corresponding to the dashed and dotted lines, respectively, where *R*_{E} represents the ratio between the minimum energy required to process a single pit and the minimum energy required to make *N*_{pit} = *N*_{parallel}. In the result obtained with the optimization, *R*_{E} was improved to 0.29. As a result of the optimization, the energy required to fabricate over 1000 pits was decreased from 69 nJ and 60 nJ to 49 nJ, respectively.

In order to investigate the performance limitations and achievable quality in parallel laser processing for various combinations of the parameters *p*_{d} and *αN*_{SLM}, reconstructions with a variety of *N*_{parallel} were applied to laser processing. Figures 6(a) and 6(b) and Figs. 6(i) and 6(j) show optical reconstructions of CGH and optical microscope images of structures fabricated on a glass surface with *N*_{parallel} = 379, 700, 1088, 1125 and 1317, respectively. The images in the upper and bottom rows show the results without (with the optimization only in the computer) and with the in-system optimization of the CGH, respectively. In each laser processing, *p*_{d}, *αN*_{SLM} and *E*_{sample} were set as shown in the figure. In the case of *αN*_{SLM} $\le $ 210 and 7.7 $\le $ *p*_{d} (*N*_{parallel} = 379 and 700), there was no major difference relating to *N*_{pit} and the quality of the structure between the results without and with the in-system optimization in spite of the improvement of the quality of the reconstruction, because the uniformities *U* in the optical reconstructions used in Figs. 6(a) and 6(c) were relatively high (0.42 and 0.36, respectively) compared with the result obtained with *N*_{parallel} = 1005. In addition, *E*_{sample} is sufficiently larger than the threshold energy required to process the glass (see the threshold energy in Fig. 5(d)). On the other hand, in the case of 210 $\le $ *αN*_{SLM} and *p*_{d} $\le $ 7.2 (*N*_{parallel} = 1088, 1125 and 1317), the difference between the results without and with the in-system optimization was clearly observed from the microscope images because *U* in the optical reconstructions used in Figs. 6(e), 6(g) and 6(i) were 0.32, 0.33 and 0.31, respectively. It means that the in-system optimization is absolutely essential for massively parallel laser processing when *N*_{parallel} is over 1000. The processing quality of the results with the in-system optimization (Figs. 6(f), 6(h) and 6(j)) also gradually decreased with increasing *αN*_{SLM} and decreasing *p*_{d} from the microscope images. Therefore, the performance limitation of massively parallel laser processing in our system was estimated at *αN*_{SLM} $\approx $ 250 and *p*_{d} $\approx $ 7.0. Based on these parameters, the maximum *N*_{parallel} was calculated to be 1189 by using Eq. (7).

The maximum value of *αN*_{SLM} was predictable from the spatial frequency response of the SLM. However, the minimum value of *p*_{d} was 2.5-times larger than the value of our previous work [33]. The reason for the discrepancy was assumed to be as follows. In the previous work, the minimum *p*_{d} = 2.8 was evaluated from the optical reconstruction captured by an image sensor. When *p*_{d} was actually set to 3.0, the quality of the fabricated structure was unexpectedly undesirable due to mutual interference between the side lobes of the diffraction beam. This is because the energy required to fabricate the glass sample is quite high compared with that required to capture the reconstruction. Therefore, the minimum *p*_{d} in the actual laser processing is usually larger than that evaluated from the optical reconstruction.

## 6. Conclusion

We demonstrated massively parallel femtosecond laser processing with more than 1000 beams. The number of parallel beams, *N*_{parallel}, which is related to the processing throughput, is mathematically given by the number of pixels in the SLM, *αN*_{SLM}, imaged on the pupil plane of the objective lens and the distance parameter, *p*_{d}, which is obtained by dividing the distance between adjacent beams by the diffraction-limited beam diameter. *αN*_{SLM} and *p*_{d} were limited by the spatial frequency response of the SLM and the diffraction limitation of the focused beam, respectively. In our system, the maximum values of *αN*_{SLM} and *p*_{d} were experimentally estimated to be 250 and 7.00, respectively. Based on these parameters, the maximum *N*_{parallel} was calculated to be 1189 by using an analytical equation.

In massively parallel laser processing of glass samples, it was experimentally demonstrated that in-system optimization of the CGH is a key method in realizing 1k-laser processing. In the case of laser processing with *N*_{parallel} = 1005, 1005 pits were successfully fabricated with irradiation pulse energies of *E*_{sample} = 59 nJ at the sample plane and *E*_{SLM} = 0.337 mJ at the SLM plane. The energy at the SLM plane was sufficiently less than the damage threshold of the SLM. We believe that our results give the useful knowledge to perform massively holographic femtosecond laser processing in practical industrial applications.

## Acknowledgments

This work was supported by Grant-in-Aid for Scientific Research (B) and Challenging Exploratory Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan and by Nippon Sheet Glass Foundation for Materials Science and Engineering.

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