Development of a Simulation Method of Three-Dimensional Ultrafine Processing by Femtosecond Laser Shunsuke Nabetani 1, a, Hideki Aoyama 1, b * 1, 2, c

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1 Development of a Simulation Method of Three-Dimensional Ultrafine Processing by Femtosecond Laser Shunsuke Nabetani 1, a, Hideki Aoyama 1, b * 1,, c, Masahiro Ueda Yoshinori Ogawa 1,, d 1,, 3, e, and Kazuo Yamazaki 1 Keio University, Hiyoshi, Kohoku-ku, Yokohama, 3-85 Japan 511A Etcheverry Hall, University of California, Berkeley, CA C, Bainer Hall, University of California, Davis, CA a nabetani@ddm.sd.keio.ac.jp, b haoyama@sd.keio.ac.jp, c m-ueda@berkeley.edu d y-ogawa@berkeley.edu, e kyamazaki@ucdavis.edu Keywords: femtosecond laser, processing simulation, laser ablation Abstract. A femtosecond laser can achieve high quality processing for multiple materials without thermal metamorphism; therefore, it can be applied to ultrafine processing of advanced functional materials that are difficult to machine. For high quality and high efficiency processing of difficult-to-machine materials, it is necessary to characterize the laser material interactions and develop a laser processing simulation and CAM (Computer Aided Manufacturing) systems. In this study, a simulation method for processing three-dimensional ultrafine shapes using a femtosecond laser is developed. Introduction A femtosecond laser is a pulsed laser with a pulse width in the femtosecond range; this enables high precision processing of high-hardness materials that are otherwise difficult to cut and dielectric materials that are difficult to process using conventional laser systems and electric discharge machining [1, ]. Therefore, femtosecond lasers are expected to be used to process materials that have useful properties, such as sapphire and diamond, but are otherwise difficult to process. In order to process materials to a desired shape using a femtosecond laser, a CAM (Computer Aided Manufacturing) system based on the ablation characteristics is required. However, to the best of our knowledge, such a system has not been developed. The femtosecond laser processing method has a shortcoming that affects the development of a CAM system: it is difficult to predict the processed shape. As such, it is necessary to profile the processed shape under various conditions (such as laser parameters, material properties, scanning speed, and processing path). While it is essential to conduct experiments to investigate processing characteristics, trial and error experimental approaches are costly and inefficient. Therefore, a simulation system based on experimental results and the principles of interactions between femtosecond lasers and materials is required. A three-dimensional processing simulation system using a femtosecond laser enables reproduction of the processed shape under various conditions with only the basic experimental data, and such a system is greatly useful for the development of the CAM system. In processing using a femtosecond laser, a phenomenon called "ablation," which is the process of removing material by focusing and irradiating the laser pulse onto a surface, is utilized. It is necessary to experimentally investigate the ablation characteristics of the material of interest in the development of the simulation system. Experimental investigation of ablation characteristics for various substances has been reported [3, 4]. In this study, the focus is on dependence of the ablation rate on the fluence for prediction of the processed shape. The ablation rate is the depth that can be processed per pulse. It was reported in a previous study

2 that the processed shape can be predicted using measurement data of the fluence dependence of the ablation rate [5], because the laser intensity distribution corresponds to the processed shape in femtosecond laser processing. By utilizing this property, three-dimensional processing simulations can be realized from experimental data. Based on the above, in this study, a femtosecond laser processing simulation method focusing on the fluence-dependence of ablation rate is proposed. First, a simulation method of single-shot ablation is proposed and evaluated for the measured shape. Then, the method is extended to simulations using multi-shot ablation, and pocket fabrication by scanning irradiation is simulated. Simulation of Single-shot Ablation Simulation Method. In this study, a threedimensional processing simulation method is proposed based on the principle that the processed shape depends on the intensity distribution of the beam of the femtosecond laser. The simulation program is written using Microsoft Visual C The simulation results are displayed using MATLAB. The flow of the simulation is as follows. First, as shown in the left side of Fig. 1, the surface of the material on which the laser pulse is irradiated is divided into a uniform mesh. The incident fluence on each mesh point can be calculated from Eq. (1) using the radial distance from the center axis of the beam r [6]: F r r = F exp ω, (1) where F is the peak fluence and ω is the beam spot radius. Next, the ablation rate L corresponding to the incident fluence F is calculated from the fitting function of the measurement data. For the fitting function, the following logarithmic function of degree n is used: ln ln n L= a + a1 F + + a F. () n Laser Pulse Distance Distance r r Fig. 1 Ablation model Degree n is in the range of 1 to 3, and determined a value at which the fitting curve fits the measurement data most. The mesh point height is set according to the height of the target material and is divided by 1/1 of the surface mesh size. By lowering the mesh point height per the ablation rate calculated from Eq., the processed shape is simulated as shown on the right side of Fig. 1. Comparison of Simulation Results and Measurement Data. Using the proposed simulation method, single-shot ablation of corundum is simulated. Data on fluence dependence of ablation rate was extracted from the plot of measurement data by Guizard et al. [7]. Fig. shows the results of fitting Eq. to the measurement data with for n = 3. The obtained fitting function is expressed by Eq. 3:

3 3 L= ln F 7. ln F ln F. (3) Simulations are performed using Eq. 3. The distance between mesh points are 1 nm. The simulation result of a crater formed by vertically irradiating a corundum surface with a laser pulse of peak fluence 5.5 J/cm is shown in Fig. 3. The beam spot radius at full-width half-maximum (FWHM) was set to 1 μm, similar to that in Ref. [7]. This result is compared with the data extracted from the crater shape plot measured by Guizard et al. [7]. Since the measurement data is the shape of the cross section of the crater, it is compared with a cross section parallel to the y-z plane passing through the Fig. Ablation rate versus fluence [7] beam axis of the simulation result. The results of the comparison are shown in Fig. 4. The crater shape of the simulation result is qualitatively close to the crater measured. The maximum depth and the hole diameter were set as evaluation criteria, and the respective values are summarized in Table 1. Percentage error is obtained from Eq. 4. The percentage errors in the maximum depth and the hole diameter are 1% and 4%, respectively, and the usefulness of the simulation method is confirmed. ( Measurement Value) ( Simulation Value) ( Measurement Value) Error Rate = 1. (4) Fig. 3 Simulation result of singleshot ablation Fig. 4 Comparison of sectional shapes of craters [7] Table 1 Maximum depth and crater diameter comparisons Data Maximum Depth [nm] Crater Diameter [μm] Measurement Simulation

4 Simulation of Multi-shot Ablation Extension of Simulation Method. When a material is processed using a femtosecond laser, processing is performed by multi-shot ablation, in which repeated pulses irradiate the target. Since the shape of the material changes during processing, the laser is not normally incident. Therefore, in order to simulate multi-shot ablation, it is necessary to extend the abovementioned simulation method to take the influence of the angle of incidence into account. In the case of non-normal incidence, it is necessary to take into account the change in the direction of travel of light inside the material due to refraction, and the change in intensity reflectance. Considering the above, reconstruct the model of the ablation. In the proposed simulation method, ablation by a laser pulse is modeled as a set of ablations by each laser pulse incident on a mesh point. First, model the pulse as a set of rays. As shown in Fig. 5(a), each ray advances in the refraction direction per the ablation rate corresponding to the incident fluence. Incident fluence is calculated based on the Gaussian distribution and then corrected based on the intensity reflectance [8]. Then, as shown in Fig. 5(b), it is assumed that the ray has a cylindrical volume and the material in that cylindrical area with the ray as its central axis is removed. A set of removal regions formed by each ray is taken as a processed shape, and the mesh point height is changed accordingly to model the ablation by laser pulses. Similar to the single-shot case, a fitting function for the fluence dependency of the ablation rate is used for calculation of the ablation rate. Incidence Surface Ray of Laser Angle of Incidence Ray of Laser Incidence Surface Removal Area Refraction Angle Ablation Rate (a) Fig. 5 Ablation model (b) When simulation is performed according to this model, it is necessary to set the incidence surface in order to define the angle of incidence of each ray. For this reason, as shown in Fig. 6, the least squares plane, where the square of the height difference from the mesh point of interest and surrounding points is minimized, is regarded as the incidence surface. The angle of incidence, the intensity reflectance, and the refraction vector can be obtained from the normal vector of the incidence surface. The direction of travel of the ray after refraction is determined by the obtained refraction vector. Incidence Surface Incidence Point Fig. 6 Setting of incidence surface

5 When simulating multi-shot ablation with this model, the incident fluence on each mesh point cannot be calculated from Eq. (1) because the incident fluence depends not only on r but also z, axial distance from the beam s waist. The beam spot radius on z is expressed as [9]: ω ( r) 1 λz = ω + πω, (5) The pulse energy is expressed as: E pulse πω F z z = (, ) = π rf r z dr, (6) Then, from Eq. (1), (5) and (6), the incident fluence can be calculated as: E, exp pulse r = F rz πω ( z) ω ( z), (7) Simulation Result. Simulation of pocket fabrication by multi-shot ablation is performed using the proposed 3 μm method. The distance between mesh points are 1 5 nm. As with simulation of a single-shot, the peak 5 μm fluence was set to 5.5 J/cm and the beam spot radius 4 was set to 1 μm (FWHM). Scanning irradiation was 3 performed in the path shown in Fig. 7 with a spacing of 1 μm between pulses in the x direction. The laser Y 1 wavelength was set at 8 nm, and the refractive index of corundum was set at Fig. 8(a) shows a pocket X of 1 layer, and Fig. 8(b) shows a pocket of 1 layers. Since there is no measurement data for multi-shot Fig. 7 Scanning path ablation, it is not possible to compare and verify the proposed method at this time. However, if the usefulness of this simulation method can be confirmed, it would be possible to simulate processed shape with arbitrary laser parameters and in arbitrary scanning paths, which could be useful for CAM system development. (a) (b) Fig. 8 Simulation results of pocket fabrication

6 Conclusion In this research, a simulation method based on experimental data was proposed for the development of a femtosecond laser processing CAM system. In the proposed method, the focus was on dependence of the ablation rate on the fluence, and single-shot ablation was simulated by correlating the distribution of incident fluence to the crater shape. The usefulness of the proposed method was confirmed by comparison with measurement data. Then, a simulation method for multi-shot ablation was proposed by extending this method to include the influences of reflection and refraction in the case of non-normal incidence. As a result, processing simulation with arbitrary laser parameters and in arbitrary scanning paths was achieved. In future work, multi-shot ablation simulation results will be compared with experimental results, and the proposed method will be evaluated for suitability. Furthermore, the number of pulses and repetition rate dependence of ablation rate [4, 1] will be incorporated into the simulation. References [1] C. Momma, B.N. Chekhov, S. Nolte, F. von Alvensleben, A. Tünnermann, H. Welling, B. Wellegehausen, Short-pulse laser ablation of solid targets, Optics Communications, Vol. 19 (1996), pp [] D. Ashkenasi, A. Rosenfeld, H. Varel, M. Wähmer, E.E.B. Campbell, Laser processing of sapphire with picosecond and sub-picosecond pulses, Applied Surface Science, Vol. 1 (1997), pp [3] M. Hashida, A. Semerok, O. Gobert, G. Petite, J.-F. Wagner, Ablation thresholds of metals with femtosecond laser pulses, Proceedings of SPIE, Vol. 443, Nonresonant Laser-Matter Interaction (NLMI-1) (1), pp [4] M.E. Shaheen, J.E. Gagnon, B.J. Fryer, Experimental study on 785 nm femtosecond laser ablation of sapphire in air, Laser Physics Letters, Vol. 1, No. 6 (15), 6613 (9 pp). [5] M. Fujita, M. Hashida, Femtosecond-Laser Processing, Journal of Plasma and Fusion Research, Vol. 81 (5), pp [6] A. Ben-Yakar, R.L. Byer, Femtosecond laser ablation properties of borosilicate glass, Journal of Applied Physics, Vol. 96, No. 9 (4), pp [7] S. Guizard, A. Semerok, J. Gaudin, M. Hashida, P. Martin, F. Quéré, Femtosecond laser ablation of transparent dielectrics: measurement and modelisation of crater profiles, Applied Surface Science, Vol. 186 (), pp [8] E. Hecht, Optics, 4th Ed. (), pp.111-1, Addison Wesley. [9] O. Svelto, Principle of Lasers, 5th Ed. (1), p.153. [1] J. Cheng, W. Perrie, S. P. Edwardson, E. Fearon, G. Dearden, K.G. Watkins, Effects of laser operating parameters on metals micromachining with ultrafast lasers, Applied Surface Science, Vol. 56 (9), pp