December 1, 2013 / Vol. 38, No. 23 / OPTICS LETTERS
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Shape control of elemental distributions inside a glass by simultaneous femtosecond laser irradiation at multiple spots Masaaki Sakakura,1,* Torataro Kurita,2 Masahiro Shimizu,2 Kouhei Yoshimura,2 Yasuhiko Shimotsuma,2 Naoaki Fukuda,1 Kazuyuki Hirao,2 and Kiyotaka Miura2 1
Hitachi Zosen Collaborative Research Division, Office of Society-Academia Collaboration for Innovation, Kyoto University, Kyoto 615-8520, Japan 2 Department of Material Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan *Corresponding author: [email protected]‑u.ac.jp Received August 21, 2013; revised October 18, 2013; accepted October 21, 2013; posted October 22, 2013 (Doc. ID 196056); published November 19, 2013 The spatial distributions of elements in a glass can be modulated by irradiation with high repetition rate femtosecond laser pulses. However, the shape of the distribution is restricted to being axially symmetric about the laser beam axis due to the isotropic diffusion of photo-thermal energy. In this study, we describe a method to control the shape of the elemental distribution more flexibly by simultaneous irradiation at multiple spots using a spatial light modulator. The accumulation of thermal energy was induced by focusing 250 kHz fs laser pulses at a single spot inside an alumino–borosilicate glass, and the transient temperature distribution was modulated by focusing 1 kHz laser pulses at four spots in the same glass. The resulting modification was square-shaped. A simulation of the mean diffusion length of molten glass demonstrated that the transient diffusion of elements under heat accumulation and repeated temperature elevation at multiple spots caused the square shape of the distribution. © 2013 Optical Society of America OCIS codes: (320.2250) Femtosecond phenomena; (140.3390) Laser materials processing; (140.6810) Thermal effects; (230.6120) Spatial light modulators. http://dx.doi.org/10.1364/OL.38.004939
Glasses can have a variety of properties, because various functional elements can be dissolved in the glass matrix [1]. Therefore, luminescence, refractive index, thermal expansion coefficients, and other physical and chemical properties of glasses have been finely tuned by changing the kinds and concentration of elements. However, the spatial distribution of these properties is difficult to control by conventional glass production methods (i.e., melt-quenching and sol-gel). One candidate technique for local modification of glass properties is laser processing [2–11]. In particular, femtosecond (fs) laser processing has been investigated as a powerful technique to modify the properties of glass three dimensionally [3–11]. Recently, several researchers found that irradiation of glass with focused fs laser pulses at high repetition rate (100 kHz–1 MHz) induces local melting around the focal region, and the elemental distribution changes in the molten region [5–14]. This laser-induced elemental distribution change allows for larger property and structural modifications in a local volume inside glasses, such as local generation of phase-separated structures [14], crystals [5,7,10] and nanoclusters [11]. However, the shape of the elemental distribution is always circular, because the shape of the molten region depends on that of the heated volume around the photoexcited region, which is radially symmetric about the beam axis [12–14]. In this study, we show that the shape of the fs laser-induced elemental distributions can be controlled more flexibly by simultaneous irradiation at multiple spots inside a glass. In this method, local melting was induced by higher repetition rate irradiation (250 kHz) at a single point, and the shape change of the elemental distribution was induced by irradiation at 0146-9592/13/234939-04$15.00/0
lower repetition rate (1 kHz) at multiple spots using a spatial light modulator [15,16]. Irradiations were performed in an alumino–borosilicate glass [52SiO2 − 9B2 O3 − 17Al2 O3 − 22CaOwt:%]. A schematic illustration of the fs laser irradiation system is shown in Fig. 1(a). We used high repetition rate (250 kHz, pulse width ∼80 fs; Coherent Inc., Mira-RegA) and low repetition rate (1 kHz; pulse width ∼120 fs; Coherent Inc., Mira-Legend) amplified fs lasers, which generated laser pulses with a central wavelength of 800 nm. The polarization orientations of the fs laser pulses at 1 kHz and
Fig. 1. (a) Experimental setup for simultaneous multispot irradiation with 1 kHz and 250 kHz fs laser pulses. M are mirrors; L1, L2: lenses (f 300 mm and 125 mm, respectively). (b) Schematic illustration of multispot fs laser irradiation inside a glass. (c) Phase hologram to modulate the 1 kHz fs laser pulses. (d) Simulated light intensity distribution at the focus. © 2013 Optical Society of America
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250 kHz were perpendicular to each other, and these laser pulses were mixed by a polarization beam splitter. The laser pulses were reflected by a spatial light modulator (LCOS–SLM, Hamamatsu) and focused inside a glass sample with an objective lens (Nicon, LU-Plan, 50×, NA 0.55) after passing a telescope with magnification of about 0.42. This LCOS–SLM could modulate the phase distribution of only horizontally polarized light. In this experiment, the polarization orientation of the 1 kHz laser pulses was horizontal and that of 250 kHz pulses was vertical. Therefore, only the spatial phase distributions of the 1 kHz laser pulses were modulated by the SLM. 250 kHz laser pulses without modulation were focused at a single spot inside a glass sample. At the same time, 1 kHz pulses were focused at multiple positions inside the sample by selecting a phase hologram on the SLM [Fig. 1(b)]. The phase hologram [Fig. 1(c)] was calculated by the Optimal Rotation Angle method [17]. To examine the element distributions in the modified region, a columnar modification was produced by translating the sample parallel to the beam axis at 2 μm/s. After the laser irradiation, the glass was polished to expose the modified region, and the elemental distributions in the modified region were analyzed with an Electron Probe Microanalyzer (EPMA; JXA-8100, JEOL). Figure 2(a) shows a transmission optical microscope image of the modification inside an alumino–borosilicate glass after irradiation with only focused 250 kHz laser pulses at the center. The pulse energy was about 2.0 μJ, and the exposure time was 5 s. During laser exposure, a bright emission appeared around the photoexcited region [the left image of Fig. 2(a)]. After the laser irradiation [the right image of Fig. 2(a)], a circular modification with mainly two boundaries appeared around the laser focal region [6,8,9,12–14]. The glass inside the inner boundary had been molten during laser exposure, because the material flow was observed in this region. On the other hand, in the outer ring structure, no material
Fig. 2. (a) Transmission optical microscope images of the modification during (left) and (b) after (right) irradiation with 250 kHz laser pulses at the center and those with multispot irradiation (250 kHz at the center and 1 kHz at the surrounding four spots). (c) and (d) Distributions of elements by EPMA in the modifications after single spot and multiple spot irradiation, respectively. The color bars indicate the signal intensities in EPMA. The signal intensities at unmodified regions are 100.
flow was observed during laser irradiation, but this structure has been attributed to visco–elastic deformation due to thermal expansion of the central heated region during laser irradiation [13]. A different modification was formed by focusing 250 kHz laser pulses at a single spot and 1 kHz laser pulses of 8 μJ/pulse-spot at four spots inside the same glass [Fig. 2(b)]. The four focal spots of the 1 kHz pulses were located at the vertices of a square 35 μm on a side, as shown in Fig. 1(d). The focal spot of the 250 kHz pulses was located at the symmetry center of the four spots. During laser irradiation, the glass in the central region became molten, and the molten region spread gradually to the four photoexcited points. After the 5 s laser irradiation, the inner boundary of the modification became square-shaped, while the outer boundary remained circular. Because the flow of molten glass during laser exposure was observed only in the square-shaped region, the squared-shaped boundary corresponds to the inner boundary of Fig. 2(a). To compare the elemental distribution change in the two modifications, we measured the EPMA mapping of Si, Ca, Al, and O [Figs. 2(c) and 2(d)]. The results show that the shapes of the elemental distributions are different between the two modifications, but the tendencies of the distributions of each element are similar; Si was located in the central region, while Ca was localized near the inner boundary and Al was located just at the inner region of the Ca-localized region. The oxygen atoms were distributed to compensate the electron charge in the modified region. The signals of B, which were not shown because of weak signal, were slightly larger near the inner boundary. The tendencies of these distributions are summarized in Fig. 3. These trends are the same as those in previously reported papers [6,9,18]. The former glass network (SiO2 ) migrates to the central region, while the modifiers (CaO) migrate to the boundary of the molten region [1,19]. Because Al2 O3 is an intermediate species [19], it is concentrated slightly inside the Ca-rich region. The remarkable point of the result by multispot irradiation is the noncircular shape of the elemental distribution. Several experiments suggested that elemental distribution is determined by the temperature distribution during laser exposure [9,18]. For example, Shimizu et al. showed that CaO components move to lower
Fig. 3. Schematic illustration of elemental distribution changes and heat modification after fs laser irradiation at a high repetition rate in the case of (a) 250 kHz irradiation at the center and (b) 250 kHz irradiation at the center and 1 kHz irradiation at the surrounding four points.
December 1, 2013 / Vol. 38, No. 23 / OPTICS LETTERS
temperature regions whereas SiO2 components move to higher temperature regions. Also, Luo et al. demonstrated a correlation between elemental distribution and temperature distribution during laser exposure. To clarify the relationship between the temperature distribution and the shape of the elemental migration region, the temperature distributions during laser irradiation were simulated. The temperature distribution was calculated by solving the thermal diffusion equation with repeated heating at 1 kHz on four spots, and that at 250 kHz on a single spot. The equations for the calculation are the same as those in [8]. The positions of the heated regions are the same as those of the photoexcited region in the experiment. We assumed that the heat sources were Gaussian-shaped and parameters for them are listed in Table 1. The material parameters for the simulation were thermal diffusion coefficient, Dth 0.54 μm2 μs−1 , heat capacity, C p 0.75 JK−1 g−1 and the density of the glass, ρ 2.6 gcm−3 . Figure 4(a) shows the simulated temperature distributions at 500 ms Δt μs after the onset of irradiation with 250 and 1 kHz pulses. Δt is the time after the 501st shot of the 1 kHz laser pulse. Heat accumulation occurred due to the repeated heating at 250 kHz at the center. At Δt 0 μs, the temperatures in the surrounding four regions were elevated by the photoexcitation with 1 kHz laser pulses. After that, the temperature distribution changed gradually by thermal diffusion, and the spatial temperature modulation at the four regions almost disappeared by Δt 250 μs. We confirmed that similar temperature distribution changes were repeated until the shutoff of the repeated photoexcitation (heating in the simulation). Although the shape of the elemental migration region looks similar to the contour line of 1000°C at Δt 50 μs, this transient temperature distribution disappears so quickly that it cannot explain the shape of the elemental distributed region. Inside a glass at high temperature, elements can migrate where the viscosity is low enough, and the viscosities of glasses decrease continuously with increasing temperature. Therefore, we estimated the boundary of the molten region based on the viscosity and diffusion constants of elements using the simulated timedependent temperature distribution. If we assumed that neutral components such as SiO2 and CaO diffused in the molten glass, the diffusion coefficient (DM ) can be evaluated by the Stokes–Einstein equation [22]:
DM T
kB T ; 6πηTr M
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(1)
where kB is the Boltzmann constant, T is temperature, ηT is the viscosity of the molten glass at the temperature of T, and r M is the radius of the diffusing component. For rough evaluation of DM , we calculated the diffusion constant by r M 0.1 nm, which is on the order of the radius of an ion [22]. Because the viscosity during laser exposure is dependent on time, we evaluated the mean diffusion length during laser exposure by the following equation: Z LD x; y
0
texp
0.5 DM Tt; x; ydt ;
(2)
where t is the time after the irradiation by the first pulse, x; y is the position, texp is the exposure time of 250 kHz and 1 kHz fs laser pulses, and Tt; x; y is the timedependent temperature distribution during laser exposure. For the temperature-dependent viscosity of the glass, we used the viscosity data of a borosilicate glass and interpolated values by Fulcher’s equation [1]. Figure 4(b) shows the distribution of the mean diffusion length at various exposure times of multispot irradiation (texp ). The region in which the mean diffusion length is longer than 1 μm (yellow–red colored region) becomes larger and gradually approaches a rounded square shape. We defined the region of LD > 1 μm as the migration region, because this length is enough for an elemental distribution change to be detected. After the 5 s laser exposure, the simulation migration region became very similar to that of the experiment. To compare the simulations, optical microscope images of the modifications inside an alumino–borosilicate glass
Table 1. Parameters for Simulation of Temperature Distribution Changea
The center (250 kHz) Four points (1 kHz)
Δtp μs
QμJ
wth μm
lz μm
4 1000
1.5 6.0
4.0 4.0
20 20
a Δtp : pulse interval; Q: generated thermal energy after a single photoexcitation at each spot; wth and lz : transverse width and longitudinal length (in the beam axis) of the heated region by a single photoexcitation, respectively. We assumed that at least 75% of laser pulse energy was transformed to thermal energy based on the evaluations in [20] and [21].
Fig. 4. (a) Simulated temporal evolution of temperature distribution inside a glass after 1 kHz irradiation at 500 ms after the onset of multiple spot laser irradiation. (b) Spatial distributions of simulated mean diffusion length of molten glass at various laser exposure times. (c) Transmission optical microscope images of modifications induced by simultaneous multispot fs laser irradiation in various exposure times. (d) Magnified images of the dotted red-squared region of (c).
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This research was supported by JSPS Grant-in-Aid for Young Scientists (B), No. 22750187 and Scientific Research (A), No. 23246121.
Fig. 5. Triangle, square, and hexagonal shapes of molten regions produced inside an alumino–borosilicate glass by irradiation with 250 kHz fs laser pulses at the center and 1 kHz fs laser pulses at three, four, and six spots, respectively.
by various exposure times are shown in Fig. 4(c). At 0.1 s, the molten region around the center and the 1 kHz photoexcited regions were separated completely. At 0.5 s it seemed that the molten glass had been ready to flow from the 1 kHz heated region toward the central region [This is indicated by a black arrow in Fig. 4(d)]. In the simulation [Fig. 4(b)], the region of LD < 1 μm between the central region and the 1 kHz heated regions was too thick for the molten glass to flow between the two regions at 0.1 s. After 0.5 s, the simulation shows that the mean diffusion length in the same regions becomes longer than 1 μm, suggesting that the molten glass could begin to flow between the two regions. After 1 s, this region of molten glass flow became wider [Fig. 4(d)], and finally the entire molten region became square-shaped. The simulation of the mean diffusion length also shows that the region of LD > 1 μm approached a square shape by 5 s. Therefore, the temporal evolution of the molten region in the experiment could be partially reproduced by the simulation of the mean diffusion length. However, this simulation does not take into account the thermal conduction caused by the flow of molten glass. To simulate the flow of molten glass more precisely, simulation of thermic fluid dynamics with thermal expansion at each photoexcitated region will be necessary to predict the shape of the elemental distribution. In conclusion, a square-shaped elemental distribution could be formed by simultaneous irradiation at multiple spots inside an alumino–borosilicate glass with 250 and 1 kHz laser pulses. The shape of the distribution could be partially explained by the mean diffusion length of molten glass under heat accumulation by 250 kHz irradiation and repeated temperature elevation by 1 kHz irradiation. Beyond just a square shape, we have succeeded in making various modified shapes using the same technique, as shown in Fig. 5. This technique will enable more flexible spatial control of properties inside various glasses.
References 1. K. Varshneya, Fundamentals of Inorganic Glasses (Academic, 1994). 2. R. Sato, Y. Benino, T. Fujiwara, and T. Komatsu, J. NonCryst. Solids 289, 228 (2001). 3. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996). 4. C. B. Schaffer, A. Brodeur, J. F. García, and E. Mazur, Opt. Lett. 26, 93 (2001). 5. Y. Yonesaki, R. Araki, K. Miura, K. Fujita, and K. Hirao, J. Non-Cryst. Solids 351, 885 (2005). 6. S. Kanehira, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 023112 (2008). 7. A. Stone, M. Sakakura, Y. Shimotsuma, G. Stone, P. Gupta, K. Miura, K. Hirao, V. Dierolf, and H. Jain, Opt. Express 17, 23284 (2009). 8. M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010). 9. F. Luo, B. Qian, G. Lin, J. Xu, Y. Liao, J. Song, H. Sun, B. Zhu, J. Qiu, Q. Zhao, and Z. Xu, Opt. Express 18, 6262 (2010). 10. C. X. Fan, B. Poumellec, M. Lancry, X. He, H. D. Zeng, A. Erraji-Chahid, Q. M. Liu, and G. R. Chen, Opt. Lett. 37, 2955 (2012). 11. J. Choi, M. Bellec, A. Royon, K. Bourhis, G. Papon, T. Cardinal, L. Canioni, and M. Richardson, Opt. Lett. 37, 1029 (2012). 12. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Y. Arai, Opt. Express 13, 4708 (2005). 13. M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008). 14. M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, Appl. Phys. A 100, 1001 (2010). 15. Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, Appl. Phys. Lett. 87, 031101 (2005). 16. M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, Opt. Express 18, 12136 (2010). 17. J. Bengtsson, Appl. Opt. 33, 6879 (1994). 18. M. Shimizu, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, K. Hirao, and K. Miura, Opt. Lett. 36, 2161 (2011). 19. K.-H. Sun, J. Am. Ceram. Soc. 30, 277 (1947). 20. M. Shimizu, M. Sakakura, M. Ohnishi, M. Yamaji, Y. Shimotsuma, K. Hirao, and K. Miura, Opt. Express 20, 934 (2012). 21. I. Miyamoto, A. Horn, and J. Gottmann, J. Laser Micro Nanoen. 2, 7 (2007). 22. P. Atkins and J. de Paula, Physical Chemistry (Oxford University, 2006), Chap. 21.
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Shape control of elemental distributions inside a glass by simultaneous femtosecond laser irradiation at multiple spots Masaaki Sakakura,1,* Torataro Kurita,2 Masahiro Shimizu,2 Kouhei Yoshimura,2 Yasuhiko Shimotsuma,2 Naoaki Fukuda,1 Kazuyuki Hirao,2 and Kiyotaka Miura2 1
Hitachi Zosen Collaborative Research Division, Office of Society-Academia Collaboration for Innovation, Kyoto University, Kyoto 615-8520, Japan 2 Department of Material Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan *Corresponding author: [email protected]‑u.ac.jp Received August 21, 2013; revised October 18, 2013; accepted October 21, 2013; posted October 22, 2013 (Doc. ID 196056); published November 19, 2013 The spatial distributions of elements in a glass can be modulated by irradiation with high repetition rate femtosecond laser pulses. However, the shape of the distribution is restricted to being axially symmetric about the laser beam axis due to the isotropic diffusion of photo-thermal energy. In this study, we describe a method to control the shape of the elemental distribution more flexibly by simultaneous irradiation at multiple spots using a spatial light modulator. The accumulation of thermal energy was induced by focusing 250 kHz fs laser pulses at a single spot inside an alumino–borosilicate glass, and the transient temperature distribution was modulated by focusing 1 kHz laser pulses at four spots in the same glass. The resulting modification was square-shaped. A simulation of the mean diffusion length of molten glass demonstrated that the transient diffusion of elements under heat accumulation and repeated temperature elevation at multiple spots caused the square shape of the distribution. © 2013 Optical Society of America OCIS codes: (320.2250) Femtosecond phenomena; (140.3390) Laser materials processing; (140.6810) Thermal effects; (230.6120) Spatial light modulators. http://dx.doi.org/10.1364/OL.38.004939
Glasses can have a variety of properties, because various functional elements can be dissolved in the glass matrix [1]. Therefore, luminescence, refractive index, thermal expansion coefficients, and other physical and chemical properties of glasses have been finely tuned by changing the kinds and concentration of elements. However, the spatial distribution of these properties is difficult to control by conventional glass production methods (i.e., melt-quenching and sol-gel). One candidate technique for local modification of glass properties is laser processing [2–11]. In particular, femtosecond (fs) laser processing has been investigated as a powerful technique to modify the properties of glass three dimensionally [3–11]. Recently, several researchers found that irradiation of glass with focused fs laser pulses at high repetition rate (100 kHz–1 MHz) induces local melting around the focal region, and the elemental distribution changes in the molten region [5–14]. This laser-induced elemental distribution change allows for larger property and structural modifications in a local volume inside glasses, such as local generation of phase-separated structures [14], crystals [5,7,10] and nanoclusters [11]. However, the shape of the elemental distribution is always circular, because the shape of the molten region depends on that of the heated volume around the photoexcited region, which is radially symmetric about the beam axis [12–14]. In this study, we show that the shape of the fs laser-induced elemental distributions can be controlled more flexibly by simultaneous irradiation at multiple spots inside a glass. In this method, local melting was induced by higher repetition rate irradiation (250 kHz) at a single point, and the shape change of the elemental distribution was induced by irradiation at 0146-9592/13/234939-04$15.00/0
lower repetition rate (1 kHz) at multiple spots using a spatial light modulator [15,16]. Irradiations were performed in an alumino–borosilicate glass [52SiO2 − 9B2 O3 − 17Al2 O3 − 22CaOwt:%]. A schematic illustration of the fs laser irradiation system is shown in Fig. 1(a). We used high repetition rate (250 kHz, pulse width ∼80 fs; Coherent Inc., Mira-RegA) and low repetition rate (1 kHz; pulse width ∼120 fs; Coherent Inc., Mira-Legend) amplified fs lasers, which generated laser pulses with a central wavelength of 800 nm. The polarization orientations of the fs laser pulses at 1 kHz and
Fig. 1. (a) Experimental setup for simultaneous multispot irradiation with 1 kHz and 250 kHz fs laser pulses. M are mirrors; L1, L2: lenses (f 300 mm and 125 mm, respectively). (b) Schematic illustration of multispot fs laser irradiation inside a glass. (c) Phase hologram to modulate the 1 kHz fs laser pulses. (d) Simulated light intensity distribution at the focus. © 2013 Optical Society of America
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250 kHz were perpendicular to each other, and these laser pulses were mixed by a polarization beam splitter. The laser pulses were reflected by a spatial light modulator (LCOS–SLM, Hamamatsu) and focused inside a glass sample with an objective lens (Nicon, LU-Plan, 50×, NA 0.55) after passing a telescope with magnification of about 0.42. This LCOS–SLM could modulate the phase distribution of only horizontally polarized light. In this experiment, the polarization orientation of the 1 kHz laser pulses was horizontal and that of 250 kHz pulses was vertical. Therefore, only the spatial phase distributions of the 1 kHz laser pulses were modulated by the SLM. 250 kHz laser pulses without modulation were focused at a single spot inside a glass sample. At the same time, 1 kHz pulses were focused at multiple positions inside the sample by selecting a phase hologram on the SLM [Fig. 1(b)]. The phase hologram [Fig. 1(c)] was calculated by the Optimal Rotation Angle method [17]. To examine the element distributions in the modified region, a columnar modification was produced by translating the sample parallel to the beam axis at 2 μm/s. After the laser irradiation, the glass was polished to expose the modified region, and the elemental distributions in the modified region were analyzed with an Electron Probe Microanalyzer (EPMA; JXA-8100, JEOL). Figure 2(a) shows a transmission optical microscope image of the modification inside an alumino–borosilicate glass after irradiation with only focused 250 kHz laser pulses at the center. The pulse energy was about 2.0 μJ, and the exposure time was 5 s. During laser exposure, a bright emission appeared around the photoexcited region [the left image of Fig. 2(a)]. After the laser irradiation [the right image of Fig. 2(a)], a circular modification with mainly two boundaries appeared around the laser focal region [6,8,9,12–14]. The glass inside the inner boundary had been molten during laser exposure, because the material flow was observed in this region. On the other hand, in the outer ring structure, no material
Fig. 2. (a) Transmission optical microscope images of the modification during (left) and (b) after (right) irradiation with 250 kHz laser pulses at the center and those with multispot irradiation (250 kHz at the center and 1 kHz at the surrounding four spots). (c) and (d) Distributions of elements by EPMA in the modifications after single spot and multiple spot irradiation, respectively. The color bars indicate the signal intensities in EPMA. The signal intensities at unmodified regions are 100.
flow was observed during laser irradiation, but this structure has been attributed to visco–elastic deformation due to thermal expansion of the central heated region during laser irradiation [13]. A different modification was formed by focusing 250 kHz laser pulses at a single spot and 1 kHz laser pulses of 8 μJ/pulse-spot at four spots inside the same glass [Fig. 2(b)]. The four focal spots of the 1 kHz pulses were located at the vertices of a square 35 μm on a side, as shown in Fig. 1(d). The focal spot of the 250 kHz pulses was located at the symmetry center of the four spots. During laser irradiation, the glass in the central region became molten, and the molten region spread gradually to the four photoexcited points. After the 5 s laser irradiation, the inner boundary of the modification became square-shaped, while the outer boundary remained circular. Because the flow of molten glass during laser exposure was observed only in the square-shaped region, the squared-shaped boundary corresponds to the inner boundary of Fig. 2(a). To compare the elemental distribution change in the two modifications, we measured the EPMA mapping of Si, Ca, Al, and O [Figs. 2(c) and 2(d)]. The results show that the shapes of the elemental distributions are different between the two modifications, but the tendencies of the distributions of each element are similar; Si was located in the central region, while Ca was localized near the inner boundary and Al was located just at the inner region of the Ca-localized region. The oxygen atoms were distributed to compensate the electron charge in the modified region. The signals of B, which were not shown because of weak signal, were slightly larger near the inner boundary. The tendencies of these distributions are summarized in Fig. 3. These trends are the same as those in previously reported papers [6,9,18]. The former glass network (SiO2 ) migrates to the central region, while the modifiers (CaO) migrate to the boundary of the molten region [1,19]. Because Al2 O3 is an intermediate species [19], it is concentrated slightly inside the Ca-rich region. The remarkable point of the result by multispot irradiation is the noncircular shape of the elemental distribution. Several experiments suggested that elemental distribution is determined by the temperature distribution during laser exposure [9,18]. For example, Shimizu et al. showed that CaO components move to lower
Fig. 3. Schematic illustration of elemental distribution changes and heat modification after fs laser irradiation at a high repetition rate in the case of (a) 250 kHz irradiation at the center and (b) 250 kHz irradiation at the center and 1 kHz irradiation at the surrounding four points.
December 1, 2013 / Vol. 38, No. 23 / OPTICS LETTERS
temperature regions whereas SiO2 components move to higher temperature regions. Also, Luo et al. demonstrated a correlation between elemental distribution and temperature distribution during laser exposure. To clarify the relationship between the temperature distribution and the shape of the elemental migration region, the temperature distributions during laser irradiation were simulated. The temperature distribution was calculated by solving the thermal diffusion equation with repeated heating at 1 kHz on four spots, and that at 250 kHz on a single spot. The equations for the calculation are the same as those in [8]. The positions of the heated regions are the same as those of the photoexcited region in the experiment. We assumed that the heat sources were Gaussian-shaped and parameters for them are listed in Table 1. The material parameters for the simulation were thermal diffusion coefficient, Dth 0.54 μm2 μs−1 , heat capacity, C p 0.75 JK−1 g−1 and the density of the glass, ρ 2.6 gcm−3 . Figure 4(a) shows the simulated temperature distributions at 500 ms Δt μs after the onset of irradiation with 250 and 1 kHz pulses. Δt is the time after the 501st shot of the 1 kHz laser pulse. Heat accumulation occurred due to the repeated heating at 250 kHz at the center. At Δt 0 μs, the temperatures in the surrounding four regions were elevated by the photoexcitation with 1 kHz laser pulses. After that, the temperature distribution changed gradually by thermal diffusion, and the spatial temperature modulation at the four regions almost disappeared by Δt 250 μs. We confirmed that similar temperature distribution changes were repeated until the shutoff of the repeated photoexcitation (heating in the simulation). Although the shape of the elemental migration region looks similar to the contour line of 1000°C at Δt 50 μs, this transient temperature distribution disappears so quickly that it cannot explain the shape of the elemental distributed region. Inside a glass at high temperature, elements can migrate where the viscosity is low enough, and the viscosities of glasses decrease continuously with increasing temperature. Therefore, we estimated the boundary of the molten region based on the viscosity and diffusion constants of elements using the simulated timedependent temperature distribution. If we assumed that neutral components such as SiO2 and CaO diffused in the molten glass, the diffusion coefficient (DM ) can be evaluated by the Stokes–Einstein equation [22]:
DM T
kB T ; 6πηTr M
4941
(1)
where kB is the Boltzmann constant, T is temperature, ηT is the viscosity of the molten glass at the temperature of T, and r M is the radius of the diffusing component. For rough evaluation of DM , we calculated the diffusion constant by r M 0.1 nm, which is on the order of the radius of an ion [22]. Because the viscosity during laser exposure is dependent on time, we evaluated the mean diffusion length during laser exposure by the following equation: Z LD x; y
0
texp
0.5 DM Tt; x; ydt ;
(2)
where t is the time after the irradiation by the first pulse, x; y is the position, texp is the exposure time of 250 kHz and 1 kHz fs laser pulses, and Tt; x; y is the timedependent temperature distribution during laser exposure. For the temperature-dependent viscosity of the glass, we used the viscosity data of a borosilicate glass and interpolated values by Fulcher’s equation [1]. Figure 4(b) shows the distribution of the mean diffusion length at various exposure times of multispot irradiation (texp ). The region in which the mean diffusion length is longer than 1 μm (yellow–red colored region) becomes larger and gradually approaches a rounded square shape. We defined the region of LD > 1 μm as the migration region, because this length is enough for an elemental distribution change to be detected. After the 5 s laser exposure, the simulation migration region became very similar to that of the experiment. To compare the simulations, optical microscope images of the modifications inside an alumino–borosilicate glass
Table 1. Parameters for Simulation of Temperature Distribution Changea
The center (250 kHz) Four points (1 kHz)
Δtp μs
QμJ
wth μm
lz μm
4 1000
1.5 6.0
4.0 4.0
20 20
a Δtp : pulse interval; Q: generated thermal energy after a single photoexcitation at each spot; wth and lz : transverse width and longitudinal length (in the beam axis) of the heated region by a single photoexcitation, respectively. We assumed that at least 75% of laser pulse energy was transformed to thermal energy based on the evaluations in [20] and [21].
Fig. 4. (a) Simulated temporal evolution of temperature distribution inside a glass after 1 kHz irradiation at 500 ms after the onset of multiple spot laser irradiation. (b) Spatial distributions of simulated mean diffusion length of molten glass at various laser exposure times. (c) Transmission optical microscope images of modifications induced by simultaneous multispot fs laser irradiation in various exposure times. (d) Magnified images of the dotted red-squared region of (c).
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OPTICS LETTERS / Vol. 38, No. 23 / December 1, 2013
This research was supported by JSPS Grant-in-Aid for Young Scientists (B), No. 22750187 and Scientific Research (A), No. 23246121.
Fig. 5. Triangle, square, and hexagonal shapes of molten regions produced inside an alumino–borosilicate glass by irradiation with 250 kHz fs laser pulses at the center and 1 kHz fs laser pulses at three, four, and six spots, respectively.
by various exposure times are shown in Fig. 4(c). At 0.1 s, the molten region around the center and the 1 kHz photoexcited regions were separated completely. At 0.5 s it seemed that the molten glass had been ready to flow from the 1 kHz heated region toward the central region [This is indicated by a black arrow in Fig. 4(d)]. In the simulation [Fig. 4(b)], the region of LD < 1 μm between the central region and the 1 kHz heated regions was too thick for the molten glass to flow between the two regions at 0.1 s. After 0.5 s, the simulation shows that the mean diffusion length in the same regions becomes longer than 1 μm, suggesting that the molten glass could begin to flow between the two regions. After 1 s, this region of molten glass flow became wider [Fig. 4(d)], and finally the entire molten region became square-shaped. The simulation of the mean diffusion length also shows that the region of LD > 1 μm approached a square shape by 5 s. Therefore, the temporal evolution of the molten region in the experiment could be partially reproduced by the simulation of the mean diffusion length. However, this simulation does not take into account the thermal conduction caused by the flow of molten glass. To simulate the flow of molten glass more precisely, simulation of thermic fluid dynamics with thermal expansion at each photoexcitated region will be necessary to predict the shape of the elemental distribution. In conclusion, a square-shaped elemental distribution could be formed by simultaneous irradiation at multiple spots inside an alumino–borosilicate glass with 250 and 1 kHz laser pulses. The shape of the distribution could be partially explained by the mean diffusion length of molten glass under heat accumulation by 250 kHz irradiation and repeated temperature elevation by 1 kHz irradiation. Beyond just a square shape, we have succeeded in making various modified shapes using the same technique, as shown in Fig. 5. This technique will enable more flexible spatial control of properties inside various glasses.
References 1. K. Varshneya, Fundamentals of Inorganic Glasses (Academic, 1994). 2. R. Sato, Y. Benino, T. Fujiwara, and T. Komatsu, J. NonCryst. Solids 289, 228 (2001). 3. K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996). 4. C. B. Schaffer, A. Brodeur, J. F. García, and E. Mazur, Opt. Lett. 26, 93 (2001). 5. Y. Yonesaki, R. Araki, K. Miura, K. Fujita, and K. Hirao, J. Non-Cryst. Solids 351, 885 (2005). 6. S. Kanehira, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 023112 (2008). 7. A. Stone, M. Sakakura, Y. Shimotsuma, G. Stone, P. Gupta, K. Miura, K. Hirao, V. Dierolf, and H. Jain, Opt. Express 17, 23284 (2009). 8. M. Shimizu, M. Sakakura, M. Ohnishi, Y. Shimotsuma, T. Nakaya, K. Miura, and K. Hirao, J. Appl. Phys. 108, 073533 (2010). 9. F. Luo, B. Qian, G. Lin, J. Xu, Y. Liao, J. Song, H. Sun, B. Zhu, J. Qiu, Q. Zhao, and Z. Xu, Opt. Express 18, 6262 (2010). 10. C. X. Fan, B. Poumellec, M. Lancry, X. He, H. D. Zeng, A. Erraji-Chahid, Q. M. Liu, and G. R. Chen, Opt. Lett. 37, 2955 (2012). 11. J. Choi, M. Bellec, A. Royon, K. Bourhis, G. Papon, T. Cardinal, L. Canioni, and M. Richardson, Opt. Lett. 37, 1029 (2012). 12. S. M. Eaton, H. Zhang, P. R. Herman, F. Yoshino, L. Shah, J. Bovatsek, and A. Y. Arai, Opt. Express 13, 4708 (2005). 13. M. Sakakura, M. Shimizu, Y. Shimotsuma, K. Miura, and K. Hirao, Appl. Phys. Lett. 93, 231112 (2008). 14. M. Shimizu, K. Miura, M. Sakakura, M. Nishi, Y. Shimotsuma, S. Kanehira, T. Nakaya, and K. Hirao, Appl. Phys. A 100, 1001 (2010). 15. Y. Hayasaki, T. Sugimoto, A. Takita, and N. Nishida, Appl. Phys. Lett. 87, 031101 (2005). 16. M. Sakakura, T. Sawano, Y. Shimotsuma, K. Miura, and K. Hirao, Opt. Express 18, 12136 (2010). 17. J. Bengtsson, Appl. Opt. 33, 6879 (1994). 18. M. Shimizu, M. Sakakura, S. Kanehira, M. Nishi, Y. Shimotsuma, K. Hirao, and K. Miura, Opt. Lett. 36, 2161 (2011). 19. K.-H. Sun, J. Am. Ceram. Soc. 30, 277 (1947). 20. M. Shimizu, M. Sakakura, M. Ohnishi, M. Yamaji, Y. Shimotsuma, K. Hirao, and K. Miura, Opt. Express 20, 934 (2012). 21. I. Miyamoto, A. Horn, and J. Gottmann, J. Laser Micro Nanoen. 2, 7 (2007). 22. P. Atkins and J. de Paula, Physical Chemistry (Oxford University, 2006), Chap. 21.
