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Local melting and modulation of elemental distributions can be induced inside a glass by focusing femtosecond (fs) laser pulses at high repetition rate (>100 kHz). Using only a single beam of fs laser pulses, the shape of the molten region is ellipsoidal, so the induced elemental distributions are often circular and elongate in the laser propagation direction. In this study, we show that the elongation of the fs laser-induced elemental distributions inside a soda-lime glass could be suppressed by parallel fsing of 250 kHz and 1 kHz fs laser pulses. The thickness of a Si-rich region became about twice thinner than that of a single 250 kHz laser irradiation. Interestingly, the position of the Si-rich region depended on the relative positions between 1 kHz and 250 kHz photoexcited regions. The observation of glass melt during laser exposure showed that the vortex flow of glass melt occurred and it induced the formation of a Si-rich region. Based on the simulation of the transient temperature and viscosity distributions during laser exposure, we temporally interpreted the origin of the vortex flow of glass melt and the mechanism of the formation of the Si-rich region.
© 2014 Optical Society of America
1. Introduction
Local heat accumulation inside a glass by irradiation with focused fs laser pulses at a high repetition rate can be used to induce local melting inside a glass [1–16]. In the melting region, formation of crystals [10–12], nanoparticles [13] or microbubbles [14] can be induced, so a number of researchers have used the heat accumulation phenomena to modify local properties inside various glasses. One of interesting phenomena induced by heat accumulation inside a glass is a spatial modulation of glass elements in the molten region [6–9]. Because various properties of a glass, such as chemical durability, refractive index, phase stability, and so on, depend on the composition of elements of the glass [17], the spatial modification of elemental distributions can serve as a space-selective control of these properties inside glasses. For example, our research group demonstrated space-selective phase separation in a Na2O-SiO2 glass by modifying the concentration of Na2O in the molten region by fs laser irradiation at 250 kHz [9].
However, there is a problem in the fs laser-induced modification of elemental distributions; the shape of the distribution is restricted to a circular or ellipsoidal shape [6–10]. In addition, the spatial confinement of the localized elements is relatively low, because the elemental distributions along the laser propagation axis spread in the laser propagation direction [8, 10]. The circular or ellipsoidal shape of the elemental distributions and the low spatial confinement are attributed to the thermal diffusion [1–5], because one of the determining factors of the shape of the elemental distribution is the temperature distribution during exposure of fs laser pulses [7]. Therefore, further control of spatial distributions of elements needs the modification of the temperature distribution during laser exposure. In our previous study, we showed the method by which the shapes of the elemental distributions in an alumino-borosilicate glass could be changed from circular to square-shaped by parallel laser irradiation at multiple spots [16]. In the method, square-shaped molten region was generated by focusing 250 kHz fs laser pulses at a single spot and 1 kHz pulses at four spots simultaneously. However, the distributions along the laser propagation axis have not been investigated. In this study, we investigated the elemental distribution in the laser propagation direction in a soda-lime glass by parallel laser irradiation at multiple spots. We found that a Si-rich layer was generated and the spread of the Si-rich layer could be suppressed compared with a single beam irradiation. In addition, we found that the position of the Si-rich layer depended on the relative focal depths between 250 kHz fs laser pulses and 1 kHz laser pulses.
2. Method
2.1 Parallel fs laser irradiation inside a glass
A schematic illustration of a parallel fs laser irradiation system with a spatial light modulator (SLM) [16, 18] is shown in Fig. 1(a). Femtosecond laser pulses at a repetition rate of 250 kHz (the wavelength was 800 nm, pulse width was ~80 fs; Coherent Inc., Mira-RegA) and 1 kHz (1 kHz; wavelength was 800 nm, pulse width was ~120 fs; Coherent Inc., Mira-Legend) were input to the same optical path using a polarizing beam splitter. The polarization orientations of the 1 kHz and 250 kHz laser pulses were perpendicular to each other. These laser pulses were reflected by an SLM (LCOS-SLM, X10468-02, Hamamatsu Photonics K. K.), propagated through a telescope (the magnification was about 0.41) and focused inside a soda-lime glass plate (Schott, B-270 Superwite [19]) using a 50 × objective lens to induce photoexcitation (Nicon, LU-Plan, NA = 0.55). The depth of the photoexcited region was about 0.2 mm from the glass surface. The beam diameters of 250 kHz and 1 kHz laser pulses just before the objective lens were about 2.5 mm and 6.5 mm, respectively. The SLM modulated the spatial phase distributions of 1 kHz laser pulses only, because it is polarization-dependent. Therefore, unmodulated 250 kHz laser pulses were focused at a single spot inside a glass sample, while modulated 1 kHz pulses were focused at multiple spots inside a glass sample. The focal positions of 1 kHz pulses were controlled by selecting a phase modulation pattern (phase hologram) on the SLM. In this study, 1 kHz fs laser pulses were focused at four spots, and 250 kHz pulses were focused at the center as shown Fig. 1(b). The phase hologram was calculated by the iterative Fourier transform method [18, 20, 21], and the focal depth of the 1 kHz laser pulses was changed by adding the phase pattern of a Fresnel lens to the phase hologram.
Fig. 1 (a) Parallel laser irradiation system with two fs laser sources and a spatial light modulator. BS: a polarization beam splitter; DM: dichroic mirror, which reflects light around 800 nm; OL is an objective lens; L1, L2: lenses of focal lengths of 220 mm and 90 mm, respectively; CCDs: charge coupled device camera. (b) Schematic illustration of focusing of 250 kHz and 1 kHz laser pulses at multiple spots.
During exposure of laser pulses, the morphology change around the photoexcited region was observed from both the top and side directions. The photoexcited region was illuminated by a blue light-emitted-diode (LEDs, HLV2-14BL, CCS Inc.) and the transmitted light through an objective lens was imaged on a charge coupled device (CCD) camera. A 10 nm bandpass filter (#65-144; Edmund Optics), which transmits light around 470 nm, was placed in front of the CCD camera to attenuate plasma emission and black body radiation from the photoexcited region.
To examine the element distributions in the laser propagation direction, the pile-shaped modification was produced by translating the glass sample perpendicular to the beam axis at 10 μm/s during laser exposure. After the laser exposure, the glass was cut perpendicular to the pile-shaped modification and polished to expose the modified region along the beam axis. The elemental distributions in the modified region were analyzed with an Electron Probe Microanalyzer (EPMA; JXA-8100, JEOL).
2.2 Simulation of temperature distribution
To interpret the mechanism of the elemental distribution change by fs laser irradiation at multiple spots, the temperature distribution during laser exposure [T(t, r)] was simulated by the thermal diffusion equation with heat sources at multiple photoexcited regions [4, 22]:
where t is the time after the photoexcitation by the first fs laser pulse, r = (x, y, z) is the Cartesian coordinate inside a glass (z is the laser propagation axis), λt, ρ and Cp are the thermal conductivity, density and heat capacity of the glass, respectively, and Q’(t, r) is the heat source by photoexcitation. To simulate the experimental result, the heat source should come from one point at 250 kHz and four points at 1 kHz. Therefore, Q’(t, r) was expressed aswhere NX, QX, ΔtX and fX(r) are the pulse numbers, thermal energy generated at the photoexcited region per pulse per focal spot, time separation between pulses and normalized spatial distribution of 250 kHz (X = 250kHz) and 1 kHz (X = 1kHz) laser pulses, respectively, δ(t) is the delta function, and Rk is the center of photoexcited region by 1 kHz laser pulses. Here, the generation of thermal energy by each photoexcitation was expressed by the delta function for simplicity, because the thermal energy is generated much faster (~ps) than thermal diffusion inside a glass (~μs) [3, 23–25]. fX(r) was normalized for the integral over the space to be 1.It is difficult to determine the spatial distributions of the heat sources f250kHz(r) and f1kHz(r) precisely, because focal distortions could be caused by the laser induced modification by multiple shots [26] and the absorption efficiency is not proportional to the light intensity in the fs laser induced modification of glasses [27]. However, in this study, rough estimation of f250kHz(r) and f1kHz(r) is sufficient for calculation of temperature distributions, because the precise shape of the initial temperature distribution have disappeared by the time range of our interest (after milliseconds). To determine the rough form of the spatial distributions of the heat sources f250kHz(r) and f1kHz(r), we assumed that f250kHz(r) and f1kHz(r) are similar to the intensity distribution along the z axis of the 250 kHz and 1 kHz laser pulses. The focusing profiles were simulated using the Fresnel diffraction integral [28], in which the spherical aberration due to the refraction at a glass surface was taken into consideration. We assumed that the laser beam (with a diameter of 2.5 mm for 250 kHz laser pulse and 6.5 mm for 1 kHz) was focused at 0.2 mm depth from the surface of a soda-lime glass (the refractive index of 1.51 [19]) by a lens of a 4 mm focal length, which were the same as the experiment. The spherical aberration by the refractive index mismatch at the glass surface was expressed by the phase aberration function given in the reference [29]. The intensity distributions of 250 kHz and 1 kHz laser pulses along the z axis were shown in Fig. 2(a).Clearly, the intensity distributions along the z axis are asymmetric due the spherical aberration and depended on the diameter of the laser beam. Because the asymmetry of the intensity distribution along z affects the temperature distribution, we took the asymmetry into the consideration in the temperature simulation. Approximately, we expressed fX(r) (X = 250kHz or 1kHz) by combination of two Gaussian functions:
where AX is the normalizing constant, which is determined for the integral of fX(r) over the space to be 1. We fitted the simulated intensity distributions along z [Fig. 2(b)] by the superposition of three Gaussian functions, in which two of them express the main peak and the rest is a minor component, and determined pX, ZX1, LX1, ZX2 and LX2 of fX(r) to express the main peak in the simulated intensity distribution. The determined parameters in Eq. (3) for X = 250 kHz and 1 kHz were listed in Table 1.The expression of the heat distribution by Eq. (3) seems very rough, because the oscillating structure in the intensity profile in Fig. 2(b) cannot be expressed by this equation. However, the rough expression of the heat distribution by Eq. (3) is enough for our study, because the important time constant in our simulation (longer than several microseconds) is long enough for the fine structure in the initial temperature distribution to disappear due to thermal diffusion.Fig. 2 (a) Simulated intensity distributions along the beam axis of 250 kHz and 1 kHz laser pulses. The red broken line indicates the geometrical focus of the laser beam. (b) Light intensity at the maximum plotted against along z. Red dots are simulated intensities, and the black lines are fitting by Eq. (3).
Table 1. Parameters for expressing the heat sources in the temperature simulation.
All the parameters for the simulation were listed in Table 2.The material parameters are of a soda-lime glass [4, 19]. The viscosities of a soda-lime glass at various temperatures in this Table were used to calculate the viscosity distribution during laser exposure by the simulated temperature distribution. The thermal energy by 250 kHz laser pulse was obtained by simulating the outer boundary of the modification induced by 250 kHz irradiation at a single spot. This thermal energy is 75% of the pulse energy just after the objective lens, which is similar to the reported absorptivity (70-90%) [30–32]. The deposited thermal energy by a 1 kHz laser pulse was calculated using the same absorptivity and pulse energy.
Table 2. Parameters for the temperature and diffusion simulation [19]. λt does not include the thermal conduction by radiation. Q250kHz was estimated by the modification by irradiation with a single 250 kHz laser pulses, and Q1kHz was estimated by the absorptivity (75%) and pulse energy just after the objective lens (10 μJ at each spot).
3. Results and discussion
3.1 Elemental distributions
Figure 3(a) shows an optical microscope image of a modification inside a soda-lime glass after focusing fs laser pulses at 250 kHz. The pulse energy was about 1.35 μJ just after the objective lens and the time of exposure by laser pulses was 5 seconds. The shape of the modification was ellipsoidal, which is due to the thermal diffusion and the focusing profile of the laser pulse. In the modification, there were two boundaries of structural changes. Inside the inner boundary, flow of molten glass melt was observed during laser exposure. Therefore, we call the region inside the inner boundary “molten region” in this paper. The outermost modification between the inner and outer boundaries was formed as a result of the visco-elastic relaxation of glass under heat accumulation and thermal expansion during laser exposure [2].
Fig. 3 (a), (b) Optical microscope images of the fs laser-induced modifications inside a soda-lime glass observed perpendicular to the laser propagation axis. (a) The modification by 250 kHz laser beam at a single spot and (b) that by multi-spots’ irradiation, respectively. (c), (d) The EPMA images of Si, Ca and K along the beam axis in the modifications of (a) and (b), respectively. The color bars indicate the relative signal intensity of Si and Ca in the EPMA. The signal intensity in the unmodified region is 100.
Figure 3(b) shows the modification inside the same glass after parallel fs laser irradiation at multiple spots. The pulse energies of 250 kHz and 1 kHz laser pulses were 1.35 μJ and 40 μJ (10 μJ at each photoexcited spot) just after the objective lens, respectively. The exposure time of laser pulses was 5 seconds. As shown in Fig. 1(b), 250 kHz laser pulses were focused at the center, and 1 kHz pulses were focused at four spots (L = 50 μm and Δd = 0 μm; L and Δd are defined in Fig. 1(b)) simultaneously. The modification in the outer region became larger and the outermost boundary remained ellipsoidal-shaped. On the other hand, the molten region changed drastically; the molten region became asymmetric and larger in the horizontal direction. In addition, the variation of the brightness in the molten region is larger than that of the single spot irradiation. This large variation of the brightness indicates that the variation of density or glass composition during laser exposure was large in this region.
Figures 3(c) and 3(d) show the EPMA mappings of Si and Ca in the modifications along the laser propagation axis. In both modifications by a single spot’s and multispots’ irradiations, the elemental distributions changed only in the molten regions. In the modification by the single spot irradiation (Fig. 3(c)), the concentration of Si became higher in the lower part of the molten region, and it decreased in the upper part of the molten region. On the other hand, in the modification by multispot irradiation, Si was also concentrated in the lower part of the molten region, but the shape of the distribution was different (Fig. 3(d)); the Si-rich region stretched in the horizontal directions. In other regions, the decrease of Si concentration was not so large as that of the single spot’s irradiation. The distribution of Ca was almost opposite to that of Si in both the cases.
The soda-lime glass contains 1-10 wt% of alkali cations such as Na and K. However, we do not discussed the distributions of these cations in detail in this paper, because the EPMA signal of Na is much weaker and Na can migrate easily during EPMA mapping, and the modifications of K were very subtle compared to Si and Ca. For example, the EPMA mappings of K ions were shown in Figs. 3(c) and 3(d). The EPMA signal changes in these mapping are much smaller than those of Si and Ca. These mappings suggest that the concentration of K ion should tend to decrease both in the Si-rich and Ca-rich regions.
Because the shape of molten region and the ion migration are affected by the temperature distribution inside a glass during laser irradiation [7, 8], the difference in elemental distributions should be due to the modulation of the temperature distributions by parallel photoexcitations at multiple spots. Because the temperature distribution during laser exposure depends on the distribution of photoexcited regions, we expected that the elemental distribution would be affected by the relative focal depths between 250 kHz and 1 kHz laser pulses (Δd, defined in Fig. 1(b)). Figure 4 shows the EPMA mappings of Si and Ca of different Δd. Δd was calculated using geometric optics based on the Fresnel lens added to the phase hologram. When the focal positions of 1 kHz laser pulses were deeper than that of 250 kHz laser pulse (Δd = −15 μm and −25 μm), the Si-rich region was located in the lower part of the molten region as that of Δd = 0 μm. The thickness of the Si-rich regions of Δd = −15 μm and −25 μm was about twice smaller than that of Δd = 0 μm. On the contrary, in the case of Δd>0, Si elements migrated to the upper part of the molten region. Especially at Δd = 15 μm, a Si-rich layer of about 10 μm thickness was formed. As Δd increased, the Si-rich region moved to the lower of the molten region again. The modulation of elemental distributions was smaller as Δd became larger; the Si-rich region of Δd = 45 μm was similar to that of a single spot irradiation.
Fig. 4 Distributions of Si and Ca of different relative depth (Δd) between the focal positions of 250 kHz and 1 kHz fs laser pulses. The broken line is the geometrically calculated focal plane of 250 kHz pulses and the cross marks ( × ) are the focal positions of the 1 kHz pulses. These focal positions were calculated based on the geometrical optics and Fresnel lens patterns added to the phase hologram.
3.2 Flow of molten glass during laser exposure
The most interesting point in the above results is that the position of a Si-rich layer depended on the relative depths of 250 kHz and 1 kHz photoexcited regions. To find the origin of the difference in the position of a Si-rich layer, we observed the flow of glass melt during laser exposure from the direction perpendicular to the laser axis by the CCD-2 in Fig. 1(a). Figure 5 shows the snap shots of the transmission optical microscope images during laser exposure. The exposure time in acquisition of these images was about 33 ms. (The movies can be obtained from web site as Media 1 and Media 2.) Just after the start of laser exposure, the glass around the 250 kHz photoexcited region melted, and the molten region spread to the 1 kHz photoexcited region after 0.5 s. After 1 s, the vortex flow of glass melt was observed near the 1 kHz photoexcited regions, and the darker region appeared gradually near the upper boundary of the molten region in the case of Δd = + 15 μm [Fig. 5(a)]. The dark regions correspond to the Si-rich regions revealed by the EPMA mapping [Fig. 4]. Also in the case of Δd = −15 μm, similar vortex flow of glass melt was observed near the 1 kHz photoexcited region, but the direction of the flow was opposite to that of Δd = + 15 μm and the darker region was generated near the lower boundary of the molten region [Fig. 5(b)]. From the observation, we found that the directions of the vortex flows depended on Δd. When the 1 kHz photoexcited region was above the 250 kHz region (Δd = + 15 μm), the directions of the vortex flows were clockwise in the right region and counterclockwise in the left region (schematically illustrated in the image at 2.0 s of Fig. 5(a)). As the result, the upward flow of glass melt appeared in the center of the molten region. On the other hand, in the case of Δd = −15 μm, the directions of the vortex flows were opposite to those at Δd = −15 μm, and the glass melt flowed downward in the center of the molten region [The observed flow was drawn in the image at 2.0 s of Fig. 5(b)]. Therefore, we speculated that the flow direction of the glass melt should be attributed to the formation of Si-rich region; the upward flow of the glass melt in the central region formed the Si-rich region in the upper region, while the downward flow formed one in the lower region.
Fig. 5 (a), (b) Snap shot of the transmission optical microscope images of glass melt during laser exposure viewed perpendicular to the laser propagation direction by the CCD-2. The differences in focal depth of 250 kHz and 1 kHz laser pulses in (a) and (b) were Δd = + 15 μm (Media 1) and −15 μm (Media 2), respectively. The cross marks ( × ) at 0.1 s indicate the focused positions of 1 kHz pulses, which were calculated using geometrical optics. The observed flows of melt were drawn by red arrows in the images at 2.0 s. (c) Proposed model of Si condensation upper in the molten region in the case of Δd = + 15 μm. The arrows indicate flow of melts. η means viscosity.
We speculated the formation of the Si-rich region near the boundary of the molten region based on the dependence of viscosity on temperature and Si concentration: It is widely known that the viscosity of a silicate glass at the same temperature becomes lower as the concentration of network modifying cations, such as Na+ and Ca2+, increases [16]. In addition, the viscosity of glasses decreases monotonously as the temperature increases. Therefore, the viscosity of glass melts increases with moving to the colder region, and the increase of the viscosity is larger in a Si-richer glass. If the spatial distribution of the composition in glass melt is inhomogeneous, i.e. there are Si-rich and Si-poor regions [33], the viscosity increase must be higher in the Si-rich region than in a Si-poor region. Therefore, when the glass melt reaches the boundary of the molten region, Si-rich melts of higher viscosity would be left near the boundary, and Si-poor melts would keep flowing due to their lower viscosity. While Si-poor melts can move back to the central region by the vortex flow induced by 1 kHz photoexcitation, highly viscous Si-rich melts would be accumulated near the boundary of molten region gradually due to their higher viscosity. This mechanism of melt flow and accumulation of Si-rich melt was schematically illustrated in Fig. 5(e).
3.3 Simulation of temperature distribution
The remaining question is what determined the direction of flow of glass melt during laser exposure. To investigate the origin of the flow, the temperature distributions during laser exposure at Δd = + 15 μm were simulated. Figure 6(a) shows the temporal evolutions of the temperature distributions along the laser propagation axis. The simulated surface includes both 250 kHz and two 1 kHz photoexcited regions. The time of the temperature distributions was 1000 ms + Δt after the start of laser exposure, in which Δt is the time after the 1001 st shot of the 1 kHz laser pulse. The temperature around the central region was high at all time during laser exposure because of highly repeative photoexcitation at 250 kHz in this region [2–5, 30–32]. Sudden increase of the temperature apart from the central region occurred after the irradiation with 1 kHz pulse, but the temperature decreased quickly in several tens microseconds by the thermal diffusion. Similar temperature changes were repeated until the stop of laser exposure.
Fig. 6 (a) Simulated temperature distribution during laser exposure at Δd = + 15 μm. (b) Viscosity distributions calculated by the temperature distribution of (a) and temperature dependent viscosity of a soda-lime glass. (c) Viscosity distributions with the regions of 103-103.5 Pa∙s drawn in black. The blown lines indicate the expected flow of glass melt through the transiently formed channels.
Figure 6(b) shows the transient viscosity distributions calculated by the simulated temperature distributions and temperature dependence of the viscosity of a soda-lime glass (Table 2). The increase of the temperature at 1 kHz reduces the viscosity around the 1 kHz photoexcited region, and the low viscosity regions spread in the lateral directions due to thermal diffusion. To show the low viscosity region clearly, the region of 103-103.5 Pa∙s, at which glass melt can flow easily [16], was drawn in black on the viscosity distributions in Fig. 6(c). The region where the viscosity is lower than 103.5 Pa∙s became wider as thermal diffusion, and after Δt = 25 μs the low viscosity regions around 1 kHz and 250 kHz photoexcited region were connected. These connected low viscosity regions mean that channels of glass melt were formed transiently after Δt = 25 μs. In our previous study, we have observed the formation of flow channel between 1 kHz and 250 kHz photoexcited regions in an alumino-borosilicate glass, in which the glass melt seemed to flow from the 1 kHz photoexcited region to the 250 kHz region [16]. The flow of the melt from 1 kHz photoexcited region could work as a trigger of the vortex flow around 1 kHz photoexcited region. The expected melt flow was illustrated schematically by arrows in Fig. 6(c).
This mechanism of melt flow is based on the simulation by only thermal diffusion equation, in which no thermal conduction by melt flow is taken into consideration. For full understanding of the elemental distribution change due to glass melt flow, fluidic simulation of glass during laser exposure is necessary.
4. Conclusion
The spread in the laser propagation direction of a Si-rich region inside a soda-lime glass could be reduced by focusing 1 kHz fs laser pulses at four spots and 250 kHz pulses at the center. The position of the Si-rich region depended on the relative positions between 1 kHz and 250 kHz photoexcited regions. The observation of glass melt during laser exposure and simulation of transient temperature and viscosity distributions suggest that the flow of the glass melt could be responsible for the formation of a Si-rich layer and the position of the Si-rich region could be controlled by formed transient channel of glass melt by irradiation of 1 kHz laser pulses at optimal positions. The results give us novel technique to control spatial distribution of glass composition.
Acknowledgments
The authors thank Prof. Qiu from South China University of Technology for useful discussion and comments. In addition, the authors thank Dr. Itoh of Hamamatsu Photonics K. K. for good advice of construction of the parallel laser irradiation system. This research was supported by Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Young Scientists (B), No. 22750187 and that for Scientific Research (A), No. 23246121.
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