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The nonlinear absorptivity of FOTURAN glass to ultrashort laser pulses is evaluated by experimental measurement and thermal conduction model at different parameters including energy and repetition rate of the laser pulse, translation speed and thermal properties of the sample. The mechanical strength of an embedded laser-melted sample and an overlapped weld sample is determined by a three-point-bending test and a shear test, respectively. The results are related to the average absorbed laser power Wab. We found the mechanical strength of an overlapped weld joint to be as high as that of the base material for low Wab, if the sample pair is pre-bonded to provide optical contact.
©2011 Optical Society of America
1. Introduction
Localized internal processing of transparent materials by ultrashort laser pulses has been drawing much attention because of the wide range of available applications such as waveguide formation [1], three-dimensional optical memory [2] and fusion welding [3,4]. Consequently, it is important to evaluate the nonlinear absorptivity and the temperature field in commercially useful transparent materials, since they will affect the laser-matter interaction process and the quality of the modification especially for high pulse repetition rate processing.
Although several authors have modeled the absorption of the ultrashort laser pulse energy in distilled water using rate equations describing the free electron formation as a result of single laser pulse [5,6], the model cannot be applied to the case of multi-pulse laser irradiation especially at high repetition rates. An experimental measurement procedure was developed to evaluate the nonlinear absorptivity of ultrashort laser pulses in bulk glass for high pulse repetition rates [4,7]. A thermal conduction model [8] was also developed to evaluate the laser energy absorbed in the laser-induced plasma at high pulse repetition rates. The model predicts that for a given pulse energy, the nonlinear absorptivity increases as the pulse repetition rate increases. This is due to increase in the density of the thermally excited free electrons, which seed electrons for avalanche ionization.
The mechanical strength of internally modified single glass samples that have been exposed to ultrashort laser pulses has been evaluated by different testing procedures including a four-point-bending test [9], a double torsion test [10] and nano-indentation [11,12], and it was found that the laser-irradiated glass samples is strengthened by creating the residual compressive stress. This is in contrast to the case of conventional nanosecond (ns) laser pulse processing where cracks form due to the development of residual stress that is in tension [13]. There is limited study on the mechanical strength of laser-weld joints, because the weld quality is significantly dependent on sample preparations. The early work of fusion welding of glass samples [3] showed that the joint strength is much lower than that of the base material, presumably because the sample preparation was not ideal. Recently a paper reported that the mechanical strength of laser-welded joint can be greatly enhanced by introducing a pre-bonding process step to the glass plates that are to be welded [14]. The paper also indicated that the attractive force caused by van der Waals interaction [15] at the interface has to be taken into account in evaluating the mechanical strength of the pre-bonded welded joint. However, the effect of welding conditions on the mechanical strength of the weld joint has not yet been reported.
In the present paper, we investigate the ultrashort laser pulse welding of FOTURANTM (Schott Glass Corp., Mainz, Germany) glass, which is widely used for three-dimensional structuring of components and is finding increasing use in devices ranging in applications from the medical to the development of miniaturized satellites [16–18]. Two specific aspects are to be studied: The characteristics of nonlinear absorptivity as it applies to ultrashort laser pulses and the mechanical strength of the weld joint. The nonlinear absorptivity is evaluated by the experimental measurement and the use of a simulation model that includes as parameters the energy and repetition rate of laser pulse, the translation speed of the sample and thermal property of the sample. The mechanical strength of an embedded melted region and of overlapped welded samples is evaluated by a three-point bending test and a shear test, respectively. It is shown that the mechanical strength of welded and internally melted samples is closely related to the average absorbed laser power Wab, suggesting the strength of the overlapped weld joint approaches that of the base material for decreasing Wab.
2. Nonlinear absorption properties of FOTURAN glass
2.1 Experimental measurement of nonlinear absorptivity
Ultrashort pulse laser system (Duetto from Time-bandwidth Products, wavelength λ = 1064nm, M2=1.1) with a pulse duration of 10ps is used to induce melting FOTURAN glass having a thickness of 1mm. The laser beam is focused by a microscope objective lens with a numerical aperture (NA) of 0.55. The exposure is done as the glass plate is transversely moved at a velocity region of 10~200mm/s. The pulse repetition rate f is varied over a wide range of 50kHz~8.2MHz, resulting in different energies per pulse. The thermal and physical properties of virgin FOTURAN are shown in Table 1 . FOTURAN is a glass but upon heating and cooling can become a glass/ceramic composite.
The nonlinear absorptivity AEx can be determined by measuring the laser pulsed energy transmitted through the sample using the following equation [4,8].
where Q0 is incident laser pulse energy, Qt is transmitted pulse energy and R is Fresnel reflectivity. The nonlinear absorptivity can be determined by this procedure with an uncertainly less than 3% [8], since the reflection and scattering by laser-induced plasma is negligible in transparent material [20]. A power meter with a rather slow response time of ≈1sec is used for measuring Qt. The experimental measurement of AEx was limited to the translation speeds below ≈30mm/s, because the sample size was limited to tens mm.Figure 1 shows the nonlinear absorptivity AEx plotted vs. pulse repetition rate f at a translation speed v=20mm/s and an average laser power of 3W. AEx is higher than 80% at f<700kHz, and quickly decreases for f>1MHz, reaching a value that is approximately 35% at f = 8.2MHz. Figure 2 shows the cross-sections of the internally melted glass sample for various pulse repetition rates. The modified structure consists of a teardrop-shaped inner structure and an elliptical outer structure like the case of borosilicate glass [9], and the size of the outer structure varies in accordance with the nonlinear absorptivity.
Fig. 1 Experimental and simulated nonlinear absorptivity of FOTURAN glass at a translation speed of 20mm/s at different pulse repetition rates with a focus position zh from the top surface of 640µm (NA0.55, τ = 10ps, average laser power 3W). The cross-sections of the sample are shown in Fig. 2.
Fig. 2 Cross-sections at different pulse repetition rates f at a constant average laser power of 3W in FOTURAN glass. (NA0.55, v=20mm/s, τ=10ps, zh=640µm).
2.2 Determination of characteristic temperature of modified structure
The simulation model used to evaluate the nonlinear absorptivity is briefly presented here. A detailed account can be found in Ref [8]. The temperature field in laser-irradiated glass sample is simulated assuming a line heat source with continuous heat delivery w(z) appears in an infinite solid moving at a constant speed of v along the x-axis. The relevant equation is
where s2 = x2 + y2 + (z-z’)2, K is the thermal conductivity and α is thermal diffusivity given by the relation K/cρ (c = specific heat and ρ=density) and T0 is room temperature. In this model, it is assumed that the thermal properties of the material are constant for the sake of simplicity. For w(z), we introduced a simple function of the formwhere l is the length of the laser-absorbed region along z-axis (light propagation axis), and a, b and m are positive constants. The function w(z) can be determined by fitting the isotherm of the maximum cycle temperatures attained in (y,z) frame at dT/dx=0 to the cross-section of the experimental modification structures, assuming the characteristic temperature of the modified structure is known. Then the nonlinear absorptivity ACal can be derived by the Eq. (4).where f is pulse repetition rate, and Q0 incident laser pulse energy. It was shown the simulated nonlinear absorptivity agrees with the experimental nonlinear absorptivity with an accuracy of 3%, assuming that the characteristic temperature of the outer structure of the modified zone in borosilicate glass is the forming temperature with a viscosity η = 104dPa.s [8].In this study the characteristic temperature of the outer structure is determined from the experimental measurement of nonlinear absorptivity, since viscosity data of FOTURAN glass is not available. Figure 3(a) shows a typical cross-section of internally melted FOTURAN glass sample obtained at Q0 = 5µJ, f = 500kHz and v = 20mm/s. Figure 3(b) shows the simulated isothermal lines fitted to the experimental structures for m = 0.5, m = 1 and m = 2, where optimized values of a, b and l are used and the characteristic temperatures of the outer and the inner structures are assumed to be Tout = 900°C and Tin = 3,000°C, respectively. Figure 3(c) shows w(z) corresoponding to each value of m. It is seen that the shape of the inner structure and its relative position with respect to the outer structures are sensitive to the value of m, and that m = 2 provides the best result. A value of m = 2 is reasonable considering that the radius of the laser beam spot is proportinal to z2 at locations away from the focus. It should also be noted that the size and shape of the outer isotherm depend little on m, suggesting that the nonlinear absorptivity can be determined even without an exact distribution of w(z), if the integrated value of w(z) is known. Figure 4 shows the effect of Tout on the evaluated value of ACal. The simulated value of ACal varies linearly with Tout. The characteristic temperature can be determined from this figure if the nonlinear absorptivity is known.
Fig. 3 (a) Cross-section of FOTURAN glass (f=500kHz, Q0=5µJ, v=20mm/s, zh=250µm), (b) Simulated isothermal lines for m=0.5, 1.0 and 2.0 (characteristic temperatures: assumed to be Tout = 900þC and Tin = 3,000þC), (c) Intensity distribution w(z) for different values of m.
Fig. 4 Relationship between characteristic temperature of the outer structure Tout and the nonlinear absorptivity ACal (f = 500kHz, Q0 = 5µJ, v = 20mm/s, m = 2).
In order to determine the value of Tout, the experimental nonlinear absorptivity AEx is determined at the same conditions as that in Fig. 3(a). The result is AEx = 70.5%. Using AEx = 70.5%, a value of Tout = 900°C is obtained for the characteristic temperature. The data indicates the effect of the accuracy of Tout on ACal is approximately 0.075%/°C.
2.3 Effect of laser processing parameters on nonlinear absorptivity
In this section, the nonlinear absorptivity of FOTURAN glass is determined by fitting the simulated isotherms at Tout = 900°C using different parameters including laser pulse repetition rate, average laser power and translation speed. For an average laser power of 3W, the focus position measured from the top surface is zh = 640µm. Figure 1 shows the nonlinear absorptivity at a translation speed of v = 20mm/s as a function of pulse repetition rate. The simulated value of ACal agrees with experimental values of AEx over a wide range of pulse repetition rate of f = 50kHz~8.2MHz within an uncertainty of 3% similar to that shown in Ref [8].
The nonlinear absorptivity ACal simulated at different average laser powers at f = 1MHz at 20mm/s is plotted in Fig. 5(a) . ACal increases with increasing laser power, because the rate of multiphoton ionization increases with increasing the laser intensity. Figure 5(b) shows ACal plotted vs. translation speed for a pulse repetition rate of f=1MHz. These results show that ACal decreases with increasing translation speed. This can be explained by the fact that the cooling rate is faster at higher translation speeds so that the laser-irradiated region cools down faster between the laser pulses. Thus as the translation speed increases, the density of the thermally excited free electrons is decreased at the moment of the laser pulse impingement, so that the density of seed electrons for avalanche ionization is decreased [8].
Fig. 5 Nonlinear absorptivity of FOTURAN glass (zh=640µm) plotted vs. (a) average laser power in comparison with D263 (f = 1MHz, v = 20mm/s), and (b) translation speed (at average laser power of 3W, f=1MHz).
2.4 Effect of thermal properties on nonlinear absorptivity
To gain more insight on the nonlinear absorption process in FOTURAN glass, a comparison has been done with another glass material that has different thermal properties. The thermal properties of the material should affect the nonlinear absorptivity because heat accumulates at high pulse repetition rates. In order to simplify the problem, our comparison was with a glass material that has similar band gap energy Eg as shown in Table 1. By placing this restriction we can possibly overlook the effects of the multiphoton ionization (MPI) rate which should be similar in the two materials. The band gap energy of FOTURAN glass was determined by a Tauc plot based on optical transmission spectroscopy data. A value of Eg = 3.6eV is obtained, which is in good agreement with the value reported in Ref [16]. In this experiment, the material D263 (Schott Glass Corp., Mainz, Germany) serves as the reference material, because the band the gap energy of Eg = 3.7eV is close to that of FOTURAN glass and the nonlinear absorptivity has been well-studied [8].
In Fig. 5(a), the nonlinear absorptivity ACal of D263 simulated at f=1MHz and v=20mm/s [8] is plotted vs. average laser power, showing ACal of FOTURAN glass is smaller than that of D263 when compared at the same average laser power. This is attributed to the larger thermal conductivity K of FOTURAN glass, since both materials have approximately the same band gap energy and cρ. Assuming the same amount of laser energy is absorbed by MPI, D263 must reach a higher temperature during laser irradiation due to a smaller thermal conductivity. This should result in a larger density of thermally excited free electrons to seed avalanche ionization.
Figure 6 is a plot of the cross-sectional area S within the isotherm of Tout as a function of average absorbed laser power Wab at v=20mm/s for both FOTURAN glass and D263. The data points include different pulse repetition rates f for D263 [8] and FOTURAN glass. It is interesting to see that data points of the both materials fall nearly on a single line, in spite of the fact that both materials have different thermal conductivities K (see Table 1). We postulate that the effect of a lower Tout in FOTURAN glass is compensated by the effect of a larger K for D263. The figure also includes a data point taken at pulse duration of τ = 400fs [4]. Note that this point also falls on the same line, suggesting avalanche ionization is the predominant absorption process at high pulse repetition rates even for 400fs.
Fig. 6 Cross-sectional area S in the isothermal line of Tout for FOTRUAN glass and D263 at pulse duration of 10ps and 400fs at translation speed of v=20mm/s.
As will be discussed in section 3, the average absorbed laser power Wab plays an important role in defining the mechanical strength of the laser-irradiated sample. We have shown the nonlinear absorptivity of FOTURAN glass can be evaluated by the experimental measurement and the application of a thermal conduction model. It is also possible to determine Wab through the measurement of the molten cross-sectional area for FOTURAN or D263.
3. Mechanical strength of weld joint
3.1 Mechanical strength of internally melted single glass sample
The mechanical strength of a weld joint is affected not only by the laser-irradiation conditions such as pulse repetition rate, pulse energy and translation speed, but by the geometry of the weld joint and the preparation of the glass plates. In order to ascertain the major factors affecting the mechanical strength of a weld joint in the laser-irradiation conditions, influences that might result from geometry of the weld joint of the glass plates were minimized. The internally melting of the single glass sample was made at an average laser power of 2.5W at different pulse repetition rates f and the translation speeds v. The embedded melted samples were lapped and polished parallel to the melt line to expose the maximum width of the melt line to the surface. These samples were then cut perpendicularly to the melt line having a width of 15mm. The mechanical strength of the molten region was determined with a three-point-bending test by applying the maximum stress at the molten region as schematically shown in the inset of Fig. 7 .
Fig. 7 Mechanical strength of internally melted single FOTURAN sample determined by a three-point-bending test at different f and v at a constant average laser power of 2.5W. A thick dotted line shows the average strength of the base material.
The mechanical strength data determined at different pulse repetition rates f and translation speeds v is shown in Fig. 7. A total of five samples were tested for each condition. The strength of the virgin material having no laser irradiation dose falls within the region of 115~200MPa (average strength: 152MPa). On the other hand, the average value of all the internally melted samples (60 data points in total) is approximately 145MPa. This is nearly equivalent to the virgin or base material. However, the strength of the internally melted single plate is approximately 30MPa lower than that of the base material for the conditions v = 20mm/s and f = 0.2MHz. The data show that the value of the strength tends to increase with increasing v and f, reaching as high as or even above that of the base material. There is some uncertainty scattering in the data set, but the general observed trend is valid.
In Fig. 8 , the bending strength data of the embedded melted single samples is re-plotted as a function of the averaged absorbed laser power Wab determined by ACal from Figs. 1 and 5(b). The colored zone in the figure highlights measured data, which is drawn assuming that the mechanical strength decreases linearly with increasing Wab, suggesting that the mechanical strength is related to Wab. Even though the mechanical strength is lower than the base material for larger Wab values, with decreasing Wab there is a net positive effect on the mechanical strength. As Wab decreases the mechanical strength increases such that in the region Wab<1.0W there is the possibility of strengthening the material beyond the strength of the base material. This conclusion is supported by other data from a previous report, where it was shown the internally melted single plate of fused silica with 10ps laser pulses was shown to be stronger than that of the base material [21]. This is also in accordance with other reports showing the strengthening of bulk glass using fs-laser pulses that were evaluated by a variety of testing procedures including the four-point bending test [9], the double torsion test [10] and the nano-indentation [11,12]. In these reports, the strengthening is attributed to the compressive residual stress produced in the laser-irradiated region. To further compare with fs-laser pulses, we examined the effect of the laser polarization vector with respect to the translation direction. No influence of the laser polarization vector could be observed, suggesting that the nano-grating structures observed in the irradiation of low laser pulse energies of fs duration [22] is not produced in the case of high repetition rate ps-laser pulses. An explanation of why the strength of the laser-irradiated samples tends to decrease with increasing Wab could be due to the fact that while the absorption of ultrashort laser pulse energy provides the compressive stress, there is also a large melt volume which generates tensile stress that compensates. The residual tensile stress is normally observed in conventional metal welding. It should be noted that approximately 75% of the strength of the FOTURAN base material is still maintained even as high as Wab≈1.8W.
Fig. 8 Mechanical strength of internally melted single glass sample and overlap-welded joint plotted vs. average absorbed laser power Wab. The result of overlap welding joint of D263 [14] is also plotted.
3.2 Mechanical strength of overlapped weld joint
Prior to the overlap welding, the glass plates have to be faced with intimate contact to confine the laser-induced hot plasma within material [8]. It was reported [14] that using sample pairs with optical contact, cracks can be prevented and that the mechanical strength of the weld joint can reach much higher than the case without optical contact [3]. The optical contact is marked by a lack of light reflections from the interface, and can be normally obtained with the glass surfaces having roughness and flatness found in float glass, if the glass surfaces are carefully cleaned [23]. Lapping and polishing are, however, needed to provide optical contact in FOTURAN glass plates, since the surface roughness and flatness of as-received FOTURAN plate are not as good as float glass. Two FOTURAN glass plates of 1mm in thickness in optical contact were overlap-welded by irradiating a focused laser beam. The focus position is placed a little below the interface to provide the maximum width of the molten region at the interface.
In evaluating the mechanical strength of the weld joint, the effect of the optical contact force has to be evaluated [14], because the measured strength of the weld joint overestimates as the result of the attractive force due to van der Waals interactions [15]. The optical contact force can be evaluated by inserting a blade with measured thickness between the contact surfaces and measuring the length of the “air wedge” extending to the contact line [24]. In the present study, the optical contact force was evaluated by applying the shear force to break the optical contact, because the glass sample having a thickness of 1mm are too thick to insert a blade. Glass samples with a width of 15mm were used for evaluating the shear force to break the optical contact at different length L as schematically shown in Fig. 9 . The sample with the minimum length of L = 1mm was produced by HF-etching of masked glass sample.
Fig. 9 Shear force to break optical contact FOC plotted vs. contact area SOC. The optical contact force per unit area σOC is also plotted.
Figure 9 shows the shear force FOC to break the optical contact plotted as a function of optical contact area SOC. The optical contact force per unit area σOC ( = FOC/SOC) is approximately 1.5MPa at L = 1mm, and decreases with increasing SOC. The values of σOC in SOC <200mm2 are in agreement with the values reported for glass materials by Kachkin et al. [25]. We also measured the optical contact force σOC of D263 glass plates, and obtained a value of 88N at L = 10mm showing good agreement with FOTURAN glass plates. This value of σOC of D263 is somewhat higher than our previous result [14], suggesting the pre-bonding process has been improved in the present study.
Overlap welding was performed using the pre-bonded sample with L=10mm corresponding to FOC≈88.2N (σOC≈0.6MPa), which is strong enough to keep optical contact in handling the sample for the welding experiment. Although σOC≈0.6MPa is approximately two orders smaller than the strength of FOTURAN glass, L=10mm is also two orders larger than typical bead width. Therefore the strength of the weld joint σW was determined by subtracting the optical contact force FOC from the rupture load FRUP, and then dividing by the cross-sectional area of the weld bead SW using
Overlap welding was performed at an average laser power of 3W at different pulse repetition rates and different translation speeds. In Figs. 10(a) and 10(b), the rupture load FRUP and the welded area SW are plotted as a function of translation speed v with a constant pulse repetition rate of f=1MHz, and as a function of pulse repetition rate at a constant translation speed of v = 20mm/s, respectively.
Fig. 10 Effect of (a) translation speed at f=1MHz and (b) pulse repetition rate at v = 20mm/s on the rupture strength and weld area of the overlap-weld samples. (L=10mm, length of weld path = 8~9mm)
Figure 8 also presents σW data for overlap-welded samples, where the data points for (a) f=1MHz and (b) v=20mm/s are shown. In the figure, the nonlinear absorptivity of the overlap welding was assumed to be equal to the values obtained at zh = 640µm, which are given by Figs. 1 and 5(b). In spite of the fact that the nonlinear absorptivity is actually affected by zh, most data points of the overlap weld are included within the aforementioned colored region that highlights the data from the internal melt single plate studies. It is noted that one single data point taken at translation speed of 100mm/s lies outside this region. Furthermore the data measured at different v but constant f has a steep dependence with translation speed. We believe this result is as a consequence of the nonlinear absorptivity for the overlap welding (zh≈1mm) which is actually smaller than that of the single plate studies at zh = 640µm. This difference is due to the larger spherical aberration which results in a lower laser power density at the focus, and the decrease in the nonlinear absorptivity due to the spherical aberration tends to increase with increasing translation speed.
In order to deduce the difference in the nonlinear absorptivity between zh=640µm and zh≈1mm (overlap welding), we measured the width of the welded region in the samples ruptured in the shear test, and compared this with the simulated width of the molten zone. It was found that the width of the weld region was approximately γ≈75% of the simulated width at 100mm/s. The measured width of the fractured region were γ≈81% and γ≈95% of the values at zh = 640µm at v = 50mm/s and 10 = mm/s, respectively, supporting the conclusion that the effect of zh on the nonlinear absorptivity increases with increasing translation speed. Assuming it is possible to revise the value for the average absorbed laser power W’ab by the relation W’ab = γ*Wab, the data values of overlap weld joint in Fig. 8 that are at higher translation speeds move to lower Wab, and approach the data taken at v = 20mm/s. Further experiments are needed to quantify this analysis.
Figure 8 also contains data of the strength of overlap-welded D263 [14]. The data point falls in the same region of FOTURAN data, suggesting that the overlap-welded samples provide the equivalent strength to the internally melted single plate, if the sample pair is appropriately pre-bonded to provide optical contact.
Figure 11 shows fracture faces observed by SEM at different translation speeds at a laser pulse repetition rate of f = 1MHz. The sample at 20mm/s (11a) with the lower joint strength appears as an irregular fracture face, suggesting that a complicated stress field is produced in the weld bead possibly as a result of the local compensation of the tensile stress on the compressive stress field. The sample at 100mm/s (11c) with the higher joint strength appears as a smooth fracture face, suggesting the compensation of the stress field due to tensile stress is smaller. For better understanding of the mechanism, further study is needed by simulating the stress field.
Fig. 11 SEM photographs of ruptured face of overlap welded sample and strength of the weld joint at 3W at f = 1MHz.
4. Summary and conclusions
The nonlinear absorptivity of FOTURAN material to incident ps laser pulses has been experimentally measured and simulated by a model that includes the effects of different processing parameters including pulse energy, the repetition rate of the laser pulse, the sample translation speed and thermal properties. The mechanical strength of an internally melted single sample and overlapped welded sample were evaluated by a three-point bending test and a shear test, respectively. The strength of the overlap weld joint is found to be as high as the internally melted single glass plate when the sample pair is prepared such that optical contact is achieved. The results show that the mechanical strength of the both single and overlap weld joint samples decreases with increasing the average absorbed laser power Wab, and is as strong as the base material when Wab<1.2W.
Acknowledgments
The authors wish to thank Dr. J. Gottmann and Dipl.-Phys. D. Schaefer, Lehrstuhl für Lasertechnik LLT, RWTH Aachen University, for their measurement of band gap energy of the glass sample. This work was partially supported by Erlangen Graduate School in Advanced Optical Technologies (SAOT).
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