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Abstract
A dynamic pulse propagation modeling for femtosecond laser bonding of Borofloat glass is presented. The temperature evolution and internal modifications are predicted by incorporating the nonlinear electron dynamics along with temperature dependent thermal properties. The modelling predicts the spatial and temporal distribution of absorption coefficient and plasma density that gives quantitative estimations of the heat affected zone and weld geometry. The impact of focusing condition on heat affected zone and weld geometry is investigated, which for the first time to our knowledge allows to numerically determine the desired relative position between the geometrical focus of a femtosecond-laser-pulse and the interface of the two substrates to be welded. The prediction of the modelling on the offset distance is applied to weld Borofloat glass plates having optical contact and can be applied to other dielectric solids.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Femtosecond laser has enormous potential in internal modification of solids for laser based bonding/welding [1,2], polishing [3] and waveguide writing [4]. The dimension of modification is greatly affected by both the heat accumulation and the nonlinear absorptivity at high pulse repetition rates [5,6]. Therefore, it is essential to understand femtosecond (fs) laser–matter interaction, through which temperature distribution within heat affected zone and the dimension of the internal modification induced by plasma generation in solid can be evaluated. Nonlinear absorptivity is needed to predict the two aforementioned phenomena. Previous works [2,7] have simulated the temperature profile during laser welding process using a measured nonlinear absorptivity from incident and transmitted power. However, the measurement is wavelength, pulse length and material specific, and cannot explain the observed asymmetrical tear drop energy distribution as the role of plasma in absorption has not been considered. Miyamoto et al. [1,5,6,8] have further calculated the nonlinear absorptivity by fitting the simulated isotherm to the experimentally obtained modification structures. However, these reported methods depend on the experimental data and cannot predict the modification prior to experiment. Sun [9,10] and Miyamoto [11,12] have incorporated the plasma absorption during laser beam propagation for modelling temperature through analytical solution to the heat conduction equation via using static value of specific heat capacity and thermal conductivity. However, in actual experimental condition these material specific thermal properties significantly vary with increasing temperature during laser mater interaction. Particularly for laser based welding by fs-pulses with high repetition rate, the heat-accumulation-induced temperature change modifies the thermal properties of the material locally [13,14]. Thus, omission of their temperature dependency will most likely over or under predict the temperature. In this work, a dynamic heat accumulation modelling is presented to study the internal modification of Borofloat (B33) glass. The differential heat conduction equation is solved numerically by finite difference modelling (FDM), where the temperature dependence of heat capacity and thermal conductivity are considered. The model incorporates the nonlinear dynamics of energy absorption and free electron/plasma generation, taking into consideration of a time and space dependent absorption coefficient that varies according to the fs-pulse propagation. The model-predicted modification region is used to optimize the laser welding process.
For ultrafast laser welding of transparent materials, most studies share a common characteristic: optical contact needs to be established prior to laser welding, and the gap between the samples is generally confined to less than λ/4 (λ=633 nm). The study presented here is more relevant when optical contact is achieved. However, in some applications, welding must be achieved with an air gap between the two glass plates. For a small gap less than 3 $\mathrm{\mu}$m, gap bridging was achieved either by optimization of welding parameters (energy and focal position) [15,16] or by employment of burst mode to eject and deposit molten material at the surface of the sample which fills an existing gap [17]. Additionally, for a large gap around 10 $\mathrm{\mu}$m, a small-scale rapid oscillating scan was used to create enough molten material to fill the gap during the welding process [18,19]. Furthermore, the adoption of beam shaping has exhibited significant advantages in relaxing the strict requirement on precisely controlling the focal position. The focal-position tolerance zone across the materials interface increases by 5.5 fold by using zero-order Bessel beam, compared with Gaussian beam [20].
The dynamic nonlinear modelling presented in this work can accurately analyze the temperature evolution and internal modifications in the solid, therefore offering a valuable tool for the dimensional analysis of heat affected zone (HAZ) for fs-laser welding and for the determination of the focal location relative to the interface of the two substrates to be welded. In section 2, theoretical modelling is presented to predict temperature evolution at the focal volume inside material. Pulse wise analysis of the change in temperature profile at the focal volume has been carried out. The Effect of laser parameters on HAZ and Internal modification region (IMR) is studied. The model was used to predict the required offset between the interface and the geometrical focus for two fs-laser welding configurations. In section 3, experimental methods are presented to describe the process of fs laser welding. In section 4, the results obtained from experiment using the model predicted offset distance are reported.
2. Theoretical modelling
In the theoretical model, internal modification by fs pulse propagation in B33 glass is analyzed to understand and optimize laser welding process. The nonlinear energy deposition of fs pulses is determined by considering beam propagation and generation of plasma. The deposited energy is used to calculate the temperature rise and the thermal conduction model is used to derive the temperature distribution. IMR and HAZ are estimated based on free-electron density and temperature distribution, respectively. The schematic diagram of the process of fs laser welding of two B33 substrates is shown in Fig. 1. The fs-pulse propagating along z-axis is focused by a microscope objective around the interface of the two substrates. The modelling predicts the size and position of the HAZ, which helps in locating the laser focus at the exact position during the laser welding process. A 300-fs pulse at 1030-nm wavelength with energy of 0.6 $\mathrm{\mu}$J and repetition rate (f) of 1 MHz is used to analyze the results of modelling. The laser is scanned with a speed of v=10 mm/s along x-axis. In modelling, scanning speed (v) is considered by pulse-to-pulse beam translation increment, xci = v×tpp, where tpp is the time separation between pulses, defined as tpp=1/ f. Here ‘xci’ is the distance covered by the beam along laser scanning direction (x-direction) between two pulses.
2.1 Nonlinear absorption and electron dynamics
When a fs-laser pulse is focused inside a transparent dielectric like glass, the energy of pulse is first absorbed by electrons in the valence band to generate free electrons via photoionization, cascade ionization while going through electron-hole recombination. This nonlinear interaction can be explained by Eq. (1) [11], a rate equation that describes the evolution of free electron density ρ(z,t) under the influence of fs pulse having intensity I(z,t).
Fig. 2. Dynamic evolution of intensity and Keldysh parameter ($\gamma $) in B33 for a 300-fs pulse propagating with pulse energy of 0.6 μJ and beam waist radius of 1.13 μm.
Table 1. List of parameters and their values used in the modelling.
The free-electron density $\mathrm{\rho }({\textrm{z},\textrm{t}} )$ is obtained by numerically solving Eq. (1) with initial condition, $\mathrm{\rho }[{\textrm{z},0} ]= {\mathrm{\rho }_{\textrm{therm}}}$, where ${\mathrm{\rho }_{\textrm{therm}}}$ is the thermally ionized free electron density that depends on temperature and bound electron density of glass [11]. As the pulse propagates through the solid, the intensity $\textrm{I}({\textrm{z},\textrm{t}} )$ and the absorption coefficient $\mathrm{\alpha }({\textrm{z},\textrm{t}} )$ are affected by the generated plasma density $\mathrm{\rho }({\textrm{z},\textrm{t}} )$ and are given by Eq. (2) and Eq. (3) respectively.
Fig. 3. (a) Laser intensity I0max (without plasma) and Imax (with plasma and absorption) along beam propagation direction, (b) Plasma density $({{\rho_{max}}} )$, absorption coefficient $({{\alpha_{max}}} )$ and deposited volume energy density Qv plotted along beam propagation direction. Pulse energy for this simulation is 0.6 μJ.
2.2 Heat generation, dissipation and accumulation
The elemental energy deposited by a single pulse, $\textrm{E} = {\textrm{Q}_\textrm{v}}(\textrm{z} )\times \textrm{dv}$ is used to calculate the temperature rise, $\textrm{T} = \textrm{E}/({{\mathrm{\rho }_m}{\textrm{c}_\textrm{p}}\textrm{dv}} )$ at each pixel of volume d$\textrm{v}$ (=dx${\times} $dy${\times} $dz) from a background temperature of 293 K. Here, ${\mathrm{\rho }_m}$ is the material density and ${\textrm{c}_\textrm{p}}$ is the specific heat capacity. The induced temperature decreases over time as heat diffuses through the material bulk. The analytical heat conduction equation [Eq. (5)] links the temporal and spatial rates of temperature change. The two important thermal properties of glass are heat capacity $({{\textrm{c}_\textrm{p}}} )$ and thermal conductivity $(\mathrm{\kappa } )$, both of which are temperature dependent. ‘${\textrm{c}_\textrm{p}}$’ causes the temperature to rise and ‘$\mathrm{\kappa }$’ causes the heat dissipation. The temperature dependencies of both ${\textrm{c}_\textrm{p}}$ and $\mathrm{\kappa }$ were taken into account using an explicit central finite difference solution to the heat conduction equation as explained in [3,14,27].
Fig. 4. (a) Temperature dependent heat capacity (${c_p}$) and thermal conductivity ($\kappa $) for B33, (b) Blue curve represents the time evolution of maximum temperature for 50 pulses, taking into consideration of the temperature dependence of ${c_p}$ and $\kappa $. The red curve represents the time evolution of maximum temperature when ${c_p}$ and $\kappa $ is kept constant at room temperature.
2.3 Prediction of temperature profile upon the incidence of single and multiple pulses
The profiles of the temperature distribution (along the laser-pulse propagation direction z) at different times up to one microsecond, after the energy deposited by a single pulse is shown in Fig. 5(a). The black curve represents the temperature profile at a time right after energy is deposited by the pulse and before the start of heat diffusion. This instant of time is designated as time ‘0 $\mathrm{\mu}\textrm{s}$’ for the analysis of heat diffusion process in Fig. 5. This temperature profile resembles the profile of the energy density (${\textrm{Q}_\textrm{v}}$) curve shown in Fig. 3(b), both having their peak locations at 5.2 μm above the geometrical focus. As time passes, heat diffusion results in the reduction of the peak values and the shift of the peak towards the surface. We further analyzed the role of ${\textrm{c}_\textrm{p}}$ on the temperature shift. Figure 5(b) shows that when using a constant ${\textrm{c}_\textrm{p}}$, the shift of the temperature profile remains the same as compared to using an increasing ${\textrm{c}_\textrm{p}}$ [Fig. 5(a)]. It further demonstrates that the temperature would have been over predicted if a constant ${\textrm{c}_\textrm{p}} $ is used. Thus, the shift of the temperature profile is predominantly due to heat dissipation rather than the increase in ${\textrm{c}_\textrm{p}} $ with temperature.”
Fig. 5. (a) Peak of T shifts towards surface due to heat dissipation. (b) For a constant Cp, the corresponding shift of T are negligible while the temperatures are over predicted. (c) Effect of previous pulse on the temperature profile of the next pulse, where solid and dotted curves are respectively the temperature right after (TAP) and before (TBP) each pulse. (d) Temperature contour at 1093 K at 0 $\mu $s for pulses 10-50. (e) Temperature contour at 1093 K at 1 μs for pulses 10-50.
The effect of heat accumulation on the temperature profile due to multiple pulses is further demonstrated in Fig. 5(c), in which TBP and TAP represent the temperature right before and after the incidence of indicated pulse number, respectively. It shows that the temperature profiles TAP2 and TAP3 are respectively raised from TBP2 and TBP3 upon incidence of each of the first three laser pulses. When comparing TAP1, TAP2 and TAP3, the temperature peak is increased from 853 K to 1216 K and its position is shifted 5.2 µm to 11.2 µm away from the geometrical focus, toward the surface. This is due to the accumulative heating effect of the previous pulse(s). In between two adjacent pulses, the available time for heat to dissipate is 1µs, controlled by the repetition rate (f) of the laser (1 MHz). For instance, TAP1 becomes TBP2 after the heat dissipation. Figure 5(c) also shows that, after heat dissipation, the peak of the temperature profile returns to the same location, around 13 µm away from the geometrical focus for all three pulses (dashed lines), but with increased peak values from 569 K to 919 K for TBP1 to TBP3 respectively. The above effect of heat accumulation makes TAP to converge to TBP when the number of pulses increases, as evident from the temperature profiles of 30th and 50th pulse.
Glass softening temperature (Tsoft = 1093 K) is chosen to define the contour of the heat modified region [32]. It is observed from temperature evolution [blue curve in Fig. 4(b) that, the diffused temperature (after 1 µs) remains above 1093 K after the 5th pulse]. The change in size and shape of the temperature contour at 1093 K (in yz-plane) for pulses starting from 10 to 50 in 10 pulse intervals are shown in Figs. 5(d) and 5(e). Although the peak temperatures of both the cases are located at around same positions, the sizes of the temperature contour are different at time 0 $\mathrm{\mu}$s and 1 $\mathrm{\mu}$s. The cross-sectional size of the contours at 1 $ \mathrm{\mu}$s are smaller than the corresponding contours at 0 $\mathrm{\mu}$s due to heat dissipation. For both cases (0 & 1 $\mathrm{\mu}$s), the size increases with pulse number and saturates towards higher pulses, whereas the center remains unchanged as explained above. The size increases with pulse number because of heat accumulation. This will lead to modification of the material within the contour due to visco-elastic deformation and glass element flow.
From the simulation results shown in Fig. 5, we conclude that, for multi-pulse interaction of fs-laser with B33 material, the center of the temperature contour continuously moves away from the geometrical focus upon incidence of each subsequent pulse, however, it always settles around the same longitudinal position after heat dissipation on the 1-µs time scale. This further provides insight to our strategy for achieving effective welding: by placing the interface of the two substrates to be welded at the position where the centers/peaks of TAP and TBP converge, which is approximately 13 µm away from the geometrical focus and toward the laser source for the case that was simulated.
2.4 Prediction of heat affected zone and internal modification region during multi-pulse processing
The complete spatial distributions (yz-section) of the temperature after 1 $\mathrm{\mu}$s for the 1st and 50th pulse are shown in Figs. 6(a) and 6(b) respectively. The red color contour in both these figures are the plasma profile within which the maximum plasma density exceeds the critical value (${\mathrm{\rho }_\textrm{c}}$ = 0.2${\times} {10^{21}}\textrm{c}{\textrm{m}^{ - 3}})$. This plasma contour represents the IMR [9]. The black contour in Fig. 6(b) covers the area having temperature higher than Tsoft and is considered as the HAZ. As the temperature does not reach to Tsoft until arrival of the third pulse [Fig. 4(b)], there is no HAZ contour identified for the first pulse in Fig. 6(a). The majority portion of the HAZ is located well above the geometrical focus, due to the nonlinear electron dynamics during pulse propagation [5]. In comparison to the 1st pulse, the peak temperature for 50th pulse has increased from 569 K to 2162 K. However, the corresponding peak location for 50th pulse is shifted only 600 nm from that of 1st pulse due to heat dissipation as explained in the previous sub-section (Fig. 5).
Fig. 6. Temperature distribution (yz-cross section) after 1 $\mu $s for the (a) 1st pulse and (b) 50th pulse. The red contour in both figures represent the IMR, which is the plasma contour at ${\rho _c}.$ Locus of temperature at Tsoft = 1093 K is shown as HAZ (black contour) in (b).
For the prediction of IMR, it is noted that the individual interactions of the free electrons in the focal volume with successive pulses are approximately the same and produce the identical deposited energy distribution Qv(z) by each pulse [9].
Figure 7(a) shows the time evolution for electron density between successive pulses. The plasma density drops down to the order of 1015 cm−3 when time reaches to nanosecond range. Therefore, it has negligible effect on the next pulse that arrives one or a fraction of one microsecond later. Because, when the time interval between successive pulses is larger than the plasma relaxation time, the free-electron density gets similar to that in the unexcited dielectrics and the interaction of dielectrics with the subsequent pulse is same to that with the former pulse [10]. Thus, for each pulse, the solid sees a similar behavior of ρmax and αmax, which is also described in [9,10]. However, the effect of thermally ionized electrons becomes significant as the pulse number increases as shown in Fig. 7(b) and has been considered in the modelling. The expression for thermally ionized electron density (${\mathrm{\rho }_{\textrm{therm}}}$) is obtained from [11], which depends on temperature and bound electron density (${\mathrm{\rho }_{\textrm{bound}}}$).
2.5 Effect of laser parameters on HAZ and IMR
The effect of pulse energy and repetition rate on HAZ is analyzed and shown in Fig. 8. For a fixed repetition rate of 1 MHz, the size of HAZ increases when pulse energy increases from 0.3 $\mathrm{\mu}$J to 1.0 $\mathrm{\mu}$J. In addition, the HAZ shifts towards the surface with increasing pulse energy as shown in Fig. 8(a).
Fig. 8. (a) Effect of pulse energy at 1 MHz repetition rate, (b) Effect of repetition rate at fixed pulse energy of 0.6 μJ.
On the other hand, repetition rate does not change the position of HAZ. As shown in Fig. 8(b), when repetition rate increases from 0.5 MHz to 2 MHz (at a fixed pulse energy of 0.6 μJ), the size of HAZ increases while the position of its center remains unchanged. Thus, for welding process, repetition rate is more effective than the pulse energy as the size is increased around the same location. This makes the parameter optimization process easier in experiment without changing the focus location with respect to the interface.
To obtain more insights into the effect of laser parameters, two different sets of welding configurations with same average power of 0.6 watt are modelled. The processing parameters and the model prediction of HAZ and IMR are summarized in Table 2.
Table 2. Comparison of the two welding configurations with same average laser power of 0.6 watt.
The laser wavelength and the focal spot radius for both the configurations are 1030 nm and 1.13 $\mathrm{\mu}$m, respectively. Figure 9(a) compares the HAZ of the two configurations. The center of the HAZ for both configurations is well above the geometrical focus, due to the nonlinear electron dynamics during pulse propagation [4]. Even if the average laser power for both configurations is same, higher pulse energy (blue contour) shifts the HAZ more towards top surface in relation to the geometrical focus as evident by the experimental results shown in [5].
During welding experiment, the laser should be focused at a location such that the interface resides inside the modification region, suitably at the widest portion. This fact has also been shown experimentally for picosecond-pulsed laser welding of Borosilicate glass substrates [33], where the focal spot was positioned 0 - 40 µm below the interfaceand the maximum shear forces are reached at focal displacements approximately around −20 micron.” This result is consistent to our model predicted offset direction and values shown in Fig. 9. Figure 9(a) shows that the widest portion of HAZ (blue contour) is located 14.2 $\mathrm{\mu}$m and 8.6 $\mathrm{\mu}$m above geometrical focus for Config-1 and Config-2, respectively. It further shows that the widest portion of IMR (blue contour) is located 12.5 $\mathrm{\mu}$m and 9.2 $\mathrm{\mu}$m above the geometrical focus for Config-1 and Config-2, respectively. The model predicted maximum transverse (along y) and longitudinal (along x) size of HAZ and IMR for both configurations are given in Table 2. The maximum transverse size of IMRs for both configurations are almost same, whereas the longitudinal size along the beam propagation is elongated for higher pulse energy. This behavior of plasma density causes the shift of the HAZ for higher pulse energy as demonstrated in Fig. 9(a). Thus, the model predicts that, to ensure that the interface is located at the wider portion of the HAZ, the focus of the laser beam for Config-2 should be 5.6 $\mathrm{\mu}$m closer to the interface than that of Config-1. Both configurations are used for welding of B33 plates, which are described in the following sections.
3. Welding experiments
3.1 Sample preparation
For fs- laser micro welding, it is easier to be welded when optical contact at the interface is created between the two substrates although welding is achievable while there is an air gap between two substrates [16,17]. Optical contact can be achieved when the sample surfaces have sufficiently high flatness (${\sim} $λ/4) and low roughness. Any kind of contaminants, dust particles or surface defects/scratches will reduce the optical contacts. Therefore, the substrates need to be cleaned properly before making optical contact. The optical contact can be established by simply putting the two plates together if the samples are clean enough optically. Applying a radially outward pressure by gently pressing the sample with fingertips will remove the air out of the interface. Interference fringe at the interface is a signal for poor optical contact. B33 glass plates of 1-inch diameter and 0.5-mm thickness are used as welding samples. These samples have surface flatness of λ/4 (λ = 633 nm). When the two samples are held together, large area optical contact (direct bond) are achieved as shown in Fig. 10 without requiring any external pressure. The remaining dust particles on the sample surface didn’t allow complete optical contact at two outer locations. This direct bond is further enhanced through laser welding.
Fig. 10. Large area optical contact (direct bond) achieved in B33 plates of 1-inch diameter and 0.5-mm thickness without external pressure.
3.2 Experimental set up for laser welding
The above samples that have optical contact are welded using femtosecond laser system (Amplitude Satsuma HP3) delivering pulses of 300 fs at central wavelength of 1030 nm. The repetition rate can be varied from 1 kHz to 2 MHz. The maximum pulse energy is 40 µJ and it can be adjusted through a Beam Shaper (LS-SHAPE, LASEA). As shown in Fig. 11, a telescope system guides the beam to a microscope objective (Nikon Plan, 20X, 0.5 NA) that focuses the pulses around the interface of two substrates to be welded. Samples are precisely positioned using a motorized three-axis translation stage (Jenny Science, Lxc80F40) with 100 nm resolution. LabVIEW program is used to control the motion of the stage and synchronize it with the laser. The laser is off during acceleration and deceleration of the stage and it is turned on when speed reaches the desired value.
The laser beam was focused 200 $\mathrm{\mu}\textrm{m}$ (136.6 $\mathrm{\mu}\textrm{m}$ in B33) below top surface. A 50X objective and camera are used to measure the beam waist (${\mathrm{\omega }_0}$) of the focused beam inside BF. The radius of the focused beam at 20 different positions around the focal position, with 0.001 mm resolution, was measured and fit with the Gaussian beam propagation equation to obtain ${\mathrm{\omega }_0}$. The ${\mathrm{\omega }_0}$ thus obtained is $1.13\; \mathrm{\mu}\textrm{m}$ with Rayleigh range (${\textrm{z}_\textrm{R}}$) of $5.15\; \mathrm{\mu}\textrm{m}$ inside material. These values were subsequently used in the simulations described in section 2. The samples are translated in x, y and z directions to allow the incident laser beam to write welding patterns at the required focusing location relative to the interface. The laser was focused at the top surface of top substrate and then at the bottom surface of bottom substrate of the assembly by observing the confocal image. The interface was determined as the middle of the top and bottom surface.
4. Welding results
Using the model predicted offset, the two configurations discussed in modelling sections were used for welding of two sets of B33 substrates. The two substrates bonded directly through optical contact are shown in Figs. 12(a) and 12(b) for configuration 1 and 2 respectively. There are a few air (grey color) patches (indicated by red dotted contours) remaining at the interface due to suboptimal optical contact achieved during the experimental process. To ensure that the interface is located at the wider portion of the HAZ, the focus of the laser beam was placed at the model-predicted position relative to the interface of the two substrates, ${\sim} $15 $\mathrm{\mu}$m and 10 $\mathrm{\mu}$m for the two configurations, respectively. Both the configurations are welded, and the welded assemblies are shown in Figs. 12(c) and 12(d) for Configuration 1 and 2 respectively. The welding pattern consists of 8 parallel seams with 2-mm gap and 21 scanned lines of 10 mm long within each seam. The optical contact has been reinforced by laser welding as the remaining air patches have clearly been reduced by the laser welding seams.
Fig. 12. Direct bonding achieved through optical contacts for (a) config-1 and (b) config-2. The red dotted contours indicate the air patches remained after optical contact. Femtosecond-Laser welded assemblies for (c) config-1 and (d) config-2. The blue dotted rectangular area are used for calculation of shear stress.
The shear strength of the welded substrates corresponding to Configuration-1 is measured, using a shear break testing method similar to what is described in [36]. Shear stress is calculated by using equation, P = F⁄S, where F is the shear force and S represents the welded area as shown by the blue rectangles in Figs. 12(c) and 12(d). The maximum force, which occurs immediately before breakage, is used to determine the weld breaking stress. Four samples were measured and the probability of survival as a function of shear stress is shown in the Weibull plot (Fig. 13). A maximum of 16 MPa of shear strength has been demonstrated and it is expected that, the statistics on the survival probability will improve with a greater number of samples tested.
It is noted that both optical contact and fs laser welding contributes to the measured shear stress. Using laser micro-welding the joining strength of above samples with previously established optical contact can be reinforced at least two to three-fold [34,35]. A detailed analysis of effect of optical contact on shear stress can be found from [36,37]. Okamoto et al. has demonstrated in Fig. 5 of [36] that the shear stress purely contributed by optical contact decreases from 1.5 MPa to 0.4 MPa while the area increases from 20 mm2 to 500 mm2. Therefore, the estimated shear stress for the samples presented in this paper is less than 1.5 MPa given the sample area of 506 mm2, which is the maximum size for optical contact. As the measured maximum shear stress of the welded samples is 16 MPa, which is an order of magnitude larger, we concluded that the used welding parameters have produced the direct bonding of the samples.
5. Conclusion
A dynamic heat accumulation modelling for femtosecond laser welding of Borofloat glass is developed to optimize the welding process. The temperature evolution and internal modifications are predicted by incorporating the nonlinear electron dynamics along with temperature dependent thermal properties. The modelling is built to predict welding geometry, that reduces experimental parameter optimization, considering temperature dependent thermal properties and absorption coefficient. To our best knowledge, this is the first model that is capable of predicting the relative position between the geometrical focus and the interface of the two glass substrates to be welded. The modelling predicts that for welding process, repetition rate is more effective than the pulse energy as the size of laser-induced modification is increased while the location is maintained. Two B33 substrates with previously established optical contact have been successfully welded by considering the size and geometry of the HAZ predicted by the simulation results. Shear strength of 16 MPa has been achieved for a typical welded assembly. The experimental validation of the model will be performed and reported in a future publication, expanding the experiments presented in this paper, including systematic study of shear stress and the cross-section images of the heat affected zone in relation to the interface for various offset distances. This study can be further extended for welding of transparent substrates having air gap by applying various beam shaping techniques.
Funding
U.S. Department of Energy (DE-AC52-07NA27344); Lawrence Livermore National Laboratory (LLNL-LDRD Program, Project 18-ERD-042).
Acknowledgments
The authors thank Dr. S. Patra and Dr. R. Haque of Lawrence Livermore National Labs, USA for measuring the shear strength of the bonded assembly.
Disclosures
The authors declare no conflicts of interest.
References
1. I. Miyamoto, K. Cvecek, and M. Schmidt, “Crack-free conditions in welding of glass by ultrashort laser pulse,” Opt. Express 21(12), 14291–14302 (2013). [CrossRef]
2. I. Miyamoto, A. Horn, J. Gottmann, D. Wortmann, and F. Yoshino, “Fusion welding of glass using femtosecond laser pulses with high-repetition rates,” J. Laser Micro/Nanoeng. 2(1), 57–63 (2007). [CrossRef]
3. L. L. Taylor, J. Xu, M. Pomerantz, T. R. Smith, J. C. Lambropoulos, and J. Qiao, “Femtosecond laser polishing of germanium [Invited],” Opt. Mater. Express 9(11), 4165–4177 (2019). [CrossRef]
4. T. Feng, P. K. Sahoo, F. R. Arteaga-Sierra, C. Dorrer, and J. Qiao, “Pulse-Propagation Modeling and Experiment for Femtosecond-Laser Writing of Waveguide in Nd:YAG,” Crystals 9(8), 434 (2019). [CrossRef]
5. I. Miyamoto, K. Cvecek, Y. Okamoto, and M. Schmidt, “Internal modification of glass by ultrashort laser pulse and its application to microwelding,” Appl. Phys. A 114(1), 187–208 (2014). [CrossRef]
6. I. Miyamoto, K. Cvecek, and M. Schmidt, “Evaluation of nonlinear absorptivity in internal modification of bulk glass by ultrashort laser pulses,” Opt. Express 19(11), 10714–10727 (2011). [CrossRef]
7. I. Miyamoto, A. Horn, and J. Gottmann, “Local melting of glass material and its application to direct fusion welding by ps-laser pulses,” J. Laser Micro/Nanoeng. 2(1), 7–14 (2007). [CrossRef]
8. I. Miyamoto, K. Cvecek, and M. Schmidt, “Simple evaluation procedure of nonlinear absorptivity in glass welding using USLP with high-pulse repetition rates,” Phys. Procedia 39, 526–533 (2012). [CrossRef]
9. M. Sun, U. Eppelt, W. Schulz, and J. Zhu, “Role of thermal ionization in internal modification of bulk borosilicate glass with picosecond laser pulses at high repetition rates,” Opt. Mater. Express 3(10), 1716–1726 (2013). [CrossRef]
10. M. Sun, U. Eppelt, W. Schulz, and J. Zhu, “Mechanism of internal modification in bulk borosilicate glass with picosecond laser pulses at high repetition rates,” inPacific Rim Laser Damage 2015: Optical Materials for High-Power Lasers, (International Society for Optics and Photonics, 2015), 953214.
11. I. Miyamoto, Y. Okamoto, R. Tanabe, Y. Ito, K. Cvecek, and M. Schmidt, “Mechanism of dynamic plasma motion in internal modification of glass by fs-laser pulses at high pulse repetition rate,” Opt. Express 24(22), 25718–25731 (2016). [CrossRef]
12. I. Miyamoto, K. Cvecek, and M. Schmidt, “Nonlinear absorption dynamics simulated in internal modification of glass at 532 nm and 1064 nm by ultrashort laser pulses,” Procedia CIRP 74, 344–348 (2018). [CrossRef]
13. R. Weber, T. Graf, P. Berger, V. Onuseit, M. Wiedenmann, C. Freitag, and A. Feuer, “Heat accumulation during pulsed laser materials processing,” Opt. Express 22(9), 11312–11324 (2014). [CrossRef]
14. F. Bauer, A. Michalowski, T. Kiedrowski, and S. Nolte, “Heat accumulation in ultra-short pulsed scanning laser ablation of metals,” Opt. Express 23(2), 1035–1043 (2015). [CrossRef]
15. J. Chen, R. M. Carter, R. R. Thomson, and D. P. Hand, “Avoiding the requirement for pre-existing optical contact during picosecond laser glass-to-glass welding,” Opt. Express 23(14), 18645–18657 (2015). [CrossRef]
16. K. Cvecek, R. Odato, S. Dehmel, I. Miyamoto, and M. Schmidt, “Gap bridging in joining of glass using ultra short laser pulses,” Opt. Express 23(5), 5681–5693 (2015). [CrossRef]
17. S. Richter, F. Zimmermann, R. Eberhardt, A. Tünnermann, and S. Nolte, “Toward laser welding of glasses without optical contacting,” Appl. Phys. A 121(1), 1–9 (2015). [CrossRef]
18. H. Chen, J. Duan, Z. Yang, W. Xiong, and L. Deng, “Picosecond laser seal welding of glasses with a large gap,” Opt. Express 27(21), 30297–30307 (2019). [CrossRef]
19. H. Chen, L. Deng, J. Duan, and X. Zeng, “Picosecond laser welding of glasses with a large gap by a rapid oscillating scan,” Opt. Lett. 44(10), 2570–2573 (2019). [CrossRef]
20. G. Zhang, R. Stoian, W. Zhao, and G. Cheng, “Femtosecond laser Bessel beam welding of transparent to non-transparent materials with large focal-position tolerant zone,” Opt. Express 26(2), 917–926 (2018). [CrossRef]
21. L. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).
22. M. Sun, U. Eppelt, S. Russ, C. Hartmann, C. Siebert, J. Zhu, and W. Schulz, “Numerical analysis of laser ablation and damage in glass with multiple picosecond laser pulses,” Opt. Express 21(7), 7858–7867 (2013). [CrossRef]
23. P. K. Kennedy, “A first-order model for computation of laser-induced breakdown thresholds in ocular and aqueous media. I. Theory,” IEEE J. Quantum Electron. 31(12), 2241–2249 (1995). [CrossRef]
24. D. J. Little, M. Ams, and M. J. Withford, “Influence of bandgap and polarization on photo-ionization: guidelines for ultrafast laser inscription,” Opt. Mater. Express 1(4), 670–677 (2011). [CrossRef]
25. N. M. Bulgakova, V. P. Zhukov, and Y. P. Meshcheryakov, “Theoretical treatments of ultrashort pulse laser processing of transparent materials: toward understanding the volume nanograting formation and “quill” writing effect,” Appl. Phys. B 113(3), 437–449 (2013). [CrossRef]
26. A. Couairon, L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, “Filamentation and damage in fused silica induced by tightly focused femtosecond laser pulses,” Phys. Rev. B 71(12), 125435 (2005). [CrossRef]
27. L. L. Taylor, J. Qiao, and J. Qiao, “Optimization of femtosecond laser processing of silicon via numerical modeling,” Opt. Mater. Express 6(9), 2745–2758 (2016). [CrossRef]
28. (Schott Borofloat 33), retrieved https://psec.uchicago.edu/glass/borofloat_33_e.pdf.
29. S. Ghosh, A. Ghosh, J. Mukherjee, and R. Banerjee, “Improved thermal properties of borosilicate glass composite containing single walled carbon nanotube bundles,” RSC Adv. 5(63), 51116–51121 (2015). [CrossRef]
30. P. Richet and Y. Bottinga, “Thermochemical properties of silicate glasses and liquids: a review,” Rev. Geophys. 24(1), 1–25 (1986). [CrossRef]
31. K. Trachenko and V. Brazhkin, “Heat capacity at the glass transition,” Phys. Rev. B 83(1), 014201 (2011). [CrossRef]
32. S. Richter, “Direct laser bonding of transparent materials using ultrashort laser pulses at high repetition rates,” 2014).
33. K. Cvecek, I. Miyamoto, J. Strauss, V. Bui, S. Scharfenberg, T. Frick, and M. Schmidt, “Strength of joining seams in glass welded by ultra-fast lasers depending on focus height,” J. Laser Micro/Nanoeng. 7(1), 68–72 (2012). [CrossRef]
34. D. Hélie, M. Bégin, F. Lacroix, and R. Vallée, “Reinforced direct bonding of optical materials by femtosecond laser welding,” Appl. Opt. 51(12), 2098–2106 (2012). [CrossRef]
35. D. Hélie, F. Lacroix, and R. Vallée, “Reinforcing a direct bond between optical materials by filamentation based femtosecond laser welding,” J. Laser Micro/Nanoeng. 7(3), 284–292 (2012). [CrossRef]
36. Y. Okamoto, I. Miyamoto, K. Cvecek, A. Okada, K. Takahashi, and M. Schmidt, “Evaluation of Molten Zone in Micro-welding of Glass by Picosecond Pulsed Laser,” J. Laser Micro/Nanoeng. 8(1), 65–69 (2013). [CrossRef]
37. K. Cvecek, I. Miyamoto, J. Strauss, M. Wolf, T. Frick, and M. Schmidt, “Sample preparation method for glass welding by ultrashort laser pulses yields higher seam strength,” Appl. Opt. 50(13), 1941–1944 (2011). [CrossRef]
