During processing of glass using ultra-fast lasers the formation of bubble-like structures can be observed in several glass types such as fused silica. Their formation can be exploited to generate periodic gratings in glasses but for other glass processing techniques such as waveguide-writing or glass welding by ultra-fast lasers the bubble formation proves often detrimental. In this work we present experiments and their results in order to gain understanding of the origins and on the underlying formation and transportation mechanisms of the gas bubbles.
© 2014 Optical Society of America
During processing of glass by ultrafast lasers with pulse durations in femtosecond and picosecond range the formation of bubble-like structures can be observed [1–4]. In the past the controlled generation of these bubbles, especially in fused silica has received considerable interest , since this effect can be exploited for the generation of periodic structures. Moreover, the formation of bubbles has impact also on the generation of waveguides as well as on glass welding by ultra-fast lasers  acting as undesirable scatter centers in the first case and reducing the strength of the welding seam in the latter case. The formation of bubbles depends strongly on the glass type used. Bubbles can be observed in fused silica and in borofloat 33 glass types whereas almost no bubbles are formed in borosilicate D263 glass and soda lime glasses.
The setup used for the glass processing experiments described in this work is shown in Fig. 1. The laser, a modelocked Nd:YVO4-laser (Fuego, TBWP, Switzerland) provides pulses with a FWHM-duration of 10 ps at 1064 nm wavelength, with adjustable (single pulse – 8.2 MHz) pulse repetition rate and up to 50 W of nominal average power. Figure 2 shows microscope images of a typical bubble formation observed in fused silica. The following irradiation conditions were used: pulse energy EP = 732 nJ, repetition rate f = 8.2 MHz, feed speed v = 50 mm/s and a numerical aperture of the microscope objective NA = 0.8. The focus (coinciding with the tip of the molten zone) was placed 200 µm below the upper surface.
The molten zone in Fig. 2 appears as a low-contrast contour with a tear drop shape (when viewed in cross section) having a width of approximately 40 µm and a height of about 70 µm. The low contrast of the molten zone is caused by a slight change of the refractive index of the glass induced by the laser processing. Clearly visible are the bubbles within the molten zone that are spaced periodically near the top of the molten zone. This periodic spacing that occurs at certain processing conditions can be exploited to structure gratings in suitable glass materials. However, as can be seen from the in the side view of Fig. 2, the gas bubbles affect the size of the molten zone particularly decreasing its height by shifting the lower end of the contour of the molten zone towards the bubbles. This is detrimental to glass welding since the interface of two glass plates to be welded should be positioned between the bubbles and the lower end of the contour of the molten zone. The reduction of the molten zone by the bubbles reduces effectively the available tolerance (especially if a gas bubble as shown in Fig. 8 forms) of a welding seam and increases the requirements on the positioning accuracy of the welding system. Moreover, in waveguide writing applications the bubbles can act as strong scatterers, thus increasing the losses of the waveguide. Due to the impact the bubble formation has on the above described glass processing techniques the knowledge of the underlying mechanisms might prove essential for the purposeful manipulation of the bubble formation. Although possible origins of the gas bubble were discussed in , the model given there was not exhaustive as many effects that can be observed were not included in the description. Thus, the aim of the present work is to characterize the bubble generation process by several additional methods such as analysis of chemical composition of the gas bubbles as well as high speed camera videos of the plasma region. We arrive at an expanded model which we discuss with other plausible theories such as in .
2. Observations of underlying processes
In this section several observations as well as experiments and their results will be described. The first part of the experiments will concentrate on macroscopic properties of the molten pool whereas the second part will analyze the underlying chemical processes. For all the experiments shown in this section fused silica has been used as glass type, because it exhibits very prominent bubble formation and it consists almost exclusively of SiO2 as no further chemical additives are present. Thus it is highly suitable for a detailed analysis of bubble formation, since the absence of additives will not distort or tarnish the experimental results by undue or unexpected interactions or reactions. The generation of gas bubbles can be classified in two parts. The first part concerns the origins of the gas, e.g. whether it is a gas at all and, if so, what kind of gas. The second part concerns the transportation and formation mechanisms of the bubble, e.g. the bubble shape or buoyancy. The experiments described here cannot give an extensive and complete understanding of all underlying effects. Our intent is, therefore, to provide experimental results that help to compose an overall picture of the bubble formation mechanism. Consequently, as there will be room for speculation some further competing bubble/void formation hypotheses will be discussed in section 2.5. Before proceeding to the experiments a brief description of the involved processes is given using glass welding by ultra-short laser pulses as an example:
In this method the pulses, at a wavelength transparent to the processing material, are tightly focused onto the joint surface of two glass pieces intended for welding. Due to the tight focusing and short laser pulse duration, the light intensity inside the focal volume reaches values high enough to lead to multi-photon absorption . For pulse durations well below 100 fs also tunnel and field ionization may occur instead. The electrons generated by this nonlinear interaction become free and are accelerated by absorbing photons directly from the laser beam. These electrons can and will scatter inelastically on other atoms consequently ionizing some of those atoms and effectively setting off avalanche ionization within the focal volume. Once started, the avalanche ionization can carry on even if the pulse intensity drops below the value necessary for multiphoton ionization. During irradiation the electron plasma builds up very quickly and reaches very high temperatures.
Subsequently, ions as well as not ionized material are heated by electron-phonon coupling. However, the presence of ionization does not necessarily mean that oxygen atoms have been liberated since even the SiO2 network could theoretically lose one electron while the network itself is more or less intact (compare E’-centers in SiO2 with + 1 net charge ). Therefore, the purpose of the following consideration is to determine how probable thermally induced dissociations of SiO2 are. If probable, free oxygen will be generated for sure, because independent of the thermal dissociation laser induced ionization processes will still take place.
Numerical simulations  show that during the laser irradiation in a steady-state case the temperatures may easily reach a temperature region between 3000 and 4000 K. Using the Saha equation  the density of thermally excited (free) oxygen atoms and ions can be calculated. Because the calculation of the internal partition functions necessary to solve the Saha equation for the dissociation process of glass SiO2 → Si + 2 O is quite involved, we will restrict our considerations only to the energetically most demanding process, namely the ionization of (already free) oxygen atoms: O → O + + e-.
That this process is indeed energetically most demanding is shown in the following. The boiling point of fused silica described in literature is 2950° C . Boiling, if it is understood as the transformation of the silica network into single SiO2 molecules, will provide a very fast decomposition of the single molecules into silicon and oxygen. This is due to the fact that SiO2 is only a total formula. In reality, for solid and liquid states, one silicon atom (excluding color centers, NBOHCs and other defects) shares 4 oxygen bonds. In order to exist in a single molecule state the SiO2 molecule would have to form double bonds to each of the oxygen atoms (similar to CO2). However, theoretical and experimental analysis shows that Si = O (double) bonds are very instable already at room temperature [12,13]. Consequently, should any gaseous SiO2 form inside the molten zone it will rapidly dissociate into silicon and oxygen, especially due to the very high temperatures present. Thus, boiling of fused silica (if possible under the high pressure inside the molten zone) will result on one hand in free oxygen. On the hand also other dissociation process are possible. The energy required for SiO2 → Si + 2 O is 857.3 kJ/mol while the energy required for O → O + + e- lies at 1313.9 kJ/mol. Thus if the second process is thermodynamically possible the first one will take place for sure because of the smaller energy it requires. Furthermore, not considered in the Saha equation is the laser induced ionization of the components. Thus, considering only the temperature-based Saha equation for thermal dissociation of oxygen atoms to oxygen ions (O → O + + e-) the calculation will yield only the minimum amount of substance of freed oxygen. In reality the amount of oxygen generated in this process will be much larger.
Figure 3 shows the dependence of the oxygen ion density in ions/µm3 in the temperature range between 2800 K and 4500 K. In order to calculate this dependence an isochoric transition from solid bulk material to the molten/plasmatic material was assumed, meaning that the initial oxygen atom concentration inside the glass melt is the same as that of bound oxygen in fused silica bulk material. Analysis of the cross-sections given by numerical simulations in  shows that the volume of the hot plasma region lies typically in a range between 103 and 104 µm3. Comparing this volume with the results in Fig. 3 yields the rough estimate that within the plasma region could exist up to 0.02 µm3 of molecular oxygen. This estimate considers only thermal oxygen ionization processes and neglects laser induced as well as thermal dissociation of SiO2 and SiO to free oxygen, the laser spot movement and subsequent oxygen accumulation as well as volume expansion due to the high temperatures present. This means that the amount of generated oxygen will be very likely considerably larger.
While besides the laser induced ionization processes also the Saha equation strongly hints at the presence of free oxygen atoms and ions within the plasma zone that could possibly react to form molecular oxygen during the cool-down phase, it does not explain how the bubbles are formed during irradiation. For a possible explanation one could assume that the free oxygen atoms or ions are generated separately and at random positions within the melt, since the laser induced or thermally induced dissociation processes act at an atomic or molecular level (even if distributed over the interaction volume at the same time). This assumption is especially valid for the here considered case, were the plasma zone is much larger than the focal spot (compare Fig. 5), since it is avalanche ionization which is responsible for the heating. Therefore, ultra-fast laser induced cavitation mechanisms [14–16] are inadequate to explain the bubble generation in an extended hot plasma zone. The potential energy of the free oxygen will be definitely higher than that of glass molecules within the melt while their mobility will be much higher due to their smaller size (compare description of oxygen and aluminum in ). Their Brownian motion will lead to a (time-dependent) fluctuation of the local concentration of free oxygen. Due to the higher potential energy of free atomic and ionic oxygen the local intrinsic energy of a melt region depends on the local concentration of free oxygen at the same location. As the free oxygen ions and atoms may gain kinetic energy by recombinations to atomic oxygen or by reacting to oxygen molecules, the local temperature may rise sufficiently to vaporize the glass melt at the same location. For a sufficiently large vaporized particle ensemble the mixture of particles will exhibit macroscopic properties such as pressure, temperature or density. This will result in a formation of an interface (surface) against the adjacent melt fluid thus forming a gaseous bubble within the melt. Due to the different density inside the gas bubble also buoyant forces will affect the bubble effectively driving it upwards. In the following several effects will be described that can be observed during bubble formation that will help clarify the origin of bubble formation.
2.1 Multi-pass irradition
One of the main questions concerning the formation of gas bubbles is whether the bubbles are formed from the excited free atoms and ions generated by laser induced ionization and thermal dissociation or if the bubbles form inside the molten zone from interstitial oxygen molecules (compare  and literature therein) that are nanoscopic inclusions of molecular gas particles that could stem from the manufacturing process of the glass. The first case assumes that the constitutional elements of glass – silicon and oxygen – are present in the correct stoichiometrical ratio necessary to form glass. This condition may not always be fulfilled since interstitial peroxy linkages are known to exist inside fused silica . In any case – independently of the oxygen’s positions in the original glass – after irradiation and bubble formation the initial stoichiometry is not preserved inside the solidified molten zone. In the second case (the one with interstitial oxygen molecules) the gas molecules are already present within the glass material and the melting of the glass is necessary to provide a fluidity and viscosity that allows the surplus gas molecules to coalesce. After cool down the stoichiometry of the constituent elements of the bulk glass should be closer to the ideal ratio.
In order to determine whether the first or the second case is valid we decided to make multi-pass irradiation runs of the same glass region. In the first case the number and overall volume of gas bubbles should increase with increasing number of melt runs since each time plasma is produced also free oxygen atoms and ions should be produced. Of course, the increase rate of the number of bubbles will decrease with increasing irradiation passes because already formed bubbles from previous irradiation passes will act as scatterers and decrease the laser incoupling efficiency as already mentioned above. In the second case most of the dissolved gas within the initial bulk material should coalesce during the first few irradiations. After the first few irradiations no further significant increase of the overall bubble volume should be observed.
Figure 4 shows the experiment carried out as shown schematically in Fig. 1. The irradiation parameters were as follows: pulse energy EP = 4 µJ, repetition rate f = 1 MHz, feed speed v = 20 mm/s and a numerical aperture of the microscope objective NA = 0.55. The microscope image in Fig. 4(a) shows that the number of bubbles increases with increasing number of irradiations. Interestingly, already for a single irradiation pass the average gas bubble volume of ~22 µm3/(µm melt run) is three orders of magnitude larger than the minimal prediction given in section 2, page 4 (~0.02 µm3 oxygen). Besides the massive simplifications for the estimated 0.02 µm3 oxygen within the plasma zone, the high volume at the first irradiation pass could be a sign for additional gas contribution from interstitial oxygen molecules. However, the volume increase in Fig. 4(b) shows a strong rise for few irradiation passes and a smaller increase for a higher number of passes. But, as already mentioned, this should be expected since the bubbles present should scatter the laser radiation thus decreasing the plasma generation efficiency. The observed volume increase even at 20 irradiation passes is a strong hint that the bubbles are generated by the ionization process and do not origante from nanoscopic inclusions within the original bulk material coalescing inside the molten zone.
2.2 Dynamics of formation
Although the results of multiple irradiation experiments strongly hint at the fact that the gas is generated within the plasma these results by themselves not conclusive enough since they do not show the formation dynamics of the bubbles. In order to observe the dynamics a high speed camera was used to observe the plasma region. The camera used a macro objective lens with a 4:1 magnification ratio and was positioned in such a way that the plasma could be observed perpendicularly to the irradiation laser from one of the polished facets of the glass plate. The frame rate of the camera was 25 kHz while the exposure time was set to 2 µs. Figure 5 shows a sequence of image frames taken at the following irradiation conditions: pulse energy EP = 12 µJ, repetition rate f = 0.5 MHz, feed speed v = 20 mm/s and numerical aperture of the microscope objective NA = 0.55. Since the frame rate of the camera would result in too many pictures to show within the scope of this paper we decided to show in Fig. 5 only each 50th frame of the original image sequence resulting in a time difference of 2 ms between each image frame displayed in Fig. 5. Additional supplementary video material can be found only in Media 1, Media 2. Media 1 shows the behavior of the plasma from −10 ms to + 10 ms in Fig. 5 (compare time stamp) while Media 2 shows a time lapse video from the beginning, where the laser generates plasma in air before the glass plate is moved into the laser beam. The time range extends form ca. −100 ms to + 130 ms (compare Fig. 6(b)).
Figure 5 shows in each frame a bright region that is supposedly the plasma region. This fact is corroborated by numerical simulations  as well as similarly shaped structures in glasses with and without bubble formation [6,9] as is also discussed in section 2.3 of this work (see Fig. 10). As can be at 4 ms. Afterwards, in the frames at 6 - 10 ms, a structure is visible behind (on the right side of) the bright region that was not present in front of the bright regions at the 0 and 2 ms frames. Obviously something must have occurred at the 4 ms frame that has reduced the incoupling efficiency of the laser. Moreover, there is also a difference between the shapes of bright regions. While the regions at the 0 and 2 ms frames are somewhat smaller and exhibit a more complex structure the regions at 8 and 10 ms are larger and have a simpler outline. Indeed, high speed movies (see Media 1 and Media 2) show that the bright region grows dynamically instable showing strong fluctuations shortly before the bubble is formed, while after the bubble has formed the bright region grows back to its previous size and is dynamically very stable for certain time until it grows instable again.
The time dependent stability of the plasma, especially its size, is shown in Fig. 6. The high speed images were evaluated in size along the profile lines “left-vertical”, “right-vertical”, “upper-horizontal” and “lower-horizontal” (compare Fig. 6(a)). Figure 6(b) shows the long-term plasma size development – the origin of the time scale corresponds to the origin of the image sequence in Fig. 5 (“0 ms” in Fig. 5 = “0 ms” in Figs. 6(b) and 6(c)). Figure 6(c) shows a zoomed-in region with the same time scale as Fig. 5. Clearly visible in Fig. 6(b) is the decrease of the plasma size down to zero. This are the moments where the gas bubbles get stuck. Before, the size of the plasma fluctuates strongly and is in general smaller. After these moments, the plasma size is in general larger and shows much smaller fluctuations. Interestingly, in the time range between 60 and 80 ms only the “upper-horizontal“ size decreases twice down to zero. Simultaneously, the other plasma sizes do also decrease but do not reach zero size. We observe in both cases in the high speed video that the gas bubbles get stuck while the plasma is still present. The plasma grows smaller but, interestingly the size of these particular bubbles is also smaller than the typical size of the other bubbles.
The complete plasma size decrease down to zero (time range 4.5 to 5.8 ms in Fig. 6(c)) makes the observation of the bubble at the laser’s spot location by high speed camera possible as the camera sensor is not overexposed from the plasma radiation. Figure 7(a) shows the image frames from 4.32 to 5.72 ms that belong to the same image sequence as shown in Fig. 5. In the image frame at 4.32 ms a small plasma spot is still present. The scattering of the laser radiation on the bubble is visible as interference fringes in the high speed movie that change in shape from image frame to image frame. While it is easy to see this in the high speed movie, the scattering is very hard to make out in an image sequence (e.g. Fig. 7(a)). In order to increase the visibility of the scattering-induced interference fringes we subtracted from all image frames in Fig. 7(a) an image frame taken at 5 ms (Fig. 7(c)) and increased subsequently the contrast of the difference image frames. The resulting image sequence is shown in Fig. 7(b). The corresponding video sequence is shown in Media 3.
It is highly improbable that such a large bubble should form suddenly. Especially, when considering the observed plasma size instabilities. The instabilities become apparent no later than 20 ms after a bubble separation event, while they grow very obvious for at least 10 ms before the bubble separation event (see Fig. 6(a)). Thus, we have to assume that the bubbles are already present inside the plasma zone. The “invisibility” of the bubbles during the presence of plasma can be attributed to two effects. First, the camera sensor is overexposed by the radiation from the plasma – the scattering on the bubble is therefore not detectable. Second, a very high portion of the laser’s power is absorbed by nonlinear absorption by the plasma  and is thus not available to provide scattered radiation.
This behavior leads to the conclusion that the gas bubbles grow during the plasma interaction and are dragged along with the plasma region. Otherwise a high number of small bubbles should be evenly distributed along the melt run. The bubble’s growth and their dragging takes place until the gas bubble becomes so large that it starts to scatter the laser radiation by which the incoupling efficiency decreases. Nonetheless, as long as the bubbles are relatively small the incoupling efficiency decreases only for the bottom part of the plasma region (the tip of the plasma). The laser can still heat the upper part of the plasma very efficiently, because at this location the heating is mainly provided by avalanche ionization. Under these circumstances also laser light scattered and reflected of the bubbles can still provide heating due to avalanche ionization. Thus the light scattered on small bubbles still contributes to the heating process. This stage is marked by the strong fluctuations of the bright region.
Only after further growth of the gas bubble and its rising due to buoyancy the bubble becomes large enough to severely decrease the laser incoupling efficiency. As a result the plasma ceases partially or completely (depending on irradiation parameters) to exist. During this stage the temperature of the molten zone decreases strongly. In consequence the viscosity of the glass material increases by a large amount so that the gas bubble cannot be dragged any further effectively staying stuck along the way. Indeed, as is shown in Fig. 8 the size of the molten zone decreases (showing the low temperature area of the process) where the bubble has formed. After the bubble has got stuck and the laser spot has moved to a different location along its path inside the glass the incoupling efficiency is back to original (without the light scattering on the bubble) and the ionization and heating processes can take place unhindered. Since in this case new gas bubbles will be formed the process will repeat itself. Under certain irradiation conditions this can lead to a periodic formation of gas bubbles as shown in Fig. 2.
It is to be expected that for lower laser power the occurrence frequency of the bubbles will increase. A smaller laser power creates a smaller plasma region that cools down faster and has thus higher average viscosity than for higher laser powers. Consequently, the drag effect should be less effective while the build-up of gas bubbles can disrupt the laser heating by avalanche ionization earlier during the process.
In the high speed movie it takes on average about 31 ms for the gas bubble to develop and get stuck. During this time the lasers focus and thus the plasma (feed speed 20 mm/s) move 620 µm through the glass. Therefore, the average bubbles distance is much larger in the (herein) discussed high speed movie than the one shown in Fig. 2 and 4(a). The decrease of the plasma size in Fig. 6 is obviously correlated to the size decrease of the molten zone around the gas bubbles – an effect that can be observed in Fig. 8 and the side- and top-views in Fig. 2.
One key question of the gas bubble formation and drag process observed by the high speed camera is what kind of effect is responsible for the drag effect of the bubbles. One very likely possibility is connected to the Eötvös rule which states that in general the surface tension of a fluid decreases with increasing temperature . The gas bubbles will be formed inside the hot plasma region or at least very near to it. As is known from numerical simulations  the temperature will decrease to the sides of the plasma. However, in most practically relevant cases a steady state will be developed during the glass processing with ultra-short laser where the plasma region and molten zone follow the movement of the laser spot inside the material. However, the gas bubbles cannot be assumed to have already a motion trajectory due to the laser movement when they are generated (except for their buoyancy of course). But the bubbles will form a gaseous phase within a fluid. This means that the surface of the gas bubbles connecting them to the molten pool will exhibit a surface tension. The surface tension is largest for a curved surface resulting in a tendency to flatten out the curved surface in order to reduce its surface energy. For a gas bubble enclosed in a fluid that has the same surface tension across its whole surface an ideally round bubble will be formed because of the equilibrium of all local surface tensions.
Nonetheless, during cool-down the bubbles can freeze in elongated shapes as shown in Figs. 4(a) and 8. The elongation is possible, because the scattering of the laser radiation on the bubble is not necessarily complete, especially, in case of large gas bubbles where strong dynamic instabilities can be observed. This allows for laser heating the material in spite of the scattering. Consequently, a small portion of the molten zone may be present. Assuming a large bubble exists already (before the scattering of laser radiation starts to increase significantly), the bubble will be forced to an elongated shape, because the surface tension will increase especially from the sides of the molten zone (left and right side beside the bubble as in cross section in Fig. 2) as soon as the laser in-coupling grows less effective.
However, as shown schematically in Fig. 9 in the case of processing glass by ultra-fast lasers the surface tension will not be in equilibrium across the complete bubble surface. It will be lower in the direction of the laser spot movement following the Eötvös rule due to the higher temperatures closer to the laser spot and plasma region. In the opposite direction where the material is cooling down the surface tension will increase due to the Eötvös rule. The higher surface tension at the “cold end” of the gas bubble will now push the bubble forward in the direction of the laser spot movement because the surface tension at the “hot end” of the bubble inside the laser spot is lower and can therefore not build up a sufficiently high counter pressure. This results in effective motion of the gas bubble with the laser spot. Of course this mechanism will be interrupted if – should the gas bubble grow too large – the laser induced ionization and heating grow too small due to the scattering of the laser radiation on the gas bubble.
2.3 Temperature dependency of buoyancy of bubbles
Figure 10 shows cross sections of molten zone generated at different feed speeds, at a pulse energy of EP = 6 µJ, a repetition rate f = 1 MHz and a numerical aperture of the microscope objective NA = 0.55. Due to the variation of the feed speed different energy input per unit length is realized resulting in varying volume sizes of the molten zones. The larger the molten zone gets the longer the time necessary for the cool-down will become. Consequently, at higher input energies per unit length the molten zone stays longer fluid at lower viscosities than for smaller input energies per unit length. Also, it has to be assumed that for higher input energies per unit length the average viscosity of the melt pool is smaller than for smaller input energies for unit length. This results in a higher mobility of the gas bubbles which improves the drag effect on the bubbles caused by the Eötvös rule. Overall the better mobility of the gas bubbles in larger molten zones leads to the formation of bigger gas bubbles because besides the lower melt viscosity the bubbles have enough time to coalesce.
The improved coalescing ability in larger molten zones is reflected also in the buoyancy of the gas bubbles. As can be seen in Fig. 10 the bubbles are located for feed speeds between 10 and 70 mm/s mainly at the top of the molten zone. Only for the feed speeds 100 and 150 mm/s can the bubble distribution be observed across the whole height of the molten zones. However for feed speeds between 20 and 70 mm/s small bubbles are visible at the bottom of the molten zone.
An explanation for this behavior can be given by the temperature-viscosity relation of glassy materials: for small molten zones the cool-down time is fairly short leading to a relatively cold molten zone with high viscosity. This is the reason why at feed speeds 100 and 150 mm/s the bubbles freeze on their way buoying towards the top of the molten zone. The viscosity of the melt is also too large for the bubbles to coalesce. However, the bubble distribution is very interesting itself, since if a highly viscous molten zone is assumed to enclose them, they have not traveled far before being frozen within the solidified melt. This means they were generated close to the locations of their later solidification. This leads to the conclusion that the bubbles are not generated within the whole of the molten zone but rather close to the middle of the molten zone. This seems to be the plasma - laser beam interaction region. Indeed, the distribution of the gas bubbles would fit well enough into the bright plasma zone shown in Fig. 5.
For feed speeds between 20 and 70 mm/s the temperature of the melt pool is high enough for most bubbles to coalesce. Due to the larger volume of the coalesced bubbles the buoyant force is strong enough to propel the coalesced bubble completely to the top of the molten zone even though the temperature might be only by a small amount higher than that of the 100 mm/s melt run. However, due to the sharp tip on the bottom side of the molten zone the tip cools faster down than e.g. the round shape on top of the melt run. This leads to smaller average temperatures of the tip even though the tip lies closer to the nominal focus point of the laser beam . Because of the lower temperature the viscosity is higher at the tip preventing the formed gas bubbles (e.g. by multiphoton ionization) from buyoing up to the top of the molten zone. At 10 mm/s the temperature and its distribution becomes obviously high and uniform enough to make buoyancy possible also for bubbles generated near the sharp tip of the molten zone.
The hitherto presented experiments and explanation show what kind of forces act on the gas bubbles and describe the relationships between melt zone temperature, viscosity and surface tension as well as the location of generation of the gas bubbles. However, in order to ascertain the underlying chemical processes the chemical composition of the gas bubbles should be determined.
2.4 Chemical composition of the gas bubbles
The analysis of the chemical composition of the gas bubbles is not an easy task due to the small size of the bubbles simply by having a very small amount of substance to analyze. The curvature of the bubbles in combination with the refractive index difference of their inside to the surrounding glass material renders most commercially available spectroscopic instruments useless. Nonetheless, for nanoscopic structural changes in glasses induced by ultra-short laser pulses the material modifications have been analyzed and a multitude of modifications has been observed [4,8,18,19]. Just to mention a few modifications there may be Si dangling bonds (SiE’s), oxygen deficiency centers (ODCs), non-bridging oxygen hole centers (NBOHC) [20,21] or peroxy linkages. It should be clear that the presence of SiE’s and ODCs shows that oxygen can be freed by pulsed laser irradiation and is thus (compared with thermal oxygen ionization possibility discussed in section 2 (Fig. 3)) an additional pathway to create free oxygen. However, this is not the same for NBOHCs and peroxy linkages, because the oxygen is not freed by the formation process. Instead an absorption band is formed. In the following we will show that even these structural changes are able to increase the production rates of free oxygen. We will explain this mechanism by using NBOHC as an example but the same conclusions are valid also for the peroxa-linkages.
The NBOHC is characterized by an oxygen atom that is disconnected to one part of the original SiO2 chain while a single chemical bond is still shared with the other part of the SiO2 chain . While the laser induced generation of NBOHCs does not free the oxygen completely, it shows that molecular bonds can be dissociated by laser radiation in solid glass materials. Furthermore, NBOHCs have absorption bands at photon energies of 2 eV and 4.8 eV , meaning that ultra-short laser pulses (as used here) can lead to multi photon absorption and, subsequently, to dissociation of the dangling oxygen atom at the wavelength (used here) of 1064 nm (~1.2 eV photon energy), thereby producing a free oxygen atom. While this process first requires the laser induced generation of NBHOCs, the subsequent dissociation of the dangling oxygen atom is much more likely than the multiphoton ionization of fused silica. This easier because with NBOHCs present the multi photon absorption and ionization processes do not have to overcome the band gap of fused silica which is with 9 eV [7,22] much higher than the absorption bands of NBOHCs.
As long as a SiO2 network – however short – is present inside the glass melt, it has to be assumed that the NBOHC generation mechanism (with a possible, subsequent laser induced dissociation of the dangling oxygen atom) is still active when the glass melt is irradiated. Being freed inside the glass melt we can expect a high mobility of the oxygen atoms due to Brownian motion. Therefore, the generation of NBOHCs as well as their absorption characteristics point strongly towards the possibility of a subsequent free oxygen generation. When freed within the glass melt the oxygen may very likely coalesce into gas bubbles. Consequently, this results – within the glass melt – in the formation of a mixture of amorphous SiO2 and amorphous silicon , that should be preserved by the rapid quenching by the subsequent cool-down of the glass melt.
In order to be able to get at least some knowledge about the chemical composition of the bubbles we assumed the only gas present in a dissociation process of SiO2 will be oxygen. For this measurement we irradiated fused silica samples by multiple passes and in several vertical and horizontal layers in order to create a large amount of bubbles. These samples were then placed into an enclosed crucible with nitrogen atmosphere containing deoxygenated water. The water was deoxygenated by boiling it for 60 min in an autoclave and filling the still boiling water into hermetically sealable canisters to cool down to room temperature. After cooling down the water was transferred to the crucible in a nitrogen atmosphere. The irradiated glass samples were also placed into the water inside the crucible and grinded under water. During the grinding process the content of dissolved oxygen in the water was monitored using a Clark sensor. Within the Clark sensor the following reaction takes place :
From the measured electrical current the partial pressure of the dissolved oxygen in water can be deduced as long the water temperature is known. Knowing the partial pressure of dissolved oxygen within the water allows to determine for a given water volume the amount of substance of solved oxygen. Estimating the overall gas bubble volume by microscope makes it possible to calculate the oxygen density within the gas bubbles inside the gas bubbles assuming all gas bubbles were destroyed during the underwater grinding process and all of the oxygen present in the bubbles dissolved in water (which might be a too optimistic assumption).
Figure 11 shows the calculated oxygen density of 4 irradiated samples. For comparison reasons the oxygen density of pure gaseous molecular oxygen at normal conditions is also shown in Fig. 11. As can be seen the density inside the bubbles is at least as high as that of pure oxygen at normal conditions. This means that the gas pressure inside the bubbles lies within the range of several 100 kPa. Indeed, this seems to be true when considering Fig. 8 which shows a microscope photograph of a gas bubble taken using crossed polarizers. The area of stress induced birefringence is clearly visible as a bright area next to the molten zone and the gas bubble. (The increased pressure inside the gas bubbles could be possibly exploited for the analysis of pressure conditions during the laser-plasma interaction.)
The high content of oxygen inside the bubbles makes it highly probable that either NBOHCs or a mixture of amorphous silicon and SiO2 or a combination of all three is formed. On the one hand the NBOHCs are rather transparent within the visual wavevelength spectra (they absorb mainly between 190 and 260 nm and exhibit fluorescence near 650 nm) which makes them hard to be observed by a conventional optical microscope. On the other hand amorphous silicon would exhibit a very strong absorption in visual and should be observable by optical microscope. However, even if 100 µm3/(µm melt run) would be generated (compare Fig. 4(b)) having an oxygen density of 10 g/l (compare Fig. 11) an oxygen mass of 10−15 kg3/(µm melt run) would have accumulated making the surplus silicon all but invisible for an optical microscope since the corresponding silicon volume would be 0.76 µm3 per µm melt run.
The intent of this chapter is to compare the presented model with other possible theories on the formation of these bubbles.
3.1 Presence of interstitial oxygen
One possible theory where the observed effects would be comparable to those described by our model would be the presence of highly concentrated interstitial oxygen molecules inside the bulk glass material . In this case the remelting of the glass could allow the interstitial oxygen molecules to diffuse through the glass and form gas bubbles that should experience a similar drag effect and buoyancy as described here. Moreover, the chemical analysis would also give similar results, since we measured an increase in oxygen when the bubbles were destroyed. However, if it is assumed that the amount of substance of interstitial oxygen is limited then repetitive remelting of the same area under same irradiation conditions the volume and amount of gas bubbles should stay constant after the first few irradiations. However, as described in section 2.1 we observe monotic increase in gas bubble volume at least up to 20x irradiation. While the contribution of interstitial oxygen to gas bubble formation cannot be ruled out for the first irradiation, the subsequent irradiations should originate on the effects described by our model. Thus, the processes in our model will be also partially responsible for the initial formation of the gas bubbles.
3.2 Cavitation mechanism
Another possibility of bubble generation would be due to cavitation induced by the ultra-short laser pulses [14–16]. In this mechanism a laser pulse creates a high energy plasma that is able to create a void at the irradiated spot due to the fast expansion of the cavity surface that acts as shock wave (supersonic propagation) or propagates as fast as the speed of sound. Rapid cool-down (quenching) can freeze the bubbles in their expanded state. Indeed, for low pulse repetition rates we observe crack formation in the glass where the cavitation mechanism may be involved. However, the cavitation mechanism is active only as long as the laser pulse irradiates solid glass or the molten zone. As soon as it irradiates the inside of the expanding cavity the expansion pressure should decrease considerably, because inside the cavity the gaseous or plasmatic material exhibits a significantly smaller density. This small density will not be sufficient to keep the cavity expansion constant.
Therefore, in order to characterize the relevance of the cavitation mechanism to formation of gas bubbles as observed here it is sufficient to consider when the expanding cavity overtakes the size of the focal spot or the plasma size and if it corresponds to the observed occurrence frequencies of the bubble, since as soon the laser spot/ plasma region is overtaken by the cavity, the material heating should stop and the cavity should get stuck. In the presented experiments the focal spot size is (without spherical or thermal distortions) ~3 µm while the (horizontal) plasma size is ~40 µm (Fig. 6). The speed of sound in glasses lies between 2800 m/s and 5600 m/s  (within the melt the velocity might be somewhat smaller). Nonetheless, even at the smaller speed of sound the front of the caviation bubble would overtake the laser spot after 0.5 ns and the plasma region after 7 ns. In contrast, it takes on average 31 ms for a bubble to develop and get stuck (see Fig. 6). Therefore, the distributed generation of oxygen across the plasma region, its coalescence and buoyancy as well as the drag effect described here are much more plausible than bubble generation by cavitation.
3.3 Formation of voids due to tensile stresses in liquid glass melt
The bubble formation could also occur due to tensile stresses within the melt during its cool-down. Initially, let us consider for simplicity that the tensile stresses of the cooling glass melt open up a void at a location where the laser spot and thus plasma have already passed by. In an ideal case the location of the void would be too far from the plasma, so that no additional oxygen originating from thermal dissociation of SiO2 (discussed on page 3 and 4) diffuses into this void. However, the multi-pass irradiation experiments as shown in section 2.1 contradict this theory, too. A repetitive remelting under the same irradiation conditions and same irradiated material should shift the glass each time to the same thermodynamic liquid state. Therefore, the tensile stresses should be very similar during cool-down for each remelting. Consequently the volume and amount of voids should not show the monotonic increase in Fig. 4. Of course, for the first melt run we cannot rule out this mechanism.
Now let us assume that the location of the void is very near to the plasma and the focal spot, so that oxygen can diffuse and fill the void directly. Again, the experiments on buoyancy and chemical composition would lead to similar results as observed in our experiments. However, due to the tensile stresses within the melt no drag effect should be observed, because the tensile stresses should be a direct function of the length of the melt that is cooled down. Since the irradiation conditions are kept constant during the melt run the voids should occur more or less periodically. This is not the case for Figs. 4(a) and 6(b). Furthermore, once the oxygen-filled voids have formed, further irradiations of the same area should lead to the formation of gas bubbles that accumulate around formerly formed gas bubbles. This is because the laser light scattering on already formed bubbles should stop efficient heating of the plasma, while the tensile stresses of the melt should stay constant. By contrast, in our model, where the gas bubbles are dragged along and increase in size, bubbles that are already present within the solid glass have the chance to be picked up and incorporated into the growing bubble. This can be seen especially in Fig. 4(a) for the 2x irradiated melt run.
3.3 Gas bubble formation by rapid quenching
Recently, another theory on the generation bubbles/voids has been presented by Richter et. al. . The authors explain the void/bubble formation by densification and subsequent rapid quenching of the glass material. The densification occurs due to the laser irradiation and leads to an increase of the material’s density as described in . Due to the small size of the highly heated material the cool-down is fast enough to quench the material in its thermodynamical state. Thus properties such as higher density and, thus correspondingly, higher refractive index are frozen and can exist at room temperature. Since the volume of the remaining glass doesn’t change, voids have to form in order to compensate for the densification. The authors did not measure the chemical composition of the voids/bubbles.
However, the main reason why the theory proposed by  does not explain all observed effects is given by section 2.1 again. As explained above, a repetitive remelting under the same irradiation conditions and same irradiated material should shift the glass each time to the same thermodynamic state. The densification and quenching postulated in  should lead for each irradiation roughly to the same volume of the voids. In contrast, Figs. 4(a) and 4(b) show that the bubble volume grows with increasing number of irradiation runs (at same conditions and despite the scattering losses on already present bubbles.) Since such growth would not occur in the quenching mechanism we have to postulate a different origin of the bubbles. We conclude that while the quenching process may be still be present, at least when the glass material is irradiated for the first time, the main effect for bubble formation is given by the dissociation of silicon dioxide.
Furthermore, in  SEM images of bubbles with a size (crossection) of approximately 5 µm x 5 µm and 10 µm x 10 µm were provided. In the experiments described here we observe larger bubbles. Since we observe a clear internal appearance (Figs. 2, 4(a) and 8) we have to deduce that our bubbles do not exhibit such inner structure. Otherwise the bubbles would appear to be optically dull due to the scatter centers on its surface. The smooth appearance of the bubble can be attributed to the fact that our bubbles have taken a longer time to form than the bubbles shown in  thus providing more time for the surface tension to smooth the bubble surface. Thus the quenching theory in  is very likely inadequate to describe the gas bubble generation as observed in our case.
4. Conclusion and outlook
In this work the generation and formation processes of gas bubbles are described that occur during processing of glass by ultra-short laser pulses. The gas bubbles occur in the first place due to the ionization processes induced by the ultra-short laser pulses (multiphoton ionization, tunnel ionization, avalanche ionization) as well as by thermal dissociation processes set off by the very high temperatures achieved inside the plasma. This leads to the generation of free atoms and ions that have the possibility to chemically react along different paths that are not directly obvious from the chemical composition of the original bulk glass material. To keep the reactional paths of the recombinations relatively simple we investigated only fused silica glass samples which consist mainly of pure SiO2. We prove in this work by measuring the oxygen density of the generated bubbles that the bubbles contain indeed a high amount of oxygen.
We have shown that for high enough temperatures of the molten zone the bubbles will coalescence and will eventually buoy up towards the top of the molten zone. Due to the Eötvös rule which describes the temperature dependency of the surface tension the bubbles may be carried along with the moving laser spot, growing larger until they scatter enough laser radiation to interrupt the laser induced nonlinear plasma generation and heating. If this occurs the temperature of the molten zone is reduced. This increases the viscosity of the melt pool which effectively freezes the gas bubble at this location. Has the laser spot moved on the laser induced ionization of the glass material can start anew making it possible for certain irradiation conditions to produce a highly periodic chain of gas bubbles (see Fig. 2) that can act as a periodic grating .
One possible exploit of the buoyancy and the drag effect due to the Eötvös rule would be to use more complex irradiation strategies such as complex probably three-dimensional laser spot and sample movement combined with synchronous laser power modulation to drag or buoy up the gas bubbles towards or away from a certain region e.g. in order to create a waveguide core without bubbles or to collect the bubbles at certain locations. This could offer multiple opportunities to create functional optical devices in glass materials.
The experiments and results described in this work are however not sufficient to describe all the thermodynamic processes that take place during ultra-fast processing of glasses. One main issue is the occurrence of bubbles in borofloat 33 glass type while in a chemically similar glass, such as borosilicate D263 glass which has roughly the same melting point no gas bubble formation can be observed. The authors believe that this has to do with certain additives such as B2O3, Na2O, K2O and Al2O3 present in these glass types. It is imaginable that one of these elements (boron, sodium, potassium or aluminum) could bind dissolved atomic and/or ionic oxygen faster than pure silicon or silicon oxide as no double bonds are required [12,13]. However, it must be assumed that the reaction equilibrium – depending among others on the melt temperature – is affected also by the cool down rate, the viscosity of the melt as well as the solubility of atomic and or molecular oxygen in the melt. Further investigations including a larger variety of glasses (such as pure GeO2 glass where oxygen filled micro bubbles were observed ) will be necessary to clarify these processes and explain why certain glass types show bubble formation and while others do not.
This work was supported by the Bayerisches Laserzentrum GmbH Erlangen (blz), theErlangen Graduate School in Advanced Optical Technologies, Friedrich-Alexander University Erlangen-Nürnberg (SAOT) as well as the Deutsche Forschungsgemeinschaft and Friedrich-Alexander University Erlangen-Nürnberg (FAU) within the funding programmme Open Access Publishing
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