Ultrafast laser induced microexplosions: explosive dynamics and sub-micrometer structures

Chris B. Schaffer * , Eli N. Glezer † , Nozomi Nishimura, and Eric Mazur

Department of Physics, Harvard University, Cambridge, MA 02138

ABSTRACT

Tightly focused femtosecond laser pulses can be nonlinearly absorbed inside transparent materials, creating a highly excited electron – ion plasma. These conditions exist only in a small volume at the laser focus. This tight confinement and extreme conditions lead to an explosive expansion — a microexplosion. In solid materials, a microexplosion can result in permanent structural changes. We find that the damage produced by femtosecond pulses in this way is surprisingly small, with only a 200- nm diameter. Material left at the center of the microexplosion is either amorphous and less dense or entirely absent. The thresh- old for breakdown and structural change is nearly independent of material. Time-resolved measurements of microexplosions in water allow us to observe the dynamics of the explosive expansion. The structural changes in solids resulting from microexplo-

sions allow for three-dimensional data storage and internal microstructuring of transparent solids.

1. INTRODUCTION

In our experiments we tightly focus femtosecond laser pulses beneath the surface of transparent materials. In the focal volume, the laser energy is tightly confined, giving intensities high enough for nonlinear absorption to take place. The light is absorbed by the electrons, producing an electron – ion plasma. Because of the short duration of the laser pulse the lattice has no time to respond, and remains unperturbed during the excitation. The electrons collisionally heat the ions in the first few picoseconds following the excitation. This absorption and energy exchange occur only in the small volume near the focal spot of the laser, so the hot electron – ion plasma is highly localized. This tightly confined, highly excited plasma expands explosively — pro- ducing a microexplosion. The expansion of the plasma is very rapid, with velocities much greater than the speed of sound in the material. Later the expansion slows leaving a bubble of ionized material, and launching an expanding pressure wave. The electron – ion plasma recombines on a nanosecond timescale, emitting a bright spark. Above a threshold, a microexplosion can

permanently damage the material.

As an estimate of the extreme conditions that are created in our experiments, consider a 1- µ J pulse instantaneously ab- sorbed in a 1- µ m 3 volume inside a transparent solid or liquid. This energy and volume are typical for our experiments. Assum- ing a typical heat capacity of 10 3 J/kgK and a density of 10 3 kg/m 3 , the material is heated to 10 6 K. The temperature rise estimate requires knowledge of the heat capacity at constant volume, which changes with temperature. However, the values of the heat capacity in the condensed state are valid as estimates well beyond the vaporization temperature because expansion has not occurred. At a temperature of 10 6 K the ionized material resembles an ideal gas at the density of a typical solid and a pres- sure of ~10 MBar. An ideal monatomic gas has a heat capacity of 7 × 10 2 J/kgK, so a heat capacity of 10 3 J/kgK is a reasonable estimate at both extremes of the heating process. From these estimates we see that the conditions created in a microexplosion

are characterized by extreme temperatures and pressures.

In a microexplosion, these extreme conditions exist only in a small volume at the focal region, allowing the creation of these conditions with micrometer-scale precision for use in applications. We recently found that sub-micrometer structures — microstructures — can be produced inside many transparent materials by tightly focused 100-fs pulses. 1 These micorstructures have a large contrast in index of refraction and can be seen with transmitted or scattered light under a standard microscope. We have demonstrated the use of these structures as data bits for permanent 3-D optical data storage. 1 The tested materials include fused silica, BK7 optical glass, plastic (acrylic), and single-crystal quartz, and sapphire. Microexplosions that lead to the for- mation of microstructures were produced in all of the tested materials, thus allowing for a storage medium that is mechanically,

*. Email: schaffer@physics.harvard.edu †. Current address: IGEN Corp., 16020 Industrial Dr., Gaithersburg, MD 20877

chemically and thermally very stable, and inexpensive.

In this report we characterize the optical and structural properties of the microstructures formed in transparent solids by microexplosions. We then determine the thresholds for such changes to be produced in several different materials. Finally, we

examine the dynamics of microexplosions from 100 fs to 100 ns, using water as the transparent medium.

2. STRUCTURAL CHARACTERIZATIONS

We tightly focus ultrashort laser pulses inside a transparent material to create localized structural changes, with an altered index of refraction. Figure 1a shows an example of a random binary pattern in fused silica, recorded using 0.5- µ J, 100-fs, 800-nm pulses from a regeneratively amplified Ti:Sapphire laser, focused by a 0.65 numerical aperture (NA) microscope objective. With this focusing, the threshold for structural change that can be seen under a microscope is 0.3 µ J. The pattern is read out in parallel using transmitted light in a microscope with a 0.95 NA objective. The spacing between adjacent bits is 2 µ m. During read-out, the depth discrimination provided by the short depth-of-field of the 0.95 NA objective is sufficient if adjacent layers are spaced by about 10 µ m or more. The longitudinal extent of the structurally altered regions is about 2.5 µ m. We recorded 10 layers spaced by 15 µ m, using a standard 0.65 NA refractive objective. Using an objective with a large working distance and an adjustment for aberrations caused by focusing into the material, it should be possible to record over 100 layers of data bits,

spaced by 10 µ m.

The consistent morphology of the microstructures in the array shown in Fig. 1a is notable. Structural changes are confined to the central region of the microexplosion. The size of the microstructures remains consistent from shot to shot, even near the threshold. Similar structures were produced in a wide variety of materials, including plastic, glass, quartz, and sapphire. The high contrast between the altered regions and the surrounding material suggests that the index of refraction of the microstruc- tures is very different from the undamaged material. By measuring the diffraction of a laser beam from similar arrays, we con- clude that the diffraction could be due to a small (~5%) difference in refractive index, but could also be due to a vacuum bubble. 2

( a ) ( b )

Fig. 1. ( a ) Binary data pattern stored inside fused silica with 2- µ m bit spacing, recorded using 100-fs, 0.3- µ J, 800-nm laser pulses, and photographed with an optical microscope using transmitted light. ( b ) Tilted SEM view of a polished cross- section through a regular array of 5- µ m spaced microstructures in fused silica produced by 100-fs, 0.3- µ J, 800-nm laser

pulses. Inset shows a single microstructure at higher magnification.

The 1- µ m diameter of the spots in the image in Fig. 1a is at the resolution limit of the optical microscope. To obtain in- formation about the lateral extent of the structural changes in the material, we polished away the fused silica sample until the microstructures were exposed, applied a 30-nm gold coat, and viewed the sample under a scanning electron microscope (SEM). Figure 1b shows such a SEM image of a 5 × 5- µ m regular array of spots recorded under conditions identical to those used in Fig. 1a. To better show the morphology the sample is tilted in the SEM. The bright spots correspond to protrusions on the surface, while the dark spot (top row second from the right) corresponds to a pit in the surface. Whether a microstructure appears as a protrusion or a pit depends on the level to which the material is polished. The inset in Fig. 1b shows a pit at higher magnification.

Both types of features have diameters of roughly 200 nm.

We have also carried out microstructural examinations with an atomic force microscope (AFM). The sample was pre- pared by polishing away material until a layer of structures was reached. In agreement with the SEM studies, the micro- structures appear as either protrusions or pits in the AFM image (see Fig. 2). The curves in Fig. 2 show depth profiles of protrusions and pits recorded by the AFM. The protrusions are 7–10 nm high, while the pits are at least 35–40 nm deep. The pit depth may be greater than the measured value, because the measurement is limited by the size of the AFM tip (which is pyramidal with a tip radius of less than 40 nm). The diameter (FWHM) of both the pits and the protrusions is

200–250 nm.

We attribute the small size of the microstructures to self-focusing. Self-focusing results from the intensity-dependent ra- dial variation in the index of refraction, n ( r ) = n o + n 2 I ( r ) , where n2 is proportional to the third-order susceptibility, χ (3). To examine the effect of self-focusing we modelled the beam propagation under our experimental focusing conditions. We find that self-focusing significantly reduces the beam waist, even under already tight external focusing conditions. For example, with 0.65-NA external focusing in fused silica, a 100-nJ, 100-fs pulse is expected to self-focus to a 150-nm beam waist diameter (FWHM) according to this model. 3 In agreement with these findings, the power in the laser at an energy of 100-nJ is approxi- mately 50% of the critical power needed for total collapse of the beam to a filament, while the power needed to produce changes visible under a microscope exceeds the critical power by 50%. 4 While other effects such as plasma absorption and defocusing need to be considered at even higher pulse energies, our analysis indicates that self-focusing plays an important role in the small

size of the voxels produced by microexplosions.

The effect of microexplosions on crystal structure in and around the voxels is observed by transmission electron micros- copy (TEM) of thin cross-sections through microstructure in single-crystal quartz and sapphire. To prepare a sample for TEM, first an array of microstructures is written inside a 100- µ m-thick transparent disk. The disk is then dimpled on both sides by grinding with diamond paste. Further material removal is done by controlled ion-milling on both sides, until the dimples ap- proach each other to form a hole at the same depth as the microstructure array. The thin edge around the hole then contains cross-sectional slices through several structures. In the case of some materials (e.g. sapphire), the ion milling makes the surface

Fig. 2. AFM images of cross-sections through microstructures produced in fused silica with 100-fs pulses. Scans through three different ( a ) pits and ( b ) protrusions are shown in the graphs. Scans are offset vertically for clarity.

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amorphous, and a thin layer must be removed by chemical etching. Finally, a thin conductive layer of carbon is deposited to avoid charge build-up in the TEM.

Figure 3a shows a TEM micrograph of a microstructure in quartz, created by a 100-fs, 2- µ J, 800-nm pulse. The oval- shaped region at the center of the microexplosion is much more transparent to the electron beam than the surrounding material, indicating it is less dense, porous, or thinner. A sharp boundary separates the oval region from the surrounding crystal, which is highly stressed. Cracks begin outside the central oval, and radiate outward. (The cracks seen in the central region in Fig. 3a originated from a nearby damaged spot.) Because crack formation requires tensile stress, the stresses outside the oval must be dominantly compressive. The crack directions are consistent from voxel to voxel, propagating along specific axes in the crystal. Figures 3b and 3c show the electron diffraction patterns from selected areas indicated in Fig. 3a. The material surrounding the oval region is crystalline, while in the oval region the material is amorphous-like. In sapphire we have observed some voxels

with a void in the center of the amorphous region.

The structures produced by 100-fs pulses differ drastically from those produced by 200-ps and 10-ns pulses. With the long- er pulses, the resulting structures are irregularly shaped, and cracks appear in the material even at energies only slightly above the threshold for structural change. Also, when the pulse energy is close to the threshold for structural change, the size of the damaged region fluctuates strongly from shot to shot. Fig. 4 shows an example of the features produced by 200-ps pulses. The focusing conditions and beam profile are identical to those used in Figs. 1a and 1b. The pulse energy is 9 µ J, which is three times the observed threshold, and the spacing between structures is 10 µ m. Note the large size of the spots, and clearly visible cracking produced with these longer pulses. With 10-ns pulses from a Nd:YAG laser, even larger, irregularly shaped spots are

produced, and the cracking is more extensive.

We attribute the differences in structures produced by femtosecond and picosecond and longer laser pulses to differing absorption mechanisms for the different pulsewidth regimes. The pulsewidth dependence of the threshold for surface damage in dielectrics has been extensively studied. 5–7 The absorption mechanisms leading to a microexplosion in the bulk are similar to those which cause surface ablation. For femtosecond laser pulses, the intensity in the focal volume is high enough to initiate a multiphoton absorption process (in our case about fifth order). The leading edge of the laser pulse ionizes a few electrons by

( a )

Fig. 3. ( a ) TEM micrograph of a cross-section through a microstructure in quartz created by 100-fs, 2- µ J, 800-nm laser pulses. ( b ) TEM diffraction pattern from the region in the left circle in ( a ), indicating an amorphous-like structure. ( c ) TEM

diffraction pattern from the area in the right circle in ( a ), indicating crystalline structure.

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the multiphoton process and these electrons can linearly absorb photons until they have enough energy to impact ionize another electron. This process of linear absorption followed by impact ionization continues in an avalanche. In the case of femtosecond pulses, it is the laser pulse itself that initiates the avalanche by providing the initial electrons through multiphoton absorption. For longer laser pulses, the intensity is too low for significant multiphoton absorption to occur, and the initial electrons for the

avalanche process must come from impurity states or thermal electrons.

For picosecond and longer pulses, the absorption relies on impurity states in the material. So, the absorption and damage is necessarily a statistical process. Furthermore, it is an all or nothing process. It takes significant energy to get the avalanche started from the few impurity electrons, but once it starts, a significant fraction of the laser energy is absorbed. For femtosecond pulses, the absorption is self-initiated and does not depend on impurity or defect states in the material, and is therefore more deterministic. Furthermore, one can get enough multiphoton absorption to initiate the avalanche with much less energy than would be required for the avalanche to proceed from impurities alone. With femtosecond pulses, we can deposit less total energy

than with longer pulses, and we can deposit that energy more consistently.

3. THRESHOLDS

To determine the threshold for structural change, and to monitor any slow (ns timescale or longer) transient effects, we moni- tored the scattering of a He:Ne laser from the pumped region of the sample in real time. For 100-fs pulses, at energies of only 50 nJ, we observed a transient scattering signal which decays with a ~5 ns lifetime. The emission lifetime of the laser-induced plasma was also measured to be 5 ns, and we attribute the transient scattering signal to plasma formation and recombination. We also measured the threshold for a non-transient scatter signal (indicating permanent damage) for the case of single laser

shots and multiple shots (~ 3000) at a single spot in the sample.

We performed experiments in glass, fused silica, single crystal quartz, and single crystal sapphire. The measured thresh- olds for plasma formation, single shot damage, and multiple shot damage for these materials are shown in Fig. 5. Thresholds were determined for both 100-fs and 200-ps pulses. For 100-fs excitation pulses, we find that there is little variation in the thresholds even between very different materials (see Fig. 5a). Note that we can produce permanent structures at energies more than a factor of 5 below the threshold for damage that is visible under a microscope. Presumably, the structures produced with less than 0.3 µ J are too small to be seen optically. The similarity of the single and multiple shot damage thresholds indicates that the damage occurs catastrophically on a single laser shot. If small changes produced by one laser shot were amplified by subsequent laser shots, one would expect to find a much lower threshold for multiple shot damage than for a single pulse. For comparison, we performed experiments using 200-ps. The thresholds for both plasma and damage were approximately a factor of 20, 30, and 40 higher than the 100-fs thresholds for glass, fused silica, and quartz, respectively (see Fig. 5b). The higher

thresholds are due to the differing absorption mechanisms for femtosecond and picosecond pulses discussed above.

Fig. 4. Damage produced inside fused silica by 200-ps pulses. Optical microscope photograph using transmitted light. Note the difference in scale relative to Fig. 1a; bits are spaced by 10 µ m.

We found the threshold for breakdown in water to be ~200 nJ using the scattering technique. The slightly higher threshold in water is likely due to spherical aberration introduced by focusing through a 180- µ m-thick window in the water cell. We also use a piezoelectric sensor to determine the breakdown threshold in water by monitoring the pressure wave produced by the mi- croexplosion. We measure the dependence of the pressure on the pulse energy, and compare this dependence for 100-fs and 200-ps pulses. Figure 6a shows the setup for piezoelectric pressure detection. A 0.65-NA objective is used to focus laser pulses 100–200 µ m inside a water cell containing a submerged piezoelectric sensor. The piezoelectric voltage is amplified and the sig- nal is recorded on a digital oscilloscope. Figure 6b shows the response of the sensor to a propagating pressure wave driven by a 100-fs, 1.8 - µ J pulse. The oscillations correspond to several vibration modes of the sensor. The amplitude of the response in- creases with increasing energy, but the shape of the response changes only slightly. Using the height of the first peak, we mea- sure the magnitude of the pressure in the wave as a function of input energy, For 100-fs excitation pulses, we find a sharp threshold of 0.2 µ J for detecting a pressure wave, followed by a nearly linear increase of pressure with input energy. The mea-

sured breakdown threshold is in excellent agreement with the result from the scattering measurement.

( a ) ( b )

Fig. 5. ( a ) Plot showing thresholds for plasma formation, multiple shot (~3000 shots) damage, and single shot damage driven by 100-fs, 800-nm pulses in glass (BK7), fused silica, single crystal quartz, and single crystal sapphire. ( b ) Comparison

plot of thresholds for 100-fs and 200-ps drive pulses.

( a ) ( b )

Fig. 6. ( a ) Water cell for piezoelectric pressure measurements. ( b ) Response of the piezoelectric sensor to the pressure wave produced by a 100-fs, 1.8- µ J pulse. The signal is averaged over 100 pulses. We use the amplitude of the first peak (see

arrow) as a measure of the pressure in the wave.

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Figure 7 shows the pressure produced by 100-fs and 200-ps pulses over three orders of magnitude in laser pulse energy. Above 10 µ J, the pressure produced by the 100-fs and 200-ps pulses is equal. In the range 10–100 µ J the logarithmic slope is 0.5 indicating that the pressure increases approximately as the square root of the input energy and that the deposited energy is proportional to the input energy. With 200-ps pulses, the breakdown occurs randomly in the vicinity of the threshold. In fact, no clear threshold exists. In the range 2–6 µ J, an increasing percentage of the laser shots produce breakdown, with no break- down below 2 µ J and breakdown on every shot above 6 µ J. In contrast, with 100-fs pulses there is little shot-to-shot variation in the pressure produced by the breakdown even very close to the threshold. Below 1 µ J, the absorbed fraction of each pulse diminishes with decreasing incident energy, but the breakdown occurs consistently from shot-to-shot. This difference in behav- ior is because the energy deposition for 100-fs pulses is initiated by multiphoton absorption, whereas the absorption of 200-ps

pulses relies on absorbing impurities to generate the initial electrons.

For pulses with energies greater than 10 µ J we find a transmission of 20% through the water sample, indicating that a large fraction of the incident energy is absorbed. Assuming 80% absorption in this energy range, we can use the pressure measure- ments to extrapolate the absorption coefficient to smaller energies. The low pressure produced by 100-fs pulses near the 0.2- µ J threshold indicates that it is possible to consistently deposit a small fraction of the incident energy into the pressure wave —

approximately 50 pJ — making it conceivable to photodisrupt biological tissue with sub-cellular precision.

4. DYNAMICS

To obtain information about the dynamics of microexplosions, we use time-resolved measurement techniques. Figure 8 shows the setup for time-resolved imaging of a cross-section through the center of a microexplosion. A 100-fs, 800-nm wavelength pump pulse from an amplified Ti:Sapphire laser is focused by a 0.6 NA microscope objective inside the sample, producing a microexplosion. The resulting dynamics are illuminated by a time-delayed, 100-fs, 400-nm wavelength probe pulse, and im- aged onto a CCD camera. The 800-nm pump is blocked by a filter. The time-delay between the pump and probe is varied from

0 to 60 ns to monitor the expansion of the pressure wave front.

Figure 9a shows an image of the pressure wave in sapphire 3.8 ns after optical excitation by a 3- µ J pulse. The figure is averaged over 30 CCD images to improve the image quality. Note the asymmetrical pressure wave expansion due to the anisot- ropy of sapphire. Figure 9b shows the measured radii of the pressure wave as a function of time for the first 10 ns of expansion. The line represents the speed of sound in sapphire (11.4 µ m/ns). It is clear that any hypersonic expansion resulting from the

Fig. 7. Comparison of the pressure produced by 100-fs pulses (filled circles) and 200-ps pulses (squares) in water. Each point is averaged over 100 pulses. In the 200-ps data, the open squares represent a range in pulse energy where some pulses

produce no signal, while others significantly exceed the average.

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extreme conditions produced in the microexplosion occurs only in the first fraction of a nanosecond and only over a few mi- crons, where imaging is difficult.

To obtain information about microexplosion dynamics more easily, we use water as the transparent medium. Because wa- ter is more compressible than most solids, the pressure wave produces a larger density change and thus has a more pronounced optical effect. We also expect supersonic expansion over a greater distance because of the greater compressibility of water, mak- ing imaging of the supersonic expansion possible. A practical advantage of using a liquid is that it recovers to its original state after the microexplosion, and thus experiments can be performed at a high repetition rate, in our case 1 kHz. Also, water serves as a good model for tissue, and allows one to study breakdown and pressure wave propagation under conditions relevant to laser

microsurgery of the eye. 8,9

Figure 10a shows an image of the small vapor bubble and the pressure wave in water 35 ns after optical excitation by a 1- µ J pulse. Figure 10b shows a larger bubble and a more visib l e pressure wave driven by a 14- µ J pulse. In Fig. 11 we plot the radial expansion of the pressure wave driven by 1- µ J, 10- µ J, and 30- µ J pulses. The radii were measured to the outer edge of the pressure wave. Included for comparison is a line representing the propagation of sound in water (1.48 µ m/ns). In the first several images (up to ~1 ns), the pressure wave and vapor/plasma bubble are indistinguishable, thus the first several open squares rep- resent the size of the entire microexplosion volume. Later data points correspond to the radius of the pressure wave. The expan- sion velocity (slope in the data) matches the speed of sound for all but the first fraction of a nanosecond. The region of

Fig. 8. Time-resolved imaging setup for observing the dynamics of laser-induced breakdown and pressure wave propagation.

( a ) ( b )

Fig. 9. ( a ) Expanding pressure wave in sapphire photographed 3.8 ns after optical excitation by 100-fs, 800-nm laser pulses of 3- µ J energy. ( b ) Radial expansion of the pressure wave driven by 3- µ J pulses in sapphire. The line represents the speed

of sound in sapphire (11.4 µ m/ns).

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supersonic expansion has a diameter of 11 µ m, 17 µ m and 20 µ m for 1- µ J, 10- µ J, and 30- µ J pulses, respectively. These findings are very different from experiments with 40-ps pulses, where there was supersonic expansion over a 200–400 µ m diameter for 25- µ J pulses. 10 The initial expansion of the vapor bubble and shock wave is extremely rapid. At 100 ps the vapor bubble diam- eter for 1- µ J pulses is already 7 µ m. The initial diameter is determined by the1- µ m laser spot size, giving an initial expansion velocity of at least 30 µ m/ns, i.e. 20 times the speed of sound in water. Such an explosive expansion suggests that it is driven by megabar pressures. Despite the extreme initial conditions, the total deposited energy is much less than that deposited with longer pulses and the supersonic expansion region is much smaller. This greater confinement of the disrupted zone might allow

for more precise photodisruption of biological tissues. 8,9

Until a few hundred picoseconds after excitation, the plasma/vapor bubble is too small to be imaged accurately. We de- veloped a time-resolved scattering technique that allows us to determine the size of the plasma from initiation (to be described in an upcoming publication). We find that it takes about 10 ps for the electrons to collisionally heat the ions, during that time the plasma remains at an approximately constant radius. Once the ions are hot, however, the expansion proceeds with a velocity of 90 µ m/ns — over 60 times the speed of sound in water. The supersonic expansion ends by 200 ps leaving a bubble of ionized material and launching the pressure wave. This is the first observation, to our knowledge, of such rapid expansion in laser-in- duced breakdown in water. Previous experiments with ultrashort pulse breakdown in water have not resolved the micrometer- scale picosecond dynamics ( i . e . the explosive expansion of the plasma/vapor bubble), and instead observed initial shock wave

propagation velocities of 2–3 µ m/ns. 9,11

We believe the microexplosion dynamics measured in water are typical of the microexplosion dynamics for many mate- rials, including solids. The similarity of the breakdown thresholds in all the systems we studied, both solid and liquid, and the similarity of the structures produced in different solids indicates that the microexplosion process is material independent. Thus, the dynamic measurements in water indicate the general features of microexplosions for a wide variety of condensed matter

systems.

5. CONCLUSIONS

In this report we have investigated ultrafast laser-induced microexplosions in transparent materials. We find that the microex- plosion process produces extreme conditions that are highly localized at the focal volume. These initial conditions lead to highly explosive dynamics and can result in permanent structural changes. We have used optical microscopy, SEM, AFM, and TEM to study the structural effects of the microexplosions. Optical scattering and acoustic techniques were used to determine the thresholds for breakdown in a wide variety of materials. Time-resolved imaging provides a view of the nanosecond dynamics of the explosion, and time-resolved scattering measurements allows us to observe the supersonic expansion of the plasma on

the picosecond time scale.

( a ) ( b )

Fig. 10. Small vapor bubbles and expanding pressure waves in water photographed 35 ns after optical excitation by 100-fs, 800-nm laser pulses of ( a ) 1- µ J and ( b ) 14- µ J energy. Each figure is averaged over 30 CCD images to improve the

image quality.

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The ultrashort laser driven microexplosions provide a unique method for internal microstructuring of transparent materi- als. The fabrication of very general three-dimensional structures is possible with this technique. The use of this method for high- density three dimensional data storage is discussed in another article. 1 Photonic bandgap materials and three dimensional dif- fractive optical elements are both also possible. The extreme conditions produced in microexplosions might provide a micro- scopic laboratory for studying the equation of state of materials at high temperature and pressure. Because the effects are so confined, microexplosions may also find applications in precise photodisruption of tissue with potential benefits in ophthalmol-

ogy, subsurface skin surgery, and biological experiments. 8

6. REFERENCES

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Fig. 11. Radial expansion of the pressure wave driven by 1- µ J ( ■ ), 10- µ J ( ▲ ), and 30- µ J ( ● ) pulses. The radii were measured to the outer edge of the pressure wave. The line represents propagation of sound in water (1.48 µ m/ns). The inset shows

the first 3 ns of expansion.

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