Thresholds for femtosecond laser-induced
breakdown in bulk transparent solids and water
Chris B. Schaffer, Nozomi Nishimura, and Eric Mazur*
Harvard University, Department of Physics, Cambridge, MA 02138
ABSTRACT
We present thresholds for optical breakdown in bulk transparent solids and water with 100-fs laser
pulses. In solids, we used microscopy and scattering techniques to determine thresholds for plasma
formation and permanent damage in a wide variety of materials. Transmission measurements show
that damage occurs at energies where there is little absorption of the laser pulse. In water, we used
scattering and acoustic techniques to measure the breakdown threshold for 100-fs pulses. In contrast
to solids, transmission measurements in water indicate that there is no plasma or bubble formation
unless there is significant absorption. For comparison, we also measured breakdown thresholds for
200-ps pulses.
Keywords: ultrafast lasers, laser-induced breakdown thresholds, multiphoton absorption, avalanche
ionization, laser-induced damage thresholds
1. INTRODUCTION
Femtosecond laser-induced breakdown in transparent materials has received much attention in recent years. When a femtosecond laser pulse is tightly focused inside a transparent material the intensity at the focus can become high enough to cause
absorption through nonlinear processes.1 This nonlinear absorption creates a high-temperature plasma at the laser focus. If the
laser is focused on the surface, the ionized material is ablated. If the laser is focused in the bulk, the plasma expands into the
surrounding volume creating a microscopic explosion — a microexplosion. In solids the microexplosion leaves behind a permanently damaged region inside the material. These microexplosions provide an ideal means for the micromachining of solid
materials,2–4 and may also offer a precise laser scalpel for microsurgery.5–8
Other authors have reported on the thresholds for surface ablation of transparent solids. The dependence of the surface
ablation threshold on pulsewidth and on material, the relative role of multiphoton and avalanche ionization, and the morphology
of damage have all been studied.9–12 In water, the dependence of the breakdown threshold on pulsewidth has been measured,
and the dynamics of pressure wave propagation and cavitation have been studied.13–17 In studies performed to date, many different techniques have been used to determine the breakdown threshold, often measuring very different physical phenomena.
No distinction has been made between thresholds measured by different techniques.
In this paper, we measure the breakdown thresholds in the bulk of transparent solids and water, distinguishing between
the thresholds for various physical phenomena. This work represents the first systematic study of femtosecond laser-induced
breakdown thresholds in the bulk (as opposed to the surface) of transparent materials. There are several thresholds that we will
discuss in solids: the threshold for plasma formation, for single- and multiple-shot damage, for visible damage, and for a change
in the transmission. We measure the threshold for plasma formation and single- and multiple-shot damage using a scattering
technique. The visible damage threshold is determined by examining irradiated samples under an optical microscope. Finally,
the transmission-change threshold is defined as the laser energy at which the transmission begins to drop, indicating the onset
of strong absorption. In water we measure the threshold for plasma formation, for bubble and pressure-wave formation, and for
transmission-change. The thresholds for plasma and bubble production are measured with the scattering technique. We use an
acoustic technique to determine the threshold for pressure-wave formation.
We find that, in solids, plasma and permanent damage can be produced below the transmission-change threshold, indicat* E-mail: mazur@physics.harvard.edu
WWW: http://mazur-www.harvard.edu/
ing that only a small fraction of the laser energy is responsible for the initial plasma and damage. For damage produced close
to the single- and multiple-shot damage thresholds, the damage produced is not large enough to be visible under a microscope.
Furthermore, we find that the threshold for visible damage coincides with the threshold for transmission-change, indicating that
the greater absorption above the transmission-change threshold leads to the production of larger damage in the material. In contrast to solids, all the thresholds in liquids coincide. We do not see plasma, bubble, or pressure-wave production below the transmission-change threshold, indicating that the laser pulse has no effect on the water until a substantial fraction of the laser energy
is absorbed.
2. THRESHOLDS IN BULK SOLIDS
We recently discovered that microexplosions induced by femtosecond laser pulses can produce sub-µ m diameter structures inside transparent materials.2,9,18 Figure 1a shows an optical picture of these structures produced about 100 µ m below
the surface of a fused silica sample by 100-fs, 800-nm, 0.5-µ J pulses that are focused with a 0.65 numerical aperture (NA) microscope objective. The apparent 1-µ m diameter in the images is at the resolution limit of the microscope. We determined the
diameter of the structures to be approximately 200 nm using a scanning electron microscope,2 an atomic force microscope,9
and a transmission electron microscope.18 The threshold for producing damage that is visible under a microscope is about 0.3
µ J for a wide variety of materials. For comparison, structures produced by 200-ps, 800-nm, 9-µ J laser pulses are shown in Fig.
1b. Note the much larger, cracked structures. The threshold for visible damage with 200-ps pulses is about 3 µ J in fused silica.
To determine the thresholds for damage not visible under a microscope, and to monitor transient effects on the nanosecond
or longer timescale, we used a scattering technique. The setup is shown in Fig. 2. A 100-fs or 200-ps pump pulse is tightly focused inside the sample with a 0.65-NA microscope objective. A He:Ne laser is weakly focused in the same region. We monitor
the scattering of the He:Ne laser beam due to disturbances induced by the pump. The directly transmitted He:Ne light is blocked,
allowing only light scattered out of the original beam path to reach the detector. Above a certain threshold we begin to see a
20 µm
20 µm
(a)
(b)
Fig. 1. (a) Structures produced in fused silica by 100-fs, 800-nm, 0.5-µ J pulses. (b) Structures produced in fused silica by 200-ps, 800-nm, 9µ J pulses. Both images were taken with an optical microscope and are shown on the same scale.
transient scattering signal which decays in 5 ns. Because we find an emission lifetime of about 5 ns for the 100-fs laser-induced
plasma, we attribute this transient signal to the presence of the plasma. The corresponding threshold is therefore referred to as
the plasma threshold. Above a higher threshold, the scattering signal does not return to zero, indicating permanent damage to
the material. This threshold is therefore called the single-shot damage threshold. We also measured the threshold for producing
damage with multiple-shots (about 3000 pulses).
We measured the thresholds for plasma formation, for single-shot damage, and for multiple-shot damage in glass, fused
silica, single crystal quartz, and single crystal sapphire. The first three columns of Table 1 summarize these thresholds for 100fs laser pulses. Surprisingly, there is little variation in the thresholds even between very different materials. Furthermore, the
sample
pump
objective
objective
beam
block
photodiode
He:Ne
laser
Fig. 2. Scattering setup for determining plasma and single- and multiple-shot damage thresholds.
thresholds for single- and multiple-shot damage in Table 1 are a factor of 3–5 below the 0.3-µ J threshold for visible damage,
indicating that any damage produced with less than 0.3 µ J is too small to be resolved optically. The coincidence of the singleand multiple-shot damage thresholds indicates that damage occurs catastrophically on the first laser shot. If small changes produced by one laser shot were amplified by subsequent laser shots, one would find a lower threshold for multiple-shot damage
than for single-shot damage.
For comparison, we repeated the scattering experiments with 200-ps pulses; the thresholds for plasma formation and single- and multiple-shot damage are listed in the last three columns of Table 1. The thresholds for these pulses are a factor of 20–
40 higher than for 100-fs laser pulses. Furthermore, the single- and multiple-shot damage thresholds with picosecond pulses are
close to the visible damage threshold (~ 3 µ J). Apparently, any damage produced with picosecond pulses is large enough to be
seen under a microscope.
material
100 fs
plasma
formation (µJ)
100 fs
single-shot
damage (µJ)
100 fs
multiple-shot
damage (µJ)
200 ps
plasma
formation (µJ)
200 ps
single-shot
damage (µJ)
200 ps
multiple-shot
damage (µJ)
glass (BK7)
0.04
0.07
0.06
0.9
1.2
1.0
fused silica
0.06
0.08
0.06
1.7
1.8
1.7
quartz
0.08
0.08
0.08
2.9
2.9
2.9
sapphire
0.07
0.1
0.1
1/N
1/N
1/N
Table 1. Thresholds for plasma formation and single- and multiple-shot damage in bulk solids for 100-fs and 200-ps laser pulses.
Figure 3 shows the transmission of a 100-fs pulse through fused silica as a function of incident laser energy. The arrows
mark the thresholds for plasma formation, single-shot damage, and visible damage. There is an abrupt drop in the transmission
at 0.3 µ J, defining the transmission-change threshold. When the laser energy is below the transmission-change threshold, the
transmission is nearly one, and, therefore, the absorption is low. This small absorption indicates that only a small fraction of the
laser energy is responsible for the plasma formation and damage produced. The transmission-change threshold coincides with
the visible damage threshold, indicating that it is only when a significant fraction of the laser pulse is absorbed that 200-nm
diameter structures are produced. Reflection and scattering of the laser pulse by the plasma is small, accounting for less than a
few percent of the laser energy. Note that at high laser energy, the transmission of this transparent material is less than 20%.
3. THRESHOLDS IN WATER
We used the He:Ne scattering technique to measure the plasma and bubble formation thresholds in water. For tightly focused 100-fs pulses, we find that a transient scattering signal is produced at an energy of 0.2 µ J. This signal, which persists for
several microseconds, is due to both a plasma and the formation of a bubble. Initially, the laser-produced plasma scatters the
plasma
visible damage
transmission
1
damage
0.1
0
0.1
1
10
100
laser energy (µJ)
Fig. 3. Transmission of 100-fs pulses through fused silica as a function of the incident laser energy.
He:Ne probe; after the plasma recombines, the bubble is responsible for the scattering. We do not see any plasma production
below the threshold for producing a bubble.
In addition to the scattering technique, we used an acoustic measurement to measure the pressure wave formation threshold in water.13 A 0.65-NA objective focuses the laser pulse inside a water cell containing a submerged piezoelectric sensor. We
use the piezoelectric transducer to detect the pressure wave launched by the laser-produced plasma. For 100-fs pulses, the
threshold for detecting a pressure wave is also 0.2 µ J. The thresholds for plasma, pressure wave, and bubble production all coincide for 100-fs laser pulses. Our acoustic measurements indicate that, for 100-fs pulses, the breakdown is very consistent,
even near threshold.13 In contrast, 200-ps pulses do not consistently produce breakdown near the 2-µ J threshold. The thresholds
for plasma, bubble, and pressure wave formation in water for 100-fs and 200-ps pulses are listed in Table 2.
100 fs
plasma (µ J)
100 fs
bubble (µ J)
100 fs
pressure wave (µ J)
200 ps
plasma (µ J)
200 ps
bubble (µ J)
200 ps
pressure wave (µ J)
0.2
0.2
0.2
2.0
2.0
2.0
Table 2. Thresholds for plasma, bubble, and pressure wave formation in water for 100-fs and 200-ps laser pulses.
Figure 4 shows the transmission of 100-fs laser pulses through water as a function of incident laser energy. The transmission is approximately one up to the transmission-change threshold of 0.2 µ J, where it begins to drop. The arrow marks the
threshold for plasma, bubble, and pressure wave formation. The transmission-change threshold coincides with the thresholds
for plasma, bubble, and pressure wave formation. This is in contrast to solids, where the plasma formation and single-shot damage thresholds were below the transmission-change threshold.
4. DISCUSSION
Let us now compare the results obtained for fused silica and water. Note that producing damage in a solid and producing
a pressure wave or a bubble in a liquid both involve mechanical effects, i.e. the motion of atoms. For simplicity we refer to the
single-shot damage threshold in fused silica and the bubble or pressure-wave formation threshold in water collectively as the
mechanical effect threshold. The various thresholds for fused silica and water for 100-fs laser pulses are listed in Table 3. In the
solid material, we find that plasma can be produced without mechanical effects, and that both plasma and mechanical effects
can be produced well below the threshold for transmission-change. We find that if the energy is above the threshold for trans-
plasma, bubble, and pressure wave formation
transmission
1
0.1
0
0.1
1
10
100
laser energy (µJ)
Fig. 4. Transmission of 100-fs pulses through water as a function of incident laser energy.
mission-change, then the mechanical effects are more extensive, producing damage large enough to be seen with a microscope
(but still quite small at only 200-nm diameter). Conversely, in water, no plasma is produced below the threshold for mechanical
effects. Furthermore, neither plasma nor mechanical effects are produced below the threshold for transmission-change.
material
plasma formation (µ J)
mechanical effects (µ J)
transmission-change (µ J)
fused silica
0.06
0.08
0.3
water
0.2
0.2
0.2
Table 3. Comparison of 100-fs pulse thresholds for plasma formation, mechanical effects, and transmission-change in fused silica and water
We can only compare the relative values the thresholds in each material, because spherical aberration caused by the cell
window is likely to increase the beam waist at the focus in water. Thus, at a given laser energy, the fluence is probably higher
in fused silica than in water.
The differences in the relative values of the various threshold for 100-fs pulses in fused silica and water can be attributed
to the differing contributions of multiphoton and avalanche ionization in the two materials. In water, the thresholds for plasma
formation, mechanical effects, and transmission-change all coincide. This “all or nothing” threshold indicates that the absorption is dominated by avalanche ionization. Because avalanche ionization is an efficient absorption mechanism, once the avalanche begins a significant fraction of the laser pulse is absorbed. This stronger absorption, in turn, leads to more energy being
deposited in the material, producing larger mechanical effects. In water, the multiphoton absorption alone is not strong enough
to produce a plasma or any mechanical effects. Instead, the electrons produced by multiphoton absorption seed the avalanche
process (thus also leading to the non-statistical threshold behavior discussed above). The avalanche, once started, causes enough
absorption that not only plasma, but also mechanical effects, are produced.
In fused silica we see plasma formation and mechanical effects at energies where there is little absorption. Because avalanche ionization leads to the absorption of a large fraction of the laser pulse, we conclude that the plasma and damage at low
laser energies are produced by multiphoton absorption. This is supported by estimating the laser fluence at the 60-nJ threshold
for plasma formation. The diffraction limited spot size of the laser under our focusing conditions has less than a 1-µ m diameter.
In solids, we focus approximately 100 µ m below the surface of the sample, where spherical and other aberrations are minimized.
Because the focusing is aberration free, we can safely take a 1-µ m diameter spot size as an upper limit. To find a lower limit,
recall that the size of the damage spots produced at high laser energy is only 200 nm in diameter, indicating that the spot size
is significantly below the diffraction limit. The decreased spot size could be due to self focusing.19 In any case, the beam diameter is between 1 µ m and 200 nm at the focus, giving a fluence between 7.6 × 10–2 and 1.9 J/m2. Stuart et al. present a model
for short pulse breakdown in fused silica12 that predicts, for 100-fs pulses with fluences above about 3 × 10–2 J/m2, that multiphoton absorption alone is sufficient to produce plasma and damage, with no avalanche necessary. Because our fluence exceeds the necessary fluence by a factor of at least two and probably closer to 60, we are certainly in the regime where
multiphoton absorption alone is responsible for plasma production and damage at threshold.
Above the threshold for transmission-change, where significant absorption occurs, larger damage, visible under a microscope, is produced. The strong absorption above the transmission-change threshold indicates that avalanche ionization is responsible for much of the absorption. Evidently, the number of electrons ionized by multiphoton absorption below the
transmission-change threshold is enough to produce plasma and some damage, but is not enough to get an avalanche started
during the laser pulse. Above the transmission-change threshold, the multiphoton absorption generates more electrons early in
the pulse because the intensity is higher. These electrons generated early in the pulse can then participate in the avalanche for
the remainder of the pulse. The increased absorption due to the avalanche process leads to more extensive mechanical effects,
in this case, visible damage.
In the study of surface ablation thresholds, various research groups have defined breakdown thresholds in different ways.
Lenzner, et al. measure the ablation depth as a function of laser energy, and extrapolate back to zero ablation depth to arrive at
a threshold.10 Du et al. measure transmission-change and plasma emission to determine the threshold.11 Stuart et al. look for
visible damage with a microscope after the sample has been irradiated by many laser shots.12 In our previous work in the bulk
of transparent materials, we defined the damage threshold as the energy required to produce damage visible under a microscope.2,9,18 Our present work indicates that, at least for the case of short (100-fs or less) laser pulses, these various thresholds
do not necessarily coincide.
5. CONCLUSIONS
In this paper we report on thresholds for femtosecond laser-induced breakdown in bulk transparent solids and water. Using
an optical scattering technique we find that the threshold for producing plasma and damage varies little between materials. From
transmission measurements in fused silica we find that plasma and damage are produced at energies where there is little absorption of the laser pulse. However, damage large enough to be seen under a microscope is only produced above the threshold for
transmission-change, where the absorption is stronger. In water, we used optical scattering and acoustic techniques to measure
the plasma and bubble formation thresholds. In contrast to solid materials, transmission measurements in water indicate that
there is no plasma or bubble production below the transmission-change threshold. This difference is attributed to differing roles
of multiphoton and avalanche ionization in water and fused silica.
6. ACKNOWLEDGMENTS
The authors would like to thank Eli N. Glezer for help with the experiments. A portion of this research was supported by the
Materials Research Science and Engineering Center at the Division of Engineering and Applied Sciences at Harvard University.
C.B.S. acknowledges support of a National Defense Science and Engineering Fellowship.
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