Appl. Phys. A 68, 525–531 (1999) / DOI 10.1007/s003399900033

Applied Physics A Materials Science & Processing  Springer-Verlag 1999

Photoacoustic cavitation in spherical and cylindrical absorbers G. Paltauf, H. Schmidt-Kloiber Institute of Experimental Physics, Karl-Franzens-Universität Graz, Universitätsplatz 5, 8010 Graz, Austria (Fax: +43-316/380-9816, E-mail: [email protected]) Received: 9 October 1998/Accepted: 5 January 1999/Published online: 31 March 1999

Abstract. Photomechanical damage in absorbing regions or particles surrounded by a non-absorbing medium is investigated experimentally and theoretically. The damage mechanism is based on the generation of thermoelastic pressure by absorption of pulsed laser radiation under conditions of stress confinement. Principles of photoacoustic sound generation predict that the acoustic wave generated in a finite-size absorbing region must contain both compressive and tensile stresses. Time-resolved imaging experiments were performed to examine whether the tensile stress causes cavitation in absorbers of spherical or cylindrical shape. The samples were absorbing water droplets and gelatin cylinders suspended in oil. They were irradiated with 6-ns-long pulses from an optical parametric oscillator. Photoacoustic cavitation was observed near the center of the absorbers, even if the estimated temperature caused by absorption of the laser pulse did not exceed the boiling point. The experimental findings are supported by theoretical simulations that reveal strong tensile stress in the interior of the absorbers, near the center of symmetry. Tensile stress amplitudes depend on the shape of the absorber, the laser pulse duration, and the ratio of absorber size to optical absorption length. The photoacoustic damage mechanism has implications for the interaction of ns and sub-ns laser pulses with pigmented structures in biological tissue. PACS: 42.62.Be; 43.35.Ud; 87.51

In many therapeutic applications of laser pulses in medicine, the interaction of laser radiation and tissue is initiated by the heating of small absorbing regions that are surrounded by less absorbing tissue. “Small” means here that the absorber is smaller than the laser-irradiated volume. Such absorbing sites are for example blood capillaries, tattoo pigments, or melanosomes in the retinal pigmented epithelium (RPE) of the eye. The interaction of a laser pulse with an absorbing structure, and in particular the photoacoustic response of the absorber, are strongly influenced by relaxation of heat and

stress [1]. In both cases, the absorber size plays a role, because it determines the characteristic times of thermal and acoustic relaxation. If the laser pulse duration exceeds these limits, the decay of heat and stress in the absorber during irradiation becomes noticeable. If the light distribution inside the absorber is uniform, the thermal relaxation time, tth , is given by tth =

a2 , 4χ

(1)

where a is the characteristic size of the absorber and χ is the thermal diffusivity (in water, χ = 1.44 × 10−7 m2 /s). Absorption of a laser pulse that is shorter than tth leads to a maximum temperature rise in the absorber. This maximizes the thermal effect, which can be thermal denaturation or a phase change. The latter effect, namely the formation of transient vapor bubbles around melanosomes has been hold responsible for retinal damage caused by irradiation of the eye by short laser pulses [2, 3]. The acoustic relaxation time, tac , for uniform irradiation is given by the acoustic transit time through the absorber of size a, tac =

a , c

(2)

where c is the speed of sound. If the pulse duration is shorter than tac , the thermoelastic stress caused by the temperature rise stays confined in the absorbing region during the laser pulse, leading to a maximum pressure. An interaction taking place under conditions of stress confinement can therefore cause mechanical damage in the absorbing volume. Since the heated volume acts as an acoustic source, the acoustic waves emitted from the absorber can also damage surrounding tissue. The acoustic relaxation time is always shorter than tth , except for very small absorbing particles with a size in the sub-nm range (assuming thermal and acoustic properties of water). Therefore, a laser pulse with a duration tp smaller than tac has the potential of causing both strong mechanical and thermal effects. However, as studies of photoacoustic damage

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in water or tissue-like media have demonstrated, it is possible to achieve stress-induced fractureat a temperature rise of only a few degrees Celsius, where no thermal damage can be expected [4–6]. This has led to the hypothesis that for small, strongly absorbing particles such as melanosomes (size around 1 µm) the damage threshold for irradiation with ps laser pulses, where stress confinement is achieved, might be determined by photoacoustic interaction [7]. Photoacoustic damage is caused by tensile stress waves with an amplitude that exceeds the tensile strength of the material in which they propagate. Two mechanisms can turn the initially compressive thermoelastic stress into tensile stress. The first one is reflection of the stress wave at a boundary to a medium with lower acoustic impedance. The second one is related to the finite size of the acoustic source. An example where reflection plays a role is irradiation of a homogeneously absorbing medium through a transparent medium with lower acoustic impedance. If the beam diameter is much larger than the optical penetration depth, plane thermoelastic waves start to propagate from the heated volume in directions perpendicular to the boundary between the two media. The wave propagating towards the boundary is immediately reflected with negative sign and can cause fracture and ejection of material (“photospallation”) if its amplitude exceeds the tensile strength [4–6, 8]. For a strong acoustic mismatch (for example, tissue irradiated through air) the tensile stress amplitude can reach half of the initial thermoelastic pressure amplitude and the damage range has a lateral extension equal to the laser beam diameter. Tensile stress generation due to the finite size of the acoustic source becomes important if the condition of plane wave propagation is not satisfied or if there is no negative reflection at a boundary. An example is the thermoelastic wave generated after transmission of a short laser pulse into an absorbing liquid via an optical fiber [9]. The wave, part of which is reflected at the water– glass interface with positive sign, is diffracted at the lateral boundary of the circular acoustic source. Thereby strong tensile stress and cavitation are created near the fiber axis. In a highly absorbing liquid, a cavitation range exceeding by far the optical penetration depth from the fiber tip has been observed. If the fiber diameter is equal to or smaller than the penetration depth, radially propagating parts of the wave cause tensile stress amplitudes that are higher than the initial thermoelastic pressure. The influence of the finite size of the heated volume on the photoacoustic wave propagation has been theoretically described as an acoustic diffraction effect [10, 11]. This treatment is particularly appropriate if the acoustic source has the shape of a flat disc with a thickness (given by the absorption length) smaller than its diameter. Generally, the occurrence of tensile stresses in photoacoustic waves follows from fundamental principles of sound generation and propagation [12, 13]. It is required that an acoustic wave emitted from a distribution of positive stress of arbitrary shape and finite size must contain equal portions of compressive and tensile stress in a way that the integral over time of the pressure at a certain point vanishes. This is also the basic assumption of this study: according to this principle, any small, absorbing structure in tissue that is irradiated with a laser pulse under conditions of stress confinement should experience tensile stresses that might cause photomechanical damage.

To verify this hypothesis, photoacoustic damage in lightabsorbing model structures is investigated. In the experiments, absorbing spheres and cylinders are irradiated with short light pulses. The propagation of stress waves and tensile-stress-induced cavitation are observed with timeresolved imaging. The experiments are compared and complemented with results from a simplified theoretical model that uses solutions of the thermoelastic wave equation. 1 Theory In the simulations, photoacoustic sound generation in a lightabsorbing region inside a non-absorbing liquid is considered. Apart from the optical contrast, the liquid is homogeneous, meaning that the refractive index as well as the acoustic impedance are matched inside and outside the absorbing volume. The absorber has spherical or cylindrical shape and is irradiated from one side with a laser pulse. This results in an acoustic wave that can be described by the solution of the thermoelastic wave equation for the velocity potential [13] ∇ 2ψ −

1 ∂2ψ β = S, 2 2 c ∂t ρCp

(3)

where ψ is the velocity potential, β is the thermal expansion coefficient, ρ is the density, Cp is the specific heat capacity at constant pressure, and S is the heat generated per unit time and volume. This equation is valid if heat conduction and viscosity effects can be neglected. The pressure p is obtained from ψ using the relation: p = −ρ

∂ψ . ∂t

(4)

First the case of instantaneous deposition of heat at time zero is considered, where the heat-source term S at a point r can be expressed as the product of the volumetric energy density W and the Dirac delta function δ(t): S(r, t) = W(r)δ(t) .

(5)

Instantaneous heating gives rise to an initial thermoelastic pressure p0 (r) that depends on material properties and on W(r): p0 (r) =

βc2 W(r) = ΓW(r) , Cp

(6)

where Γ is the Grüneisen parameter. It has to be noted that the Grüneisen parameter depends on the temperature and thus on the energy density. Therefore, the relation between absorbed energy density and pressure is only linear for small temperature changes. The solution of the wave equation for a Delta heating pulse is given by the integral [9, 12] ZZ t βc2 ψ(r, t) = − W(r0 ) ds = 4πρ Cp |r−r0 |=ct ZZ t − p0 (r0 ) ds , (7) 4πρ |r−r0 |=ct

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where r0 is a point in the source volume and ds is the surface element on a unit sphere. The integration has to be performed on the surface of a sphere with radius ct around the observation point r. After deriving the pressure from (7) using relation (4), convolution with the temporal profile of the laser pulse yields the solution for a pulse of finite duration. For a pulse with a Gaussian temporal profile, one obtains R +∞ p(r, t) =

−∞

0

e−(2t /tp ) pδ (r, t − t 0 ) dt 0 , R +∞ −(2t 0 /t )2 p dt 0 −∞ e 2

(8)

where pδ is the solution for Delta pulse irradiation. A fundamental property of a photoacoustic wave that is emitted from a source of finite size, namely that this wave must contain compressive and tensile stress, follows immediately from (4) and (7). If the pressure signal at a certain point starts after a time t1 and ends before t2 , the integral over the pressure is given, according to (4), as the difference between two values of the velocity potential, Zt2

  p dt = ρ ψ(t1 ) − ψ(t2 ) = 0 ,

(9)

t1

each of them given according to (7) as the integral of the energy density over the surface of a sphere with radius ct. The sphere with radius ct2 includes the source volume, whereas the smaller one with radius ct1 does not (Fig. 1). Both ψ1 and ψ2 must be zero, because neither of the spheres intersects the acoustic source. Consequently also their difference and thus the integral over the pressure must vanish, which is only possible if the wave contains both positive and negative parts. The same arguments are valid if the observed point lies inside the source volume, provided the laser pulse starts at t > t1 . It remains to define the distribution of absorbed energy density. Figure 2 shows a section through an absorbing sphere that is irradiated by a laser pulse being incident in positive z-direction. The distribution of the energy density inside the sphere depends on the distance l of the observed point (z 0 , r 0 in cylindrical coordinates) from the surface of the absorber in direction of the incident laser beam. W(z 0 , r 0 ) = µa H0 exp(−µal) , p l = a2 − r 0 2 + z 0 .

(10)

Fig. 2. Cross section of an absorbing sphere that is irradiated by a laser pulse being incident in positive z-direction. The shaded area represents the heated volume. The energy density at a point (r 0 , z 0 ) depends on the distance l from the irradiated surface

H0 is the incident radiant exposure in a plane perpendicular to the direction of the laser beam axis. The energy distribution in a cylinder irradiated in a direction perpendicular to its axis is obtained in a similar manner. The following dimensionless quantities are introduced in order to generalize the results of the simulation: p∗ =

p , Γµa H0

a∗ = aµa ,

tc , a tp c tp∗ = . a t∗ =

(11)

Pressure and time are replaced by p∗ , the normalized pressure and t ∗ , the dimensionless time. p∗ is defined in a way that its maximum initial value in the absorbing volume after instantaneous heating is equal to one. The dimensionless time is in units of the acoustic transit time tac . The dimensionless radius a∗ is used to describe the light distribution inside the absorber and is given by the ratio of the absorber radius to the optical penetration depth. Nearly homogeneous heating of the absorber is achieved if a∗  1, whereas a∗  1 describes the case where only a thin shell on the side of the incident laser radiation is heated. tp∗ is the dimensionless pulse duration in units of tac . As long as a∗ < 1, stress confinement is achieved, if tp∗ < 1. If a∗ > 1, the heated volume occupies only a part of the absorber, and the condition of stress confinement depends on the absorption coefficient, requiring that tp < 1/µa c or tp∗ < 1/a∗ . The integration in (7) and the convolution with the temporal profile of the laser pulse (8) are performed numerically. Results are presented either in terms of pressure as a function of time at a fixed point or pressure as a function of space along a straight line at a fixed time. 2 Experiment

Fig. 1. Sketch illustrating the recording of a photoacoustic wave at point r outside the acoustic source. The source is the volume where W(r0 ) 6 = 0. Due to the finite source volume the wave is limited in time between t1 and t2

Small absorbers of different shape were irradiated with laser pulses and imaged with a time-gated video camera to observe cavitation and stress wave propagation inside and outside the absorbing volume (Fig. 3). Samples were water droplets (ρ = 1000 kg/m3 , c = 1500 m/s) suspended in silicone oil (ρ = 960 kg/m3, c = 1000 m/s) or gelatin filaments (ρ = 1080 kg/m3 , c = 1600 m/s) in castor oil (ρ = 960 kg/m3, c =

528 Table 1. Experimental parameters for taking the images in Figs. 4 and 7

Spheres

Cylinders

a∗

tp∗

a/mm

µa /mm−1

∆T/◦ C

0.22 1.2 14.8 0.18 1.09 10.4

0.08 0.08 0.06 0.09 0.1 0.09

0.11 0.11 0.15 0.1 0.09 0.1

2 10.9 99 1.8 12.1 104

3.4 17 99 8 32 310

Fig. 3. Experimental setup for taking time-resolved images of absorbing spheres and cylinders

1540 m/s). The samples contained Orange G, which has an absorption maximum at a wavelength of 490 nm. Gelatin was prepared with 75 wt. % dye solution and 25% gelatin powder. The concentration of Orange G in the dye solution was 10 g/l. The samples were irradiated with 6-ns-long pulses from an optical parametric oscillator (OPO) via a 600-µmcore-diameter optical fiber. By tuning the wavelength of the OPO from 500 to 540 nm the absorption coefficient of the samples could be varied from 100 to 2 mm−1 . Images were taken with an exposure time of 10 ns and after variable delay time with respect to the incident laser pulse. Back illumination of the samples using a fiber-transmitted flash (3-µs duration) from a Xenon lamp yielded shadowgraphs in which pressure gradients of the traveling stress waves are visible. 3 Results Figure 4 shows images of absorbing water droplets in silicon oil after irradiation with a laser pulse. The optical fiber

Fig. 4a–i. Cavitation in absorbing water droplets suspended in oil after irradiation with OPO pulses. The tip of the 600-µm-core-diameter fiber is seen in the upper part of each image. The absorption coefficient was varied yielding a∗ = 0.22 (a–c), 1.2 (d–f), and 14.8 (g–i). Images were taken at different delay times after the laser pulse: 70 ns (a, d, g); 1.1 µs (b, e, h); 3.1 µs (c, f), 15 µs (i)

is seen in the upper part of the images. The size of the droplets ranged from a = 0.11 mm to 0.15 mm. By changing the wavelength of the OPO pulses, the values of a∗ were varied from 0.22 to 14.8. Experimental parameters are listed in Table 1. The dark spot seen in the center of the droplets after 70 ns is cavitation. The cavities grow more or less with time (images after 1.1 and 3.1 µs) and disappear after a few µs. It is possible to estimate the maximum temperature rise in the absorbing spheres, using ∆T =

µa H0 . ρCp

(12)

At a∗ = 0.22 and a∗ = 1.2, the final temperature did not exceed the boiling point. Only at a∗ = 14.8, where ∆T = 99 ◦ C, water vaporization occurred, turning the upper half of the droplet in the image dark (image after 15 µs). The images in Figs. 5 and 6 show the initial phase of stress wave propagation and the onset of cavitation in a spherical droplet. The images are compared with calculations of the pressure along the common symmetry axis of the sphere and the laser beam (the z axis in Fig. 2) at the respective delay times. At low absorption (a∗ = 0.2, Fig. 5) the temperature and the resulting initial pressure are nearly uniform in the sphere. Stress waves are seen as circular shadows around and within the droplets. Since the calculation assumes an identical sound speed inside and outside the sphere, stress wave propagation was only calculated and compared in the interior of the droplets. A good correlation between the maximum pressure gradient in the calculation and the circular shadow in the images is observed. Best visibility of the collapsing

Fig. 5a–d. Images of stress wave propagation and cavitation in a sphere with a∗ = 0.2 (a = 0.15 mm, µa = 1.3 mm−1 ), taken 60 ns (a), 80 ns (b), 100 ns (c), and 140 ns (d) after the laser pulse. The diagrams show calculated stress distributions on the symmetry axis of the absorbing sphere along the direction of the incident laser radiation. The relative position is defined as z ∗ = z/a. At the center, z ∗ = 0

529

Fig. 6a–d. Images and calculated stress distributions along the z ∗ axis for a sphere with a∗ = 3.0 (a = 0.185 mm, µa = 16 mm−1 ). Delay times are 60 ns (a), 100 ns (b), 120 ns (c), and 160 ns (d)

stress wave is achieved in the image that was taken at a delay time of 80 ns. The calculation yields a maximum tensile stress in the center after about 100 ns with a relative amplitude of −16. The dark spot that is seen in the center of the droplet after 100 and 140 ns is again cavitation. The image taken after 140 ns also shows the expanding stress wave. Images and calculations at a∗ = 3.0 are shown in Fig. 6. Due to

Fig. 7a–f. Cavitation in absorbing gelatin cylinders suspended in oil. Values of a∗ are 0.18 (a, b), 1.09 (c, d) and 10.4 (e, f). Delay times: 70 ns (a, c, e); 570 ns (b, d); 50 µs (f)

the higher absorption, stress waves start to propagate only in and around the upper, heated hemisphere. The tensile stress component grows during propagation towards the center and reaches a maximum of −11 after 120 ns. At this time, also the onset of cavitation is seen. The image taken after 160 ns and the corresponding calculated p(z) curve show cavitation near the center and the stress wave approaching the bottom of the droplet. The images in Fig. 7 show the photomechanical response of gelatin filaments to irradiation with laser pulses. The values of a∗ together with the other experimental parameters are again listed in Table 1. In the images that were taken after a delay time of 70 ns, a dark line is seen at the cylinder axis, indicating the formation of cavitation. At a∗ = 10.4 the estimated maximum temperature strongly exceeds the boiling point (∆T = 310 ◦ C), causing the large vapor bubble that is observable after 50 µs. In the other experiments the temperature stayed below the boiling point. The diagrams in Fig. 8 show pressure as a function of time in the center of a sphere (a) and on the axis of a cylinder (b). The laser pulse starts at t ∗ = 0 and has a duration of tp∗ = 0.09, corresponding closely to the experimental values used for taking the images in Figs. 4 and 7. In all cases, tensile stress occurs at t ∗ ≈ 1 + tp∗ . The amplitude of the negative stress rises with decreasing a∗ . This tendency can be also seen in Fig. 9, where the positive and negative stress amplitudes in the center of a sphere (a) and on the axis of a cylinder (b) are depicted as a function of a∗ , for two different values of tp∗ . The curves reveal a decrease of the normalized tensile stress amplitude with rising a∗ and also with increasing tp∗ .

Fig. 8a,b. Stress as a function of time in the center of a sphere (a) and on the axis of a cylinder (b), calculated for different values of a∗ . The dimensionless pulse duration is tp∗ = 0.09

530

Fig. 9a,b. Positive and negative normalized amplitudes of photoacoustic waves in the center of a sphere (a) and on the axis of a cylinder (b), calculated as a function of a∗ for different values of tp∗

4 Discussion We have presented experimental results that demonstrate the generation of photoacoustic tensile stress waves and of cavitation in small optical absorbers after irradiation with a short laser pulse. One important observation was that cavitation occurred even if the peak temperature caused by absorption of laser radiation stayed well below the boiling point. This is particularly important when the damage mechanism in biological tissue is considered. The results indicate that photoacoustic fracture inside small absorbing regions can occur at levels of incident radiant exposure that do not cause any thermal damage. In some experiments with highly absorbing samples an energy density was achieved that raised the temperature above the boiling point. This caused both vaporization and photoacoustic cavitation in the absorbers. The two phenomena were clearly separated: Vaporization occurred near the surface that was heated by the laser pulse, while photoacoustic cavitation was generated near the center, where no laser radiation was absorbed due to the small optical penetration depth. This shows that even if vapor bubble formation seems to be the dominant photomechanical damage mechanism, internal fracture due to tensile stress waves has to be considered. The theoretical simulations support the main experimental findings, by showing that tensile stress occurs inside the absorbers and is focused in the center of symmetry, where the onset of cavitation is observed experimentally. It has to be examined, however, to what extent the calculations, which are based on some idealized assumptions, may be compared with the experiments. One of these assumptions is the validity of the thermoelastic wave equation (3), requiring that heat conduction and viscosity can be neglected. The first condition is satisfied, because only pulse durations below or at the limit of

stress confinement are considered in this study (for the largest values of the absorption coefficient, tp∗ ≈ 1/a∗ ). For such short pulses, heat is automatically confined as long as the absorber size is not too small (i.e. not in the sub-nm range). Also the influence of viscosity depends on the size of the absorber and can be neglected for absorbers larger than about 100 nm [14] (assuming water properties). Another assumption that was made in the simulation and was not entirely fulfilled in the experiments is the match of optical refractive index and acoustic impedance between interior and exterior of the absorbing region. In all cases, the refractive index inside is smaller than outside (1.332 in water and 1.405 in gelatin compared to 1.402 in silicone oil and 1.470 in castor oil). This causes slight deviations from the theoretical light distributions, but no optical focusing into the absorber that would give rise to local heating and thermal cavity formation. The acoustic mismatch is stronger for the combination water– silicone oil than for gelatin and castor oil. In both cases, the acoustic impedance is lower outside than inside (36% for water in silicone oil and 14% for gelatin in castor oil) and would give rise to a negative reflection of the wave at the boundary. However, the experiments in gelatin cylinders, where the reflection coefficient is only 0.08, demonstrate that tensile stress is generated nearly without acoustic reflection. Additional experiments have been made with water droplets in castor oil, where the acoustic match is nearly perfect, and have qualitatively yielded the same results as with the other samples. The images are not shown here, because the interior of the droplets can barely be seen due to the large mismatch of the optical refractive index. From these experiments and from the theoretical results it can be concluded that the simplified simulation, which assumes an acoustic match, is appropriate, because the main cause of tensile stress is not acoustic reflection but the geometry and limited size of the absorber. The maximum tensile stress depends on the shape of the absorber, the dimensionless pulse duration (indicating the degree of stress confinement) and on the light distribution, given by a∗ . The normalized tensile stress amplitude is much higher in a sphere than in a cylinder, because of the higher degree of symmetry. The spherically collapsing wave causes a very short tensile peak with high amplitude. In contrast, the infinite extension of a cylinder in z-direction causes a longer tensile phase. Because the areas under the positive and negative parts of the p(t) curves have to be equal (as stated in (9)), the longer tensile pulse on the cylinder axis has a lower amplitude. Similar arguments can be used for the influence of the pulse duration. An increasing pulse duration causes a temporal broadening of the tensile part of the wave, thereby decreasing the stress amplitude. The influence of the light distribution, namely an increase of the maximum tensile stress with decreasing factor a∗ , can be explained in terms of a higher degree of symmetry for a more homogeneous light distribution. Here it has to be noted that in many cases an absorber in biological tissue is irradiated by scattered light. This has the consequence that the light distribution inside the absorber will be more symmetric than for collimated irradiation, even if the absorber size is much larger than the absorption length. Since the photoacoustic wave generated in an absorber of given shape depends only on the light distribution and

531

on the degree of stress confinement, the results obtained for one absorber size can be scaled to another size, provided that a∗ and tp∗ are preserved. As an example the photoacoustic response of a melanosome in the RPE can be estimated from the results presented here. Taking a representative value for the absorption coefficient of a melanosome in the visible spectral range, µa = 100 mm−1 and a typical size of a = 1 µm [3], we get a∗ = 0.1, indicating nearly homogeneous heating. In order to obtain tp∗ < 1 for stress confinement, the pulse duration has to be shorter than 700 ps. The shape of a typical melanosome is reported to be slightly ellipsoidal [7]. Therefore the tensile stress amplitude will be lower than in a sphere, but still somewhat higher than in a cylinder. Assuming properties of water and a temperaturedependent Grüneisen parameter [15], a thermoelastic pressure of about 900 bar can be calculated for an instantaneous temperature rise from 20 ◦ C to 100 ◦ C. This results in a tensile stress amplitude in the kbar range inside a melanosome, if some focusing inside the particle occurs. The question is whether a few kbar of negative stress is sufficient to cause cavitation in the particle. For comparison, cavitation thresholds near −8 bar have been reported for water exposed to dynamic tensile stress [16]. Such a low threshold is due to heterogeneous nucleation in the liquid at small impurities. The threshold of homogeneous nucleation in pure water is estimated to be near −1.3 kbar [17]. It can be expected that in the tiny volume around the center of an absorbing droplet where high tensile-stress amplitudes are achieved, nucleation sites are not readily available and the cavitation threshold approaches that for homogeneous nucleation. This assumption is supported by measurements of cavitation thresholds in absorbing droplets. These measurements were done by observing the pulse energy necessary to cause cavitation with a probability of 50%. For a∗ ≈ 1 we found a typical energy density threshold of 40 J/cm3 , giving about 50 bar of positive thermoelastic pressure and about −500 bar for the cavitation threshold. Although the time-resolved images partly showed violent cavitation inside the samples, in no case could a disintegration of the absorber be observed. Only in the gelatin filaments was a permanent damage near the axis seen in some experiments. The high stability of the liquid and gelatin samples is due to surface tension and the confinement by the surrounding oil. Biological structures, however, are more sensitive and are ex-

pected to be permanently damaged by internal photoacoustic cavitation. 5 Conclusion The experiments and their theoretical analysis have shown that irradiation of a finite-size absorbing volume with a laser pulse in the regime of stress confinement causes strong tensile stress and leads to cavitation inside the absorber. This photoacoustic damage mechanism is important for medical applications of laser pulses in the nanosecond and sub-ns range, where it partly determines the interaction of laser radiation with pigmented regions or particles within the tissue. This has particular implications for safety considerations in the short-pulse regime. Acknowledgements. This work has been supported by the Austrian Science Foundation (FWF), Project number P10769 Med. G. Paltauf is supported by the Austrian Programme for Advanced Research and Technology (APART) of the Austrian Academy of Sciences.

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