Focusing of high-amplitude surface acoustic waves leading to material damage is visualized in an all-optical experiment. The optical setup includes a lens and an axicon that focuses an intense picosecond excitation pulse into a ring-shaped pattern at the surface of a gold-coated glass substrate. Optical excitation induces a surface acoustic wave (SAW) that propagates in the plane of the sample and converges toward the center. The evolution of the SAW profile is monitored using interferometry with a femtosecond probe pulse at variable time delays. The quantitative analysis of the full-field images provides direct information about the surface displacement profiles, which are compared to calculations. The high stress at the focal point leads to the removal of the gold coating and, at higher excitation energies, to damage of the glass substrate. The results open the prospect for testing material strength on the microscale using laser-generated SAWs.

Surface acoustic waves (SAWs), also known as Rayleigh waves, play an important role in many areas of science and technology from seismology1 to signal processing2 and non–destructive material characterization.3–5 Similar to other types of waves, SAWs can be focused to a small spot, ultimately limited by the wavelength. Focusing can, for instance, be performed by a lens–shaped thin film structure or a curved interdigital transducer (IDT).6 The enhancement of the SAW amplitude by focusing has found applications in the design of acousto-optic devices7,8 and, more recently, in microfluidics.9–11 The use of laser pulses to generate SAWs makes it possible to achieve focusing by shaping the excitation laser beam12–16 without any structures on the surface. One can imagine that focused SAWs may be able to reach the limit of the material strength and cause damage. This aspect of SAW focusing has not hitherto been explored. The fact that high-amplitude SAWs can cause material damage has generally been well recognized. For example, SAWs are the leading cause of damage produced by earthquakes.17 On the microscale, brittle fracture by SAWs has been previously observed in the nonlinear regime of SAW propagation,18–20 wherein the increase in stress at the surface occurred due to the formation of “surface shock waves” without the aid of focusing. With this approach, multiple randomly located linear cracks were formed in the path of the SAW propagation. By contrast, SAW focusing is expected to produce material damage at a well-defined location.

In this work, high-amplitude focused SAWs are generated by ring-shaped laser pulses in an arrangement resembling the one that was used to focus shock waves in a thin liquid layer21,22 and in highly–ordered pyrolytic graphite.23 The “acoustical breakdown” takes place at the focal point in the linear regime of the SAW propagation. The magnitude of stress in the material is quantified based on interferometric images of the surface displacement field.

The experimental setup and sample configuration are shown schematically in Fig. 1. A 300-ps, 800-nm wavelength, laser pulse with energy varying from 80 μJ to 2.4 mJ was focused onto the surface of a 300 μm-thick glass substrate (Schott D263) sputter-coated with an 80 nm-thick gold film. Using a 0.5° axicon prism and a lens with a 30-mm focal length, the excitation pulse was focused into a ring with a 200-μm diameter and a 10-μm width. The gold coating was ablated from the glass substrate at the laser ring location, launching surface acoustic waves. An inward-propagating surface wave converged towards the center, whereas an outward-propagating wave diverged out of the excitation ring. A variably delayed 180-fs duration, 400-nm wavelength probe pulse derived from the same laser system was used to record interferometric images of the sample surface using a Michelson interferometer. The reference mirror of the interferometer was tilted in order to obtain parallel interference fringes with a desired fringe density of about 250 fringes/mm.

FIG. 1.

Optical setup and sample configuration. (a) The axicon-lens combination is used to focus the excitation into a ring on the gold-coated surface of the glass substrate. The surface is imaged onto a CCD camera at 10× magnification using a variably-delayed femtosecond probe pulse and a Michelson interferometer configuration to obtain interferometric images of the surface displacement. (b) Sample configuration schematically showing the ring-shaped excitation and propagation of focusing and diverging SAWs.

FIG. 1.

Optical setup and sample configuration. (a) The axicon-lens combination is used to focus the excitation into a ring on the gold-coated surface of the glass substrate. The surface is imaged onto a CCD camera at 10× magnification using a variably-delayed femtosecond probe pulse and a Michelson interferometer configuration to obtain interferometric images of the surface displacement. (b) Sample configuration schematically showing the ring-shaped excitation and propagation of focusing and diverging SAWs.

Close modal

Figure 2 shows a typical set of interferometric images captured at an excitation fluence of 2.5 J/cm2 at six representative delays, showing the convergence of the SAW and subsequent divergence after passing through the focal point. We note that this is not a real-time sequence, as each image was taken using a separate laser shot, and the sample was translated laterally between the shots to move the laser spot to an undamaged area of the sample. Fringes of the constant phase bended as the surface was displaced vertically, and the optical path, directly proportional to the surface displacement, was changed; hence, the SAW profiles were directly observable in the images.

FIG. 2.

Interferometric images of propagating SAWs recorded with varying delay between the excitation pulse and the imaging probe pulse at a laser excitation fluence of 2.5 J/cm2. (a) CCD image at a delay of 15.6 ns. The propagating SAW is characterized by a bend in the interference fringes. The directions of the SAW propagation, inward and outward, are indicated by yellow arrows. The dark ring is formed due to the removal of the gold coating along the laser irradiation ring. (b)–(f) Cropped CCD images at increasing delays show focusing (b)–(d) of the SAW followed by divergence (e) and (f). After the convergence of the SAW, a black spot appears at the focal point, revealing damage in the gold film caused by the SAW (e) and (f).

FIG. 2.

Interferometric images of propagating SAWs recorded with varying delay between the excitation pulse and the imaging probe pulse at a laser excitation fluence of 2.5 J/cm2. (a) CCD image at a delay of 15.6 ns. The propagating SAW is characterized by a bend in the interference fringes. The directions of the SAW propagation, inward and outward, are indicated by yellow arrows. The dark ring is formed due to the removal of the gold coating along the laser irradiation ring. (b)–(f) Cropped CCD images at increasing delays show focusing (b)–(d) of the SAW followed by divergence (e) and (f). After the convergence of the SAW, a black spot appears at the focal point, revealing damage in the gold film caused by the SAW (e) and (f).

Close modal

As shown in Fig. 2(e), a dark area appeared at the focal point after the passage of the SAW, revealing the damage of the gold film. Permanent damage was also caused by direct laser exposure and is evidenced in Fig. 2(a) by a dark ring area (now bare glass) where the laser was focused. These damage features were confirmed by post-mortem scanning electron microscopy (SEM) images shown in Fig. 3. At a smaller excitation energy and therefore smaller acoustic amplitude, the gold coating at the center delaminated from the glass substrate but was not removed [Fig. 3(a)]. The resulting bump at the center, measured with a surface profilometer, showed a height of about 270 nm. At a fluence of 2.5 J/cm2, the center portion of the gold film was removed, in agreement with time-resolved images in Figs. 2(e) and 2(f). With increased laser excitation energy, the damage was not restricted to the gold layer but extended to the glass substrate. A higher acoustic amplitude led to a more dramatic acoustical breakdown of the glass at the focus [Fig. 3(c)]. In addition to crater formation, the entire gold film inside the laser ring was removed from the substrate. A set of time-resolved interferometric images at high laser fluences has not yet been obtained, as the extensive gold film damage substantially worsened the image quality.

FIG. 3.

Post-mortem SEM micrographs for three different excitation fluences: (a) 1.3 J/cm2, (b) 2.5 J/cm2, and (c) 38.2 J/cm2. Insets show the close-up views of the center region.

FIG. 3.

Post-mortem SEM micrographs for three different excitation fluences: (a) 1.3 J/cm2, (b) 2.5 J/cm2, and (c) 38.2 J/cm2. Insets show the close-up views of the center region.

Close modal

The vertical surface displacement field, u Z ( x , y ) , of the gold–coated substrate can be obtained from interferometric images by comparing the fringe patterns before and after excitation. The relationship Δ φ / 4 π = u Z / λ was used to extract the displacement profile quantitatively, where Δ φ , u Z , and λ denote the phase shift with respect to the reference image, the surface displacement, and the wavelength of the probe beam, respectively. The surface displacement profile was extracted for multiple delays along a ring diameter, taking advantage of the cylindrical symmetry of the experiment22,24 (see the supplementary material for more details). The surface displacement profiles extracted from the images are presented in Fig. 4 for five representative delays for a laser excitation fluence of 2.5 J/cm2. As expected, the amplitude of the SAW increased as it focused towards the center: from a peak–to–peak value of 80 nm at 11.2 ns to 270 nm near the center at 40.4 ns. The dispersion of SAWs due to the presence of the 80 nm–thick gold layer was clearly visible from the surface displacement plots, particularly at later times. For example, at a delay of 32.0 ns (Fig. 4), the lower frequency component of the acoustic wave reached the center, while the highest observable frequencies were still tens of microns away from it. It is also worth noting that, simultaneously with the SAW generation, a blast wave was generated and propagated in air above the sample. The density change in air, caused by this blast pressure wave, also induced a phase shift in the probe beam and was therefore detected in the deformed fringe pattern. However, the measurements of the SAW were not affected by the blast wave as the latter travelled at a lower speed than the SAW (at approximately 1.1 km/s).

FIG. 4.

Measured (solid curves) and calculated (dashed curves) vertical surface displacement profiles at different delays at an excitation fluence of 2.5 J/cm2. The SAW propagation direction is indicated by red solid arrows. The weaker surface skimming longitudinal wave (SSLW) is also detected. Positive values correspond to outward displacements. The blast wave contribution to the phase shift is indicated by dotted black arrows.

FIG. 4.

Measured (solid curves) and calculated (dashed curves) vertical surface displacement profiles at different delays at an excitation fluence of 2.5 J/cm2. The SAW propagation direction is indicated by red solid arrows. The weaker surface skimming longitudinal wave (SSLW) is also detected. Positive values correspond to outward displacements. The blast wave contribution to the phase shift is indicated by dotted black arrows.

Close modal

While interferometric images yield SAW profiles in terms of the surface displacement, the stress distribution causing material damage is not directly observable. In order to determine the stresses associated with focusing SAWs, numerical simulations were carried out. The SAW propagation was simulated using the finite element time domain method with a commercial software package PZFlex. The simulated surface displacements shown in Fig. 4 yield good agreement with the experimental data. The discrepancies arise from uncertainty in the experimentally measured time delays; this is particularly noticeable in the 40.4 ns profile (close to the maximum focusing) when the amplitude at the center is very sensitive to the time delay (see the supplementary material). Having established that the simulations reproduce the surface displacement measured in the experiment, we can compute the stresses in the sample which are not accessible to experimental observations.

The time evolution of the stresses close to the focus computed at the film-substrate interface for the last numerical element in the gold film is shown in Fig. 5. (The corresponding strain maps presented in the supplementary material yielded strain rates up to 6 × 107 s−1.) We believe that the delamination of the gold film is caused by the tensile stress σzz, which reaches its maximum value of 0.92 GPa at 40.4 ns. The in-plane tensile stress σrr, reaching a much greater value in excess of 7 GPa, cannot cause delamination, but it can fracture the gold film, thus facilitating its removal. The relatively small values of σzz are due to the fact that its value at the free surface ought to be identically zero, and the interface is located at a small depth compared to the SAW wavelength (the same is true for σrz; in addition, the latter is identically zero at the focus r = 0 due to the symmetry constraints). The maximum positive (tensile) σzz value of 2.4 GPa is reached inside the glass substrate at a depth of 3.5 μm. It should be noted that both σrr and σzz greatly exceed the static tensile strength of both gold and borosilicate glass (30 to ∼400 MPa for gold depending on the film thickness and 20–200 MPa for glass).25–27 However, in our case, the tensile stress is only applied for about a nanosecond. It is known, largely from shock spallation experiments,28–30 that the dynamic material strength can greatly exceed the static strength: for example, it was found that the spall strength of copper exceeded 10 GPa and approached the theoretical limit predicted by the equation of state at strain rates over 108 s−1;30 in another shock spallation experiment, soda lime glass was found to withstand a tensile stress of up to 3 GPa without damage.28 

FIG. 5.

Stresses computed close to the focus r 10 μ m at the film-substrate interface for the last numerical element in the gold film 67 n m z 80 n m . The scale bars show the maximum and minimum values reached for each stress component.

FIG. 5.

Stresses computed close to the focus r 10 μ m at the film-substrate interface for the last numerical element in the gold film 67 n m z 80 n m . The scale bars show the maximum and minimum values reached for each stress component.

Close modal

Unlike in previous studies of material damage by high-amplitude nonlinear SAWs,18–20 in our experiment, the SAW propagation was in the linear regime as indicated by a good agreement between the experiment and the simulations based on the linear model. The absence of nonlinear effects is explained by the SAW dispersion caused by the gold film. The linear SAW propagation regime has an advantage in terms of quantifying the stress magnitude. Indeed, in the nonlinear regime, the formation of a shock front leads to a singularity in the in-plane stress at the surface.18–20 Quantifying the stress magnitude requires the knowledge of the width of the shock front, which cannot be measured due to the limited spatial resolution of the optical probe. In the linear regime, this difficulty does not arise: once the simulations match the measured displacement profile, we have a high confidence in the calculated stress pattern.

In conclusion, we have demonstrated material damage caused by focusing of laser-induced high-amplitude SAWs. This approach opens a prospect for testing material strength and adhesion of coatings at ultrahigh strain rates. SAWs offer some possibilities not accessible in the more conventional shock spallation approach, such as studying crack initiation at the free surface. Practical advantages include a smaller excitation laser energy required and the fact that only one surface of the sample needs to be optically accessible. An intriguing possibility is testing approaches proposed for preventing damage by earthquake-generated SAWs31 in a microscale experiment. Studying SAW focusing on an uncoated surface in the nonlinear regime presents yet another avenue for future research.

See supplementary material for the image analysis procedure, materials properties, simulations details, strain maps, and effect of time delay adjustment.

The authors would like to thank Ryan Duncan, Doug Shin, Lingping Zeng, and Jeff Eliason for their help in the sample characterization. This work was supported in part by the U.S. Army Research Laboratory and the U. S. Army Research Office through the Institute for Soldier Nanotechnologies, under Contract No. W911NF-13-D-0001. The authors acknowledge financial support from CNRS (Centre National de la Recherche Scientifique) under grant Projet International de Coopération Scientifique.

1.
A.
Mordret
,
T. D.
Mikesell
,
C.
Harig
,
B. P.
Lipovsky
, and
A.
Prieto
,
Sci. Adv.
1
,
e1501538
(
2015
).
2.
C.
Campbell
,
Surface Acoustic Wave Devices and Their Signal Processing Applications
(
Academic Press
,
Boston, MA
,
1989
).
3.
A. G.
Every
,
Meas. Sci. Technol.
13
,
R21
(
2002
).
4.
J. A.
Rogers
,
A. A.
Maznev
,
M. J.
Banet
, and
K. A.
Nelson
,
Annu. Rev. Mater. Sci.
30
,
117
(
2000
).
5.
B.
Sherman
,
H.-C. C.
Liou
, and
O.
Balogun
,
J. Appl. Phys.
118
,
135303
(
2015
).
6.
I. M.
Mason
,
J. Acoust. Soc. Am.
53
,
1123
(
1973
).
7.
H. E.
Engan
,
T.
Myrtveit
, and
J. O.
Askautrud
,
Opt. Lett.
16
,
24
(
1991
).
8.
M. M.
de Lima
,
F.
Alsina
,
W.
Seidel
, and
P. V.
Santos
,
J. Appl. Phys.
94
,
7848
(
2003
).
9.
M.
Tan
,
J. R.
Friend
, and
L. L.
Yeo
,
Phys. Rev. Lett.
103
,
24501
(
2009
).
10.
Y.
Ai
and
B. L.
Marrone
,
Microfluid. Nanofluid.
13
,
715
(
2012
).
11.
G.
Destgeer
,
S.
Im
,
B.
Hang Ha
,
J.
Ho Jung
,
M.
Ahmad Ansari
, and
H.
Jin Sung
,
Appl. Phys. Lett.
104
,
023506
(
2014
).
12.
A. A.
Kolomenskii
,
S.
Jerebtsov
, and
H.
Schuessler
,
Opt. Lett.
30
,
2019
(
2005
).
13.
S. D.
Sharples
,
M.
Clark
, and
M. G.
Somekh
,
Ultrasonics
41
,
295
(
2003
).
14.
P.
Cielo
,
F.
Nadeau
, and
M.
Lamontagne
,
Ultrasonics
23
,
55
(
1985
).
15.
S.
Dixon
,
T.
Harrison
,
Y.
Fan
, and
P. A.
Petcher
,
J. Phys. D. Appl. Phys.
45
,
175103
(
2012
).
16.
F.
Bruno
,
J.
Laurent
,
P.
Jehanno
,
D.
Royer
, and
C.
Prada
,
J. Acoust. Soc. Am.
140
,
2829
(
2016
).
17.
H.
Kawase
,
Seismol. Res. Lett.
67
,
25
(
1996
).
18.
V.
Kozhushko
,
A.
Lomonosov
, and
P.
Hess
,
Phys. Rev. Lett.
98
,
195505
(
2007
).
19.
G.
Lehmann
,
A. M.
Lomonosov
,
P.
Hess
, and
P.
Gumbsch
,
J. Appl. Phys.
94
,
2907
(
2003
).
20.
A. M.
Lomonosov
and
P.
Hess
,
Phys. Rev. Lett.
89
,
95501
(
2002
).
21.
T.
Pezeril
,
G.
Saini
,
D.
Veysset
,
S.
Kooi
,
P.
Fidkowski
,
R.
Radovitzky
, and
K. A.
Nelson
,
Phys. Rev. Lett.
106
,
214503
(
2011
).
22.
D.
Veysset
,
A. A.
Maznev
,
T.
Pezeril
,
S.
Kooi
, and
K. A.
Nelson
,
Sci. Rep.
6
,
24
(
2016
).
23.
D.
Veysset
,
T.
Pezeril
,
S.
Kooi
,
A.
Bulou
, and
K. A.
Nelson
,
Appl. Phys. Lett.
106
,
161902
(
2015
).
24.
D.
Veysset
,
A. A.
Maznev
,
G.
Saini
,
S. E.
Kooi
,
T.
Pezeril
, and
K. A.
Nelson
,
AIP Conf. Proc.
1426
,
1597
1600
(
2012
).
25.
Handbook of Precious Metals
, edited by
E. M.
Savitskii
and
A.
Prince
(
Hemisphere Publishing Corporation
,
1989
).
26.
J.-H.
Kim
,
A.
Nizami
,
Y.
Hwangbo
,
B.
Jang
,
H.-J.
Lee
,
C.-S.
Woo
,
S.
Hyun
, and
T.-S.
Kim
,
Nat. Commun.
4
,
2520
(
2013
).
27.
Data provided for the glass by the manufacturer. Schott Technical Glasses. Physical and technical properties. www.us.schott.com.
28.
Z.
Rosenberg
,
D.
Yaziv
, and
S.
Bless
,
J. Appl. Phys.
58
,
3249
(
1985
).
29.
D. E.
Grady
,
J. Mech. Phys. Solids
36
,
353
(
1988
).
30.
E.
Moshe
,
S.
Eliezer
,
Z.
Henis
,
M.
Werdiger
,
E.
Dekel
,
Y.
Horovitz
,
S.
Maman
,
I. B.
Goldberg
, and
D.
Eliezer
,
Appl. Phys. Lett.
76
,
1555
(
2000
).
31.
S.
Krödel
,
N.
Thomé
, and
C.
Daraio
,
Extreme Mech. Lett.
4
,
111
(
2015
).

Supplementary Material