Time-domain extreme ultraviolet diffuse scattering spectroscopy of nanoscale surface phonons

Surface acoustic wave (SAW) propagation is central to phenomena ranging from seismic activity activity to modern telecommunications. SAWs are confined to a thin region near a solid’s surface and generally travel more slowly than bulk acoustic waves, with their velocity determined by both the material and the specific wave mode. At the macroscopic level, Rayleigh and Love seismic waves — and even ocean waves — are familiar examples of surface-bound acoustic motion. At the microscopic scale, SAWs underpin key technologies in communication systems, satellite navigation, and sensing. Their high surface sensitivity, compact footprint, and compatibility with electronics make them essential components in devices for wireless communication standards, including 5G. SAW filters, for example, operate through the piezoelectric effect: an electrical signal applied to a piezoelectric substrate generates surface acoustic waves that traverse the material and are subsequently converted back into electrical signal.

In a recent experiment at the DiProI end station of the FERMI free-electron laser (FEL) facility, an international research team uncovered a surprising way to generate and visualize sound waves that travel along solid surfaces with nanometer-scale wavelengths. When materials are excited by ultrafast laser pulses, their extreme ultraviolet (EUV) diffuse scattering patterns exhibit evolving ring-like features that reveal coherent SAWs radiating in all directions. These surface vibrations, with wavelengths as short as 60 nanometers, arise not from engineered nanostructures but from the material’s intrinsic surface roughness, which couples light absorption to mechanical motion. Laser-driven SAWs have long been used as a contactless probe of elastic properties, but their wavelengths typically match the size of the optical excitation spot — about 300 micrometers in this study. The emergence of SAWs that are thousands of times shorter was therefore entirely unexpected.

Figure 1(a) illustrates the experimental geometry: optical pump and FEL probe pulses impinge on the sample at 45°, and the diffuse EUV scattering (DES) signal is captured in reflection geometry on a CCD detector. At fixed time delay between the pump and probe pulses, the excitation induces substantial changes — up to several percent — in the static DES intensity $I_{\mathrm{DES}}^{\mathrm{pumped}}$, which appear as concentric rings in the differential image $\Delta I_{\mathrm{DES}} = I_{\mathrm{DES}}^{\mathrm{pumped}} - I_{\mathrm{DES}}^{\mathrm{static}}$ ,  shown in Fig.1(b). The radial average of these fringes evolves with the pump–probe delay, encoding the motion of surface ripples across a broad range of acoustic phonon wavevectors (Fig. 1(c)). The ability to probe a wide range of momentum transfer simultaneously allows direct extraction of the SAW dispersion relation, which agrees closely with theoretical predictions (Fig. 1(d)). The researchers further demonstrate that this effect is universal across metals, semiconductors, and multilayer films that absorb laser light.

Figure 1: (a) Sketch of the experimental setup. (b) Differential ΔI_(DES ) (Q_x,Q_y,t=250 ps)  intensity pattern recorded by the CCD detector on the Pt/Al multilayer sample. (c)  Radial average of the differential DES intensity collected at different time delays.  (c) Fourier transform of the data in panel (c). The red dashed line represents the calculated Rayleigh surface phonon dispersion relation for the Pt/Al multilayer sample.

Although the EUV scattering patterns clearly arise from coherent surface phonons, the precise mechanism that allows optical radiation — whose wavelength is orders of magnitude larger — to generate nanoscale SAWs is still not fully understood. Two complementary effects likely contribute. First, the presence of surface roughness can cause incident light to interfere with light scattered from the surface, producing a highly non-uniform absorption profile. This uneven energy deposition creates localized thermal stresses that act as randomly distributed mechanical sources, thereby launching a broadband spectrum of surface waves.

A second pathway stems from the acoustic response of the material itself. When a laser pulse is absorbed in a thin subsurface layer, it produces a longitudinal acoustic pulse that propagates both into the bulk and toward the surface. At an ideally flat interface, the upward-traveling pulse would simply reflect with reversed strain. Real surfaces, however, are never perfectly smooth; their inherent roughness scatters part of this reflected pulse into both bulk and surface acoustic modes, offering another route for generating the unexpectedly short-wavelength SAWs observed in the experiment.

Because all materials possess some degree of surface roughness, this discovery opens a new route for probing and manipulating surface dynamics at the nanoscale. The method provides access to surface vibrations far beyond the reach of conventional optical techniques and could be widely applied — even using compact tabletop coherent EUV sources.

F. Capotondi¹, A.A. Maznev², F. Bencivenga¹, S. Bonetti³, D. Engel⁴, D. Fainozzi^1,5, D. Fausti^1,6,7, L. Foglia¹, C. Gutt⁸, N. Jaouen^9,3, D. Ksenzov⁸, C. Masciovecchio¹, Keith A. Nelson², I. Nikolov¹, M. Pancaldi^1,3, E. Pedersoli1, B. Pfau⁴, L. Raimondi^1,10, F. Romanelli11, R. Totani¹, M. Trigo^12,13
1 Elettra Sincrotrone Trieste, Basovizza, Trieste, Italy 
² Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
³ Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, Venice, Italy
⁴ Max Born Institute, Berlin, Germany
⁵ Institute of Applied Physics, University of Bern, Bern, Switzerland
⁶ Department of Physics, University of Trieste, Trieste, Italy
⁷ Department of Physics, University of Erlangen-Nürnberg, Erlangen, Germany
⁸ Department of Physics, University of Siegen, Siegen, Germany 
⁹ Synchrotron SOLEIL, Saint-Aubin, Gif-sur-Yvette Cedex, France  
¹⁰ Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, USA
¹¹ Department of Mathematics, Informatics and Geosciences, University of Trieste, Trieste, Italy
¹² Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California, USA
¹³ Stanford PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, California, USA

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