Breaking the Fourier barrier: time-domain Brillouin scattering

The dynamics of acoustic phonons in matter contain relevant information on several physical properties, such as elasticity, intermolecular interactions and transport phenomena. Phonons are characterized by a frequency (ω) that changes as a function of the phonon wavevector (k). The relevant (ω,k)-space ranges from zero to a boundary called “first Brillouin zone” (ω1BZ,k1BZ), featured by material-depended values of ω1BZ ≈ 50 THz and k1BZ ≈ 10 nm-1. Such a wide range is traditionally probed by Brillouin spectroscopy, combining different probes: from infrared or visible light to hard X-rays or thermal neutrons. However, the k = 0.1-1 nm-1 sub-range, which is relevant for nanotechnology, is currently precluded, since it corresponds to length-scales L = 2π/k ≈ tens of nanometers. This gap is largely due to the impossibility of using extreme ultraviolet (EUV) light in conventional Brillouin spectroscopy, a situation related to the twofold hurdles: (i) the unavailability of EUV spectrometers with the required resolving power (>106) and (ii) the short EUV penetration depth, which inherently limits the scattering volume.

Researchers at FERMI have overcome these limitations by using the EUV transient grating (EUV TG) technique, available at the TIMER beamline, in a special configuration capable of revealing in the time domain the stimulated Brillouin scattering of EUV light. In this configuration, the short EUV penetration is particularly favorable, as it enables acoustic phonons (magenta waves in Figure 1a) to be excited in a large k spectral range by the ultrafast EUV pulses from FERMI. Since the EUV TG excitation is periodic in space, with a period LTG, it also excites counter-propagating surface acoustic waves (SAWs) with a wavevector kSAW = 2π/LTG (blue waves in Figure 1a). An EUV probe pulse impinging at near-normal incidence can be both (i) diffracted by the coherent modulations of surface displacement due to SAW propagation, resulting in a signal that deviates from the specular reflection (dashed green line in Figure 1a), and (ii) back-scattered by a phonon with a wavevector about twice that of the EUV probe (kph ≈ 2kprobe), resulting in a nearly counter-propagating signal (dotted green line in Figure 1a). The former is the regular EUV TG signal, which is bright because surface modulations are spatially extended, while the latter is a Brillouin back-scattering signal, which is expected to be much weaker because of the limited scattering volume.

Figure 1 of the Elettra top-story from the article by D. Fainozzi et al. Phys. Rev. Lett. 2024

Figure 1: (a) Sketch of the experiment. Red arrows are FEL pulses that generate the EUV TG excitation (red wave), which excite counter propagating surface acoustic waves (SAW; blue waves) and bulk phonons (magenta waves), the thick green arrow is the EUV probe (the thin green arrow is its specular reflection), dashed and dotted green arrows are the TG and the back-scattered Brillouin signal, respectively. (b) The red line is the initial portion of the experimental signal, featured by the first modulation due to SAW propagation (blue line) and faster oscillations due to bulk phonons. (c) Fourier transform of the difference between the red and blue line in panel (a), green and red peaks highlight the presence of the expected two Brillouin frequencies.

In the employed experimental geometry, these two signals overlap in space, and, since they originate from different interactions within the same pulse, they also overlap in time. They can thus interfere. When the delay between the EUV TG excitation and the EUV probe is varied, the weak Brillouin signal is revealed as a time-dependent modulation of the brighter EUV TG signal, as shown in Figure 1b. Furthermore, the chosen sample (a monoclinic β-Ga2O3 crystal) and values of kSAW and kph resulted in an easily distinguishable dynamics, i.e., a slow sinusoidal shape for the TG signal and a faster double-frequency modulation for the Brillouin back-scattering signal; see Figure 1c.

The experimental results perfectly match predictions. They demonstrate Brillouin scattering at EUV light up to large wavevectors (≈ 1 nm-1), thus filling the gap between light and X-ray (or neutron) Brillouin scattering. This phenomenon, observed on β-Ga2O3, is expected to occur in any material, given the constraint of having a substantial EUV reflectivity from the sample, to ensure a detectable TG signal around which the Brillouin modulations appear. We used an EUV probe with a fixed wavelength (13.3 nm), changing this wavelength will enable changing kph, thus permitting the dispersion relations of the phonon frequency to be mapped in a previously inaccessible range. This ingenious approach could be "downscaled" to a table-top setup, where the EUV probe comes a from a laser-driven source and the EUV TG is replaced by an optical TG, provided that the latter is absorbed by the sample in a few tens of nm. This would enhance the capabilities of table-top Brillouin setups towards the range achieved by the more complex and costly instruments operating at large scale facilities, with potential benefits for a much wider scientific community.

This research was conducted by the following research team:

Danny Fainozzi1, Laura Foglia1, Claudio Masciovecchio1, Riccardo Mincigrucci1, Nupur N. Khatu1,2,3, Ettore Paltanin1 and Filippo Bencivenga1

1 Elettra - Sincrotrone Trieste S.C.p.A., Trieste, Italy.
2 Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice, Venice, Italy.
3 European XFEL, Schenefeld, Germany.

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D. Fainozzi, L. Foglia, N.N. Khatu, C. Masciovecchio, R. Mincigrucci, E. Paltanin and F. Bencivenga, “Stimulated Brillouin Scattering in the Time Domain at 1 nm−1 Wave Vector”, Phys. Rev. Lett. 110, 033802 (2024). DOI: 10.1103/PhysRevLett.132.03380.

Last Updated on Wednesday, 19 June 2024 08:20