Optical generation and detection of gigahertz shear acoustic waves in solids assisted by a metallic diffraction grating

Osamu Matsuda, Kandai Tsutsui, Gwenaëlle Vaudel, Thomas Pezeril, Kentaro Fujita, and Vitalyi Gusev

Phys. Rev. B 101, 224307 – Published 22 June 2020

Abstract

Absorption of ultrashort laser pulses in a metallic grating deposited on a transparent sample launches in the material both compression/dilatation (longitudinal) and shear coherent acoustic pulses in directions of different orders of acoustic diffraction. The propagation of the emitted acoustic pulses can be monitored by measuring the variation of the optical reflectivity of the time-delayed ultrashort probe laser pulses. The direction of probe light incidence and its polarization relative to the sample surface as well as the orientation of the metallic grating should be specifically chosen for efficient Brillouin scattering of the probe light from shear phonons propagating in the elastically isotropic materials. As theoretically predicted, the obtained experimental data contain multiple frequency components which are due to a variety of possible Brillouin scattering angles for both shear and compression/dilatation coherent acoustic waves. All these different frequency components are explained through multiplexing the propagation directions of probe light and coherent sound by the metallic diffraction grating. Our experimental scheme of time-domain Brillouin scattering with metallic gratings operating in reflection mode provides access to monitoring the shear acoustic waves launched in the direction of the first diffraction order by backward Brillouin scattering process. Applications include simultaneous determination of several different acoustic mode velocities and optical refractive index and, potentially, measurements of the acoustic dispersion of samples with a single direction of possible optical access.

Received 11 April 2020
Revised 30 May 2020
Accepted 2 June 2020

DOI:https://doi.org/10.1103/PhysRevB.101.224307

Physics Subject Headings (PhySH)

Acoustic measurements Acoustic wave phenomena Elasticity Light-matter interaction Mechanical & acoustical properties Microstructure Optical transient phenomena Ultrasonics

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Osamu Matsuda ^1,*, Kandai Tsutsui¹, Gwenaëlle Vaudel ², Thomas Pezeril², Kentaro Fujita ¹, and Vitalyi Gusev ^3,†

¹Division of Applied Physics, Faculty of Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan
²Institut des Molécules et Matériaux du Mans, UMR 6283 CNRS, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans, France
³Laboratoire d'Acoustique de l'Université du Mans, UMR 6613 CNRS, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans, France

^*omatsuda@eng.hokudai.ac.jp
^†vitali.goussev@univ-lemans.fr

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Issue

Vol. 101, Iss. 22 — 1 June 2020

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Images

Figure 1
Schematic diagram of the generation of shear acoustic waves by the optical excitation of metallic gratings. The upper half-space is an isotropic medium. The metallic grating rods are formed on its surface: their cross sections are shown as the yellow rectangles, and their expansion along the $y$ direction is indicated by red arrows. The blue waves schematically show the displacement of the generated shear acoustic waves propagating along the first-order diffraction (white arrow).
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Figure 2
Momentum conservation and induced electric polarization $Δ P$ in the scattering process of the incident light ( $k_{i}$ ) into the scattered light ( $k_{s}$ ) by the acoustic waves ( $k_{B}$ ). (a) The $p$ incident light and the $x_{2}$ -polarized shear waves. (b) The $s$ incident light and the $x_{2}$ -polarized shear waves. (c) The $p$ incident light and the $x_{1}$ -polarized shear waves. (d) The $s$ incident light and the $x_{1}$ -polarized shear waves.
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Figure 3
Rotation of the sample. (a) Initial orientation. (b) Rotation with respect to $y$ (or $Y$ ) by an angle $α$ . (c) Rotation with respect to $x^{'}$ by an angle $β$ (side and top views). In the top view, $y^{''}$ and $z^{''}$ appear to be overlapped, but in fact, the former is directed upwards from the $X - Z$ plane, whereas the latter is directed downwards.
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Figure 4
Transient reflectivity changes for the sample rotations indicated on the plots.
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Figure 5
Norm of Fourier amplitude of the transient reflectivity changes obtained for the sample orientations indicated on the plots. The $+$ and $\times$ symbols indicate the calculated Brillouin frequencies for the longitudinal and shear waves, respectively. For convenience of presentation, the amplitudes in the low-lying part of the spectra ( $< 11$ GHz) are diminished five times.
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Figure 6
The possible Brillouin scattering configurations for the sample rotated to the orientation $[α, β] = [0 . 0^{\circ}, 33 . 1^{\circ}]$ . The wave vectors of photons before the scattering $k_{i}$ are shown by blue arrows. The wave vectors of the photons after the scattering $k_{s}$ are shown by green arrows. The wave vectors of the absorbed phonons $k_{B}$ are shown by red arrows. The $y$ and $z$ axes are shown at the bottom. In the left column the state of the photon incident on the acoustic grating is identified by the diffraction order $m_{i}$ and the direction of its propagation along the $z$ axis, $d_{i} = \pm 1$ , in the form $(m_{i}, d_{i})$ . In the top row the state of the photon scattered by the acoustic grating is identified by the diffraction order $m_{s}$ and the direction of its propagation along the $z$ axis, $d_{s} = \pm 1$ , in the form $(m_{s}, d_{s})$ . The distance between the dash-dotted vertical lines is equal to the wave number of the gratings $q$ . The vertical and horizontal solid lines indicate the distinction of forward and backward scattering processes: The top left and bottom right processes involve the backward scattering, whereas the top right and bottom left processes involve the forward scattering. The configurations $(0, 1) \to (0, 1)$ and $(- 1, - 1) \to (- 1, - 1)$ are, in fact, not the scattering, but just the light passing through the sample.
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