Three-dimensional elasto-optical interaction for reflectometric detection of diffracted acoustic fields in picosecond ultrasonics

Abstract

The three-dimensional ͑3D͒ photoelastic interaction involved in the detection mechanism of picosecond ultrasonics is investigated in micrometric metallic films. In pump-probe experiments, the laser source beam is focused to a spot size of less than 1 m. A 3D diffracted acoustic field is generated at high frequencies of several tens of gigahertz, containing longitudinal and shear waves altogether. Their propagation changes the dielectric permittivity tensor and the material becomes optically heterogeneous. Consequently, the detection process is modeled through the propagation of the laser probe beam in a material with dielectric properties varying in all directions. Thus, the solution of Maxwell's equations leads to a differential system, the source term of which is proportional to the acoustic field itself. In the frame of small perturbation theory, the latter is decomposed into a continuous sum of monochromatic plane waves. The scattered electromagnetic field is described using the matricant, and the ensuing analytical solution then allows analyzing the 3D photoelastic interaction. The contribution of acoustic diffraction and shear wave detection to the reflectometric signal is put into relief. Good agreement with experiments performed in a 1 m thick aluminum film is found.

Coherent shear phonon generation and detection with picosecond laser acoustics

“…However, the range of measurable physical properties can be greatly increased by the use of shear waves. With this goal in mind, material anisotropy [13][14][15][16][17] and three-dimensional propagation involving mode conversion 18,19 have been recently exploited to optically generate and detect picosecond shear waves. For the generation of high-frequency shear waves in thin films, the use of material anisotropy is preferable because this method generates plane shear waves propagating perpendicular to the sample surface.…”

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

“…The heating of the metallic rods by laser radiation and heat transfer from the rods to the transparent substrate induce a temperature rise that gives rise to isotropic thermoelastic stresses in both of these media exhibiting isotropic thermal expansion. The isotropic thermoelastic stresses generate only compression/dilatation (longitudinal) acoustic waves [12,13,21]. However, both in the elastically isotropic substrate (SiO 2 in our case) and in the metallic grating (polycrystalline Al in our case), the compression/dilatation waves obliquely incident on the surfaces and interfaces get partially mode converted into shear acoustic waves.…”

“…It is, however, highly desirable to generate and detect shear acoustic waves in addition to longitudinal acoustic waves in order to get the full mechanical information of the elasticity of the medium. Such attempts require lower symmetry in the medium and/or excitation configurations: for example, the use of an anisotropic medium [9][10][11][12][13][14][15][16][17][18][19] or the use of acoustic waves propagating along the direction non-normal to the surface [20,21]. It has also been suggested that optically induced gratings formed by the illumination of the sample surface with two nonparallel light beams may generate shear acoustic waves [22,23].…”

Theory and illustration of the three-dimensional elasto-optic interaction in picosecond ultrasonics

“…2 of this paper, attention is drawn on the matrix formalism of the resulting linearized equations in the Fourier domain. Then, this differential system is solved using the matricant method [8]. Finally, in Sect.…”

“…where the index q = h, s stands for the homogeneous and scattered solutions, respectively. The differential systems (6) are then solved using the matricant [8], and the change of reflectivity r s p is obtained for each polarization p = 2, 3. Finally, r s p is multiplied by the spectrum of the functions defining the spatial distributions of intensity along x 2 of the pump and probe pulses.…”