Generation and propagation of coherent phonon beams

Abstract

Narrow coherent beams of longitudinal acoustic waves are injected into a single crystal of PbMoO 4 at gigahertz frequencies, and their properties are observed by means of Brillouin scattering. The waves are generated via the thermoelastic strain that results from periodic surface heating of a thin metallic transducer by interfering cw dye lasers. Frequency tuning is achieved simply by varying the optical difference frequency. A theoretical description based on heat diffusion and thermoelastic expansion agrees with the observed frequency dependence of the acoustic intensity, inclusive of acoustic resonances within the transducer, as well as its quadratic dependence on the laser power. The propagation of the acoustic beams is found to be governed by Fresnel diffraction provided due account is taken of phonon focusing. The beam furthermore is responsive to the phase profile over the laser-illuminated area, which allows us to manipulate the beam in various ways, such as modifying its divergence as if an acoustic lens were positioned just below the transducer or sweeping the beam sideward by a moving grating. Combined with Brillouin detection, distinguishing between phase and group velocities, this provides a direct measurement of phonon focusing. Finally, the decay of the acoustic beam with the distance is measured at various frequencies, to find confirmation of Herring's asymptotic theory for anharmonic phonon decay in anisotropic crystals.

Vibrational coupling in plasmonic molecules

“…This trend can be quantitatively accounted for with our coupled harmonic oscillator model by assuming that the vibrational coupling is mediated by coherent phonons of the substrate. These phonons are excited by a nanodisk vibration and propagate with an intensity (deformation amplitude) proportional to (44,45): Iðω, dÞ = βe −αω η d [1] where I is the local deformation amplitude, β is the initial vibration amplitude, α is the attenuation coefficient, d is the propagation distance, and ω is the phonon frequency. The nonnegative materials parameter η has a value of 2 (46).…”

Transmission of coherent phonons through a metallic multilayer

“…The thickness d 0 of the transducer derives from the acoustic intensity ⌽ 0 injected into the crystal by the bare transducer, which exhibits maxima at multiples of 1.50 Ϯ0.04 GHz as a result of double-fixed-end resonances. 12 Comparison with the theoretical ⌽ 0 ͑cf. the case Nϭ0 in Fig.…”

“…Partial coverage of a crystal face with the superlattice allows us to measure the acoustic intensity ⌽ N after passage through the superlattice with reference to the intensity ⌽ 0 injected by the bare transducer. Taking the ratio ⌽ N /⌽ 0 eliminates the Brillouin cross section, the effects of acoustic attenuation in the PbMoO 4 substrate, 12 and the uncertainties associated with realignment of the Brillouin spectrometer from one frequency to the next. To integrate the Brillouin intensities over the acoustic beam as necessary for an accurate determination of ⌽ N and ⌽ 0 , we scanned perpendicularly to the pencil-shaped detection volume in 5-m steps and fitted Gaussians to the acoustic profiles so measured.…”

Experimental verification of Herring’s theory of anharmonic phonon relaxation:TeO2

“…In the present paper this is achieved by making use of a recently developed technique for the generation of monochromatic Fresnel-diffracted phonon beams in the gigahertz range. 11 The method relies on cw laser-induced thermomodulation of a metallic transducer evaporated onto the crystal, and permits measurement as a function of T at various . In addition to monochromaticity and tunability, the technique features substantial narrowness of the phonon beam with minimum divergence.…”