A. A. Maznev

Reciprocity in reflection and transmission: What is a ‘phonon diode’?

Abstract The newly popular topic of ‘phonon diodes’ is discussed in the context of a broader issue of reciprocity in reflection/transmission ( R – T ) of waves. We first review a theorem well known in electromagnetism and optics but underappreciated in acoustics and phonon physics, stating that the matrix of R – T coefficients for properly normalized amplitudes is symmetric for linear systems that conform to power conservation and time reversibility for wave fields. It is shown that linear structures hitherto proposed for ‘acoustic diodes’ in fact do obey R – T reciprocity, and thus should not strictly be called diodes or isolators. We also review examples of nonlinear designs violating reciprocity, and conclude that an efficient acoustic isolator has not yet been demonstrated. Finally, we consider the relationship between acoustic isolators and ‘thermal diodes’, and show that ballistic phonon transport through a linear structure, whether an acoustic diode or not, is unlikely to form the basis for a thermal diode.

Anisotropy of the thermal conductivity in GaAs/AlAs superlattices.

We combine the transient thermal grating and time-domain thermoreflectance techniques to characterize the anisotropic thermal conductivities of GaAs/AlAs superlattices from the same wafer. The transient grating technique is sensitive only to the in-plane thermal conductivity, while time-domain thermoreflectance is sensitive to the thermal conductivity in the cross-plane direction, making them a powerful combination to address the challenges associated with characterizing anisotropic heat conduction in thin films. We compare the experimental results from the GaAs/AlAs superlattices with first-principles calculations and previous measurements of Si/Ge SLs. The measured anisotropy is smaller than that of Si/Ge SLs, consistent with both the mass-mismatch picture of interface scattering and with the results of calculations from density-functional perturbation theory with interface mixing included.

Surface acoustic modes in thin films on anisotropic substrates

Propagation of surface acoustic modes on the (001) and (111) surfaces of Si coated by a thin isotropic overlayer is studied theoretically and experimentally. It is shown that when a surface acoustic wave (SAW) coexists with a pseudosurface wave (PSAW) of the uncoated substrate, the second-order acoustic mode of the film/substrate system originates from a PSAW and the first-order one from a SAW. The polarization pattern of either mode varies from Rayleigh type (saggital plane polarization) to Love type (horizontal polarization) depending on the propagation direction and the product of the wave vector q and film thickness d. It is also shown that the isolated off-symmetry pure mode point within the PSAW branch disappears at some critical qd value. Experimentally, surface acoustic modes of Ti-coated Si wafers are measured with the impulsive stimulated thermal scattering (ISTS) technique based on laser generation and detection of acoustic waves at a specified wave vector. ISTS data are shown to be determined ...

Broadband terahertz ultrasonic transducer based on a laser-driven piezoelectric semiconductor superlattice

Spectral characteristics of laser-generated acoustic waves in an InGaN/GaN superlattice structure are studied at room temperature. Acoustic vibrations in the structure are excited with a femtosecond laser pulse and detected via transmission of a delayed probe pulse. Seven acoustic modes of the superlattice are detected, with frequencies spanning a range from 0.36 to 2.5THz. Acoustic waves up to ∼2THz in frequency are not significantly attenuated within the transducer which indicates excellent interface quality of the superlattice. The findings hold promise for broadband THz acoustic spectroscopy.

Monte Carlo study of non-diffusive relaxation of a transient thermal grating in thin membranes

The impact of boundary scattering on non-diffusive thermal relaxation of a transient grating in thin membranes is rigorously analyzed using the multidimensional phonon Boltzmann equation. The gray Boltzmann simulation results indicate that approximating models derived from previously reported one-dimensional relaxation model and Fuchs-Sondheimer model fail to describe the thermal relaxation of membranes with thickness comparable with phonon mean free path. Effective thermal conductivities from spectral Boltzmann simulations free of any fitting parameters are shown to agree reasonably well with experimental results. These findings are important for improving our fundamental understanding of non-diffusive thermal transport in membranes and other nanostructures.

Point source in a phononic grating: stop bands give rise to phonon-focusing caustics

We use locally-excited gigahertz surface phonon wavepackets in microscopic line structures of different pitches to reveal profound anisotropy in the radiation pattern of a point source in a grating. Time-domain data obtained by an ultrafast optical imaging technique and by numerical simulations are Fourier transformed to obtain frequency-filtered real-space acousticfield patterns and k-space phononic band structure. The numerically-obtained k-space images are processed to reveal an intriguing double-horn structure in the lowest-order group-velocity surface, which explains the observed non-propagation sectors bounded by caustics, noted at frequencies above the bottom of the first stop band. We account for these phonon-focusing effects, analogous to collimation effects previously observed in two- and three-dimensional lattices, with a simple

Extraordinary focusing of sound above a soda can array without time reversal

Recently, Lemoult et al. [Phys. Rev. Lett. 107, 064301 (2011)] used time reversal to focus sound above an array of soda cans into a spot much smaller than the acoustic wavelength in air. In this study, we show that equally sharp focusing can be achieved without time reversal, by arranging transducers around a nearly circular array of soda cans. The size of the focal spot at the center of the array is made progressively smaller as the frequency approaches the Helmholtz resonance frequency of a can from below, and, near the resonance, becomes smaller than the size of a single can. We show that the locally resonant metamaterial formed by soda cans supports a guided wave at frequencies below the Helmholtz resonance frequency. The small focal spot results from a small wavelength of this guided wave near the resonance in combination with a near field effect making the acoustic field concentrate at the opening of a can. The focusing is achieved with propagating rather than evanescent waves. No sub-diffraction-limited focusing is observed if the diffraction limit is defined with respect to the wavelength of the guided mode in the metamaterial medium rather than the wavelength of the bulk wave in air.

Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves.

Contact-based vibrations play an essential role in the dynamics of granular materials. Significant insights into vibrational granular dynamics have previously been obtained with reduced-dimensional systems containing macroscale particles. We study contact-based vibrations of a two-dimensional monolayer of micron-sized spheres on a solid substrate that forms a microscale granular crystal. Measurements of the resonant attenuation of laser-generated surface acoustic waves reveal three collective vibrational modes that involve displacements and rotations of the microspheres, as well as interparticle and particle-substrate interactions. To identify the modes, we tune the interparticle stiffness, which shifts the frequency of the horizontal-rotational resonances while leaving the vertical resonance unaffected. From the measured contact resonance frequencies we determine both particle-substrate and interparticle contact stiffnesses and find that the former is an order of magnitude larger than the latter. This study paves the way for investigating complex contact-based dynamics of microscale granular crystals and yields a new approach to studying micro- to nanoscale contact mechanics in multiparticle networks.

Surface thermal expansion of metal under femtosecond laser irradiation

Transient surface displacement of gold under femtosecond laser irradiation is studied using a probe beam deflection technique. A surface thermal expansion rise time of about 100 ps is explained in terms of nonequilibrium diffusion and thermalization of photoexcited electrons. Transient displacement provides direct information on the lattice temperature profile established once the electron-lattice relaxation is completed.

Thermal transport in suspended silicon membranes measured by laser-induced transient gratings

Studying thermal transport at the nanoscale poses formidable experimental challenges due both to the physics of the measurement process and to the issues of accuracy and reproducibility. The laser-induced transient thermal grating (TTG) technique permits non-contact measurements on nanostructured samples without a need for metal heaters or any other extraneous structures, offering the advantage of inherently high absolute accuracy. We present a review of recent studies of thermal transport in nanoscale silicon membranes using the TTG technique. An overview of the methodology, including an analysis of measurements errors, is followed by a discussion of new findings obtained from measurements on both “solid” and nanopatterned membranes. The most important results have been a direct observation of non-diffusive phonon-mediated transport at room temperature and measurements of thickness-dependent thermal conductivity of suspended membranes across a wide thickness range, showing good agreement with first-princ...