Parity-Time Synthetic Phononic Media.

Classical systems containing cleverly devised combinations of loss and gain elements constitute extremely rich building units that can mimic non-Hermitian properties, which conventionally are attainable in quantum mechanics only. Parity-time (PT) symmetric media, also referred to as synthetic media, have been devised in many optical systems with the ground breaking potential to create nonreciprocal structures and one-way cloaks of invisibility. Here we demonstrate a feasible approach for the case of sound where the most important ingredients within synthetic materials, loss and gain, are achieved through electrically biased piezoelectric semiconductors. We study first how wave attenuation and amplification can be tuned, and when combined, can give rise to a phononic PT synthetic media with unidirectional suppressed reflectance, a feature directly applicable to evading sonar detection.

Extraordinary absorption of sound in porous lamella-crystals.

We present the design of a structured material supporting complete absorption of sound with a broadband response and functional for any direction of incident radiation. The structure which is fabricated out of porous lamellas is arranged into a low-density crystal and backed by a reflecting support. Experimental measurements show that strong all-angle sound absorption with almost zero reflectance takes place for a frequency range exceeding two octaves. We demonstrate that lowering the crystal filling fraction increases the wave interaction time and is responsible for the enhancement of intrinsic material dissipation, making the system more absorptive with less material.

Tunable acoustic double negativity metamaterial.

Man-made composite materials called "metamaterials" allow for the creation of unusual wave propagation behavior. Acoustic and elastic metamaterials in particular, can pave the way for the full control of sound in realizing cloaks of invisibility, perfect lenses and much more. In this work we design acousto-elastic surface modes that are similar to surface plasmons in metals and on highly conducting surfaces perforated by holes. We combine a structure hosting these modes together with a gap material supporting negative modulus and collectively producing negative dispersion. By analytical techniques and full-wave simulations we attribute the observed behavior to the mass density and bulk modulus being simultaneously negative.

Curved nanowire structures and exciton binding energies.

Growth of quantum-confined semiconductor structures is a complicated process that may lead to imperfect and complex shapes as well as geometrical nonuniformities when comparing a large number of intended identical structures. On the other hand, the possibility of tuning the shape and size of nanostructures allows for extra optimization degrees when considering electronic and optical properties in various applications. This calls for a better understanding of size and shape effects. In the present work, we express the one-band Schrödinger equation in curved coordinates convenient for determining eigenstates of curved quantum-wire and quantum-dash structures with large aspect ratios. Firstly, we use this formulation to solve the problem of single-electron and single-hole states in curved nanowires. Secondly, exciton states for the curved quantum-wire Hamiltonian problem are found by expanding exciton eigenstates on a product of single-particle eigenstates. A simple result is found for the Coulomb matrix elements of an arbitrarily curved structure as long as the radius-of-curvature is much larger than the cross-sectional dimensions. We use this general result to compute the groundstate exciton binding energy of a bent nanowire as a function of the bending radius-of-curvature. It is demonstrated that the groundstate exciton binding energy increases by 40 meV as the radius-of-curvature changes from 20 to 2 nm while keeping the total length (and volume) of the nanowire constant.

Electronic properties of semiconductor nanowires.

This paper provides a review of the state-of-the-art electronic-structure calculations of semiconductor nanowires. Results obtained using empirical k.p, empirical tight-binding, semi-empirical pseudopotential, and with ab initio methods are compared. For conciseness, we will restrict our detailed discussions to free-standing plain and modulated nanowires. Connections to relevant experimental data, particularly band gaps and polarization anisotropy, will be made since these results depend crucially on the electronic properties. For completeness, a brief review on the synthesis of nanowires is included.

Flow acoustics in periodic structures.

A recent paper [A.A. Krokhin, J. Arriaga, L.N. Gumen, Speed of sound in periodic elastic composites, Phys. Rev. Lett. 91 (2004) 264302-1-4] addresses the speed of sound in periodic elastic composites (phononic crystals) with particular emphasis to the case where air bubbles are present in water and arranged periodically. In such periodically arranged mixtures, the well-known phenomena of the drop of the speed of sound may occur and applications related to, e.g., sound-beam focusing and acoustic surgery are possible [F. Cervera, L. Sanchez, J.V. Sanchez-Perez, R. Martinez-Sala, C. Rubio, F. Meseguer, C. Lopez, D. Caballero, J. Sanchez-Dehesa, Phys. Rev. Lett. 88 (2002) 023902]. In this paper, the analysis is extended theoretically to include cases where a background flow in a periodic structure is maintained. Calculations of dispersion relations and group velocities are presented in cases with one- and two-dimensional material periodicity for background flow values in the range: 0-1m/s. Materials considered in the calculations are periodic water-air mixtures. It is shown that acoustic waves couple to the group velocities only if the (acoustic) wave vector has a component along the background flow velocity direction.

Flow acoustics modelling and implications for ultrasonic flow measurement based on the transit-time method.

A comparison between three mathematical models frequently used in flow acoustics is presented and discussed with respect to ultrasonic flow-meter performance based on the transit-time method. The flow-meter spoolpiece geometry is assumed to be a cylindrical pipe. Semi-analytical calculations employing the Frobenius power series expansion method are shown for the cases of a constant-, linear-, parabolic-, and cubic-flow profiles although the Frobenius method presented can be applied to any smooth flow profile. It is shown that the so-called deviation of measurement, often used as a measure of the flow-meter accuracy, is strongly dependent on the acoustic mode excited and the flow profile. Furthermore, differences with respect to deviation of measurement results exist among the three mathematical models analyzed.

Ultrasonic flow measurement and wall acoustic impedance effects.

An examination of the influence of wall acoustic impedance effects on sound propagation in flowing liquids confined by cylindrical walls is presented. Special focus is given to the importance of the wall acoustic impedance value for ultrasonic flow meter performance. The mathematical model presented allows any radially-dependent axial flow profile to be examined in the linear flow acoustics regime where fluid flow speed is much smaller than the fluid sound speed everywhere in the fluid medium.

Acoustic cavity modes in lens-shaped structures.

A method for solving exactly the Helmholtz equation in parabolic rotational coordinates is presented using separability of the eigenfunctions and the Frobenius power series expansion technique. Two examples of interest in acoustics are considered and analyzed quasianalytically: The acoustic pressure in a cavity defined by two paraboloids (forming a lens-shaped structure) with (I) rigid wall boundary conditions and (II) pressure-release boundaries. The rigid-wall (pressure-release) acoustic enclosure problem is a Neumann (Dirichlet) boundary condition problem. In both cases, eigenfunctions and eigenmodes are calculated and the shape dependence of the eigenvalue for the ground state is examined.

Eigenmodes of triaxial ellipsoidal acoustical cavities with mixed boundary conditions.

The linear acoustics problem of resonant vibrational modes in a triaxial ellipsoidal acoustic cavity with walls of arbitrary acoustic impedance has been quasi-analytically solved using the Frobenius power-series expansion method. Eigenmode results are presented for the lowest two eigenmodes in cases with pressure-release, rigid-wall, and lossy-wall boundary conditions. A mode crossing is obtained as a function of the specific acoustic impedance of the wall; the degeneracy is not symmetry related. Furthermore, the damping of the wave is found to be maximal near the crossing.

Ultrasonic flowmeters: temperature gradients and transducer geometry effects.

Ultrasonic flowmeter performance is addressed for the case of cylindrically shaped flowmeters employing two reciprocal ultrasonic transducers A and B so as to measure time-of-flight differences between signals transmitted from transducer A towards B followed by an equivalent signal transmitted from transducer B towards A. In the case where a liquid flows through the flowmeter's measuring section ("spoolpiece"), the arrival times of the two signals differ by an amount related to the flow passing between the two transducers. Firstly, a detailed study of flow measurement errors with mean flow in the laminar flow regime is carried out as a function of the mode index and the transducer diameter/cylinder diameter ratio in the case where no temperature gradients are present in the flowmeter sensor. It is shown that all modes except the fundamental mode overestimate the mean flow by a factor of 33.33% while excitation of the fundamental mode solely give error-free measurements. The immediate consequences are that the flowmeter error decreases as the transducer diameter/cylinder diameter ratio approaches 1 from 0 reflecting the fact that the excitation level of the fundamental mode increases from almost 0 to 1 as this ratio approaches 1 from 0. Secondly, the effect on flowmeter performance due to flow-induced temperature gradients is examined. It is shown that the presence of temperature gradients leads to flowmeter errors at the higher-flow values even in the case where the fundamental mode is the only mode excited. It is also deduced that flowmeter errors in general depend on the distance between transducers A and B whether temperature gradients exist or not. This conclusion is not reflected in the usual definition of flowmeter errors given by the so-called mode-dependent deviation of measurement introduced in earlier works.

Ultrasound transducer modeling--general theory and applications to ultrasound reciprocal systems.

A tutorial presentation on the theory of reciprocal ultrasound systems is given, and a complete set of modeling equations for one-dimensional multi-layer ultrasound transducers is derived from first principles. The model includes dielectric losses and mechanical losses in the transducer material layers as well as sound absorption in the transmission medium. First, the so-called constitutive relations of a piezoelectric body are derived based on general thermodynamic considerations, assuming that transducer operation takes place under almost isentropic conditions. Second, full attention is given to transducers oscillating in the thickness mode, discarding all other vibration modes. Dynamic transducer equations are determined using Newton's Second Law, Poisson's equation, and the definition of strain applied to a piezoelectric transducer with one or more non-piezoelectric layers on the front surface (multilayer transducer). Boundary conditions include continuity of normal velocity and stress across material interfaces as well as a subsidiary electrical condition over the piezoceramic electrodes. Sound transmission is assumed to take place in a water bath such that the Rayleigh equation can be used to obtain the incoming pressure at the receiver aperture from the acceleration of the opposing transmitter. This allows, e.g., a detailed treatment of receiver signal variations as the receiver moves from the near-field zone to the far-field zone of the transmitter. In the remaining part of the paper, receiver voltage and current signals are obtained by solving the full set of dynamic equations numerically. Special attention is given to transducers consisting of a) a pure piezoceramic layer only, b) a piezoceramic layer and a quarter-wavelength matching layer of polyphenylensulphide (PPS), c) a piezoceramic layer and a half-wavelength matching layer of stainless steel, and d) a piezoceramic layer and a half-wavelength matching layer of stainless steel tuned to resonance by a parallel inductance. Results are also given for receiver incoming pressure and receiver voltage signals when sound reception takes place in the near-field and far-field zones of the transmitter.

Perturbation theory applied to sound propagation in flowing media confined by a cylindrical waveguide.

First-order perturbation theory is employed to examine sound propagation in flowing media confined by a cylindrical waveguide. The use of perturbation theory allows examination of mode phase-speed changes due to any radially dependent flow w(r) as long as the flow magnitude is sufficiently small. The condition to be fulfilled is satisfied in the flow range: 0-0.3 m/s for the specific values of cylinder radius, ultrasound frequency, and sound speed analyzed in the present work [in the general case, however, the condition in Eq. (1) of the present work must be fulfilled]. This freedom of choice, i.e., the possibility to handle any radial flow profile, is used to analyze two flow profile cases: (1) where w(r) is a linear combination of a laminar flow profile and a flat profile corresponding to turbulent flow, and (2) where w(r) is a linear combination of a laminar flow profile and a more realistic logarithmic-dependent turbulent flow profile. In both cases, it is shown that large errors may result in ultrasound flow measurements if several modes are excited by the transmitting transducer, and that a logarithmic flow profile in the turbulent regime leads to somewhat larger measurement errors at high flow values as compared to assuming a simple flat profile in the turbulent regime.

Ultrasound transducer modeling-received voltage signals and the use of half-wavelength window layers with acoustic coupling layers.

A general set of modeling equations for lossless one-dimensional multilayer ultrasound transducers is presented based on first principles. In particular, a direct relationship between ultrasound transducer results and the underlying physical principles of electroacoustics is given. As such, the model may provide better physical understanding for designers not fully versed in electrical circuits theory or in linear system analyses. The model is suitable for time-domain analysis and monofrequency design. Special attention is given to the determination of the time-dependent voltage across the receiver electrodes subject to a general voltage input, but information on any (dynamic) variable of interest is provided. The basic equations governing the dynamics of the multilayer structure acting as transmitter as well as receiver are solved by Fourier analysis and by imposing continuity of velocity and pressure between layers. Sound transmission between the two piezoelectric circuits is assumed to take place in a water bath such that the Rayleigh equation can be used to obtain the incoming pressure at the receiver aperture from the acceleration of the opposing transmitter aperture. Comparison with experimental results is possible by allowing coupling to external electric impedances. A numerical test case using a multilayered 1-MHz transducer for flow meter applications was considered and good agreement with experiments was obtained in terms of voltage signals. The transducer contains a half-wavelength stainless steel layer needed to resist corrosion, the ability to operate at temperatures in a wide range from 20 to 150 degrees Celsius, resistance to impact from flowing particles in the medium, high pressure or vacuum, and pH values up to 10 in some locations. The influence of epoxy glue and grease acoustic coupling layers-between the piezoceramics and the stainless steel layer-in the range from 1 to 70 mum was examined. It was shown that, for the same layer thickness, epoxy glue is preferred as compared with grease, both in terms of signal shapes and amplitudes. Finally, inclusion of appropriate electric impedances in the transmitter and receiver circuits is found to affect signal pulses strongly.