Andreas P. Mayer

Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).

The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented.

3. Laser-based surface acoustic waves in materials science

Publisher Summary This chapter discusses the application of laser-based surface acoustic waves (SAWs) in materials science. Laser sources are widely used in investigations by means of SAWs of elastic properties of solids, various films, and coatings on surfaces. These sources are noncontact; they allow a SAW transmitter of desired shape to be created and thus an acoustic beam with predetermined properties to be formed. All laser-based methods of SAW generation in solids can be divided into two groups. The first group is connected with heating of the solid by the absorbed laser radiation and all consequences of this heating, such as thermal expansion, evaporation, and ablation. The second group combines the processes of interaction of the electromagnetic field with the lattice or electronic structure of the solid, including electrostriction, deformation because of carrier density modulation by laser radiation, and nonradiative recombination in semiconductors. The chapter considers thermal laser sources of SAWs, because they are universal and in general more effective. Among thermal methods, it is convenient to distinguish between two limiting cases according to the relation between the absorbed energy density and specific heat of fusion and evaporation of the solid. The low-energy limit is the linear thermoelastic regime of SAW generation. All thermal and elastic parameters are assumed constant. Local pulsed heating causes transient thermal expansion and elastic stresses, which subsequently lead to emission of bulk and surface waves. In the high-energy case, strong evaporation or ablation occurs in the irradiated area.

On the Coriolis effect in acoustic waveguides

Rotation of an elastic medium gives rise to a shift of frequency of its acoustic modes, i.e., the time-period vibrations that exist in it. This frequency shift is investigated by applying perturbation theory in the regime of small ratios of the rotation velocity and the frequency of the acoustic mode. In an expansion of the relative frequency shift in powers of this ratio, upper bounds are derived for the first-order and the second-order terms. The derivation of the theoretical upper bounds of the first-order term is presented for linear vibration modes as well as for stable nonlinear vibrations with periodic time dependence that can be represented by a Fourier series.

Guided acoustic waves propagating at surfaces, interfaces and edges

Surface and interface acoustic waves are two-dimensionally guided waves, as their displacement field is plane-wave like regarding its dependence on the spatial coordinates parallel to the guiding plane, while it decays exponentially along the axis normal to that plane. When propagating at the planar surface or interface of homogeneous media, they are non-dispersive. Another type of non-dispersive acoustic waves which is, however, one-dimensionally guided, has displacement fields localized near the apex of a wedge made of an elastic material. In this short review, their propagation properties are described as well as theoretical and experimental methods which have been used for their analysis. Experimental findings are discussed in comparison with corresponding theoretical work and potential applications of this fascinating type of acoustic waves are presented.

Nonlinear surface acoustic waves: theory.

A theoretical description is given for the propagation of surface acoustic wave pulses in anisotropic elastic media subject to the influence of nonlinearity. On the basis of nonlinear elasticity theory, an evolution equation is presented for the surface slope or the longitudinal surface velocity associated with an acoustic pulse. It contains a non-local nonlinearity, characterized by a kernel that strongly varies from one propagation geometry to another due to the anisotropy of the substrate. It governs pulse shape evolution in homogeneous halfspaces and the shapes of solitary surface pulses that exist in coated substrates. The theory describing nonlinear Rayleigh-type surface acoustic waves is extended in a straightforward way to surface waves that are localized at a one-dimensional acoustic waveguide like elastic wedges.

Rigorous COM and P-matrix approaches to the simulation of third-order intermodulation distortion and triple beat in SAW filters

In this work a set of nonlinear coupled COM equations at interacting frequencies is derived on the basis of nonlinear electro-elasticity. The formalism is presented with the aim of describing intermodulation distortion of third-order (IMD3) and triple beat. The resulting COM equations are translated to the P-matrix formalism, where care is taken to obtain the correct frequency dependence. The scheme depends on two frequency-independent constants for an effective third-order nonlinearity. One of these two constants is negligibly small in the systems considered here. The P-matrix approach is applied to single filters and duplexers on LiTaO3 (YXl)/42° operating in different frequency ranges. Both IMD3 and triple beat show good agreement with measurement.

Silicon edges as one-dimensional waveguides for dispersion-free and supersonic leaky wedge waves

Acoustic waves guided by the cleaved edge of a Si(111) crystal were studied using a laser-based angle-tunable transducer for selectively launching isolated wedge or surface modes. A supersonic leaky wedge wave and the fundamental wedge wave were observed experimentally and confirmed theoretically. Coupling of the supersonic wave to shear waves is discussed, and its leakage into the surface acoustic wave was observed directly. The velocity and penetration depth of the wedge waves were determined by contact-free optical probing. Thus, a detailed experimental and theoretical study of linear one-dimensional guided modes in silicon is presented.

On the stability of surface acoustic pulse trains in coated elastic media

Coating a planar surface of a homogeneous elastic halfspace by a thin film gives rise to dispersion of Rayleigh waves that, together with the second-order nonlinearity of the substrate or surface nonlinearities, leads to the existence of surface acoustic solitary pulses. Their shapes are computed and their stability with respect to small changes of their initial conditions and partly to collisions with each other is analyzed numerically. The existence of gap solitary waves in the case of a periodically structured film is demonstrated, and periodic solitary pulse train solutions on a small oscillatory background are found. Their stability is investigated by means of a Floquet analysis.

Application of a rigorous nonlinear P-matrix method to the simulation of third order intermodulation in test devices and duplexers

Recently a P-matrix and COM formalism was presented, which predicts third order intermodulation (IMD3) and triple beat with good accuracy and needs only a single nonlinearity constant. This formalism describes frequency dependence correctly. In this work the dependence of this nonlinearity constant on metalization ratio is investigated for aluminum metalization on LiTaO3 (YXl)/42°. By comparison to test devices the nonlinearity constant is shown to be largely independent of metalization ratio. The nonlinear effect, however, strongly depends on metalization ratio, which is well described by the model. The linearity of a duplexer is optimized by reduction of metalization ratio and redesign of Tx branch topology.

Nonlinear acoustic waves localized at crystal edges

Anisotropy has been found to play an important role for the existence of edge-localized acoustic modes as well as for nonlinear effects in rectangular edges. For a certain propagation geometry in silicon, the effective second-order nonlinearity for wedge waves was determined numerically from second-order and third-order elastic moduli and compared with the nonlinearity for Rayleigh waves propagating in the direction of the apex on one of the two surfaces forming the edge. In the presence of weak dispersion resulting from modifications of the wedge tip or coating of the adjacent surfaces, solitary pulses are predicted to exist and their shape was calculated.