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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.
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.
A simple model is introduced that describes the interaction of surface acoustic waves (SAWs) with a 2D periodic array of objects on the surface that give rise to internal resonances. Such objects may be high-aspect ratio structures like micro-pillars fabricated of a material different from that of the substrate. The model allows for an approximate determination of the band structure for the acoustic modes in such systems. Results are presented for the dependence on structural parameters of a total bandgap in the non-radiative regime of a semi-infinite substrate, and it is shown how the frequency and radiation damping of vibrational modes can be determined that are associated with defects in the periodic 2D array.
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.
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.
Silicon edges as one-dimensional waveguides for dispersion-free and supersonic leaky wedge waves
(2012)
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.
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 LiTaO 3 (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.
A laser-operated, angle-tunable transducer was employed to excite selectively elastic waves guided along the apex of a solid wedge. The propagation of wedge waves at anisotropic monocrystalline silicon edges with different symmetry properties was studied by optical detection. The reduced symmetry in crystals, as compared to isotropic media, causes a number of new features, such as the existence of supersonic leaky wedge waves, tilted spatial pulse profiles, and other peculiarities of their localization. Experimental and theoretical results are presented for three different types of symmetry configurations: the wedge symmetric about its midplane, the wedge symmetric about the plane normal to its apex line, and the wedge symmetric about one of its faces. The experiments include accurate measurements of the phase velocity and the wave field distribution, providing information on localization and coupling of wedge waves with other waves. Theoretically, the wedge waves were treated by the Laguerre function method, extended to modes that are not localized at the tip of the wedge. This approach allowed an accurate description of the observed localized and leaky wedge waves in anisotropic wedges.
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.