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The existence of acoustic waves with displacements localized at the tip of an isotropic elastic wedge was rigorously proven by Kamotskii, Zavorokhin and Nazarov. This proof, which is based on a variational approach, is extended to rectangular anisotropic wedges. For two high-symmetry configurations of rectangular edges in elastic media with tetragonal symmetry, a criterion is derived that allows identifying the boundary between the regions of existence for wedge modes of even and odd symmetry in regions of parameter space, where even- and odd-symmetry modes do not exist simultaneously. Furthermore, rectangular edges with non-equivalent surfaces are analyzed, and it is shown that at rectangular edges of cubic elastic media with one (110) surface and one (001) surface, a tip-localized guided wave always exists, apart from special cases that are characterized.

Laser pulses focused near the tip of an elastic wedge generate acoustic waves guided at its apex. The shapes of the acoustic wedge wave pulses depend on the energy and the profile of the exciting laser pulse and on the anisotropy of the elastic medium the wedge is made of. Expressions for the acoustic pulse shapes have been derived in terms of the modal displacement fields of wedge waves for laser excitation in the thermo-elastic regime and for excitation via a pressure pulse exerted on the surface. The physical quantity considered is the local inclination of a surface of the wedge, which is measured optically by laser-probe-beam deflection. Experimental results on pulse shapes in the thermo-elastic regime are presented and confirmed by numerical calculations. They pertain to an isotropic sharp-angle wedge with two wedge-wave branches and to a non-reciprocity phenomenon at rectangular silicon edges.

Among the various types of guided acoustic waves, acoustic wedge waves are non-diffractive and non-dispersive. Both properties make them susceptible to nonlinear effects. Investigations have recently been focused on effects of second-order nonlinearity in connection with anisotropy. The current status of these investigations is reviewed in the context of earlier work on nonlinear properties of two-dimensional guided acoustic waves, in particular surface waves. The role of weak dispersion, leading to solitary waves, is also discussed. For anti-symmetric flexural wedge waves propagating in isotropic media or in anisotropic media with reflection symmetry with respect to the wedge’s mid-plane, an evolution equation is derived that accounts for an effective third-order nonlinearity of acoustic wedge waves. For the kernel functions occurring in the nonlinear terms of this equation, expressions in terms of overlap integrals with Laguerre functions are provided, which allow for their quantitative numerical evaluation. First numerical results for the efficiency of third-harmonic generation of flexural wedge waves are presented.

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.

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.