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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 acoustic waves are propagated toward the edge of an anisotropic elastic medium (a silicon crystal), which supports leaky waves with a high degree of localization at the tip of the edge. At an angle of incidence corresponding to phase matching with this leaky wedge wave, a sharp peak in the reflection coefficient of the surface wave was found. This anomalous reflection is associated with efficient excitation of the leaky wedge wave. In laser ultrasound experiments, surface acoustic wave pulses were excited and their reflection from the edge of the sample and their partial conversion into leaky wedge wave pulses was observed by optical probe-beam deflection. The reflection scenario and the pulse shapes of the surface and wedge-localized guided waves, including the evolution of the acoustic pulse traveling along the edge, have been confirmed in detail by numerical simulations.
Nonlinear acoustic waves are considered that have displacements localized at the tip of an elastic wedge. The evolution equation governing their propagation is discussed and compared with its analogues pertaining to nonlinear acoustic surface and bulk waves. Solitary wave solutions of the evolution equation have been determined numerically for the cases of two rectangular edges which may be viewed as generated by splitting a half-space, consisting of crystalline silicon, into two quarter-spaces. For these two geometries, the kernel in the nonlinear terms of the evolution equation has been calculated from the second-order and third-order elastic constants of silicon, and weak dispersion due to tip truncation has been considered. Solitary pulse shapes have been computed and collisions of solitary pulses have been simulated for various relative speeds of the two collision partners. Collision scenarios for the two wedge geometries were found to differ considerably. Special attention is paid to the peculiar interaction of two initially identical solitary pulses.
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.
Acoustic waves are investigated which are guided at the edge (apex line) of a wedge-shaped elastic body or at the edge of an elastic plate. The edges contain a periodic sequence of modifications, consisting either of indentations or inclusions with a different elastic material which gives rise to high acoustic mismatch. Dispersion relations are computed with the help of the finite element method. They exhibit zero-group velocity points on the dispersion branches of edge-localized acoustic modes. These special points also occur at Bloch-Floquet wavenumbers away from the Brillouin zone boundary. Deep indentations lead to flat branches corresponding to largely non-interacting, Einstein-oscillator like vibrations of the tongues between the grooves of the periodic structure. Due to the nonlinearity of the elastic media, quantified by their third-order elastic constants, an acoustic mode localized at a periodically modified edge generates a second harmonic which partly consists of surface and plate modes propagating into the elastic medium in the direction vertical to the edge. This acoustic radiation at the second-harmonic frequency is investigated for an elastic plate and a truncated sharp-angle wedge with periodic inclusions at their edges. Unlike nonlinear bulk wave generation by surface acoustic waves in an interdigital structure, surface and plate mode radiation by edge-localized modes can be visualized directly in laser-ultrasound experiments.
In a SAW device comprises a SAW chip bearing a SAW transducer arranged within a first signal line parasitic signals due to higher harmonics of the operating frequency of the SAW devices are electrically eliminated by compensating means comprising at least one second signal line having means for producing a cancelling signal different in sign or phase to the parasitic signal, or a shunt line to electrically connect the SAW transducer to a back side metallization of the SAW chip.
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.
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 LiTaO 3 (YXl)/42° operating in different frequency ranges. Both IMD3 and triple beat show good agreement with measurement.
The laser ultrasound (LU) technique has been used to determine dispersion curves for surface acoustic waves (SAW) propagating in AlScN/Al2O3 systems. Polar and non-polar Al0.77Sc0.23N thin films were prepared by magnetron sputter epitaxy on Al2O3 substrates and coated with a metal layer. SAW dispersion curves have been measured for various propagation directions on the surface. This is easily achieved in LU measurements since no additional surface structures need to be fabricated, which would be required if elastic properties are determined with the help of SAW resonators. Variation of the propagation direction allows for efficient use of the system’s anisotropy when extracting information on elastic properties. This helps to overcome the complexity caused by a large number of elastic constants in the film material. An analysis of the sensitivity of the SAW phase velocities (with respect to the elastic moduli and their dependence on SAW propagation direction) reveals that the non-polar AlScN films are particularly well suited for the extraction of elastic film properties. Good agreement is found between experiment and theoretical predictions, validating LU as a non-destructive and fast technique for the determination of elastic constants of piezoelectric thin films.
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.