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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.
In anisotropic media, the existence of leaky surface acoustic waves is a well-known phenomenon. Very recently, their analogs at the apex of an elastic silicon wedge have been found in experiments using laser-ultrasonics. In addition to a wedge-wave (WW) pulse with low speed, a pseudo-wedge wave (p-WW) pulse was found with a velocity higher than the velocity of shear bulk waves, propagating in the same direction. With a probe-beam-deflection technique, the propagation of the WW pulses was monitored on one of the faces of the wedge at variable distance from the apex. In this way, their depth structure and the leakage of the p-WW could be visualized directly. Calculations were carried out using a method based on a representation of the displacement field in Laguerre functions. This method has been validated by calculating the surface density of states in anisotropic media and comparing the results with those obtained from the surface Green's tensor. The approach has then been extended to the continuum of acoustic modes in infinite wedges with fixed wave-vector along the apex. These calculations confirmed the measured speeds of the WW and p-WW pulses.
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.