V.G. Mozhaev

A new type of surface acoustic waves in solids due to nonlinear elasticity

Abstract It is shown that in a nonlinear elastic semi-infinite medium possessing the property of self-focusing of shear waves, besides bulk nonlinear shear waves, new surface acoustic waves exist, localization of which near the boundary is entirely due to nonlinear effects.

Some New Ideas in the Theory of Surface Acoustic Waves in Anisotropic Media

Considerable progress in the theory of surface acoustic waves in crystals has followed the application of computers. Nevertheless, possibilities for the development of corresponding analytic theories still exist. This is demonstrated in the present paper by four different problems. The first three are solved exactly and the last is solved by a perturbation method.

Subsonic leaky Rayleigh waves at liquid-solid interfaces.

The paper is devoted to the study of leaky Rayleigh waves at liquid-solid interfaces close to the border of the existence domain of these modes. The real and complex roots of the secular equation are computed for interface waves at the boundary between water and a binary isotropic alloy of gold and silver with continuously variable composition. The change of composition of the alloy allows one to cross a critical velocity for the existence of leaky waves. It is shown that, contrary to popular opinion, the critical velocity does not coincide with the phase velocity of bulk waves in liquid. The true threshold velocity is found to be smaller, the correction being of about 1.45%. Attention is also drawn to the fact that using the real part of the complex phase velocity as a velocity of leaky waves gives only approximate value. The most interesting feature of the waves under consideration is the presence of energy leakage in the subsonic range of the phase velocities where, at first glance, any radiation by harmonic waves is not permitted. A simple physical explanation of this radiation with due regard for inhomogeneity of radiated and radiating waves is given. The controversial question of the existence of leaky Rayleigh waves at a water/ice interface is reexamined. It is shown that the solution considered previously as a leaky wave is in fact the solution of the bulk-wave-reflection problem for inhomogeneous waves.

New data concerning surface Mandelstamm-Brillouin light scattering from the basal plane of germanium crystal

Abstract The intensity of Mandelstamm-Brillouin satellites (MBS) corresponding to leaky surface waves (LSW) was rigistered for Ge crystal of z -cut. The intensity was found to reach its largest values for two orientations of the light scattering plane: first, when the plane was parallel to [110], and second, when parallel to [cos 35°, sin 35°, 0]. A broad additional surface spectral line located at a frequency ≈ 1.4 times higher than those of MBS related to generalized surface waves and LSW was detected.

Nearly backward reflection of bulk acoustic waves at grazing incidence in a TeO2 crystal

Reflection of bulk acoustic waves in a TeO2 acoustooptic single crystal is studied for the case of a grazing incidence on the free crystal-vacuum boundary. The propagation and reflection of elastic waves is considered in the XOY plane of the material cut out in the form of a rectangular prism. An extraordinary case of reflection at the grazing incidence, when the energy flow of one of the two reflected waves in the crystal is directed opposite to that of the incident wave, is studied. It is shown that the transformation of the incident elastic energy into the energy of the backward-reflected wave can occur with an efficiency close to 100% and can be observed in a wide range of crystal cut angles. An abrupt change of the reflection coefficients in the vicinity of the critical angle is predicted.

Prolonged acousto-optic interaction with Lamb waves in crystalline plates

The propagation and acousto-optic interaction of Lamb modes in an anisotropic plate of tellurium dioxide (TeO2) are studied numerically and analytically. In the case of a Y-cut X-propagating TeO2 plate, the very high elastic anisotropy of the crystal greatly modifies the dispersion curves, giving rise to their multiple oscillations. The existence ranges of backward Lamb modes increase with the mode order contrary to the case of isotropic plates. The quasi-collinear light scattering by Lamb waves is considered. Owing to the structure of Lamb wave field, a simultaneous light diffraction at two different optical frequencies can take place while Lamb waves are excited only at the single frequency. It is demonstrated with the Z-cut (110)-propagating plate that a small change in the acoustic frequency can result in a significant shift in the frequency of the scattered light.

OBLIQUE ACOUSTIC AXES IN TRIGONAL CRYSTALS

A general analysis on the subject of acoustic axes for bulk acoustic waves in trigonal crystals is presented. It is shown that the eect of piezoelectricity increases the maximum allowable number of acoustic axes in the plane of elastic symmetry from three to ve for trigonal crystals of class 3m, and from 3 to 7 for trigonal crystals of class 32. The theory of acoustic axes of general orientation developed by Khatkevich (1962) is revised. A new, simpler and more general derivation of the conditions for the occurrence of acoustic axes of general orientation in crystals is presented. It is found that the previous analytical results and conclusions stating the absence of such axes in trigonal crystals are incorrect. New correct equations for acoustic axes of general orientation in trigonal nonpiezoelectric crystals are derived and conrmed by independent numerical calculations. Acoustic axes of general orientation oblique to the elastic symmetry planes are found to exist in berlinite (class 32) and in nonpiezoelectric lithium niobate (class 3m), however piezoelectricity eliminates these axes in the latter crystal. Some illustrative examples of the relationship between leaky surface acoustic wave branches and acoustic axes in trigonal crystals are given.

Incredible negative values of effective electromechanical coupling coefficient for surface acoustic waves in piezoelectrics

The extraordinary case of increase in velocity of surface acoustic waves (SAW) caused by electrical shorting of the surface of the superstrong piezoelectric crystal potassium niobate, KNbO3, is numerically found. The explanation of this effect is based on considering SAWs as coupled Rayleigh and Bleustein-Gulyaev modes. A general procedure of approximate decoupling of the modes is suggested for piezoelectric crystals of arbitrary anisotropy. The effect under study takes place when the phase velocity of uncoupled sagittally polarized Rayleigh waves is intermediate between the phase velocities of uncoupled shear-horizontal Bleustein Gulyaev waves at the free and metallized surfaces. In this case, the metallization of the surface by an infinitely thin layer may cause a crossover of the velocity curves of the uncoupled waves. The presence of the mode coupling results in splitting of the curves with transition from one uncoupled branch to the other. This transition is responsible for the increase in SAW velocity, which appears to be greater than its common decrease produced by electrical shorting of the substrate surface.

Unusual energy properties of leaky backward Lamb waves in a submerged plate

&NA; It is found that leaky backward Lamb waves, i.e. waves with negative energy‐flux velocity, propagating in a plate submerged in a liquid possess extraordinary energy properties distinguishing them from any other type of waves in isotropic media. Namely, the total time‐averaged energy flux along the waveguide axis is equal to zero for these waves due to opposite directions of the longitudinal energy fluxes in the adjacent media. This property gives rise to the fundamental question of how to define and calculate correctly the energy velocity in such an unusual case. The procedure of calculation based on incomplete integration of the energy flux density over the plate thickness alone is applied. The derivative of the angular frequency with respect to the wave vector, usually referred to as the group velocity, happens to be close to the energy velocity defined by this mean in that part of the frequency range where the backward mode exists in the free plate. The existence region of the backward mode is formally increased for the submerged plate in comparison to the free plate as a result of the liquid‐induced hybridization of propagating and nonpropagating (evanescent) Lamb modes. It is shown that the Rayleighs principle (i.e. equipartition of total time‐averaged kinetic and potential energies for time‐harmonic acoustic fields) is violated due to the leakage of Lamb waves, in spite of considering nondissipative media. HighlightsAbnormal energy properties of leaky backward Lamb waves.Zero total energy flux.Violation of the Rayleighs principle of equipartition of kinetic and potential energies.Inequality of group and energy velocities.

Types of leaky SAW degeneracy in crystals

Various types of leaky surface acoustic wave (SAW) degeneracies in crystals are considered and systematically classified, Concrete examples of these degeneracy types are given. The possibility of existence of subsonic leaky SAWs is numerically predicted. New correct equations for acoustic axes oblique to symmetry planes in trigonal crystals are derived. It is found that the maximum number of acoustic axes in trigonal crystals is equal to 16 rather than 10 as was previously stated in the literature.