Abstract
In 1887 Lord Rayleigh(1) showed that a semi-infinite, isotropic, elastic medium, bounded by a single, stress-free, planar surface, can support surface vibration modes that are wavelike in directions parallel to the surface of the solid, but whose amplitudes decay exponentially with increasing distance into the solid from the surface, with a decay length that is of the order of the wavelength of the wave along the surface. The displacement vector of these waves lies in the sagittal plane, i.e. in the plane defined by the direction of propagation of the wave and the normal to the surface. These waves are acoustic waves in that their frequencies are linear in the magnitude of the two-dimensional wave vector characterizing their propagation along the surface. They are consequently non dispersive, i.e. their speed of propagation is independent of their wavelength parallel to the surface, which is due to the absence of a characteristic length in the system under consideration. Their frequencies also lie below the continuum of frequencies allowed the normal vibration modes of an infinite elastic medium for the same value of the two-dimensional wave vector. Such surface acoustic waves are now known as Rayleigh Waves.
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Maradudin, A.A. (1985). Surface Acoustic Waves. In: Bron, W.E. (eds) Nonequilibrium Phonon Dynamics. NATO ASI Series, vol 124. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2501-7_10
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