Introduction to Surface and Superlattice Excitations by Michael G. Cottam

By Michael G. Cottam

Cottam and Tilley offer an creation to the homes of wave-like excitations linked to surfaces and interfaces. The emphasis is on acoustic, optic and magnetic excitations, and, except one part on liquid surfaces, the textual content concentrates on solids. the real subject of superlattices can also be mentioned, during which the various forms of excitation are thought of from a unified standpoint. in the course of the e-book the authors are cautious to narrate thought and scan and all the most vital experimental options are defined. The theoretical remedy assumes just a wisdom of undergraduate physics, apart from eco-friendly functionality tools which are utilized in a couple of sections; those tools are built in an appendix. The ebook additionally includes vast references to allow the reader to refer to the learn and evaluate literature, and difficulties are supplied in all of the major chapters to permit the reader to enhance themes awarded within the textual content.

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Thus the transverse modes occupy a bulk continuum defined by co ^ vTqx. At higher frequencies still is the longitudinal bulk continuum, co ^ vLqx. The bulk continua are represented by shaded regions in Fig. 5. It is of interest to see how the above calculation is modified in an elastic slab with a second free surface, at a distance L say from the first. t For a given qx these are degenerate in frequency. If, as a thought experiment, we let L decrease, the displacements of the Rayleigh waves overlap and the degeneracy is lifted.

18) The solutions for real q are those shown in Fig. 2. 18) admits solutions for complex q. 18) gives sin2(qa)>l while in the latter sin2 (qa) < 0. The corresponding expressions for q are n/2a + \y and iy, where y is real. 1. Although they are at first sight of only formal significance, they serve to introduce the idea that the complex value of q in the stop band is associated with a surface excitation. The results we shall derive were first found by Wallis (1957), using a somewhat different method.

The simplest surface-related wave in s-polarisation is the Love wave, which occurs in a film of thickness L on a semi-infinite substrate provided the transverse acoustic velocity v'T of the substrate exceeds the transverse acoustic velocity vT of the film. 78) in the substrate, which is assumed to occupy the region z < —L. 80) In order for Love waves to exist, both qz and KZ must be real, so that the displacement is an oscillatory function of z in the film and a decaying function in the substrate.

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