Context

With few exceptions this book has concerned itself with the propagation of vibrational waves in the bulk of a crystal. As indicated in Section B of Chapter 12, there are also vibrational modes associated with the surface of the medium. They are known as Rayleigh surface waves (RSWs) and pseudo–surface waves (PSWs). As with bulk waves, the velocities of these surface waves depend on the propagation direction, so one might reasonably expect phonon-focusing effects. Indeed, Tamura and Honjo and Camley and Maradudin have predicted phonon-focusing patterns for Rayleigh waves in a variety of media. An example of the latter results is shown in Figure 1: (a) is the slowness curve for Rayleigh waves on the (111) surface of Ge and (b) shows the corresponding singular directions of energy flux emanating from a point source in this plane. Phonon caustics arise from the zero-curvature regions of the slowness surface, just as discussed with bulk waves in Figure 8 of Chapter 2.

Unfortunately, high-frequency surface phonons are likely to have much shorter mean free paths than bulk phonons, due to the sensitivity of these waves to surface irregularities. The scattering of surface phonons from such defects, plus the potentially huge background of scattered bulk phonons, makes it extremely difficult to observe the ballistic propagation and phonon focusing of surface phonons. A recent study by Höss and Kinder, however, has reported experimental evidence for the focusing of surface phonons on a laser-annealed Si surface.