PHONON IMAGING

Abstract
Investigations of phonon propagation and scattering in solids use either coherent microwave phonons or incoherent phonons in the form of heat pulses¹ generated by current flow through thin metallic films and bolometer detection, or monochromatic incoherent phonons generated and detected with superconducting tunneling junctions². Applying these techniques to a perfect single crystal, quantitative measurements require knowledge on phonon propagation in anisotropic media. In contrast to optic properties the acoustic propagation in anisotropic media is much more complicated by the large number of elastic constants. An additional complication arises if the dispersion of acoustic phonons is included. Whereas the propagation of coherent phonons is simply described by the anisotropic constant-energy surfaces in q-space, the propagation of incoherent phonons (generated by a point source) is determined by the distribution of group velocities. These distributions were first calculated by Taylor, Maris and Elbaum³ with the result that specific propagation directions and modes show strong and sharply peaked intensity maxima. This phenomenon was called "phonon focussing". In later work also names as phonon channeling, phonon caustics etc. have been used. The pronounced sharpness of these distributions with strong intensity changes within angles of 1 degree raised strong experimental and theoretical interest for a more complete spacial description, or for imaging the phonon distributions. First, three-dimensional directivity patterns were obtained by computer analysis⁴. More recently, direct measurements of phonon intensity distributions⁵ and, for instance, measurements with computer-aided spacial display⁶ of the phonon intensity have led to impressive phonon images on crystal surfaces. Alternatively, it is also possible to obtain direct phonon images⁷, observing the thickness increase of a superfluid ⁴He-film on the crystal surface by the fountain effect in regions of high phonon intensity. In this lecture the fundamentals of phonon focussing and phonon imaging techniques will be reviewed.