On diffraction and focusing in anisotropic crystals

This paper discusses various aspects of diffraction and focusing for waves in anisotropic crystals, and the concepts are applicable to electromagnetic, ultrasonic bulk, or ultrasonic surface waves in homogeneous but arbitrarily anisotropic crystals. A numerical technique based on an angular spectrum of plane waves representation is shown to produce theoretical intensity profiles in good agreement with acoustooptic probe measurements of the diffraction field of a slit-type ultrasonic transducer launching quasi-longitudinal and quasi-shear waves in quartz along on axis of extreme anisotropy where the wave normal and the direction of energy flow are separated by angles greater than 20°. A theoretical study of two-dimensional focusing structures for use in anisotropic crystals reveals that a launching transducer fabricated in the shape of the relevant group-velocity surface can be far superior in producing a well-defined focus to a structure having the shape of a circular arc. The computation techniques can be applied to obtain the diffraction field of any arbitrary aperture function and the examples described, theoretical and experimental, concern acoustic waves in crystals demonstrating extreme elastic anisotropies, in fact much more extreme than would be encountered in analogous cases of optical diffraction. Because of current relevance to device research, emphasis in the latter sections of the paper is placed on ultrasonic surface waves.