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In non-isotropic single crystals the normals to the wavefronts of elastic waves are not colinear with the vectors representing either the energy flow or the particle displacement. Calculations have been carried out on the propagation characteristics of sound waves in two particular trigonal crystals, α-quartz and sapphire.The development of the eigenvalue equation for the velocity and the formulae for the components of the displacement and energy-flow vectors are summarized. The assumption that the wave has a plane wavefront normal to a given direction leads to three solutions, one representing a quasi-longitudinal wave and the other two representing quasi-transverse waves. The velocities of propagation, directions of displacement, and directions of energy flow for the three waves have been calculated for many orientations of the wave normal. Detailed results for propagation near one of the pure-mode axes are presented.

A homogeneous dielectric sphere illuminated by a small external source of electromagnetic radiation will be free, because of its special symmetry, from all off-axis aberrations such as coma and astigmatism. If the only monochromatic aberration, namely spherical aberration, is not too excessive or if it is partially corrected by a suitably designed source, a sphere could be used for purposes of rapid scanning of a microwave beam through an angle of 360° of arc without moving the lens. This possibility was investigated by computations based on geometrical optics and on the diffraction theory of optical aberrations. The results suggest that a sphere of fairly small refractive index and less than about 30 wavelengths in diameter will produce a good diffraction image of a point source. Methods are also discussed of designing appropriate sources for use with larger spheres.

Detailed measurements at a wavelength of 3.2 cm have been made of the phase distribution in the diffraction image produced by an aberration-free lens illuminated from a point source. The behavior of the phase of the electric field is shown by contours of constant phase (wavefronts) in the plane of the image space containing the axis and the H-vector of the radiating source. The region of the image space considered extends from the solid dielectric lens to a surface somewhat beyond the focus. Results are also shown of the phase distribution measured within about one wavelength of certain phase singularities which occur at the minima of intensity on the focal arc and on the axis. In general, there is very good agreement between plots of measured phase contours and plots of phase contours previously calculated from scalar diffraction theory.

The paramagnetism of the color centers in smoky quartz is caused by the electron which is missing from a nonbonding oxygen orbital near an aluminum impurity. The effects produced by externally introduced microwave phonons on the spin-resonance signal from these color centers have been studied in detail as a function of the relative phonon and spin-resonance frequencies, the phonon power, the spectrometer power, the magnetic field angle, and the phonon polarization. As has been noted previously, these interactions do not conform with those observed in other paramagnetic crystals. Effects of an applied electric field on the resonance lines and various further experiments on the color centers in smoky quartz are reported; two in particular suggest that the ''hole'', the missing electron, makes thermally excited transitions between two different sites adjacent to a given impurity atom. One of the experiments is a measurement of the cross relaxation which takes place between the various lines of the spectrum, while the other is a measurement of the low-frequency dielectric loss found at liquid helium temperatures. An attempt is made to discuss the spin-phonon results in terms of such transitions for the holes. (Author)

The usefulness of the immersion–reflection technique for the measurement of the angular dependence of the dispersion curves for elastic surface waves in anisotropic thin-film, substrate combinations is demonstrated. The example chosen consists of gold films on a substrate of Y-cut lithium niobate, the latter being both highly anisotropic and piezoelectric. The velocity accuracy of the measurements is about ±0.3% and the frequency of operation is limited by the attenuation in the liquid medium in which the test specimen is immersed.