Propagation-invariant waves in acoustic, optical, and radio-wave fields

Abstract

The physical phenomena considered in this thesis are associated with electromagnetic and acoustic waves that propagate in free space or in homogeneous media without diffraction. The concept of rotationally periodic wave propagation is introduced in the first journal article included in the thesis and it is subsequently used to analyse waves that avoid diffractive deterioration by repeatedly returning to their initial shape, possibly rotated around the optical axis. Such waves constitute an essential generalisation to several kinds of acoustic and optical beams, such as Bessel beams and self-imaging waves. Additionally, rotationally periodic waves also comprise pulsed wave forms that may propagate with a velocity independent of the speed of light (or sound) in the particular medium. This does not, however, lead to any violation of relativistic principles, as the pulse is continuously reformed by signals that have synchronously been transmitted from different locations. The individual articles in this dissertation mainly concentrate on the properties of pulsed waves.

Two specific issues are also treated in the dissertation: (i) Acoustic nondiffracting waves are considered in anisotropic, piezoelectric crystals. Their propagation may differ drastically from that of ordinary (plane) waves, and nondiffracting waves may also include effects such as internal diffraction, phonon focusing, and caustics. Possible transducer structures are considered for the generation of nondiffracting waves into bulk crystals. (ii) Generation of Bessel beams have also been verified with the use of radio holograms in the millimetre-wave regime. Hologram techniques developed have allowed the investigation of various other wave forms and their propagation, such as tapered plane waves and radio-wave vortices. A back-propagation algorithm has also been introduced for designing holograms that form wave fields of an arbitrary design.