A New Approach to Obtain Limited Diffraction Beams

Limited diffraction beams were first discovered by Durnin in 1987 (formerly named nondiffracting or diffraction-free beams by Durnin). Since then, new families of limited diffraction beams have been discovered. Theoretically, limited diffraction beams can propagate to infinite distance without diffracting or spreading. Even if they are produced with a finite aperture radiator, limited diffraction beams have a large depth of field. Because of this property, limited diffraction beams could have applications in medical imaging, tissue characterization, and nondestructive evaluation, as well as other wave related areas such as electromagnetics and optics. In this paper, we develop a novel approach that can convert any diffracting solution of the isotropic-homogeneous wave equation to a limited diffraction solution. As an example, this approach was applied to an n-dimensional wavelet solution that we generalized from the three-dimensional solution obtained by Kaiser et al. This example establishes a relationship between localized limited diffraction beams and the wavelet theory. The resulting limited diffraction beam was compared with those discovered previously.