Theory and acoustic experiments of nondiffracting X-waves [medical US imaging application]

Families of nondiffracting solutions of the isotropic-homogeneous wave equation have been discovered recently by the authors. These families of solutions contain some of the nondiffracting beams known previously, such as the plane wave, Durnin´s nondiffracting beams, etc. One subset of the new families of nondiffracting solutions represents waves of X-like shape in a plane through the axis of the waves, which the authors termed X-waves. The theoretical implications of one family of the nondiffracting solutions are reported, and the nondiffracting X-waves with finite apertures are simulated using the Rayleigh-Sommerfeld formulation of diffraction. An acoustic superposition experiment of the nondiffracting X-waves in water was performed to test the theory, and the experiment agrees closely with the theory