A study of simulation methods of limited diffraction beams

Limited diffraction beams such as Bessel beams and X waves have been studied extensively because of their potential applications in many areas such as medical imaging and optical communications. Computer simulations have been powerful tools for understanding the fundamentals of these beams. In this study, limited diffraction beams, specifically, Bessel beams and X waves, were simulated. The simulations were based on the frequency‐domain method (Rayleigh–Sommerfeld diffraction formula), time‐domain method, and finite‐element or finite‐difference method. For Bessel beams, a circular transducer divided into multiple rings was assumed. For pressure distributions on axial axis, the simulations were simplified due to the symmetry. In the case of X waves, the differential property of acoustic waves was used. The results of the simulation methods were compared with each other. Advantages and disadvantages of these methods will be reported. In all cases, the results are very close to those predicted by theory. [This work was supported in part by Grant HL 60301 from the National Institute of Health of the U.S.A.]