Angular-spectrum representation for localized waves

The angular-spectrum representation provides an elegant mathematical formulation, which is apt to study wave propagation and diffraction in problems described by the scalar wave equation. Nondiffracting waves are localized wave solutions of the scalar wave equation characterized by a cross-sectional intensity distribution which is invariant under wave propagation. Approximate nondiffracting solutions exist for surface-acoustic waves (SAW) on piezoelectric materials through crystal symmetries. The angular dependence of the wave number is here shown to have an important influence on the diffraction properties. In this paper we simulate SAW diffraction through periodic and nonperiodic structures in YZ-LiNbO₃ with a numerical technique based on the angular-spectrum representation. We also apply the angular-spectrum representation, for the first time, to the recently proposed X waves, which are exact nondiffracting solutions of the scalar wave equation