A Design Scheme for Arbitrary 3-D Caustic Beam Field Patterns

An algorithm for designing an aperture field that radiates caustic (Airy-beam type) beams along a predefined 3-D beam trajectory in free-space, with arbitrary curvature and torsion is presented. The predefined beam-axis trajectory sets the aperture field's phase to form a smooth caustic surface. The aperture amplitude distribution is constructed to manipulate both the on-axis intensity profile and the off-axis beam-width, via an iterative procedure. Once the aperture distribution is calculated, the radiation from a finite sampled aperture is computed numerically using a fast numerical technique. The algorithm is demonstrated for the case of helical trajectory beam.