Pulsed Three-Dimensional Planar Caustic Beams

We present an algorithm for designing and manipulating pulsed caustic (accelerating) beams that propagate along a predefined planar curved beam-axis trajectory in free space. These pulsed beams are localized time-dependent wave packets. We evaluate the pulsed aperture field (source) distribution that radiates the beam along the desired trajectory. The aperture field is evaluated by setting its delay to form the caustic surface about the beam-axis skeleton and to control the lateral beamwidth, and the amplitude is chosen to form a uniform intensity profile of the beam along its axis. Numerical examples are included.