Shapes of mirrors that convert a collimated incident field arriving (a) from the top or (b) from the front into a focused field whose caustic (shown in c as well as in a,b) is a non-paraxial analog of that of paraxial Airy beams, and which nearly traces a complete circle.
Miguel Alonso recently published a paper, ‘Generation of nonparaxial accelerating fields through mirrors. I: two dimensions ,’ in Optics Express. This is the first of a series of two papers on this topic. The second one can be found here.
Abstract: Accelerating beams are wave packets that preserve their shape while propagating along curved trajectories. Recent constructions of nonparaxial accelerating beams cannot span more than a semicircle. Here, we present a ray based analysis for nonparaxial accelerating fields and pulses in two dimensions. We also develop a simple geometric procedure for finding mirror shapes that convert collimated fields or fields emanating from a point source into accelerating fields tracing circular caustics that extend well beyond a semicircle.
Spring 2014