[PDF] Axially symmetric focusing as a cuspoid diffraction catastrophe: Scalar and vector cases and comparison with the theory of Mie | Semantic Scholar

Axially symmetric focusing as a cuspoid diffraction catastrophe: Scalar and vector cases and comparison with the theory of Mie

@article{Kofler2006AxiallySF,
title={Axially symmetric focusing as a cuspoid diffraction catastrophe: Scalar and vector cases and comparison with the theory of Mie},
author={J. Kofler and N. Arnold},
journal={Physical Review B},
year={2006},
volume={73},
pages={235401}
}

An analytical description of arbitrary strongly aberrated axially symmetric focusing is developed. This is done by matching the solution of geometrical optics with a wave pattern which is universal for the underlying ray structure. The corresponding canonical integral is the Bessoid integral, which is a three-dimensional generalization of the Pearcey integral that approximates the field near an arbitrary two-dimensional cusp. We first develop the description for scalar fields and then… CONTINUE READING