Wavefronts, light rays and caustic associated with the refraction of a plane wave by a conospherical lens

TL;DR

This paper analyzes the wavefronts, light rays, and caustics produced by a novel conospherical lens illuminated by a plane wave, revealing complex caustic structures with potential applications in generating specialized optical beams.

Contribution

It introduces a new lens shape combining conical and spherical surfaces and characterizes its caustic structures and optical properties.

Findings

Caustic has two branches: a real and a virtual line segment, and a 2D surface with a cusp ridge.

The two caustic branches are disconnected.

Potential to generate scalar optical accelerating and Bessel-like beams.

Abstract

The aim of the present work is to introduce a lens whose faces are a conical surface and a spherical surface. We illuminate this lens by a plane wavefront and its associated refracted wavefronts, light rays and caustic are computed. We find that the caustic has two branches. The first is constituted by two segments of a line, one part of this caustic is real and the other one virtual. The second branch of the caustic is a two-dimensional surface with a singularity of the cusp ridge type. It is important to remark that the two branches of the caustic are disconnected. Because of this property we believe that using this optical element one could generate a scalar optical accelerating beam in the region where the caustic is a two-dimensional surface of revolution, and at the same time a scalar optical beam with similar properties to the Bessel beam of zero order in the region were the real caustic is a segment of a line along the optical axis.