Wavefronts, light rays and caustic associated with the refraction of a spherical wave by two interfaces: the axicon and the plano-convex parabolic lenses

Abstract

In this work we assume that we have three optical media with constant refraction indexes n0, n1 and n2 separated by arbitrary refracting surfaces. In the optical medium with refraction index n0 we place a point light source at an arbitrary position. The aim of the present work is to obtain exact expressions for the wavefront train and the caustic associated with the evolution of the spherical wave emitted by the point light source. To this end, we construct a complete integral of the eikonal equation and we show that the evolution of the refracted wavefronts and light rays are described by a map between two subsets of . The caustic is computed as the image of the critical set associated with this map. The general results are applied to an axicon and a plano-convex parabolic lenses (glass made) when the point light source is placed on the optical axis. We find that, due to the change in the index of refraction, the spherical wavefront emitted by the point light source during its evolution experiences a metamorphosis in such a way that at the caustic region the wavefronts develop singularities and self-intersections.