Needle beams are highly attractive for applications which take advantage from a spatial and
temporal localization of photons. High intensities, high resolution and extended depth of …

By using the quantum potential approach, we show that: the Airy beam determines a
Hamiltonian system with one degree of freedom for a particle of mass m= 1 evolving under …

In this work, the propagation of vortex beams is treated using a catastrophe theory approach.
Analytic expressions are deduced to describe caustic surfaces produced by vortex lenses …

In this paper, we consider the comparative formation of perfect optical vortices in the non-
paraxial mode using various optical elements: non-paraxial and parabolic toroidal vortex …

In this work we compute the wavefronts and the caustics associated with the solutions to the
scalar wave equation introduced by Durnin in elliptical cylindrical coordinates generated by …

From a geometric perspective, the caustic is the most classical description of a wave function
since its evolution is governed by the Hamilton–Jacobi equation. On the other hand …

The aim of the present work is to show that any monochromatic solution to the scalar wave
equation in free space defines a conservative Hamiltonian system, describing a particle of …

The aim of the present work is to introduce two monochromatic solutions to the scalar wave
equation in free space, characterized by a caustic with a singularity of the hyperbolic …

The aim of this work is to present a geometrical characterization of parabolic non-diffracting
beams. To this end, we compute the corresponding angular spectrum of the separable non …

We construct exact solutions to the paraxial wave equation in free space characterized by
stable caustics. First, we show that any solution of the paraxial wave equation can be written …