Properties of the Airy beam by means of the quantum potential approach

Abstract

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 the influence of a quantum potential, such that its associated quantum force is constant, the integral curves of the Poynting vector are parabolic ones and turn out to be a subset of solutions of the corresponding Hamilton equations, the geometrical light rays associated with the Airy beam, are given by the tangent lines to the zeroes of the quantum potential, and the caustic coincides with the zeros of the quantum potential. Furthermore, we present a derivation of the Airy beam from the quantum potential equations by assuming that the quantum force is constant.