Exact analytical solutions for micrometer structured vortex beams with applications to optical tweezers

Abstract

Bessel beams are widely known by their non-diffracting properties, i.e. beams that sustain their transverse profile along the propagation. It is also well known that by a suitable superposition of Bessel beams of the same frequency, but different longitudinal wave numbers, amplitudes and phases, it is possible to obtain a resulting beam whose longitudinal intensity pattern can be shaped along the propagation z-axis. Such approach, named Frozen Wave method, can be implemented through discrete or continuous superposition, the latter being more appropriate for obtaining spatially structured beams in micrometer domains. In previous studies, authors constructed analytical solutions for micrometer zero-order (i.e., null topological charge) Frozen Wave and, thereafter, of order one and two, by making use of a topological charge raising operator. In this paper, we present an analytical closed solution for the general case where the topological charge raising operator is applied an arbitrary number of times to a micrometer zero-order Frozen Wave beam, thus generating one of arbitrary topological charge. We also apply the new solutions to model optical tweezers (in Rayleigh regime) considering different light polarizations.