Analysis of optical forces over spherical particles in the ray optics and Rayleigh regimes for Bessel beams and their discrete superpositions

Abstract

This paper aims to provide the basic notions on scalar Bessel beams (paraxials) and their discrete superposition (Frozen Waves) to an undergraduate student, focusing on mili and micrometer applications in optical trapping, through the evaluation of the optical forces exerted on spherical particles in the Rayleigh regime and under the ray optics regime. Firstly, it is expected that the student be acquainted with the basic theory of scalar Bessel beams and their experimental generations through holography, axicons and light modulators. Secondly, we shall advance in the field of biomedical optics, in order to understand some of the physical mechanisms involved in the effective trapping of biologic particles. At this stage, it is expected that the student develops optical forces analysis over spherical particles in the ray optics regime and in the Rayleigh regime. Numerical calculations of optical forces will be developed in Matlab, Mathematica or similar commercial ou freely available softwares. Finally, we will incorporate in our analysis discrete superpositions of scalar Bessel beams, all with same order and frequency but with distinct longitudinal(or radial) wave number - the so-called "Frozen Waves". The difficulties in realizing an effective three-dimensional trapping with single Bessel beams and Frozen Waves will be considered in both optical regimes, with their trapping features and characteristics being compared with those available in the literature and associated with highly focused Gaussian beams.