The design and implementation of a multiplexed spiral phase mask in an experimental optical tweezers setup are presented. This diffractive optical element allows the generation of multiple concentric vortex beams with independent topological charges and without amplitude modulation. The generalization of the phase mask for multiple concentric vortices is also shown. The design for a phase mask of two multiplexed vortices with different topological charges is developed. We experimentally show the transfer of angular momentum to the optically trapped microparticles by enabling nearly independent orbiting dynamics around the optical axis within each vortex. The angular velocity of the confined particles versus the optical power in the focal region is also discussed for different combinations of topological charges.

Optical manipulation is interfacing disciplines in the micro and nanoscale, from molecular biology to quantum computation. Versatile solutions for increasingly more sophisticated technological applications require multiple traps with which to maneuver dynamically several particles in three dimensions. The axial direction is usually overlooked due to difficulties in observing particles away from an objective-lens focal plane, a normal element in optical tweezers, and in managing interparticle distances along the trapping beam propagating direction, where strong radiation pressure and shadowing effects compromise the simultaneous and stable confinement of the particles. Here, aperiodic kinoform diffractive lens based on the m-Bonacci sequence are proposed as a new trapping strategy. This lens provides split first-order diffractive foci whose separation depends on the generalized m-golden ratio. We show the extended manipulation capabilities of a laser tweezers system generated by these lens, in which concomitant trapping of particles in different focal planes takes place. Positioning particles in the axial direction with computer-controlled distances allows dynamic three-dimensional all-optical lattices, useful in a variety of microscale and nanoscale applications.

In this work, we present a comparative analysis of different numerical methods to obtain the focusing properties of the zone plates based on Fibonacci and Cantor sequences. The Fresnel approximation was solved numerically in order to obtain the axial irradiance provided by these diffractive lenses. Two different methods were applied. The first one is based on numerical integration, specifically the Simpson integration method and the two-dimensional Gaussian quadrature. The second consisted in the implementation of the Fast Fourier Transform in both one and two dimensions. The axial irradiance of the lenses, the relative error with respect to the analytical solution, and the calculation time required by each method are analyzed and compared. From this analysis it was concluded that the Gauss method presents the best balance between accuracy and computation time. This analysis could be useful to decide the most convenient numerical method to be used for the study of more complex diffractive structures.

A characterization of a draining container is performed by measuring the pressure change at its bottom while the container drains through a small orifice. The Physics model is based on the continuity equation and Bernoulli’s principle. The pressure is measured with the barometer of the smartphone which is placed inside a hermetically sealed bag and laid at the bottom of the container. The expected theoretical relationship between the pressure at the bottom of the container and time was observed. The value for the coefficient of discharge is also estimated. The results of a survey applied to students and teachers at secondary school level indicate that the use of the pressure sensor of the smartphones helped the students to understand the basic concepts of hydrostatics and hydrodynamics at the same time their motivation for physics was increased.