An interferometric pattern between two annular laser beams is used to construct three-dimensional (3D) trapped structures within an optical tweezers setup. In addition to being fully translatable in three dimensions, the trapped structure can be rotated controllably and continuously by introducing a frequency difference between the two laser beams. These interference patterns could play an important role in the creation of extended 3D crystalline structures.

The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates.

Since their invention in 1986 by Arthur Ashkin and colleagues, optical tweezers have become an essential tool in several fields of physics, spectroscopy, biology, nanotechnology, and thermodynamics. In this tutorial, we provide a primer on how to calibrate optical tweezers and how to use them for advanced applications. After a brief general introduction on optical tweezers, we focus on describing and comparing the various available calibration techniques. Then, we discuss some cutting-edge applications of optical tweezers in a liquid medium, namely, to study single-molecule and single-cell mechanics, microrheology, colloidal interactions, statistical physics, and transport phenomena. Finally, we consider optical tweezers in vacuum, where the absence of a viscous medium offers vastly different dynamics and presents new challenges. We conclude with some perspectives for the field and the future applications of optical tweezers. This tutorial provides both a step-by-step guide ideal for non-specialists entering the field and a comprehensive manual of advanced techniques useful for expert practitioners. All of the examples are complemented by the sample data and software necessary to reproduce them.

An experimental demonstration of the mechanical transfer of orbital angular momentum to matter from acoustical vortices in free field is presented. Vortices with topological charges $l=\pm 1$ and $l=\pm 2$ were generated and a torsion pendulum was used to study the angular momentum transfer to hanging disks of several sizes. This allowed us to make a comparative study of the effective acoustical torque in terms of topological charge of the vortex, the disk radius, and its position along the main propagation axis. A theoretical discussion of the generated sound fields is also provided.

We demonstrate the transfer of orbital angular momentum from a light beam to a trapped low-index particle. The particle is trapped in a dark annular region of a high-order Bessel beam and rotates around the beam axis due to scattering from the helical wave fronts of the light beam. A general theoretical geometrical optics model is developed that, applied to our specific situation, corroborates tweezing and transfer of orbital angular momentum to the low-index particle. Good quantitative agreement between theory and experiment for particle rotation rates is observed.

Polarization singularities and topological polarization structures are generic features of inhomogeneous vector wave fields of any nature. However, their experimental studies mostly remain restricted to optical waves. Here, we report the observation of polarization singularities, topological Möbius-strip structures, and skyrmionic textures in 3D polarization fields of inhomogeneous sound waves. Our experiments are made in the ultrasonic domain using nonparaxial propagating fields generated by space-variant 2D acoustic sources. We also retrieve distributions of the 3D spin density in these fields. Our results open the avenue to investigations and applications of topological features and nontrivial 3D vector properties of structured sound waves.