Optical forces in the T-matrix formalism

Optical tweezers are a crucial tool for the manipulation and characterisation, without mechanical contact, of micro- and nanoparticles, ranging from biological components, such as biomolecules, viruses, bacteria, and cells, to nanotubes, nanowires, layered materials, plasmonic nanoparticles, and their composites. Despite the many interdisciplinary applications, only recently it has been possible to develop an accurate theoretical modelling for the mesoscale size range. This goes beyond the strong approximations typically used for the calculation of optical forces on particles much smaller (dipole approximation) or much larger (ray optics) than the wavelength of the trapping light. Among the different methods used to calculate optical forces on model particles, the ones based on the transition matrix (T-matrix) are currently among the most accurate and efficient, particularly when applied to non-spherical particles, both isolated and interacting, or in composite structures. Here, we first give an overview of the theoretical background on optical forces, optomechanics, and T-matrix methods. Then, we focus on calculations of optical trapping on model polystyrene nanowires with the aim to investigate their scaling with nanowire length at the mesoscale. We compare the force constant dependence with approximations at small or large length with respect to the trapping wavelength and with calculations on spheres, pointing out the role of shape.