Optical forces, helicity, angular momentum and how they are all intertwined

The theoretical description of optical forces and torques on micron-sized particles is a crucial area of research and has formed the foundation for advancements in optical trapping and manipulation technologies. In this study, we derive analytical expressions for optical forces and torques on micron-sized spherical particles illuminated by focused Laguerre–Gaussian (LG) beams, employing the well-defined helicity multipolar decomposition of electromagnetic fields and Mie theory. We developed a multifunctional program, Multipolar Optical Forces Toolbox, based on this theoretical framework. The program, available on GitHub, was used to generate optical trapping stability maps. These maps predict trap stability across a wide range of system parameters and serve as a practical tool for designing advanced optical trapping experiments. Our analysis reveals the important role of helicity p and orbital angular momentum ℓ on the dynamics of particles trapped off-axis in LG beams and demonstrates the unique nature of the tangential torque. Our findings also highlight notable differences in longitudinal optical forces resulting from pure helicity modifications in Gaussian beams. Furthermore, we showcase the ability of LG beams to isolate Mie resonances, offering a novel approach to locate the spectral positions of the resonances of high multipolar modes. These insights deepen the understanding of helicity in LG optical traps and pave the way for the development of more advanced optical manipulation techniques.