Superposition of shifted Laguerre-Gaussian beams

In this research, the superposition of shifted Laguerre-Gaussian (LG) beams and their intensity distribution are studied in cylindrical coordinates. By complex transverse shifting of conventional LG beams, the symmetry of intensity structure is lost and deformed to the crescent. Increasing the amount of beam pure imaginary shift causes the beam is focused on a smaller crescent. The obtained results from applying changes on the real transverse shift, topological charge, and radial index parameters of superposed LG beams depict the possibility of these beams to apply in optical trapping. As the radial index increases, in addition to the radial variation of the intensity distribution, the position and shape of the crescents are changed. Besides, analytical formulate for the angular spectrum of the superposed beams is derived and the relation of their orbital angular momentum (OAM) obtained. It is observed, by increasing the OAM, the radius of intensity distribution is increased. By the combination of these difference adjustable parameters, the localized intensity distribution has been prepared, which could be used for the production of controllable optical traps. The obtained experimental results confirm the simulation results.