Description of a multifocal arrangement of asymmetric Kummer-beam optical vortices

Abstract

In this work, we derived an analytic expression for the optical field generated by an off-axis Gaussian beam diffracted by a Discretized Vortex-Producing Lens. With this system, a multifocal arrangement of asymmetric optical vortices is obtained whose topological charge values change with the position along the optical axis. This scheme allows both, obtaining a principal asymmetric vortex corresponding with the topological charge value of the phase mask, and other asymmetric vortices with charges different from the phase mask charge. With the analytical expression, the effects induced by the discretization and misalignment on the irradiance and phase of each vortex can be simultaneously studied. A signal-to-noise ratio expression is derived to verify if the noise of the multifocal system might affect the optical vortices of interest in a significant way: We found that noise is not a problem. In conclusion, a Discretized Vortex-Producing Lens can be used as a continuous Spiral Phase Plate. Finally, we explored the feasibility that the vortex phase could be employed as a displacement estimator.