Description of a multifocal arrangement of asymmetric Kummer-beam optical vortices
In this work, an analytic expression is derived for the optical field generated by an off-axis Gaussian beam diffracted by a Discrete 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 obtaining a principal asymmetric vortex corresponding with the topological charge value of the phase mask and secondary ones with different charges. 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 importantly the optical vortices of interest. Finally, we proposed new metrics to measure the off-axis displacement using the phase of the vortex. We concluded that noise is not a problem, then a Discrete Vortex-Producing Lens can be used as a continuous Spiral Phase Plate with the bonus that secondary optical vortices can be used in the same way as principal optical vortices.