Generation of elliptic helical Mathieu optical vortices

Elliptic Helical Mathieu Optical Vortices (EHMOVs) are a family of elliptical vortex beams that are different from the classical circular vortex or high-order Bessel beams. We introduced the stationary phase method to efficiently generate EHMOVs by using the combined amplitude-phase modulation. Experimental results showed that EHMOV modes take the form of an ellipse folded through Cartesian axes unlike the vortices with radial circular symmetries. The optical morphology of the EHMOV beams can be flexibly adjusted by controlling two of their parameters, namely, order number and ellipticity. In addition, the derived expression for the orbital angular momentum (OAM) of the EHMOV beams indicates that the OAM of EHMOVs is in fractions, whereas that of Bessel beams is in integers. The EHMOVs with tunable or fractional-order OAM and elliptical optical vortex structures are expected to play a new and unique role in optical manipulation.