Adjustable anomalous hollow vortex beam and its properties

A new beam named adjustable anomalous hollow vortex beam (AAHVB) is proposed, and the expressions of an AAHVB in uniaxial crystal are derived. The evolutions of intensity distributions of an AAHVB in free space and uniaxial crystal are investigated. The relationships between intensity distributions with beam parameters, uniaxial crystal, and distance are analyzed in detail. It is found that intensity distributions of an AAHVB in uniaxial crystal can be manipulated by setting source parameters a $a$, c x ${c}_{x}$, c y ${c}_{y}$, M $M$, and n e / n o ${n}_{e}/{n}_{o}$.