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To manipulate orbital angular momentum (OAM) carried by light beams, there isa great interest in designing various optical elements from thedeep-ultraviolet to the microwave. Normally, the OAM variation introduced byoptical elements can be attributed to two terms, namely the dynamic andgeometric phases. Up till now, the dynamic contribution induced by opticalelements has been clearly recognized. However, the contribution of geometricphase still seems obscure, especially considering the vector vortex beams. Inthis work, an analytical formula is derived to fully describe the OAM variationintroduced by the nonabsorbing optical elements, which perform space-variantpolarization-state manipulations. It is found that the geometric contributioncan be further divided into two parts: one is directly related to opticalelements and the other one explicitly relies solely on the vortices before andafter the transformations. Based on this result, the same OAM variation can beachieved with different combinations of the dynamic and/or geometriccontributions. With numerical simulations, it is shown that transformation ofthe optical vortices can be fully and flexibly designed with a family ofoptical elements. We believe that these results are helpful to understand theeffect of optical elements and offer a new perspective to design the opticalelements for manipulating the OAM carried by light beams.

Orbital angular momentum induced by nonabsorbing optical elements through space-variant polarization-state manipulations