Vortex families generated by Fermat spiral photon sieve

Fermat spiral photon sieve (FSPS) containing many circular holes arranged along several Fermat spiral lines is an interesting element to generate vortex beam because of its special chiral structure. This work models the FSPS and derive the diffraction field analytically. In addition to the familiar azimuthal periodicity at the focal plane in previous works, we find the longitudinal periodicity of the generated vortex beams which present themselves as many families and therefore the multi-foci property is also discovered. We relate the vortex families with the parameters of FSPS and shows the rules. This work is helpful for design of FSPS and generation of vortex beams.