Arbitrary control of the polarization state and intensity of non-diffracting beams along their propagation direction

We experimentally demonstrate a class of non-diffracting beams with state of polarization (SoP) and intensity that can both be controlled along the propagation direction. The beams are composed of a superposition of equal frequency co-propagating Bessel beams (BBs) with different transverse and longitudinal wavenumbers. The BBs are weighted by suitable complex coefficients derived from closed-form analytic expressions. The desired polarization states (i.e., linear, radial, azimuthal and elliptical) are each independently encoded onto a set of BBs with the suitable polarizations. For experimental generation, the resulting field is decomposed into two orthogonal polarizations (horizontal and vertical). Via constructive (and destructive) interference of BBs, specific SoPs can be designed to switch on (and off) during propagation. This effectively alters the resultant SoP and intensity of the beam throughout propagation. We envision our proposed method to be of great interest in many applications, such as optical tweezers, atom guiding, material processing, microscopy, and optical communications.