Arbitrary Control of Polarization and Intensity Profiles of Diffraction-Attenuation-Resistant Beams along the Propagation Direction

Controlling the state of polarization (SoP) of light could find use in many fields, such as materials processing, polarimetry, microscopy, and optical communication, but applications typically involve interaction with absorbing media, which limits a light beam's range. Current methods for longitudinal control of SoP cannot overcome medium losses, and are either limited or not systematic in terms of SoP variations. The authors present a fully analytic, systematic methodology to engineer both the SoP and intensity of nondiffracting, attenuation-resistant beams in both lossless and absorbing media. This method is envisioned as an important advance for applications of structured light.