Longitudinal modulation on light field polarization

The polarization of light, a fundamental property governing light-matter interactions, has historically been engineered in the transverse plane perpendicular to its propagation direction and produced a various spatially structured light fields, namely, vector beams, exhibiting intriguing phenomena and effects in focusing and light-matter interaction. With the increasing demand for light field manipulation and multiplexing in more dimensions, the polarization modulations along the propagation direction have unveiled the potential of spatially varying polarization states along the optical axis, with significant propagation properties such as self-activity. This review synthesizes recent research on the longitudinal polarization engineering, emphasizing its theoretical foundations, generation methodologies, and transformative implications. We begin by outlining the polarization evolution dynamics of structured light fields during propagation, highlighting the three-dimensional (3D) variation of state of polarizations. Key techniques for realizing the longitudinal engineering of polarization without changing of transverse intensity profile are discussed. Finally, we discuss the prospect and challenges in longitudinal modulation of polarization such as achieving precise spatiotemporal control and dynamic reconfigurability.