Shaping of Vector Beams Based on Caustic Design

Appropriate wavefront design can endow light fields with many useful properties, such as accelerating, anti-diffracting, self-healing, and the capability to exhibit customizable intensity shapes. The strategy of arbitrarily combining these properties to develop novel optical fields mainly relies on caustic methods. However, caustic methods have rarely been applied to the construction of vector fields. Here, slowly changing polarization information is introduced to the caustic rays, aiming to establish direct connections between conventional rays and vector beams in the physical representation. In this manner, a technique is developed to create non-diffracting vector beams with polarization states that can vary along the caustic curves as needed. It is also demonstrated that the superposition of intersecting ray families can basically determine the polarization states of the other points in the fields. This may provide a new route for designing various novel vector fields and directly promote research in wave and focal field shaping, thereby offering more flexible beam options for applications such as material processing, particle manipulation, and microscopic imaging. Assuming that the rate of variation in the state of polarization (SOP) is much slower than that of phase, the polarization information can be almost independently introduced to the caustic rays of optical fields. For instance, a theoretical expression for non-diffracting vector beams is derived, allowing for free manipulation of both caustic shape and SOP along the caustic curve. image