Structured beam designed by ray-optical Poincaré sphere method and its propagation properties

Abstract

Structured beam plays an important role in optical communication, microscopy and particle manipulations. Traditionally, structured beam can be obtained by solving Helmholtz wave equation. This method involves complex mathematical procedures, and the properties of solved light beam are obscure. It is worth noting that the structured beam can also be constructed by ray-optical Poincaré sphere method: this method is a rather intuitive and convenient for designing the structured beam with novel properties. This method also provides a ray-based way to study the propagation properties of structured beam. In this paper, the ray-optical Poincaré sphere method combined with plum-blossom curve is used to build a family of structured beams. The optical field distributions on beam waist, including intensity and phase, are calculated by the ray-optical Poincaré sphere method. The shape of inner and outer caustics of optical field are also detailed in order to demonstrate the self-healing or non-diffraction features of beams. By using angular spectrum diffraction, the free space evolutions of such structured beams are demonstrated. The results show that the structured beam turns to be the well-known Laguerre-Gaussian beam when the leaf number of plum-blossom curve is 0. While the leaf number equals 1, the structured beam has non-diffraction property, for its inner caustic concentrates onto two points. In geometrical optics sight, all light rays are tangent to the inner caustic, and the optical fields carried by rays interfere near the caustic, leading the beam to possess a self-healing capacity. The self-healing property is demonstrated in terms of rays. With the beam's propagating, rays which launch from the inner side of beam gradually reach the outer side of beam. On the contrary, the rays launching from the inner side of beam arrive at the outer side of beam. When the center of beam is blocked, the inner rays are also blocked. After propagating, outer side rays will reach the inner side, fill up the hole of beam, and recover the injury of optical field. Furthermore, we demonstrate the structured beam with a 5leave plum-blossom curve. In this case, the inner caustic of this beam turns into a decagonal star structure; our simulation results show that this beam has relatively strong self-healing capability. Theoretically, one can simply change the parameters of plum-blossom curve or choose other kind of Poincaré sphere curve to create more complex structured beams.