Generation of high-dimensional caustic beams via phase holograms using angular spectral representation.

Using angular spectral representation, we demonstrate a generalized approach for generating high-dimensional elliptic umbilic and hyperbolic umbilic caustics by phase holograms. The wavefronts of such umbilic beams are investigated via the diffraction catastrophe theory determined by the potential function, which depends on the state and control parameters. We find that the hyperbolic umbilic beams degenerate into classical Airy beams when the two control parameters are simultaneously equal to zero, and elliptic umbilic beams possess an intriguing autofocusing property. Numerical results demonstrate that such beams exhibit clear umbilics in 3D caustic, which link the two separated parts. The dynamical evolutions verify that they both possess prominent self-healing properties. Moreover, we demonstrate that hyperbolic umbilic beams follow along a curve trajectory during propagation. As the numerical calculation of diffraction integral is relatively complex, we have developed an effective approach for successfully generating such beams by using phase hologram represented by angular spectrum. Our experimental results are in good agreement with the simulations. Such beams with intriguing properties are likely to be applied in emerging fields such as particle manipulation and optical micromachining.

Customizing non-diffracting structured beams.

We demonstrate a universal approach to designing and generating non-diffracting structured light beams with arbitrary shapes. Such light beams can be tailored by predefining suitable spectral phases that match the corresponding beam shapes in the transverse plane. We develop a practical spectral superposition algorithm to discuss the non-diffracting properties and experimentally confirm our numerical results. Our proposed approach differs from that of classical non-diffracting beams, which are always constructed from wave equation solutions. The various non-diffracting structured beams could help manipulate particles following arbitrary transverse shapes and are likely to give rise to new applications in optical micromachining.