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

Abstract

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.