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.
A new class of (2+1)‐dimensional circular butterfly beams (CBBs) is first demonstrated based on high‐dimensional butterfly catastrophes. The intensity of CBBs increases abruptly by two orders of magnitude right before they propagate to the focal plane, implying that they possess an abruptly autofocusing (AAF) ability induced by accelerating properties. The autofocusing performance can be further improved by introducing vortices. Owing to the flexibility of high‐dimensional catastrophes, butterfly beams exhibit diverse optical light structures; thus, the focal length, focal intensity, and light field structures of CBBs are tunable. Experimental results are consistent with numerical findings. Therefore, CBBs enrich the family of AAF beams and will be advantageous for optical micromachining, medical treatments, optical tweezers, and nonlinear processes.
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