Manipulating self-focusing beams induced by high-dimensional parabolic umbilic beams

Abstract

The excellent property that the intensity of autofocusing beams in the focal plane increases exponentially, makes them especially beneficial for biomedical treatment. We experimentally generate tunable (2+1)-dimensional circular parabolic umbilic beams (CPUBs) for the first time based on the high-dimensional diffraction catastrophe integral, which is determined by the potential function. Such CPUBs have circular and symmetrical intensity distributions in space through radial symmetry transformation. Due to the flexibility of high dimensionality, these light beams have rich light field structures and self-focusing property. Where, the maximum intensity suddenly increases by orders of magnitude in the focal plane. Unlike the classical circular Airy beams, CPUBs exhibit multiple self-focusing points along the optical axis and a needle-like structure during propagation, which can be affected by manipulating the control parameters. The rich properties provide a new perspective for exploring the novel physical mechanisms and phenomena in autofocusing beams. The experimental results verify the correctness of the numerical simulations. CPUBs greatly enrich the autofocusing beam family and will be advantageous for medical treatments, optical micromanipulation, and microscopic imaging.

Keywords

• Circular parabolic umbilic beams
• Self-focusing
• Optical caustics
• Catastrophe theory