Generation and characterization of customized Laguerre–Gaussian beams with arbitrary profiles

We experimentally demonstrate the generation of customized Laguerre–Gaussian (LG) beams whose intensity maxima are localized around any desired curves. The principle is to act with appropriate algebraic functions on the angular spectra of LG beams. We characterize the propagation properties of these beams and compare them with non-diffraction caustic beams possessing the same intensity profiles. The results manifest that the customized-LG beams can maintain their profiles during propagation and suffer less energy loss than the non-diffraction caustic beams, and hence are able to propagate a longer distance. Moreover, the customized-LG beam exhibits self-healing ability when parts of their bodies are blocked. This new structure beam has potential applications in areas such as optical communication, soliton routing and steering, and optical tweezing.