  We experimentally demonstrate the generation of customized perfect
Laguerre-Gaussian (PLG) beams whose intensity maxima localized around any
desired curves. The principle is to act appropriate algebraic functions on the
angular spectra of PLG 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-PLG 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. This new structure beam would have potential applications in areas
such as optical communication, soliton routing and steering, optical tweezing
and trapping, atom optics, etc.
