Fourier-invariant autofocused Laguerre-Gaussian beams

We study a new Laguerre - Gaussian (LG) beam, which differs from conventional LG mode beams that preserve the structure of the intensity distribution up to scale. The proposed beam does not retain its structure upon free-space propagation but shows some interesting properties. This beam is Fourier invariant and has extended dark regions in the initial (waist) plane and in the far field. Thus, while maintaining the beam topological charge, the effective diameter of the central dark intensity spot can be increased or decreased by changing the radial index of the Laguerre polynomial. In addition, this beam has the property of autofocusing, that is, at the Rayleigh distance from the waist, the intensity distribution has the form of a light ring (for any value of the radial index) with a minimum diameter and maximum intensity on the ring. This beam can be used to manipulate microparticles without using an additional focusing spherical lens.