Controllable two-dimensional diffraction-free polygon beams (Q2079080)

The authors study the problem of finding diffraction-free and accelerating beams which are very important in laser optics, due to their characteristics of keeping shape invariant and highly-localized intensity distributions during transmission. The problem, which was studied by many authors, is solved numerically by the means of the diffraction-free Laguerre-Gaussian solutions of the two-dimensional paraxial wave equation in linear media. In \S. 2, the theoretical mode and its exact solution are given and different polygon beams are obtained by he superposition of Laguerre-Gaussian modes, which represent common forms of stable transmissions through optical fibers. Finally, in \S. 3, numerical solutions are provided and discussed.