Controlling the propagation of an optical vortex through two-dimensional ordered and disordered waveguide arrays using topological charge.

In this paper, we study the propagation of a radially symmetric optical vortex whose amplitude is independent of topological charge in ordered and disordered 2D arrays of coupled waveguides. It is first demonstrated that the topological charge variation affects the beam spreading in the completely ordered arrays. For a low refractive index contrast between waveguides and their surroundings, the effective width at the output end of the optical lattice versus topological charge shows an oscillatory behavior. However, for a higher refractive index contrast, as the topological charge increases from 0 to 10, the effective width reaches a maximum value and then falls. Then, we investigate the effects of topological charge variation on the wave propagation through the waveguide array in the presence of different disorder strengths. Our results here confirm that the behavior of effective width versus the topological charge in the disordered array significantly depends on the average of the refractive index of the waveguides. Although the intensity of the input radially symmetric vortex beam is independent of the topological charge, for low disorder levels, the effective width and intensity distribution at the output end is strongly sensitive to the topological charge or the polar phase of the vortex beam. It is also demonstrated that, for strongly disordered arrays, the effective width and output beam profile shows no considerable change with variation of the topological charge. These effects are due to the discrete diffraction phenomenon and its dependence on the helical wavefront of the optical vortex whose form is determined by the topological charge. Therefore, it is demonstrated here that angular phase affects the beam broadening in an array of coupled optical waveguides.