Tunable beam propagation based on cylindrically symmetric gradient index system

In this work, a cylindrically symmetric gradient-refractivity two-dimensional electromagnetic system isconstructed by using the magnetic metamaterials consisting of an array of ferrite rods. With the change of thebias magnetic field, the different gradient-refractivity systems can be obtained, based on which a tunableflexible beam is demonstrated. Based on the effective-medium theory, the effective electric permittivity and theeffective magnetic permeability can be retrieved and thus the effective refractive index is obtainedstraightforwardly. It is shown that with the variation of the ferrite rod radius, an effective refractivity profilewith particular gradient can be realized, which exhibits the electromagnetic "black-hole-like" effect. Especially,the gradient refractivity profile is also designed by introducing the gradient bias magnetic field, which, inprinciple, results in the refractivity profile with many different gradients. Finally, the propagation of a Gaussianbeam in the gradient-refractivity system is simulated by using the multiple scattering theory. A few differentphenomena are observed such as the " black-hole" effect, the interior beam deflection, the exterior beamdeflection, and the beam splitting. Furthermore, the functionalities can be switched between each other bycontrolling the bias magnetic field and adding an additional degree of freedom for beam propagation.