Twisting light with hyperbolic metamaterials.

We propose a novel, miniaturized astigmatic optical element based on a single biaxial hyperbolic metamaterial that enables the conversion of Hermite-Gaussian beams into vortex beams carrying an orbital angular momentum and vice versa. As an example, we design a biaxial anisotropic metamaterial that introduces a π/2 phase shift between two orthogonal components of a Hermite-Gaussian beam due to the optical path difference and at the same time astigmatically focuses these orthogonal components such that they recombine in a symmetric Laguerre-Gaussian beam. We design the proposed device using an array of silver nanowires in an MgF(2) matrix. The advantages of the proposed approach over the existing bulk optics based techniques include compactness and therefore, compatibility with ultra-compact opto-electronic circuits, potential re-configurability and an increased tolerance to misalignment.