Modulation instability of structured-light beams in negative-index metamaterials

One of the most fundamental properties of isotropic negative-index metamaterials (NIMs), namely opposite directionality of the Poynting vector and the wavevector, enable many novel linear and nonlinear regimes of light–matter interactions. Here, we predict distinct characteristics of azimuthal modulation instability (MI) of optical vortices with different topological charges in NIMs with Kerr-type and saturable nonlinearity. We derive an analytical expression for the spatial modulation-instability gain for the Kerr-nonlinearity case and show that a specific condition relating the diffraction and the nonlinear lengths must be fulfilled for the azimuthal MI to occur. Finally, we investigate the rotation of the necklace beams due to the transfer of orbital angular momentum of the generating vortex on the movement of solitary necklace beams. We show that the direction of rotation is opposite in positive- and negative-index materials. (paper)