Stabilization of hollow Gaussian beams in nonlinear metamaterial waveguides

Hollow Gaussian beams which possess the dark hollow spatial intensity distribution were found to have interesting applications in trapping nano-sized particles and free-space optical communication. Many applications demand stable dynamics of higher dimensional beams. Here we theoretically study the dynamics of hollow Gaussian beams in cubic and quintic nonlinear negative index metamaterial. We adopt Lagrangian variational analysis and explore the parametric regions characterizing the metamaterial in which the hollow Gaussian beam can execute stable dynamics as well as it can undergo filamentation due to intrinsic collapse. We confirm the analytical results obtained through variational analysis by direct numerical analysis based Crank Nicolson method implemented in Python programming.