Propagation dynamics of elliptical super-Gaussian bullets in nonlinear metamaterial waveguide

The characteristics of an optical beam propagating in a medium should be preserved for many applications related to fiber optic communication. The phenomenon of self-trapping due to adequate balance among linear and nonlinear effects may preserve the characteristics of an optical beam. In this work, we perform a theoretical investigation on the propagation of a spatiotemporal elliptical super-Gaussian beam in a Kerr nonlinear metamaterial waveguide. We follow the Lagrangian variational method and numerical analysis using the appropriate trial function for the input elliptical super-Gaussian beam and analyze the self-trapping and deformation of the propagating beam in metamaterials. We obtain special conditions to observe the self-trapping and stabilize the dynamics of the elliptical super-Gaussian beam in both negative and positive index regimes of the metamaterial. It is found that in the negative index regime of metamaterial, the phenomenon of self-trapping may exist in the normal dispersion regime with defocusing Kerr nonlinearity. However similar to the conventional medium, the robust balance among the anomalous dispersion and focussing Kerr nonlinearity supports the self-trapping in the positive index regime. There is a critical optical power for the input beam to observe the pulse trapping phenomena. This power is found to be a function of the super-Gaussian parameter as well as the ellipticity of the input beam. The period of self-trapping is also a function of the super-Gaussian parameter and the ellipticity of the input beam.