Study of plasmonic slot waveguides with a nonlinear metamaterial core:   semi-analytical and numerical methods
  Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a nonlinear metamaterial core of Kerr-type embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assumed that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and the nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical, it is based on the finite-element method in which all the components of the electric field are considered in the Kerr-type nonlinearity with no presumptions on the nonlinear refractive index change. Our finite-element based model is valid beyond weak nonlinearity regime and generalize the well-known single-component fixed power algorithm that is usually used. Examples of the main cases are investigated including ones with strong spatial nonlinear effects at low powers. Loss issues are reduced through the use of gain medium in the nonlinear metamaterial core. 
Mahmoud M. R. Elsawy and Gilles Renversez
physics.optics nlin.PS physics.comp-ph