An Adaptive Fourier Bessel Split-Step Method and Variational Techniques Applied to Nonlinear Propagation in Negative Index Materials

摘要

Starting from a simple dispersion relation that models negative index materials, we derive and develop the underlying partial differential equation for wave propagation in such a medium. In the first part we study the linear characteristics of wave and beam propagation in NIMs. In the second part we heuristically perform a nonlinear extension of the linear partial differential equation by adding cubic nonlinear terms as in the nonlinear Klein Gordon equation, and (d+1+1)-dimensional envelope solitary wave solutions are derived. Also, using variational techniques and an adaptive Fourier Bessel split-step numerical method, we show that nonlinearity management through a periodic variation of the nonlinearity coefficient helps in stabilization of spatial solitons.