27 September 2006 An adaptive Fourier Bessel split-step method and variational techniques applied to nonlinear propagation in negative index materials
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Abstract
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.
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P. P. Banerjee, G. Nehmetallah, "An adaptive Fourier Bessel split-step method and variational techniques applied to nonlinear propagation in negative index materials", Proc. SPIE 6320, Complex Photonic Media, 63200E (27 September 2006); doi: 10.1117/12.675638; https://doi.org/10.1117/12.675638
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