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27 September 2005 Analytical model for the optical propagation in a nonlinear left-handed material
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Left-handed materials have attracted growing attention in recent years. Although many efforts have been concentrated on the study of linear devices filled with left-handed materials, it was only recently that the nonlinear optical properties and optical response of such materials have been described. However, no analytical description of light propagation in these media has been proposed. In this communication, we develop an analytical model describing the interaction of coherent electromagnetic radiation in structures containing both right- and left-handed materials with a Kerr type nonlinearity. We study the paraxial propagation of electromagnetic radiation in such structures. Using a multiple time and space scales analysis, we derive a system of two coupled nonlinear Schrödinger equations for the amplitudes of the fields, allowing for both forward and reflected waves to be present in the structure. Diffraction, group velocity dispersion and Kerr nonlinear effects are taken into account. Appropriate boundary conditions are derived. Finally, we point out the differences between propagation in right- and left-handed materials.
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P. Tassin, G. Van der Sande, I. Veretennicoff, M. Tlidi, and P. Kockaert "Analytical model for the optical propagation in a nonlinear left-handed material", Proc. SPIE 5955, Metamaterials, 59550X (27 September 2005);

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