Gap solitons in metamaterials

Electromagnetic localization and existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band - where the magnetic permeability $\mu(\omega)$ is positive and the dielectric permittivity $\epsilon(\omega)$ is negative - is described by a nonlinear Klein-Gordon equation with a dispersive nonlinear term. A family of standing and moving localized waves for both electric and magnetic fields is found, and the role played by the nonlinear dispersive term on solitary wave stability is discussed.