Dark electromagnetic solitons in the anomalous group-velocity dispersion regime in metamaterials

摘要

Solitons have been found in many physical branches. Previous investigations on solitons mainly focused on various nonlinear dispersive media in nature. It is well known that in the nonlinear dispersive medium, soliton formation is due to the exact balance between the nonlinearity and the group velocity dispersion (GVD). When the signs of nonlinearity and GVD are the same, that is, the positive (focusing) nonlinearity vs. positive (normal) GVD, or the negative (defocusing) nonlinearity vs. negative (anomalous) GVD, the interaction between nonlinearity and GVD may lead to the generation of dark solitons. In this paper, we study the formation and propagation of dark electromagnetic solitons in the metamaterials, artificial structures that display properties beyond those available in naturally occurring materials We use an extended Tanh-function expansion method to solve the nonlinear equation for ultrashort electromagnetic pulse propagation in metamaterial with a nonlinear polarization, and get dark solitary solutions under various conditions. It is found that, due to the role of the second-order nonlinear dispersion resulted from the dispersive magnetic permeability, dark solitons can be formed in the absence of linear dispersion, or even in the case of anomalous linear GVD for a focusing nonlinearity, challenging the traditional conditions for dark soliton formation.