Frequency characteristics of the dark and bright surface solitons at a nonlinear metamaterial interface

We investigate the generation and properties of dark and bright surface waves at the interface of a conventional medium and a metamaterial. It is shown that the stable dark and bright surface solitons can coexist even when the nonlinear Kerr coefficients of the two media are negative, completely different from those at the interface between two conventional media. Most importantly, both the dark and bright surface solitons exist only within a certain range of the effective refractive index of the metamaterial, greatly depending on the frequency of the electromagnetic wave propagating in it. Therefore, the generation conditions for surface solitons, and the properties of the generated surface solitons such as the peak positions and the intensity of the dark and bright surface solitons, can be controlled by adjusting the structure parameters of the metamaterial and/or the frequency of the electromagnetic wave.