Nonlinear responses of the periodic structure composed of single negative materials

We investigate the nonlinear responses of the one-dimensional periodic structure containing alternate single negative materials. The transmission property of this nonlinear periodic structure is studied and the bistable behavior is found. Similar as in the linear periodic structure, the transmission property of this nonlinear structure in the zero phase (zero-?) gap region is found to be relatively insensitive to the incident angle from 0° to 30°, in comparison with that in the Bragg gap. Especially, the transmissions associated with the zero-? gap reach the peaks at almost the same input intensity for different incident angles. Another merit of the transmission property in the zero-? gap is that a lower threshold is needed to achieve the bistability than in the Bragg gap. The electric field distribution in the system is further studied. We observe the zero-? gap soliton and compare it with the usual Bragg gap soliton. The differences between these two kinds of solitons are analyzed, and the zero-? gap soliton is shown to be insensitive to the incident angle. In the end, we find that the transmission and the soliton in the zero-? gap are also weakly dependent on the loss and the scaling in contrast to that in the Bragg gap.