Soliton excitations in a one-dimensional nonlinear diatomic chain of split-ring resonators

We present a systematic analytical study of the dynamics of nonlinear magnetoinductive waves in a one-dimensional diatomic lattice of split ring resonators (SRRs) with Kerr nonlinear interaction between nearest neighbors. The linear spectrum of this model have two branches and exhibits a gap, which is proportional to the difference between two types of SRRs. We analyze the nonlinear excitations genuine of the discreteness and nonlinearity in such a diatomic chain based on an extended quasidiscreteness approach. Gap solitons (with vibrating frequency lying in the gap), resonant kinks (with the vibrating frequency lying in the frequency bands), and intrinsic localized modes (with the vibrating frequency being above all the frequency bands) are obtained explicitly. It is also shown that the existence of different localized structures depend strongly on the type of nonlinearity of the embedded medium (a self-focusing or defocusing one).

Figure 1

(Color online) Dispersion curves in the diatomic chain of SRRs

Figure 2

The pattern of the gap solitons in 1D diatomic lattice of SRRs: (a) acoustic upper cutoff mode; (b) optical lower cutoff mode.