Role of coupling of discrete breathers in split-ring-resonator-based metamaterials

Through detailed quantum calculations, the presence of classical discrete breathers and, subsequently, a two-phonon bound state (TPBS) or quantum breather (QB) state have already been shown in nonlinear photonic materials such as ferroelectrics. The latter was done in a periodic boundary condition in terms of the variations of TPBS parameters against impurity that is related to nonlinearity. Metamaterials are also nonlinear optical materials for applications as a split-ring-resonator (SRR) in antenna arrays. By using a Klein-Gordon approach, first multi-solitons and classical breathers are shown. For QBs, by using a periodic boundary condition, the variation of the TPBS parameters with coupling within the SRR elements is observed. Finally, in a non-periodic boundary condition approach, the temporal evolution of the number of quanta is shown eventually in order to derive the critical time of redistribution of quanta that is proportional to the QB's lifetime in femtoseconds, which also shows variation with coupling in the SRR system. (paper)