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

Abstract

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.

Fano resonance due to discrete breather in nonlinear Klein–Gordon lattice in metamaterials

“…However, in case of defocusing nonlinearity, the intensities of the peaks increase to some extent. Our preliminary simulation work based on Floquet analysis for threedimensional figures also show some changes in the profile of discrete breathers [23]. A change in the value of coupling (λ) from 0.03 to 0.04 shifts the peaks, as shown in Fig.…”

“…However, as mentioned later in [21,22], the Hamiltonian developed by us for ferroelectrics can also take care of certain issues involved in metamaterials, if we suitably add a magnetic component in it. This is again mentioned in our recent paper on the effect of coupling on the temporal evolution of quanta for quantum breathers in metamaterials in a Klein-Gordon lattice under a nonperiodic boundary condition [23].…”

“…3, where the sharpness of the Fano peak is seen to increase with increasing coupling, thereby making a useful consideration for various biosensing applications [8,12]. For quantum discrete breathers, the coupling that can be changed through engineering of design parameters has a significant role on breather lifetime in femtosecond in terms of critical time of redistribution of the number of quanta [23,30]. An attempt will be made in the future to relate these two issues.…”