Rectification of Energy Transport in Nonlinear Metamaterials via Ratchets

Abstract:

The presence of discrete breathers is already described in nonlinear photonic materials, such as ferroelectrics and metamaterials by Klein-Gordon approach. Rectification of energy transport in metamaterials in presence of an appropriate external field has been studied via symmetry breaking leading to directed energy transport or ratchet behavior. Based on the earlier development of Klein-Gordon equation in metamaterial (MM) system with split-ring resonator for antenna application, a theoretical model for current density has been worked out by symmetry analysis and its violation to characterize the ratchet effect. The time-average current shows interesting results against phase shift in the ac driver. These data are further related to various parameters, such as coupling and damping in the system. For metamaterials, this opens a new application for rectification by using ratchets.

Keywords: Metamaterials, Ratchets, Rectification, Symmetry Breaking.

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The physics behind the ratchet phenomenon is described as due to Kerr-type nonlinear medium in which SRRs are placed in the MM system. In such MMs, the magneto-inductive (MI) waves are observed to propagate within a frequency band near the resonant frequency of the SRRs. Due to nonlinearity of the system, the MI waves form localized structures. It is shown that these MI waves, in terms of current density, can be controlled by tuning the phase shift of the applied field leading to MI waves propagating only in a specific direction, and hence the formation of ratchets. This was explained on symmetry analysis. Obviously, the ratchet properties are also dependent on other material parameters such as coupling between the SRRs, damping, focusing and defocussing nonlinearity, etc.

The unidirectional motion of topological solitons under the influence of zero mean (ac) external driver can be realized if certain symmetries of the system are broken, i.e. by symmetry violation, with applications: (a) molecular motors and other non-equilibrium biological systems, (b) electric currents in superlattices, (c) voltages in coupled systems, i.e. in annular Josephson junctions revealing unidirectional fluxon motion that is driven by biharmonic microwaves, d) magnetic flux cleaning in superconducting films, e) Abrikosov vortex diodes, and f) voltage rectifiers.
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J. Phys. D: Applied Physics, Vol. 46 [20], 205102 (2013).