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Discrete breathers in magnetic metamaterials
G. P. TsironisDepartment of Physics, University of Crete, and FORTH
Metamaterials, typically comprised of discrete resonant elements, exhibit electromagnetic
properties not available in naturally occuring materials. More specically magnetic metamateri-
als (MMs) show signicant magnetic properties up to Terahertz and optical frequencies . The
most common realization of a MM is comprised of periodically arranged split-ring resonators
(SRRs), which are just metallic rings with a slit. The SRRs can become nonlinear either by the
insertion of a nonlinear dielectric or a nonlinear electronic component in their slits, resulting
in a nonlinear MM . The combination of nonlinearity and discreteness makes possible the
generation of nonlinear excitations in these materials in the form of discrete breathers (DBs)
. Recently, a novel MM comprised of two types of SRRs was investigated theoretically and it
was demonstrated that in the nonlinear regime such binary MMs are suited for the observation
of phase-matched parametric interaction and enhanced second harmonic generation .
The binary structure of the lattice allows for generation of breathers through direct external
induction [5,6]. The dispersion curves for a binary MM do not contain any acoustic-like branch;
the two curves are of the 'optical' type, and they are separated by a gap . For a frequency
gapped linear spectrum, some of the modes become unstable at large amplitude. If the curvature
of the dispersion curve in the region of that mode is negative and the lattice potential is hard
then, the large amplitude mode becomes unstable with respect to formation of a DB in the gap
above the linear spectrum. In order to generate DBs with frequency chirping for a dissipative-
driven MM we initiate the driver with a frequency just below the top of the upper linear band,
which is then chirped with time to produce enough vibrational amplitude to induce modulational
instability, which then leads to spontaneous DB generation. At the end of the frequency chirping
phase, the driver frequency is well above the top of the upper linear band, and only supplies
energy into the DB(s) that are locked to the driver and they are trapped at particular SRRs.
After that, the driver frequency is kept constant and the DBs continue to receive energy falling
into a stationary state.
MMs are driven by alternating elds and thus it is expected that dissipative DBs are relevant
to these type of experiments when nonlinearity is present. We have generated numerically
dissipative DBs in a model nonlinear MM with frequency chirping of the driver . Since SRR-
based MMs with approximatelly cubic capacitive nonlinearities have been already constructed,
at least in the microwave frequency range, the realization of a binary array is in principle possible.
We propose that an experiment with frequency chirped applied eld can lead to dissipative DB
generation in a fashion very similar to that described above.
 S. Linden et al., IEEE J. Selec. Top. Quant. Electron. 12, 1097 (2006).
 I.V. Shadrivov, et al., Appl. Phys. Lett. 93, 161903 (2008).
 N. Lazarides, M. Eleftheriou, G.P. Tsironis, Phys. Rev. Lett. 97, 157406 (2006).
 M.V. Gorkunov, I.V. Shadrivov, Yu.S. Kivshar, Appl. Phys. Lett. 88, 071912 (2006).
 M. Sato et al., Phys. Rev. Lett. 90, 044102 (2003).
 M.E. Manley et al., Phys. Rev. B 79, 134304 (2009).
 M.I. Molina, N. Lazarides, G.P. Tsironis, arXiv:09054474 (2009).
Host: Panagiotis Maniadis