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                           COLOQUIOS DEL DEPARTAMENTO DE FÍSICA FCEyN - UBA

                                      http://coloquios.df.uba.ar/

                                         Charla, café y galletitas
                                    En el Aula Federman, 1er piso Pabellón I,
                                            Ciudad Universitaria


                                       Jueves 8 de julio, 14hs,


                        Metamateriales, Magnetismo a Altas Frecuencias
                               y el Argumento de Landau-Lifshitz


                                          Roberto Merlin

                                      University of Michigan




Homogeneous composites, or metamaterials, made of dielectric or
metallic particles are known to show magnetic properties that
contradict arguments by Landau and Lifshitz [Electrodynamics of
Continuous Media (Pergamon Press, Oxford, 1960 ), p. 251] indicating
that the magnetization and, thus, the permeability loses its meaning
at relatively low frequencies. Here we show that these arguments do
not apply to composites made of substances with ks = Im (sqrt(eps_s))
  >> lambda/l or ns = Re(sqrt(eps_s)) sim lambda/l  (eps_s and l are
the complex permittivity and the characteristic length of the
particles, ks and ns are, respectively, the extinction coefficient and
the refractive index, and lambda is the vacuum wavelength). Our
general analysis is supported by studies of split-rings, one of the
most common constituents of electromagnetic metamaterials, and
spherical inclusions. An analytical solution is given to the problem
of scattering by a small and thin split ring of arbitrary
permittivity. Results reveal a close relationship between eps_s and
the dynamic magnetic properties of metamaterials. For sqrt(eps_s) <<
lambda/a  (a is the ring cross-sectional radius), the composites
exhibit very weak magnetic activity, consistent with the
Landau-Lifshitz argument and similar to that of molecular crystals. In
contrast, large values of the permittivity lead to strong diamagnetic
or paramagnetic behavior characterized by susceptibilities whose
magnitude is significantly larger than that of natural substances. The
double constraint ks >> lambda/l >> 1 (or ns sim lambda/l >> 1 if ks
<< ns ) poses severe limitations for attaining magnetism at
arbitrarily high frequencies. Because they have a large extinction
coefficient, metals are to be favored at optical frequencies. Since
eps_s sim -wp^2/w^2  for w tau >> 1, the constraint becomes lambda >>
l >> lambda_p . The measured values of the permittivity for noble
metals indicate that magnetism can coexist with the effective-medium
condition for frequencies up to ~ 1.5 10^14 Hz (lambda ~ 2.5 um).