Negative Permeability of Single-ring Split Ring Resonator in the Visible Light Frequency Region
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0919-J03-08
Negative Permeability of Single-ring Split Ring Resonator in the Visible Light Frequency Region Takuo Tanaka, Atsushi Ishikawa, and Satoshi Kawata Nanophotonics Lab., RIKEN, 2-1 Hirosawa, Wako, Saitama, 351-0198, Japan ABSTRACT Negative magnetic permeability of split-ring resonators (SRRs) is theoretically investigated from THz to the visible light region. To describe the frequency dispersion of metal throughout the frequency range, we consider the exact expression of the internal impedance formula. This formula can describe not only the conduction characteristics but also the dielectric behavior of metal in the optical frequency region. Based on these investigations, we successfully determine the magnetic responses of the SRRs from THz to the visible light region. Our results indicate that the behavior of the SRR is changed completely at the transition frequency of 100 THz at which the effect of the reactance in the ring becomes more dominant than that of the resistance in the ring on the SRR. INTRODUCTION In 1999, Pendry et al. have successfully extended the frequency range of magnetic properties of effective materials by introducing an array of metallic subwavelength-structured objects referred to as “split ring resonator (SRR) ” [1]. By using the SRR, left-handed materials (LHMs) [2] exhibiting unique electromagnetic phenomena [3] have already been demonstrated in the microwave region. The SRR also gives us the opportunity to develop artificial active magnetic materials in the optical frequency region. µ of most natural materials in the optical frequency region is known to be unity because the unpaired electron spins are not able to follow a high-frequency magnetic field. In order to overcome this common understanding, much experimental effort to increase the operating frequency of the SRR up to near IR has been made recently in spite of difficulties in their fabrication [4-7]. On the other hand, some theoretical studies to describe the behavior of the SRR have been also reported from THz to near IR [8-10], and particularly in the visible range [11,12]. Since the operation of the SRR is based on the LC resonant circuit coupled with magnetic field, we must determine the frequency dispersion of conduction characteristics of metal to fully describe the SRR’s behavior. The behavior of the SRR depends on its structure as well as the dispersive properties of metal, and this makes it increasingly difficult to understand overall picture of the SRR’s behavior throughout the frequency range. THEORY In the optical frequency region, the conductivity of a metal is described as σ (ω ) =
ω 2pε0 , γ − iω
(1)
where ω is the angular frequency, ωp is the plasma frequency, ε0 is the permittivity of vacuum,
and γ is the damping constant of the metal. According to the Maxwell’s equations, the current distribution along the depth direction z of the metal is given by ⎧ σ (ω )⎫ , J (ω,z ) = J 0e ik(ω )z , k (ω ) = ω ε0µ0 ⎨1+ i ⎬ ωε0 ⎭ ⎩
(2)
where J0 is the magnitude of the current density at the surface, µ0 is the pe
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