Artifical electric and magnetic atoms

The basic physics of "magnetic atoms" is quite simple: In order to obtain a magnetic response from a metal structure the incident light field has to excite local currents circulating in loops (solenoidal currents). These currents in turn give rise to a magnetic dipole-moment. By properly designing the metal structure, one can obtain a resonant enhancement of the local currents leading to a strong magnetic response and potentially a negative magnetic permeability.
A Split Ring Resonator (SRR) is the prototype of a "magnetic atom”. It is made up of a sub-wavelength metallic ring which features a small gap. The ring forms the winding of a magnetic coil with inductance L while the gap acts as a capacitor with capacitance C. Thus, a SRR mimics an LC-oscillator with resonance frequency ωLC. If the frequency of the incident light lies within a spectral band slightly above the LC-resonance frequency, the effective magnetic permeability of a SRR array can indeed be negative.
In analogy, one can understand the physics of "electric atoms". For example, an array of long wires acts as a diluted Drude metal if the electric field is oriented along the wire axis. These wire arrays allow for a negative permeability below the effective plasma frequency.

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Split Ring Resonator compared with an LC circuit, which consists of a coil L and a capacitor C.