Magnetic plasmon resonance

It is demonstrated that metallic horseshoe-shaped (also referred to as u-shaped) nanostructures can exhibit a magnetic resonance in the optical spectral range. This magnetic plasmon resonance is distinct from the purely geometric $LC$ resonance occurring in perfectly conducting split rings because the plasmonic nature of the metal plays the dominant role. Similarly to the electrical surface plasmon resonance, the magnetic plasmon resonance is determined primarily by the metal properties and nanostructure geometry rather than by the ratio of the wavelength and the structure's size. Magnetic plasmon resonance occurs in nanostructures much smaller in size than the optical wavelength. Electromagnetic properties of periodically assembled horseshoe-shaped nanostructures are investigated, and the close proximity of the electrical and magnetic plasmon resonances is exploited in designing a negative index metamaterial. Close to the magnetic plasmon resonance frequency both magnetic permeability $\mu$ and electric permittivity $\epsilon$ can become negative, paving the way for the development of subwavelength negative index materials in the optical range.

Figure 1

Currents in two parallel metal wires excited by external magnetic field $\mathbf{H}$. Displacement currents, “closing” the circuit, are shown by dashed lines.

Figure 2

Optical magnetic permeability $\mu ={\mu }_1+i{\mu }_2$ (${\mu }_1$: continous line, ${\mu }_2$: dashed line) estimated from Lorenz-Lorentz formula for the composite containing $⊏$ shaped silver nanoantennas; volume concentration $p=0.3;$ left curves: $a=200\mathrm{nm}$, $d=50\mathrm{nm}$, $b=13\mathrm{nm}$; right curves $a=600\mathrm{nm}$, $d=90\mathrm{nm}$, $b=13\mathrm{nm}$.

Figure 3

(Color online) Magnetic plasmon resonance in a silver horseshoe-shaped nanoantenna placed in a maximum of external field $H_0$ which is directed perpendicular to the plane; the frequency corresponds to $\lambda =1.5\mathrm{\mu }\mathrm{m}$; silver dielectric constant is calculated from the Drude formula (5).

Figure 4

Optical magnetic permeability $\mu ={\mu }_1+i{\mu }_2$ (${\mu }_1$: continuous line, ${\mu }_2$: dashed line) of the composite containing silver nanoantennas shown in Fig. 3 organized in a square lattice; volume concentration $p=0.4$.

Figure 5

(Color online) Wave propagation through a two-dimensional (infinitely extended in the normal to the page direction) plasmonic crystal near the plasmon magnetic resonance. The crystal is composed of the u-shaped nanoantennas shown in Fig. 3, volume filling ratio $p=0.4$, $\lambda =1.4\mathrm{\mu }\mathrm{m}$. Magnetic field $\mathbf{H}$ of the incident em wave is directed along $z$ axis perpendicular to plane of picture; $H_z=1$ in the incident wave. (Top) Spaces between the horseshoes are filled with vacuum: no propagation. (Bottom) Spaces between the horseshoes are filled with a hypothetical $\epsilon =-3$ material: wave propagates into the structure.

Figure 6

(Color online) Plasmonic crystal composed from the u-shaped metal nanoantennas; separation between antenna centers is $80\mathrm{nm}$. Magnetic (color and contours) and electric (arrows) fields inside a periodic array of horseshoe-shaped nanoantennas at the cutoff $(k_x=0)$. (b) Dispersion relation $\omega$ vs $k_x$ for a left-handed electromagnetic wave.