Dynamical theory of artificial optical magnetism produced by rings of plasmonic nanoparticles

We present a detailed analytical theory for the plasmonic nanoring configuration first proposed by Alù et al. [Opt. Express 14, 1557 (2006)], which is shown to provide negative magnetic permeability and negative index of refraction at infrared and optical frequencies. We show analytically how the nanoring configuration may provide superior performance when compared to some other solutions for optical negative-index materials, offering a more “pure” magnetic response at these high frequencies, which is necessary for lowering the effects of radiation losses and absorption. Sensitivity to losses and the bandwidth of operation of this magnetic inclusion are also investigated in detail and compared with other available setups.

Figure 1

(Color online) A nanoring made of $N$ nanoparticles symmetrically displaced around the origin of a Cartesian reference system in the $x\text{−}y$ plane. The electric polarization response to a uniform magnetic excitation is depicted in the figure, ensuring purely rotational induced electric dipoles (black arrows).

Figure 2

(Color online) Electric-field distribution in the $\theta =\pi /2$ ($x\text{−}y$) plane varying the distance $r$ from the origin for the resonant loop of Fig. 1 with (a) $R={\lambda }_b/100$, $N=6$, (b) $R={\lambda }_b/10$, $N=6$, (c) $R={\lambda }_b/100$, $N=4$, (d) $R={\lambda }_b/10$, $N=4$, (e) $R={\lambda }_b/100$, $N=2$, and (f) $R={\lambda }_b/10$, $N=2$.

Figure 3

(Color online) (a) Real and (b) imaginary parts of the effective permeability for a cubic lattice with number density $N_d={\left(160\text{nm}\right)}^{-3}$ made of nanoloops with radius $R=60\text{nm}$ each of which is composed of $N$ silver particles with radius $a=24\text{nm}$.