Faraday rotation spectrum of magneto-optical nanoparticle aggregates

The interaction of light with a cluster of gyrotropic spherical particles is studied in view of a miniaturized Faraday rotator. The electromagnetic fields are expanded in terms of the vector multipole fields and the expansion of the scattered field is related to that of the incident field. An incident linearly polarized light with polarization azimuth $\psi$ becomes elliptically polarized upon scattering from the cluster. The polarization azimuth rotation and ellipticity angle variation are almost sinusoidal functions of $2\psi$. With planar disordered clusters of bismuth-substituted yttrium iron garnet nanoparticles of radius 50 nm, polarization rotations about $\pm 4^{\circ }$ are achievable.

Figure 1

Schematics of (a) a dimer, (b) a linear cluster, (c) a rectangular array, and (d) a disordered cluster of particles.

Figure 2

(a) $\chi -\psi$ and (b) $\beta$ as a function of $\psi$ for a dimer of Bi:YIG nanoparticles. The dimer is along the $\widehat{\mathbf{y}}$ axis, $a=50$ nm, $\lambda =365$ nm, ${\widehat{\mathbf{k}}}_I\parallel \widehat{\mathbf{z}}$, and ${\widehat{\mathbf{k}}}_S\parallel \widehat{\mathbf{z}}$.

Figure 3

(a) $\chi -\psi$ and (b) $\beta$ versus $\psi$ for a linear cluster. The cluster is along the $\widehat{\mathbf{z}}$ axis. $d=0.4a=20$ nm. (c) $\chi -\psi$ and (d) $\beta$ versus $\psi$ for a rectangular cluster. (e) $\chi -\psi$ and (f) $\beta$ versus $\psi$ for a disordered cluster. The clusters are composed of 64 Bi:YIG nanoparticles of radius $a=50$ nm. ${\widehat{\mathbf{k}}}_I\parallel \widehat{\mathbf{z}}$ and ${\widehat{\mathbf{k}}}_S\parallel \widehat{\mathbf{z}}$ are assumed. For clusters composed of anisotropic particles with ${\epsilon }_k=0$, the corresponding plots are shown in (g)–(l).

Figure 4

(a) $\mathrm{\Delta }\chi$ and (b) $\mathrm{\Delta }\beta$ as a function of $\lambda$. Here $\psi =0^{\circ }$. The plots corresponding to $\psi ={45}^{\circ }$ are shown in (c) and (d), respectively. ${\widehat{\mathbf{k}}}_I\parallel \widehat{\mathbf{z}}$ and ${\widehat{\mathbf{k}}}_S\parallel \widehat{\mathbf{z}}$ are assumed.

Figure 5

${\sigma }_{\text{CD}}/\left(\pi N{a}^2\right)$ for a monomer, dimer, and octamer of Bi:YIG nanoparticles. Here $a=d=50\mathrm{nm}$ and ${\widehat{\mathbf{k}}}_I\parallel \widehat{\mathbf{z}}$. The dimer and octamer are along the $\widehat{\mathbf{z}}$ axis.