Multipolar Decomposition of Magnetic Circular Dichroism in Arbitrarily Shaped Magneto-Dielectric Scatterers

TL;DR

The paper tackles the challenge of analyzing electromagnetic scattering from magnetized dielectric scatterers by extending a spherical-marmonics multipole framework to include magnetization currents via vector spherical harmonics $\mathbf{X}_{lm}$. It derives exact electric and magnetic multipole coefficients $a_E(l,m)$ and $a_H(l,m)$ with separate polarization and magnetization components, enabling complete decomposition of scattering, extinction, and absorption into P- and M- contributions and their interference. The method is validated against Mie theory and finite-element simulations for diverse geometries and material parameters, and is applied to ferrite cylinders in the Faraday configuration to reveal strong magnetization resonances that can dominate dielectric resonances. The results illuminate the role of magnetization currents in far-field responses and enable optimized design of non-reciprocal devices and dielectric–magnetic metasurfaces by explicitly accounting for magnetic contributions to multipolar scattering.

Abstract

Multipole expansion methods have been primarily used for analyzing the electromagnetic scattering from non-magnetic isotropic dielectric scatterers, and studies about the scattering from magnetic objects seem to be lacking. In this work, we used the multipolar expansion framework for decomposing the electromagnetic scattering by dielectric particles with magnetic properties. Magnetization current contributions were explicitly accounted for by using the vector spherical harmonics to compute the electric and magnetic multipole contributions of arbitrary order. The exact analytical expressions for the corresponding spherical multipole coefficients were employed, with the scattering efficiencies being used to distinguish the dielectric and magnetic contributions of each multipole. This enables the analysis of scattering from arbitrarily shaped, anisotropic, and inhomogeneous magnetic scatterers. It also provides a tool for studying non-reciprocal devices that exploit magnetic resonances in magnetic-dielectric materials. Calculations were made for an experimentally feasible system, namely for ferrite-based scatterers operating in the microwave regime. These materials are of interest in radio frequency (RF) applications due to their magnetic activity. We demonstrated analytically that the magnetic circular dichroism in a magnetic-dielectric scatterer in the Faraday geometry can be decomposed into individual multipole contributions. The analytical results indicate that multipole resonances associated with magnetization currents can be even stronger than multipole contributions from conventional dielectric currents. It is worth noting that these analytical results were verified through comparison with numerical results from finite element method (FEM) simulations in COMSOL Multiphysics.

Figures (10)

• Figure 1: The scatterers considered are millimeter-scale structures with constant material properties. The three geometries analyzed include a pyramid, a sphere, and a cube. For each structure, the defining geometric parameters are as follows: the edge length of the cube, the diameter of the sphere, and both the height and base length of the pyramid are all set to $H=65$ mm. These particles are illuminated by a monochromatic plane wave propagating along the $z$-axis, with the electric field $\mathbf{E}$ polarized along the $x$-axis.
• Figure 2: The scattering efficiency coefficient and corresponding multipole decomposition contributions were calculated for (a) three distinct particles: a sphere, a cube, and a pyramid, and (b) for various scalar relative permittivity and permeability values for the cube. In detail, for a cube with material parameters $\varepsilon_p = \mu_p = 5 + i$, the extinction ($Q_{\text{ext}}$), scattering ($Q_{\text{scat}}$), and absorption ($Q_{\text{abs}}$) efficiency coefficients are presented in (c), while the scattering cross sections attributed to polarization, magnetization, interaction between the EM fields generated by both bound currents and the total contribution are illustrated in (d). The particles are considered to be immersed in a vacuum ($\varepsilon_s = \mu_1 = 1$) and irradiated by a linearly polarized plane wave incident from above.
• Figure 3: This is a graphical representation of a ferrite cylinder (yttrium iron garnet (YIG)) with height $H$ and radius $r$, positioned in an external static magnetic field $H_0$, oriented in the Faraday configuration, meaning it is parallel to the propagation direction of the incident radiation ($\mathbf{H}_0 \parallel \mathbf{k}$). The cylinder is excited by incident waves from below, specifically by (a) left-hand circularly polarized (LHCP) and (b) right-hand circularly polarized (RHCP) waves.
• Figure 4: The total scattering efficiency coefficients ($Q_{\text{scat}}$) and their respective contributions from polarization and magnetization currents are shown for a ferrite cylinder with varying radii ($r = 4, 8, 12, 16$ mm). The cylinder is irradiated by circularly polarized waves in the Faraday configuration: (a), (c), and (e) depict results for left-hand circularly polarized (LHCP) waves, while (b), (d), and (f) correspond to right-hand circularly polarized (RHCP) waves.
• Figure 5: The extinction ($Q_{\text{ext}}$), scattering ($Q_{\text{scat}}$), and absorption ($Q_{\text{abs}}$) efficiency coefficients, along with the multipole decomposition of the scattering efficiency coefficient ($Q_{\text{Mult}}$), are analyzed for a ferrite cylinder irradiated by (a) left-hand circularly polarized (LHCP) and (b) right-hand circularly polarized (RHCP) waves in the Faraday configuration. The multipole decomposition contributions up to the fourth order, including dipole and quadrupole terms, are shown for (c) LHCP and (d) RHCP cases.