Modal and excitation asymmetries in magnetodielectric particle chains

We study the properties of dipolar wave propagation in linear chains of isotropic particles with independent electric and magnetic response, embedded in vacuum. It is shown that the chain can support simultaneously right-handed modes (RHMs) and left-handed modes (LHMs) of transverse polarization. The LHMs are supported by the structure even if the chain's particles possess positive polarizabilities and no Bi isotropy; the needed structural Bi isotropy is provided by the propagator instead of by the particle's local properties. In contrast to the transverse modes in chains that consist of purely electric particles that are inherently RHM, the LHM dispersion lacks the light-line branch since the dipolar features are not aligned with the electric and magnetic fields of a right-handed plane-wave solution in free space. Furthermore, it is shown that the spatial width of the LHM is significantly smaller than that of the RHM. Excitation theory is developed, and it is shown that the chain possesses modal and excitation asymmetries that can be used to eliminate reflections from the chain's termination.

Figure 1

A linear chain of magnetic-electric particles. The particles are made of simple $\epsilon ,\mu$ material, and no coupling between $\mathit{E},\mathit{H}$ occurs within the material.

Figure 2

Dispersion for the transverse modes for $kd=0.2$, where $k$ is the free-space wave number. Left-handed modes—the $D^{-}$ dispersion curve—exist also for positive real polarizabilities.

Figure 3

Spatial width of the LHMs and RHMs under guiding conditions, with the same parameters as in Fig. 2.

Figure 4

The dispersions of the diagonalized problem in Eqs. (14a)–(14c): (a) $q=1$ yields the $D^{+}$ curve only, and (b) $q=2$ yields the $D^{-}$ curve only.

Figure 5

Dispersion for a chain of unbalanced particles for $\delta =100$.

Figure 6

Residue (excitation magnitude) of the LHM and RHM under guiding conditions, with the same parameters as in Fig. 2.

Figure 7

Response to a (1,1) Huygens source. The chain inverts it's properties.

Figure 8

Response to a Huygens source $(1,1)$ with ${\left(k^3\alpha \right)}^{-1}=-400$ located near the termination of a finite chain. There is no reflection from the chain end.

Figure 9

The integration contours for the IZT. Poles are marked by $\times$, branch points by $•$, and branch cuts by wiggly lines. Singularities inside (outside) the unit circle contribute to $n\ge 0 \left(n<0\right)$.