Reinterpreting the magnetoelectric coupling of polarizability tensors of infinite cylinders using symmetry: A simple TM/TE view

Recently, Strickland et al. [Phys. Rev. B 91, 085104 (2015)] retrieved dynamic polarizabilities of infinitely long wires at oblique incidence, reporting nonzero magnetoelectric coupling, seemingly defying existing theorems which forbid this in centrosymmetric scatterers. We reconcile this finding with existing symmetry restrictions on microscopic polarizabilities using a property of line dipoles. This motivates a reformulation of cylinder polarizability, yielding diagonal tensors that decompose the response into TM and TE contributions, simplifying subsequent treatment by homogenization theories. A transformation is derived between the formulation of Strickland et al. and our reformulation, allowing magnetoelectric coupling to be identified as the contrast between TM and TE responses, and enabling simple geometric insights into all its scaling and symmetry properties.

Figure 1

Various components of polarizability, indicated by the legends, as a function of wave number $k$ and cylinder radius $a$. The geometry is a dielectric cylinder $\epsilon =40$ in vacuum excited at polar angle of incidence $\theta =\pi /4$. Shown are (a) magnetoelectric coupling, (b) electric polarizabilities, and (c) magnetic polarizabilities, where (a) is calculated using (15) and (b) and (c) using (17). TM and TE polarizabilities are respectively plotted in blue and red, while real and imaginary parts are respectively indicated by solid and dashed lines.

Figure 2

As in Fig. 1, but shows TM and TE polarizabilities at differing polar incidence angles $\theta =\pi /12$ (solid blue), $\theta =\pi /4$ (dashed-dotted red), and $\theta =5\pi /12$ (dotted black). At near-normal incidence, the first resonance manifests primarily in the TE response and the second resonance in the TM. At oblique incidence, this continues to be true, though to a lesser extent for the first resonance.

Figure 3

Three examples of incident plane waves demonstrating various properties of the magnetoelectric coupling, where $\vartheta$ indicates inclination above the $x\text{−}y$ plane. (a) Changing the angle of incidence $\vartheta \to -\vartheta$, or equivalently $\beta \to -\beta$, also changes the sign of the induced moment $p_x$. This originates from the change in sign of $E_x$, while $H_y$ and $E_z$ remain unchanged. (b) Two counterpropagating waves are incident, arranged so that $E_x$ and $E_z$ fields cancel while $H_y$ fields constructively interfere. No electric dipole moments $\mathit{p}$ are induced. (c) Switching to isometric view, two incoming plane waves of both TM and TE polarization are shown, with identical $\vartheta$ but orthogonal azimuthal angles $\varphi$. Magnitudes are chosen such that $E_x$ fields cancel, but $H_y$ fields do not. A $p_x$ moment is nevertheless induced. The only other nonzero fields are $E_z$ and $H_z$.