Metallic Helix Array as a Broadband Wave Plate

This study demonstrates theoretically and experimentally that a metallic helix array can operate as a highly transparent broadband wave plate in propagation directions perpendicular to the axis of helices. The functionality arises from a special property of the helix array, namely, that two branches of elliptically right-handed and left-handed polarized states are nearly rigidly shifted in frequency and their dispersions are controlled by different mechanisms that can be independently tuned by structural parameters.

Figure 1

A Slab of helices as wave plate for transversely propagating waves. (a) The schematic configuration of transverse propagation through helices, the helices are arranged in a square array; (b) the photo of the 7-layered sample and the corresponding dispersion diagram $\omega (k_x,k_y=k_z=0)$. The geometric parameters are the pitch $p=4\mathrm{mm}$, helix radius $a=3\mathrm{mm}$, wire diameter $\delta =0.6\mathrm{mm}$, the lattice constant $d=11\mathrm{mm}$; and the comparative results by (c) varying pitch only to $p=1\mathrm{mm}$, and (d) varying helix radius only to $a=1\mathrm{mm}$, all other parameters are fixed to their respective values in Fig. 1b.

Figure 2

Polarization characters of eigenmode. Axial ratio $AR=⟨E_y⟩/⟨i{E}_z⟩$, and longitudinal ratios $|⟨E_x⟩|/|⟨E_y⟩|$, $|⟨E_x⟩|/|⟨E_z⟩|$ are calculated for (a), (b) $B_R$, and (c), (d) $B_L$ modes. Black squares for $\mathrm{Re}(AR)$, red circles for $\mathrm{Im}(AR)$, green up-triangles for $|⟨E_x⟩|/|⟨E_y⟩|$, and blue down-triangles for $|⟨E_x⟩|/|⟨E_z⟩|$. $⟨···⟩$ denotes the spatial average in a unit cell.

Figure 3

Equifrequency surfaces of the BR and BL branches in Fig. 1b.

Figure 4

Polarization transformation. Axial ratio $ar$ of the transmitted waves as a function of the polarization angle of linearly polarized incidence when the slab thickness satisfies to $\Delta k·L=\pi$ and the ellipticity of the eigenstates is at (a) $\alpha /\beta =\sqrt{2}+1$ or (b) $\alpha /\beta =3$. The ratio $ar$ is defined as $ar=E_y/i{E}_z$, similar to the axial ratio for eigenstates illustrated in Fig. 2.

Figure 5

Transmission spectra of helix samples as wave plate. Transmission spectra are calculated and measured for three samples with 7, 14, and 21 periods along the propagating direction ($x$ direction). (a) and (b), (g) and (h) for 7-period sample, (c) and (d), (e) and (f) for 14-, 21-period samples, respectively. The first and the second subscripts, $i$, and $j$, of the transmission spectra $T_{i,j}$ refer to the polarized state of the incident and the transmitted waves, respectively. The letter $Y$ or $Z$ denotes a linear polarization along $y$ or $z$ direction. The symbol $\pi /4$ or $-\pi /4$ denotes linear polarization with a polarization angle at $\pi /4$ or $-\pi /4$ about $y$ axis. The transmission spectra are normalized to the total power of the incidence.