Asymmetric Metal-Dielectric Metacylinders and Their Potential Applications From Engineering Scattering Patterns to Spatial Optical Signal Processing

We propose a bianisotropic hybrid metal-dielectric structure comprising dielectric and metallic cylindrical wedges wherein the composite metacylinder enables advanced control of electric, magnetic, and magnetoelectric resonances. We establish a theoretical framework in which the electromagnetic response of this meta-atom is described through the electric and magnetic multipole moments. The complete dynamic polarizability tensor, expressed in a compact form, is derived as a function of the Mie-scattering coefficients. Further, the constitutive parameters—determined analytically—illustrate the tunability of the structure’s frequency and strength of resonances in light of its high degree of geometric freedom. Flexibility in the design makes the proposed metacylinder a viable candidate for various applications in the microscopic (single meta-atom) and macroscopic (metasurface) levels. We show that the highly versatile bianisotropic meta-atom is amenable to being designed for the desired electromagnetic response, such as electric dipole-free and zero or near-zero (backward and forward) scattering at the microscopic level. In addition, we show that the azimuthal asymmetry gives rise to normal polarizability components, which are vital elements in synthesizing asymmetric optical transfer function at the macroscopic level. We conduct a precise inspection, from the microscopic to the macroscopic level, of the metasurface synthesis for emphasizing on the role of normal polarizability components for spatial optical signal processing. It is shown that this simple two-dimensional asymmetric meta-atom can perform first-order differentiation and edge detection at normal illumination. The results reported herein contribute toward improving the physical understanding of wave interaction with artificial materials composed of asymmetric elongated metal-dielectric inclusions and open the potential of its application in spatial signal and image processing.

Figure 1

(a) Schematic sketch of the proposed bianisotropic meta-atom and its microscopic and macroscopic-level applications. (b) two-dimensional (2D) view, and (c) three-dimensional (3D) view of meta-atom orientation.

Figure 2

(a) Schematic showing a metal-dielectric metacylinder (${ϵ}_r=18$) with a wedge angle of $\pi$, which is excited by TM-polarized waves propagating on the -$x$ direction. Far-field scattering pattern from a mentioned meta-atom with different radius (b) 600 nm, (c) 800 nm, and (d) $1\mu \mathrm{m}$ using Mie scattering, full-wave simulation, and excited multipole moments.

Figure 3

Polarizability tensor extraction setup based on the standing-wave method introduced in Refs. [66, 67]. In each setup, we can calculate the (a) ${\alpha }_{zz}^{ee}$, ${\alpha }_{yz}^{me}$, ${\alpha }_{zy}^{em}$, ${\alpha }_{yy}^{mm}$, ${\alpha }_{xy}^{mm}$; (b) ${\alpha }_{yy}^{ee}$, ${\alpha }_{xy}^{ee}$, ${\alpha }_{zy}^{me}$, ${\alpha }_{yz}^{em}$, ${\alpha }_{xz}^{em}$, ${\alpha }_{zz}^{mm}$; (c) ${\alpha }_{xx}^{ee}$, ${\alpha }_{yx}^{ee}$, ${\alpha }_{zx}^{me}$; and (d) ${\alpha }_{xz}^{me}$, ${\alpha }_{zx}^{em}$, ${\alpha }_{xx}^{mm}$, ${\alpha }_{yx}^{mm}$ individual polarizability components.

Figure 4

Static and dynamic transverse magnetic polarizability, and longitudinal electric polarizability of a dielectric cylinder (${ϵ}_r=18$) excited by a TM-polarized incident wave. We vary here the electrical size $k_0{r}_0$. The star-shaped markets represent a validation based on Refs. [32, 33]. The plot shows the real parts of the polarizability components.

Figure 5

Real (solid lines) and imaginary parts (dashed lines) of (a) electric, (b),(c) magnetoelectric, and (d) magnetic normalized dipole polarizability of the asymmetric metal-dielectric metacylinder (${\epsilon }_r=18$), which is excited by the TM-polarized incident wave for variant values of $\beta$ with respect to radius.

Figure 6

Real (solid lines) and imaginary parts (dashed lines) of (a) electric, (b),(c) magnetoelectric, and (d) magnetic normalized dipole polarizability of the asymmetric metal-dielectric metacylinder (${\epsilon }_r=18$), which is excited by the TE-polarized incident wave for variant values of $\beta$ with respect to radius.

Figure 7

(a) Magnitude of electric polarization $P_z$ and transverse magnetic polarization $M_t$ with respect to radius and 3D scattering pattern for optimized electric dipole-free meta-atom. (b) Total extinction cross section (${\sigma }_{\mathrm{ext}}$) and forward scattering [${\sigma }_{\phi }(0)$] with respect to radius and polar scattering pattern of the optimized meta-atom for near-zero forward scattering and (c) backward scattering.

Figure 8

(a) Array of metal-dielectric metacylinders (include silicon and gold [81] materials ) as the metasurface processor. SWT and SWR are spatial wave transmitter and receiver, respectively. (b) Solid line: the amplitude and phase of synthesized OTF. Dashed line: the ideal OTF for the first-order differentiation operation. Simulation parameters: ${\lambda }_0=4.16\mu \mathrm{m}$, $r_0=0.9\mu \mathrm{m}$, $\beta ={60}^{\circ }\alpha ={150}^{\circ }$, and $d_x=2.5\mu \mathrm{m}$.

Figure 9

(a),(c) Gaussian-shape incident-field profile with (b),(e) the transmitted derivative-field profile. (d) The exact derivative signals are also presented for the sake of comparison.

Figure 10

Spatial signal processing by exploiting the proposed metasurface processor. (a) Complex input signal and normalized output and ideal case. (b) Input images and (c) edge-detected images when metasurface differentiator differentiates the input image along $x$ direction. For the 2D image, differentiation is performed line by line along the $x$ axis.