Interference-induced asymmetric transmission through a monolayer of anisotropic chiral metamolecules

We show that asymmetric transmission for linear polarizations can be easily achieved by a monolayer of anisotropic chiral metamolecules through the constructive and destructive interferences between the contributions from anisotropy and chirality. Our analysis is based on the interaction of electromagnetic waves with the constituent electric and magnetic dipoles of the metamaterials, and an effective medium formulation. In addition, asymmetric transmission in amplitude can be effectively controlled by the interference between spectrally detuned resonances. Our findings shed light on the design of metamaterials for achieving strong asymmetric transmission.

Figure 1

(a) A chiral structure can be modeled as coupled electric and magnetic dipoles, forming an angle of θ and ϕ, respectively, with the $x$ axis. (b) Schematic of a chiral SRR made of gold, with the geometric parameters indicated in the figure. (c) The transmission spectra $t_{xx}$ (black) and $t_{yx}$${}^{+}$ (blue), and $t_{yx}$${}^{-}$ (red) for a metamaterial consisting of an array of chiral SRRs. (d) The phase of transmission for $t_{yx}$${}^{+}$ (blue) and $t_{yx}$${}^{-}$ (red), and their difference (green). The inset shows a top view of chiral SRR. The structure is arranged periodically with equal periods of 30 μm in both directions.

Figure 2

(a), (b) Schematics of the metamaterial unit cell consisting of an achiral SRR (R2). The gap of the achiral SRR is filled with a material with dielectric constant ε $=$ 4. (c) The transmission spectrum $t_{xx}$ of the achiral metamaterial. The dashed line indicates the resonance frequency of the chiral resonator as in Fig. 1c. In the simulation, the unit cell is the same as that shown in Fig. 1b.

Figure 3

(a) Schematic of a metamaterial unit cell consisting of both the chiral and achiral SRRs. The size of the unit cell is 60 μm × 30 μm. The orientation of the achiral SRR is indicated by the angle ${\theta }_2$ formed between the base metal strips and the $y$ axis. (b)–(d) Transmission spectra for $t_{xx}$ (black), $t_{yx}$${}^{+}$ (blue), and t${}_{yx}$${}^{-}$ (red) at different orientations of the achiral element ${\theta }_2$ $=$ 0°, −15°, $+$15°, while the permittivity of the gap material of R2 [blue area in panel (a)] is fixed at ε $=$ 4. (e), (f) Transmission spectra for different gap material permittivities ε $=$ 5.3 and 7, respectively, while the orientation of the achiral element is fixed at ${\theta }_2$ $=$ 15°.

Figure 4

(a) The real and imaginary parts of the anisotropy term (${\varepsilon }_{xy}$ − μ${}_{xy}$). (b) The real and imaginary parts of the chiral term (${\xi }_{xx}$ $+$ ${\xi }_{yy}$). (c), (d) The amplitude and phase of the ratio between $t_{yx}$${}^{+}$ and $t_{yx}$${}^{-}$ calculated by simulation (black) and by Eq. (7) (red).