Dispersion management of anisotropic metamirror for super-octave bandwidth polarization conversion

Abstract

Dispersion engineering of metamaterials is critical yet not fully released in applications where broadband and multispectral responses are desirable. Here we propose a strategy to circumvent the bandwidth limitation of metamaterials by implementing two-dimensional dispersion engineering in the meta-atoms. Lorentzian resonances are exploited as building blocks in both dimensions of the dedicatedly designed meta-atoms to construct the expected dispersion. We validated this strategy by designing and fabricating an anisotropic metamirror, which can accomplish achromatic polarization transformation in 4-octave bandwidth (two times of previous broadband converters). This work not only paves the way for broadband metamaterials design but also inspire potential applications of dispersion management in nano-photonics.

Figure 1. Principle of the dispersion engineering for polarization conversion.

(a) Concept diagram of proposed metamirror, which is composed of a metasurface, dielectric spacer and metallic ground plane. To make the analysis as general as possible and suitable for both isotropic and anisotropic metamaterials, we take the metasurface as a thin impedance sheet without special structure, which is normally illuminated with a linear polarization. The amplitude of incident E field is denoted as A while the total reflection coefficient of the metamirror is denoted as S_ii. J is the current flowing in the metasurface. (b) Unit cell of adopted metasurface, which is constructed by two split ring resonators sitting back to back positioned on a thin substrate. (c) Perspective view of proposed metamirror, which is able to convert the LCP waves achromatically to the RCP after reflection.

Figure 2. Optimal impedances for achromatic polarization conversion.

(a) The given impedance Z_x (red solid line) and derived optimal impedance Z_y for 1/4 wave plate (blue dash line), 1/2 wave plate (blue solid line), and 3/4 wave plate (blue dot line). The real part is zero since no material loss is considered. The region above zero is inductive and the region below zero is capacitive. (b) The given ϕ_xx and derived optimal ϕ_yy for achromatic 1/4, 1/2, and 3/4 wave plates.

Figure 3. Numerical simulation and experimental verification.

(a) Simulated polarization conversion ratio from LCP to RCP (blue line) and measured polarization conversion ratio from x- to y-polarization (red asterisk). (b) Photograph of the fabricated metasurface. (c) Simulated reflection amplitude of x- and y-polarization. (d) Simulated reflection phase of x- (blue solid line) and y-polarization (blue dash line), which sharing almost the same constant gradient between 3.5 GHz and 16.5 GHz. There are five intersection points between the simulated phase difference and constant π, which corresponds to the five conversion extrema in (a). In the green shaded area, the phase difference changes severely from π to 0 or 2π, corresponding to the sharp band edges.

Figure 4. Anisotropic impedances sheet in macroscopic model and microscopic picture.

(a) Effective impedance Z_x retrieved from effective material theory (macroscopic model) and electric circuit model (microscopic picture). (b) Effective impedance Z_y retrieved from effective material theory (macroscopic model) and electric circuit model (microscopic picture). Dash line in (b) shows the optimal impedance Z_y for given Z_x. (c) and (d) Effective permittivity of the metasurface ε_x and ε_y retrieved from effective material theory, manifesting Loreantzian dispersion.

Figure 5. Circuit model of the proposed structure under the x- polarization.

(a) Origination of the inductor and capacitor when the electric field is polarized along the x-direction. (b) Equivalent circuit model for the x-polarization. (c) Electric field distributions and (d) volumetric current flows at f₁ = 6.5 GHz (zero point of Z_x). (e) Electric field distributions and (f) volumetric current flows at f₂ = 15 GHz (polar point of Z_x).

Figure 6. Circuit model of the proposed structure under the y-polarization.

(a) Origination of the inductor and capacitor when the electric field is polarized along the y-direction. (b) Equivalent LC circuit model for the y- polarization. (c) Electric field distributions and (d) volumetric current flows at f₃ = 3.5 GHz (zero point of Z_y). (e) Electric field distributions and (f) volumetric current flows at f₄ = 5.3 GHz (polar point of Z_y). (g) Electric field distributions and (h) volumetric current flows at f₅ = 13.8 GHz (zero point of Z_y).