High-efficiency tunable circular asymmetric transmission using dielectric metasurface integrated with graphene sheet

Huan Jiang; Wenyu Zhao; Yongyuan Jiang

doi:10.1364/OE.25.019732

1. Introduction

Asymmetric transmission phenomenon, like unidirectional conduction of diode, was discovered in planar chiral metamaterial first [1], and it is found that AT shows a circular conversion dichroism effect, i.e. different cross-polarization transmission coefficients. This AT behavior is quite distinct from 3D chiral response associated with different co-polarization transmission coefficients [2, 3]. Subsequently, AT has quickly become a topic of research interest as its promising to be used in polarization devices, such as rotators, polarization transformers, diode-like devices, polarizers and isolators [4, 5]. The effort to create artificial metamaterials with AT was focused on different types of planar metamaterials [6–8], but these earlier proposed single-layered chiral metamaterials seriously suffer from low efficiency. Later, helical metamaterials [9, 10], achiral twisted bi-layer [11–13], and multi-layered structures [14–18] have been proposed to enhance AT efficiency. In spite of gaining higher asymmetric parameters, most reported structures composed of complex metallic components face the challenges of large absorptive losses and costly fabrication. However, dielectric materials without intrinsic Ohmic losses could further enhance AT efficiency and simultaneously simplify the shapes of unit cells due to their Mie-type electric dipole resonance (EDR) and magnetic dipole resonance (MDR) [19]. Moreover, spatial symmetry breaking caused by oblique illumination will also extremely simplify the shape of nanoparticles compared with the one in intrinsic chiral metamaterials [20, 21]. Therefore, simple-shape dielectric metasurface based on extrinsic chirality becomes a good candidate for high-efficiency AT.

On the other hand, due to the demand of tunability in laser beam steering, axial scan focusing and tunable polarization control, some tunable devices based on flexible substrates [22], phase-changed materials [23], the control of incident angles [24], and graphene [25, 26] have been proposed. Among these tunable devices, only a few frequency-tunable AT effects have been reported with asymmetric parameters no more than 0.25 [25, 26]. In this paper, we achieve high-efficiency (0.92) and dynamically tunable AT in the mid-infrared (MIR) region by incorporating simple-shape dielectric array with a graphene sheet. The high AT efficiency, i.e. one near-unity cross-polarization transmission and the other near-zero cross-polarization transmission, originates from the difference in spectral superposition of EDRs and MDRs. Such a propagation direction-dependent polarization sensitive transmission effect results from extrinsic chirality induced by oblique illumination. In addition, the working waveband of AT is shifted by electrically controlling graphene’s Fermi energy without reoptimizing geometric parameters of structures. The high-efficiency and frequency-tunable AT effect based on simple-shape array is first reported, which provides a novel paradigm for polarization-sensitive devices, sensing, and other potential applications.

2. Design and simulations

To gain high-efficiency tunable AT with simple-shape metasurface, we first excite extrinsic chirality in symmetric array using oblique incident CPL. As a geometrical definition, chirality can be obtained from achiral structures simply by tilting their symmetry axis out of incident plane to yield the three dimensional asymmetry, which is so-called extrinsic chirality [3, 27]. To satisfy the extrinsically chiral excitation criteria, we break the mirror symmetry and C₂ rotational symmetry of strip array by considering wavevector k direction of propagation neither parallel nor perpendicular to mirror planes or rotational axes. As shown in Fig. 1(a), our array is located in x-y plane and incident light propagating in the direction with θ representing the angle of k off -z axis and with the angle φ off x axis. In this way, the polarization components of obliquely incident CPL are not along x or y direction, instead, the polarization fields in x and y directions are contributed by the projections of these two polarization components. The incident angles $θ = \pm 45 °, φ = \pm 45 °$ assures the maximum projections of incident electric field in x and y directions simultaneously, which means the largest symmetry breaking. If the normally incident CPL is decomposed into two polarization components along x and y directions with 90 degree phase delay, the transmission coefficients of x- and y-polarized incident light ( $t_{x}$ and $t_{y}$ ) are related to the electric and magnetic surface polarizabilities [28],

\begin{array}{l} t_{x} = \frac{1 - {(k_{0} /2)}^{2} α_{e x} α_{m y}}{1 + {(k_{0} /2)}^{2} α_{e x} α_{m y} - i k_{0} (α_{m y} - α_{e x}) /2}, \\ t_{y} = \frac{1 - {(k_{0} /2)}^{2} α_{m x} α_{e y}}{1 + {(k_{0} /2)}^{2} α_{m x} α_{e y} + i k_{0} (α_{e y} - α_{m x}) /2} . \end{array}

where

k_{0}

is the wavenumber in free space, the transmission of x- and y-polarized light can be controlled independently by constructing the surface electric and magnetic polarizabilities (

α_{e x}

,

α_{e y}

,

α_{m x}

and

α_{m y}

). In principle, both unit and zero circular polarization transmission can be achieved by constructing the asymmetric structure with different phase delay for CPL. For obliquely incident CPL, if the two orthogonal polarization components are regarded as normally incident light after coordinate transformation, the strip array becomes asymmetric, which means there are more freedom to control polarization transmissions. Thus we optimize microstructure by CST Microwave Studio as shown in Fig. 2(b), where a = 9 μm and b = 4.05 μm. The period of the silicon array is p = 14 μm in x and y directions, and the thicknesses of strips and substrate are 7.1 μm and 0.5 μm, respectively. Refractive index of silicon is 3.45 in MIR and substrate is assumed to be FR-4 (n = 2.04) [29, 30]. The simulation is based on the frequency-domain finite integration technology, using a unit cell boundary coupled with Floquet ports. Meanwhile, a Finite Difference Time Domain (FDTD) method software, FDTD Solutions from Lumerical, Inc. was also used to monitor field distributions.

Fig. 1 (a) The scheme of optimize silicon nanostrip array placed on FR-4 substrate. (b) The top view of a unit cell, where a = 9 μm, b = 4.05 μm and p = 14 μm in both x and y directions.

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Fig. 2 (a), (b) Transmission coefficients of CPL with $θ = \pm 45 ° φ = \pm 45 °$ incidences, $t_{- -}$ , $t_{+ -}$ , $t_{- +}$ , $t_{+ +}$ represent left-to-left, left-to-right, right-to-left, right-to-right transmitted circularly polarized light, respectively. (c), (d) Transmission spectra with $θ = \pm 45 °, φ = \pm 45 °$ incidences, (e), (f) Asymmetry parameters spectra with $θ = \pm 45 °, φ = \pm 45 °$ incidences.

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Next, we combine graphene sheet with silicon array to gain the frequency-tunability. Graphene, an atom-thick sheet with two-dimensionally arranged carbon atoms, is regarded as an anisotropic material with different conductivities in- and out-of-plane [31, 32]. The in-plane conductivity is calculated using Random Phase Approximation [33, 34],

σ (ω) = \frac{2 e^{2} ω_{T}}{π ℏ} \frac{i}{ω + i τ^{- 1}} \log [2 \cos h (\frac{ω_{F}}{2 ω_{T}})] + \frac{e^{2}}{4 ℏ} [H (\frac{ω}{2}) + i \frac{2 ω}{π} \int_{0}^{\infty} \frac{H (\frac{ω'}{2}) - H (\frac{ω}{2})}{ω^{2} - ω'^{2}} d ω']

where H (ω) = sinh (ω/ω_T)/[cosh (ω_F/ω_T) + cosh (ω/ω_T)],

ω_{F} = E_{F} / ℏ

,

ω_{T} = κ_{B} T / ℏ

, e and

κ_{B}

are the charge of an electron and Boltzmann constant, and

ℏ = h/2π

represents the reduced Planck constant. According to Eq. (2), graphene’s in-plane conductivity depends on the angular frequency of incident light ω, temperature T, Fermi energy

E_{F}

and relaxation time τ. In our simulation, we assume T = 300 K, τ = 1 ps and Fermi energy

E_{F}

ranges from 0 eV to 0.6 eV, which requires about 100 V bias voltage in experiment. Graphene is modeled as an anisotropic material with out-of-plane (z direction) dielectric constant 2.25 and in-plane (x-y plane) permittivity derived from ε(ω) = 1 + iσ (ω)/ωε₀t [35], where ε₀ represents the permittivity in the vacuum, t = 1 nm is the thickness of graphene.

3. Results and discussion

Figure 2 shows the transmission coefficient spectra of silicon array under the excitations of obliquely incident CPL, where “→” and “←” denote incident angles $θ = 45 °, φ = 45 °$ and $θ = - 45 °, φ = - 45 °$ , respectively. Right-to-left polarization transmission coefficient ( ${\vec{t}}_{- +}$ ) is much higher than the left-to-right one ( ${\vec{t}}_{+ -}$ ) near 12.68 THz, while the left-to-right transmission coefficient ( ${\vec{t}}_{+ -}$ ) is higher than the right-to-left one ( ${\vec{t}}_{- +}$ ) near 14.32 THz in Fig. 2(a). Co-polarization transmission coefficients spectra ( ${\vec{t}}_{- -}$ , ${\vec{t}}_{+ +}$ ) marked by pink and black lines are also different especially near 14.32 THz, which denotes the existence of circular dichroism (CD). The appearance of CD due to symmetry breaking brings more applications (discussed below). The indexes (“ $+$ ” and “ $-$ ”) of transmission efficient in Fig. 2(b) are exchanged each other compared with Fig. 2(a), this is because the change of incident angle induces the exchange of two enantiomeric arrangements.

For the transmitted intensity spectra of $T_{-} = {| t_{- -} |}^{2} + {| t_{+ -} |}^{2}$ and $T_{+} = {| t_{+ +} |}^{2} + {| t_{- +} |}^{2}$ , two obvious peaks and valleys are observed at 12.68 THz and 14.32 THz in Fig. 2(c). The transmission of RCP light reaches 0.93 at 12.68 THz, which originates from artificially constructed Huygens surface characterized by simultaneous excitations of strong EDR and MDR. The electric field components of strong EDR and MDR with orthogonal electric and magnetic polarizabilities are in the same direction, thus the constructive superposition of electric field components from two strong resonances and incident wave leads to a near-unity RCP transmission. While the transmission of LCP light is near zero at the same spectral position because of the deconstructive superposition of electric field components from two weak resonances and the incident wave. Differently, LCP transmission is much higher than RCP transmission at 14.32 THz owing to the variation in excitations of resonance modes, which means opposite polarization-state selectivity in the other waveband. In addition, the spectra of LCP transmission backwards ( $θ = 45 °, φ = 45 °$ ) in Fig. 2(d) is equal to that of RCP transmission forwards ( $θ = - 45 °, φ = - 45 °$ ) in Fig. 2(d). This is because AT phenomenon originates from the fact that an incident CPL see different handedness for two opposite propagation directions.

To estimate AT efficiency, we calculate the spectra of asymmetry parameters defined as $Δ_{cir}^{+} = T_{+} - T_{-} = ({| t_{+ +} |}^{2} + {| t_{- +} |}^{2}) - ({| t_{- -} |}^{2} + {| t_{+ -} |}^{2}) = - Δ_{cir}^{-}$ [7] in Fig. 2(e). The maximum asymmetry parameter of RCP light reaches 0.92 at 12.68 THz, which represents a significant improvement in efficiency and simple-shape configuration. For the case of opposite-direction incidence, the sign of asymmetry parameter for both LCP and RCP are changed upon reversal of propagation direction. As expected, the asymmetry parameter of RCP with the incident _{angle of $θ = - 45 °, φ = - 45 °$} in Fig. 2(f) equals to that of LCP one with $θ = 45 °, φ = 45 °$ incidence in Fig. 2(e). The sensitivity to incident direction at dual bands means two kinds of selectivities of polarization state at each waveband by controlling incident directions.

In order to verify AT phenomenon visually, we plot the distributions of electric field magnitude in the middle of nanoparticles at y-z and x-z planes under the excitations of RCP light at 12.68 THz. Figures 3(a) and 3(b) show the electric field distributions under RCP light _{incidence backwards ( $θ = 45 °, φ = 45 °$}). The field below and above periodic array (marked by black line frame) are homogeneous, which means RCP light passes through freely. However, there are obvious differences in field distributions below and above the black line marked _{metasurface when RCP light illuminates forwards ( $θ = - 45 °, φ = - 45 °$}), which confirms that RCP light cannot propagate along the opposite direction as shown in Figs. 3(c) and 3(d).

Fig. 3 (a), (b), (c), (d) The distributions for electric field magnitude driven by RCP light backwards and forwards, respectively (by FDTD). $(a')$ , $(b')$ , $(c')$ , $(d')$ The field vectors distributions of a unit cell by CST, the black dashed line frame marks a strip in one unit cell.

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To analyze the contributions of different resonance modes to the giant AT effect, we give out the electric field vector distributions of a unit cell as magnified red dashed line frame marked. The electric field vectors flow from top-left to bottom-right as shown in Fig. 3 $(a')$ mimicking the radiation pattern of electric dipole in far field, which means strong EDR dominates in y-z plane. The EDR contributes to the electric polarizability components in y and -z directions. While the distribution of electric field vectors in Fig. 3 $(b')$ shows the cross section of a ring-like electric current in x-z plane, which denotes strong MDR with magnetic polarizability components in z and y directions. The components of electric polarizabilities in y and -z direction and the components of magnetic polarizabilities in z and y direction constitute a vectorial Huygens metasurface, which is characterized by high transmission [36, 37]. In other words, the simultaneous excitations of two-set components of EDR and MDR lead to near-unity RCP transmission in Fig. 2(c). Because the electric fields scattered by y-direction electric polarizability and z-direction magnetic polarizability are in the same direction (y direction), similarly, the electric fields scattered by y-direction electric polarizability and z-direction magnetic polarizability are in the same direction (-z direction) [37]. Therefore, the amplitude of the vectorial sum of two-direction electric fields and incident field is near-unity. However, the field vector distribution in Fig. 3 $(c')$ characterized by ring-like electric current in y-z plane denotes a weak MDR mode with small magnetic polarizability in x direction. The distribution of field vectors in top-right region outside the unit structure in Fig. 3 $(d')$ represent a weak electric resonance with a small electric polarizability in z direction. The electric field components from incident wave and two weak resonances are counteracted leading to near-zero RCP transmission in Fig. 2(d). Noted the selectively excited resonance modes of RCP forwards described in Figs. 3 $(c')$ and 3 $(d')$ also represents the resonance modes of LCP excitations backwards, which is also responsible for the near-zero LCP transmission in Fig. 2(c). Generally, the constructive and deconstructive superpositions of electric field components from incident wave and different resonance modes result in a significant difference in the transmission of RCP and LCP waves.

After discussing the giant AT effect, we continue to analyze the frequency-tunability by integrating graphene sheet to the former silicon array. As shown in Fig. 4(a), we place graphene sheet on substrate and fabricate nanostrip array on graphene. Asymmetry parameter spectra of this structure are plotted in Fig. 4(b), which exhibits a clear blue-shift when Fermi energy ranges from 0 eV to 0.6 eV. The asymmetry parameter above 0.7 in the tunable spectra ranges from 12.52 THz to 13.13 THz as dash area marked, which makes great progress in efficiency compared with the tunable AT in [3, 27]. The large blue shift (1100 nm) results from the changes in graphene’s conductivity induced by the rises of Fermi energies. Different conductivities bring different disturbed fields. These fields affect EDRs and MDRs at various degree when the dielectric microstructures are fabricated close to graphene sheet. Concretely, the changes in resonant frequency can be interpreted using perturbation theory as [38, 39]

\frac{Δ ω}{ω_{0}} = - \frac{\underset{V}{∭} d V [(Δ \overset{\leftrightarrow}{μ} \cdot {\vec{H}}_{0}) \cdot {\vec{H}}_{0}^{*} + (Δ \overset{\leftrightarrow}{ε} \cdot {\vec{E}}_{0}) \cdot {\vec{E}}_{0}^{*}]}{\underset{V}{∭} d V (μ \cdot {\vec{H}}_{0} \cdot {\vec{H}}_{0}^{*} + ε \cdot {\vec{E}}_{0} \cdot {\vec{E}}_{0}^{*})} = - \frac{Δ W_{m} + Δ W_{e}}{W_{m} + W_{e}}

where

ω_{0}

is resonant angular frequency,

{\vec{E}}_{0}

and

{\vec{H}}_{0}

are unperturbed electric and magnetic fields whose complex conjugates are represented by

{\vec{E}}_{0}^{*}

and

{\vec{H}}_{0}^{*}

. Moreover,

Δ \overset{\leftrightarrow}{ε}

and

Δ \overset{\leftrightarrow}{μ}

are the changes in dielectric permittivity and magnetic permeability regarded as the material perturbation,

W_{e}

and

W_{m}

are the total electric and magnetic energies. The value of ∆ω relies on not only the material perturbation caused by graphene

Δ \overset{\leftrightarrow}{ε}

, but also the local enhancement of optical fields generated by dielectric array

{\vec{E}}_{0}

. The change in resonant frequency (∆ω) is large when a perturbation encounter with strong EDR and MDR simultaneously, because the enhanced fields will make great contribution in frequency-tunability as described in Eq. (3). Thus, we obtain frequency-tunability of giant AT by dynamically adjusting graphene’s Fermi energy.

Fig. 4 (a) A diagram of silicon-graphene hybrid metasurface with frequency-tunable AT effects, (b) Solid and dashed lines represent the ATs of RCP and LCP light with different Fermi energies.

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4. Application in polarization devices: sensor and circular polarizer

The proposed AT microstructure possessing the merits of high efficiency, simple-shape inclusions and frequency-tunability provide a novel paradigm to achieve tunable polarization devices, such as polarization sensor and circular polarizer. Figure 5(a) shows polarization transmission spectra of silicon array from 12.33 THz to 14.50 THz, which is defined as $T_{i n}^{+} = ({| t_{+ +} |}^{2} + {| t_{- +} |}^{2})$ and $T_{i n}^{-} = ({| t_{+ -} |}^{2} + {| t_{- -} |}^{2})$ . Such a metasurface with giant AT can be used to distinguish the polarization of incident waves as a polarization sensor. In addition, CD (different $t_{- -}$ and $t_{+ +}$ ) together with AT (different $t_{- +}$ and $t_{+ -}$ ) makes $T_{i n}^{\pm}$ different from $T_{o u t}^{\mp}$ , which leads to another application, a circular polarizer. Figure 5(b) gives out the polarization transmission spectra of $T_{o u t}^{+} = ({| t_{+ +} |}^{2} + {| t_{+ -} |}^{2})$ and $T_{o u t}^{-} = ({| t_{- +} |}^{2} + {| t_{- -} |}^{2})$ , whose definition of transmission is different from the polarization transmission in Fig. 5(a). So the transmission peak at 14.23 THz (0.93) becomes higher than that at 12.75 THz, which means the polarizer can gain LCP or RCP light efficiently at both wavebands by controlling incident angles. Furthermore, the frequency-tunability based on graphene offers our polarization sensor and circular polarizer the capacity to serve as dynamically tunable polarization devices.

Fig. 5 (a) Transmission spectra for sensing polarization state of incident light as a polarization sensor, (b) Transmission spectra for generating desired CPL as a circular polarizer.

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5. Summary and Conclusion

In conclusion, a high-efficiency and frequency-tunable AT based on simple-shape inclusions operating in MIR is demonstrated numerically in this paper. The AT effect originates from extrinsic chirality induced by oblique illumination in a symmetric array system, which not only provides flexible way to overcome complex chiral structures, but also shows even stronger AT than the intrinsic one. Specifically, our achiral strip array passes 93% RCP/LCP light and nearly blocks all LCP/RCP light with the incident angle of $θ = \pm 45 °, φ = \pm 45 °$ at 12.68 THz. In addition, the working wavebands of AT can be shifted by adjusting graphene’s Fermi energy, which offers a certain metasurface more functions without refabricating structures. In general, the realization of tunable circular AT effect in MIR makes great progress in efficiency and simple-shape construction, which facilitates many significant applications in polarization devices.

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High-efficiency tunable circular asymmetric transmission using dielectric metasurface integrated with graphene sheet

Abstract

1. Introduction

2. Design and simulations

3. Results and discussion

4. Application in polarization devices: sensor and circular polarizer

5. Summary and Conclusion

References and links

Cited By

Figures (5)

Equations (3)

Optics Express