Functionality-switchable terahertz polarization converter based on a graphene-integrated planar metamaterial

Wei Zhang; Jianli Jiang; Jing Yuan; Shuang Liang; Jisong Qian; Jing Shu; Liyong Jiang

doi:10.1364/OSAC.1.000124

1. Introduction

In the electromagnetic spectrum, the typical terahertz band is in the frequency range of 10¹¹–10¹³ Hz, which is located between the edges of far-infrared and microwave bands. Terahertz beam has low radiation, good transmission, perfect directivity and large communication capacity, thus it is of great significance in both civilian and military fields, such as bio-imaging, material component analysis, security check, military target detection and short-range communication [1–4]. As a result, over the past two decades, great efforts have been made by researchers from all over the world to develop the terahertz related sources, modulators and detectors [5–10]. Among them, terahertz polarization converters based on planar metamaterials have drawn extensive attentions and the studies have been concentrated on two main directions. One direction is broadening the working bandwidth of terahertz polarization converters [11–28]. In particular, recent studies have demonstrated that the working bandwidth of terahertz quarter-wave and half-wave plates can be broadened by carefully designing the unit cell of planar metamaterials or using multilayer and hybrid planar metamaterials [11,12,16,21,25,27,28].

The other direction is realizing tunable terahertz polarization converters by integrating the phase-change material or electro-optic material with planar metamaterials [29–36]. For example, Wang et al. [29] used the phase-change material to modulate the working frequency of a quarter-wave plate. When the temperature was increased from 300 K to 400 K, the working frequency was changed from 0.468 THz to 0.502 THz. Zhang et al. [33] used graphene-strip metamaterial to control the working state of a quarter-wave plate. When the chemical potential of graphene is 0 eV, the planar metamaterial does not change the linear polarization state of an incident terahertz beam, while the planar metamaterial works as a quarter-wave plate when the chemical potential of graphene is 0.5 eV. Ji et al. [34] demonstrated a broadband controllable THz quarter-wave plate with double layers of graphene grating and a layer of liquid crystals, where the ‘on’ and ‘off’ states of quarter-wave plate can be controlled by the graphene gratings and the working frequency of quarter-wave plate can be modulated by the liquid crystals. Besides these tunable single-function terahertz polarization converters, functionality-switchable polarization converters have also been reported recently. For instance, Vasić et al. [37] proposed an electrically tunable terahertz polarization converter based on over coupled metal isolator-metal metamaterials infiltrated with liquid crystals and realized a switch from half-wave plate to quarter-wave plate at frequency of 2.32 THz when different external gate voltages were applied. Yu et al. [38] proposed a graphene-wire integrated planar metamaterial model and demonstrated a switch from half-wave plate to quarter-wave plate with a working bandwidth of 0.12 THz.

In the current study, we would like to report a new functionality-switchable terahertz polarization converter from quarter-wave plate to half-wave plate based on a planar metamaterial integrated with a single-layer graphene. In contrast to the phase-change material and liquid crystal, graphene-based polarization converter can be designed more compactly and operated in a safer manner. In contrast to the graphene wires, a graphene sheet is more practical in fabrication and it can work more conveniently and reliably when applying an external gate voltage to change its chemical potential. In addition, we will show that our proposed functionality-switchable polarization converter has improved response in bandwidth and performance simultaneously.

2. Models and methods

Figure 1(a)

Fig. 1 (a) Schematic of the terahertz tunable polarization converter based on a planar metamaterial integrated with a graphene sheet on the hBN/Si/SiO₂/Ag substrate. (b) Unit cell of the planar metamaterial.

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shows the schematic of the terahertz tunable polarization converter. A planar metamaterial is arranged on a graphene/hBN/Si/SiO₂/Ag substrate. The unit cell of the planar metamaterial is composed of an L-shaped gold resonator, as shown in Fig. 1(b). The length and width of each arm of the L pattern are l and w, respectively. The periodical constant is a. A single layer of graphene is used to modulate the function of polarization converter. A single layer of graphene can be treated as an ultra-thin active layer and its conductivity and permittivity can be modulated by changing its chemical potential, which can be controlled on purpose by applying a gate voltage (a static electric field) or by means of chemical doping.

The conductivity of graphene contains the intraband electron-phonon scattering term σ_intra and the interband electron transition term σ_inter, which can be derived from the Kubo formula [39]:

σ (ω, Γ, μ_{c}, T) = σ_{intra} (ω, Γ, μ_{c}, T) + σ_{inter} (ω, Γ, μ_{c}, T),

σ_{intra} (ω, Γ, μ_{c}, T) = \frac{i e^{2} k_{B} T}{π ℏ^{2} (ω + i 2 Γ)} [\frac{μ_{c}}{k_{B} T} + 2 \ln (\exp (\frac{μ_{c}}{k_{B} T}) + 1)],

σ_{inter} (ω, Γ, μ_{c}, T) = \frac{i e^{2}}{4 π ℏ^{2}} ln (\frac{2 | μ_{c} | - ℏ (ω + i 2 Γ)}{2 | μ_{c} | + ℏ (ω + i 2 Γ)}),

where ω is the angular frequency, Γ = 1/2τ (τ is relaxation time) represents scattering rate. The relaxation time and the temperature are assumed to be τ = 2 ps and T = 300 K, respectively [40,41]. μ_c, e, ħ and k_B are the chemical potential, the electron charge, the reduced Plank constant and the Boltzmann constant, respectively. In the terahertz region, graphene behaves like a Drude-type material and the intraband conductivity plays a dominated role since the photon energy

ℏ ω

is far less than E_F. In order to obtain large-scale and high-purity monolayer graphene with a long relaxation time, the graphene sheet can be fabricated by the chemical vapour deposition (CVD) method on hBN substrate. The chemical potential of graphene can be controlled by applying an external gate voltage, which can be described by [32]:

E_{F} = μ_{c} \approx ℏ ν_{f} \sqrt{\frac{π ε_{r} ε_{0} V_{g}}{e t_{s}}},

where

ε_{r}

and

t_{s}

are the dielectric constant and thickness of the insulating layer, respectively.

ε_{0}

is the dielectric constant of vacuum.

ν_{f}

is the Fermi velocity (1.1 × 10⁶ m/s in graphene).

V_{g}

and

e

are external voltage and electron charge, respectively. In our model, in order to achieving a practical external gate voltage, a 3nm-thick hBN insulating layer (

ε_{r}

= 2.95) [42] is used between the graphene sheet and a 5nm-thick silicon conducting layer. In our simulation, we considered a medium-level doped silicon with a conductivity less than 10³ S/m, under which condition, the loss from doped silicon is insignificant and thus the doped silicon can be treated as a dielectric with a fixed refractive index (n = 3.4) [43]. For application purpose, the maximum chemical potential of graphene is limited to be 0.45 eV and the corresponding transverse field is far below the breakdown electric field of the thin hBN layer [44]. The silver mirror used here can also be replaced by a gold mirror. Both of them can work as a high-performance mirror at terahertz region.

At the same time, graphene can be modeled by using a uniaxial anisotropic permittivity. The permittivity tensor contains two in-plane (x-y plane) components and one out-of-plane (z direction) component, which can be described by [45]:

ε_{x x} = ε_{y y} = ε_{r} + i \frac{σ_{intra} (ω, Γ, μ_{c}, T)}{ε_{0} ω t} and ε_{z z} = ε_{r},

where ε₀ is the vacuum permittivity, ε_r is the relative permittivity of background media, and t is the thickness of the graphene sheet.

We employed a commercial three-dimensional finite-difference time-domain (3D-FDTD) software package, “Lumerical FDTD Solutions,” for the simulation of polarization converter. In simulations, a periodic boundary condition was set along both x and y directions and a perfectly matched layer (PML) absorbing boundary condition was used along z direction. The mesh step is 100 nm along all three directions. A single layer of graphene was treated as a 2D material, the thickness of which can be ignored.

3. Results and discussion

3.1 High-performance quarter-wave plate design

We first designed a quarter-wave plate based on the model in Fig. 1(a) by assuming that the chemical potential of graphene is zero. When the planar metamaterial is illuminated by x-polarized plane waves, the horizontal arm of Au L resonator becomes an x resonator along with partial energy transferred to the horizontal arm (y resonator) through near-field scattering. Then, terahertz wave transmitting through the planar metamaterial and underlying layers will be reflected by the bottom silver mirror. At last, scattering waves from top resonators and reflected waves from bottom mirror will superpose in the backward far-field free space to realize a quarter-wave plate function when the strengths of x and y polarization components are the same and their phase difference is equal to odd times of π/2. It should be noted that both near-field scattering from top resonators and reflected waves from bottom mirror can be modulated by the graphene sheet, hBN insulating layer, silicon conducting layer, and SiO₂ spacer. As a result, when graphene is unbiased, the SiO₂ spacer will play a vital role in designing a quarter-wave plate [46,47].

For terahertz application, we employed an optimized L-shape resonator from ref. 46 with ten times enlarged structural parameters, i.e., l = 12.2 μm, w = 1.2 μm, and a = 15.5 μm. The thicknesses of gold pattern and Ag reflector are 0.12 μm and 0.3 μm, respectively. We then scanned the thickness of SiO₂ from 7 μm to 11 μm to find the thickness dependent amplitude ratio and phase difference of x and y polarization components in the far-field reflected waves. As shown in Figs. 2(a) and 2(b)

Fig. 2 (a) and (b) Dependences of the amplitude ratio (a) and phase difference (b) between x and y polarization components in the reflected light on SiO₂’s thickness. (c)-(e) Polarization separated reflection spectra (c), phase difference (d) and the ellipticity (e) at the thickness of 8.94 μm. r_xx and r_yx are reflectivity. Spatial distributions of |E|, E_x, and E_y in x-y [(f)-(h)], x-z [(i)-(k)], and y-z [(l)-(n)] planes at the central frequency of 4.95 THz when the chemical potential of graphene is zero. Sliced position of x-y plane is at the Au/graphene interface and sliced positions of x-z and y-z planes are represented by the dashed lines in (f).

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, when the thickness of SiO₂ is near 9 μm (white dotted line), the amplitude ratio of r_yx/r_xx is close to 1 (yellow area) and the phase difference is near 90 degrees (yellow area). In particular, we found the maximum range of the phase difference equal to 90 degree can be obtained at the thickness of 8.94 μm. More details about the amplitude ratio and phase difference are given by Figs. 2(c) and 2(d), from which we can confirm a quarter-wave plate with an optimal working bandwidth from about 4.80 THz to 5.10 THz. As shown in Fig. 2(e), the linearly polarized incident terahertz beam can be converted into a circularly polarized one, having an ellipticity more than 0.97 within this bandwidth. We calculated the sliced spatial distributions of |E|, E_x, and E_y at the central frequency of 4.95 THz, as shown in Figs. 2(f)–2(n). When the chemical potential of graphene is zero, the electric field is strongly localized in the near field of two arms and the contribution from E_x and E_y is almost uniform in the x-y plane for the quarter-wave plate. It can also be found from the x-z and y-z planes that the resonance mainly occurs at the Au/graphene interface and there is no resonance in the dielectric spacer.

3.2 High-performance functionality-switchable polarization converter

We then studied the effect of graphene’s chemical potential on the working performance of quarter-wave plate. We initially roughly scanned the polarization separated reflection spectra when the chemical potential of graphene is changed from 0.1 eV to 0.45 eV with a step of 0.05 eV. We found that a small chemical potential of 0.1 eV can cause a drastic change in x and y polarization components. When the chemical potential is increased to 0.3 eV [Figs. 3(a)

Fig. 3 (a)-(d) Polarization separated reflection spectra when the chemical potential of graphene is 0.3 eV, 0.45 eV, 0.32 eV, and 0.36 eV, respectively.

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], an apparent reversal of r_yx and r_xx can be observed, which means a half-wave plate can be realized at this chemical potential value. When the chemical potential reaches the maximum value of 0.45 eV [Figs. 3(b)], the reversal response still occurs but the reflectivity of the x polarization component is no longer efficiently suppressed, which means the performance of half-wave plate is not satisfactory at relatively large chemical potential values.

In order to find the acceptable range of chemical potential that can support a half-wave plate with overlapped band to the quarter-wave plate in Fig. 2, we further elaborately scanned the polarization separated reflection spectra when the chemical potential is increased from 0.3 eV to 0.4 eV with a fine step of 0.02 eV. The optimal range of chemical potential for supporting high-performance half-wave plate is found from 0.32 eV [Figs. 3(c)] to 0.36 eV [Figs. 3(d)], where the r_xx keeps almost zero in a broad band. The corresponding external gate voltage is calculated from 45 V to 57 V, which is realistic in experiment. At the same time, it is not hard to find that the effective working frequency band of the half-wave plate is gradually blue shifted as the chemical potential increases. We will explain this blue shift behavior later.

Figures 4(a) and 4(b)

Fig. 4 (a) and (b) Linearity and polarization angle of half-wave plate when the chemical potential is 0.32 eV, 0.34 eV and 0.36 eV. Spatial distributions of |E|, E_x, and E_y in x-y [(c)-(e)], x-z [(f)-(h)], and y-z [(i)-(k)] planes at the central frequency of 4.98 THz when the chemical potential of graphene is 0.34 eV. Sliced position of x-y plane is at the Au/graphene interface and sliced positions of x-z and y-z planes are represented by the dashed lines in (c).

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show the linearity and polarization angle of the half-wave plate under different chemical potentials. Linearity can be used to evaluate the linearly polarized light and it is defined as the axial ratio of the polarization ellipse in the far-field reflection space, i.e., A_long-axis/A_short-axis. At the same time, the polarization conversion rate (PCR) which is defined as PCR = r_yx/(r_yx + r_xx) is usually used to evaluate the performance of a half-wave plate. As shown in Fig. 4(a), when the chemical potential is 0.32 eV, 0.34 eV and 0.36 eV, the corresponding working bandwidth with linearity over 10 (dashed line) for the half-wave plate is 4.40 ~4.90 THz (PCR>98.5%), 4.90 ~5.02 THz (PCR>98%) and 5.02 ~5.10 THz (PCR>97%), respectively. At the same time, as shown in Fig. 4(b), the polarization angle keeps near 90 degrees in a broad band and it is less influenced by the chemical potential. Figures 4(c)–4(k) show the spatial distributions of |E|, E_x, and E_y in x-y, x-z, and y-z planes at the frequency of 4.98 THz when μ_c is 0.34 eV. We can find that the electric field is mainly distributed in the far field of two arms and the contribution from E_y is critical for the half-wave plate. Meanwhile, the resonant energy is mainly localized at the Au/graphene interface and there is no resonance in the dielectric spacer, which is in agreement with the quarter-wave plate case in Fig. 2. As a result, a high-performance terahertz half-wave plate can be demonstrated with a tunable working bandwidth from 4.40 ~5.10 THz, which has fully covered the working bandwidth (4.80 ~5.10 THz) of the quarter-wave plate in Fig. 2(c). In another word, a functionality-switchable polarization converter between quarter-wave and half-wave plates can be realized by tuning the chemical potential of graphene from zero to a proper range.

As shown in Table 1

Table 1. A Comparison Between Our Polarization Converters and Reported Tunable and Functionality-Switchable Wave Plate Designs

View Table

, we compared our design with other recently reported tunable and functionality-switchable wave plate designs. Compared with the tunable wave plate, the functionality-switchable wave designs currently still show clear disadvantage in bandwidth. As compared to the similar models in previous works, our model based on a single layer graphene sheet has shown improved response in bandwidth and performance simultaneously, making it more practical in terahertz applications. However, the reflection efficiency of our model is inferior to the graphene wire model [38] due to higher absorption at the Au/graphene interface.

3.3 Physical mechanism

The physical mechanism of our designed functionality-switchable polarization converter can be explained from both macroscopic and microscopic sides. As we know, one basic thought for wave-plate functional switch design relies on the broken of different polarization components. For example, in previous work [38], a graphene wire is arranged along one direction to change the structure symmetry and two orthotropic polarization components were generated under 45°-polarized excitation. When the graphene wire is biased, the balance of two orthotropic polarization components can be effectively broken. In our model, L resonator shows symmetry along x and y directions and the presence of graphene sheet does not change the structure symmetry. Two orthotropic polarization components were generated through near-field scattering coupling under x-polarized excitation and their amplitude ratio and phase difference can be modulated by the substrate of top L-shape resonators. Specifically, the realization of quarter wave plate function with unbiased graphene sheet is due to co-contribution from the top L-shape resonators and underlying layers, where the thickness of dielectric spacer is vital for the modulation of amplitude ratio and phase difference of different polarization components. When graphene sheet is in biased state, both near-field scattering from top resonators and reflected waves from bottom mirror will be mainly modulated by the active graphene rather than the dielectric spacer since the spacer’s thickness is fixed. As a result, the realization of half wave plate function is determined by the coupling efficiency of near-field scattering since the phase difference makes no sense for cross-polarization conversion.

The near-field scattering coupling from horizontal arm to vertical one in L-shape resonator can be simply described as:

E_{x} = E_{0} e^{- j (ω t + φ_{0})},

E_{y} = κ_{y x} E_{x} = η_{y x} e^{- j Δ φ} E_{x},

where

κ_{y x}

is the coupling function.

η_{y x}

and

Δ φ

are related to the amplitude ratio and phase difference between x and y components, respectively. Both

η_{y x}

and

Δ φ

are sensitive to the dielectric constant of the background, which can be manipulated dynamically by the graphene’s conductivity.

Figures 5(a) and 5(b)

Fig. 5 (a) and (b) Real and imaginary parts of graphene’s conductivity plotted as a function of frequency for different chemical potentials. (c) Phase difference of the half-wave plate when the chemical potential is 0.32 eV, 0.34 eV and 0.36 eV. (d) Real part of gold’s permittivity at different plasmon frequencies based on the Drude model ε(ω) = ε_∞-ω_p²/(ω² + iωγ), where ε_∞ = 9.1 and γ is 1.07E14.

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show the dispersion relation of graphene’s conductivity for different chemical potentials. When the chemical potential is 0 eV, the real and imaginary parts of graphene’s conductivity will gradually decrease and increase with the growing frequency, respectively. When the chemical potential is gradually increased to 0.1 eV, 0.3 eV, and 0.45 eV, for a specific frequency, the real part of graphene’s conductivity will first decrease at μ_c = 0.1 eV and then gradually increase, while the imaginary part is consistently growing. According to Eq. (5), the real and imaginary parts of graphene’s in-plane dielectric constant are determined by the imaginary and real parts of graphene’s conductivity, respectively. Since the imaginary part of graphene’s conductivity is much larger than the real part, the performance of polarization converter is mainly affected by the former one. When the chemical potential is increased from 0 eV to 0.45 eV, the imaginary part of graphene’s conductivity is enhanced more than 10 times, so it will strongly modulate the

η_{y x}

and

Δ φ

which are critical for realizing a switchable polarization converter from a quarter-wave plate to a half-wave plate [Figs. 3(a)–3(d)]. In particular, when the chemical potential is increased from 0.32 eV to 0.36 eV, a gradually enhanced imaginary part of graphene’s conductivity will bring a growing

Δ φ

. Since the half-wave plate should satisfy a quite similar phase difference condition [Fig. 5(c)], the effective working frequency band of half-wave plate is forced to move to higher frequencies to satisfy the phase condition and thus causes a blue-shifted behavior in Figs. 3(e)–3(h).

From the microscopic side, the growing graphene’s conductivity could improve the electron density (n) and plasmon frequency (ω_p² = ne²/ε_rm_e) of the adjacent gold film. As shown in Fig. 5(d), a growing plasmon frequency of gold will cause a decrease of the real part of gold’s permittivity and result in a blue shift of resonant frequency based on the well-known Drude model and Mie scattering theory [48].

4. Conclusions

In conclusion, we have demonstrated an idea of functionality-switchable terahertz polarization converter based on a planar metamaterial integrated with a single-layer graphene on the hBN/Si/SiO₂/Ag substrate. When the graphene sheet is in the unbiased state, by carefully designing the thickness of SiO₂, we obtained a high-performance quarter-wave plate (ellipticity more than 0.97) with a working bandwidth from 4.80 THz to 5.10 THz. When the graphene sheet is in the biased state, a growing chemical potential allows a dynamically switch from a quarter-wave plate to a half-wave plate. In particular, the best range of chemical potential for a high-performance half-wave plate (PCR>97%) is from 0.32 eV to 0.36 eV, during which the working bandwidth of the half-wave plate is gradually blue-shifted as chemical potential grows and the superposed working bandwidth can fully covered the working bandwidth of the quarter-wave plate. Our proposed active terahertz polarization converter not only is working with high performance but also is compact in structure as well as convenient in fabrication and gate-voltage operation, which shows a practical value in terahertz imaging, detection, and communication.

Funding

National Natural Science Foundation of China (NSFC) (61675096, 61205042); Natural Science Foundation of Jiangsu Province (BK2014021828).

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References	Function	Active material	Central working frequency (THz)	Bandwidth (THz)	Performance	Transmission/reflection efficiency
[33]	1/4 switch	Graphene wires	1.37	0.55	ellipticity>0.94	~90% (1/4)
[34]	1/4 switch	Graphene wires	0.99	0.38	ellipticity>0.95	~80% (1/4)
[37]	1/2 to 1/4	Liquid crystals	2.32	Single frequency	ellipticity>0.96,PCR>99%	~50% (1/4), ~50% (1/2)
[38]	1/2 to 1/4	Graphene wires	0.56	0.12	ellipticity>0.96,PCR>88%	~90% (1/4), ~70% (1/4)
Present study	1/4 to 1/2	Graphene sheet	4.90	0.30	ellipticity>0.97,PCR>97%	~80% (1/4), ~55% (1/2)

Functionality-switchable terahertz polarization converter based on a graphene-integrated planar metamaterial

Abstract

1. Introduction

2. Models and methods

3. Results and discussion

3.1 High-performance quarter-wave plate design

3.2 High-performance functionality-switchable polarization converter

3.3 Physical mechanism

4. Conclusions

Funding

References

Cited By

Figures (5)

Tables (1)

Equations (7)

OSA Continuum