1. Introduction

THz radiation falls in between infrared and microwave radiation and shares properties of them, such as THz radiation is non-ionizing and can penetrate many non-conducting materials [1], therefore, there is an increasingly high interest in THz science and technology. Besides rapid updates of THz sources and sensors [2–6], various THz devices have been reported to modulate intensity, phase, polarization, and even wavelength of THz radiation [7–9], thus remarkably promoting THz techniques to mature and practical applications just as nowadays visible light optics. Among various THz devices, polarization converters play an important role in manipulating the polarization states of THz radiation and often work as modulators and switches, thus they are widely used in THz sensing, imaging and communication [10, 11].

Similar to visible light optics, birefringence materials [12] and dichroic crystals [13] as natural materials can achieve polarization conversion, but they often suffer from bulky sizes and expensive costs because these conventional THz polarization converters rely on long THz propagation distances to accumulate phase for polarization conversion. In order to obtain polarization conversion using cost-effective thin-layer devices, metamaterials as artificially structured materials have been used for THz polarization converter designs, such as Grady et al. demonstrated a metal cut wire array to realize high-efficient linear polarization conversion [14]; Liu et al. designed a structure with rotationally symmetric “F” shapes for broadband cross-polarization conversion [15]; Jiang et al. proposed a double split square gold ring array to obtain linear-to-circular polarization conversion [16] and so on.

However, these THz polarization converters still suffer from fixed polarization conversion band. As graphene can support strong surface plasmon in THz band [17, 18], graphene-based THz polarization converters become solutions for active polarization conversion band adjustment. Guo et al. designed a THz elliptical polarization converter by placing periodic rectangular graphene patches over a dielectric substrate [19]. Zeng et al. reported a THz cross-polarization converter via introducing a hollow-carved graphene on the top layer of zirconium dioxide [20]. Amin et al. adopted L-shape graphene elements on the quartz material to construct a linear polarization converter [21]. Though these reported THz polarization converters can successfully manipulate THz polarization even with adjustable polarization conversion band, they still have shortcomings, such as polarization conversion band is limited, polarization conversion is highly sensitive to incident THz radiation angle, and co-polarized THz radiation is still mixed with cross-polarized output even polarization conversion ratio (PCR) reaches a rather high level. Structure optimizations can be implemented via numerical simulations such as finite difference time domain method and finite element method to improve the performance of these THz polarization converters; however, the empirical optimization is time-consuming and lacks physical explanations, and more importantly, it is very difficult to obtain the optimal design. In other words, there still lacks theoretical model for graphene-based THz polarization converter design and optimization.

In order to solve the problem, we adopt multiple interference theoretical model for graphene metamaterial-based tunable broadband THz linear polarization converter design and optimization. The optimal THz linear polarization converter achieves PCR over 0.97, polarization azimuth angle of almost ±90° and rather low ellipticity within a broad polarization conversion band from 2.68 THz to 3.93 THz; and additionally, its polarization conversion band can be actively tuned by adjusting the graphene chemical potential and almost insensitive to the incident THz radiation angle when it is below 50°. This work not only offers a way in high-quality manipulation of THz radiation polarization; but also delivers a theoretical model for tunable broadband THz polarization converter design and optimization.

2. Multiple interference theoretical model of graphene metamaterial-based tunable broadband THz linear polarization converter

2.1 Multiple interference theory

Multiple interference theory is a theoretical interpretation based on interference. It was first used in explaining the principle of antireflection coating [22], and has now been extended to many other optical devices such as metal metamaterial-based absorbers and polarization converters [23, 24]. In this article, multiple interference theory is used aiming at graphene metamaterial-based tunable broadband THz linear polarization converter, not only for principle understanding, but also for structure design and optimization.

According to the often adopted graphene-polymide-gold configuration, the THz linear polarization converter structure acts as an essential resonance cavity supporting multiple reflection and transmission as described in Fig. 1. The x-polarized wave impinging on the top surface of the polarization converter is partially reflected back to the air (A), and the rest transmits into the polymide layer (P). Meanwhile, the reflected (r) and transmitted (t) wave are divided into cross-polarized (cro) and co-polarized (co) components defined as $r_{cro}^{AP}$, $r_{co}^{AP}$, $t_{cro}^{AP}$ and $t_{co}^{AP}$, respectively. Afterwards, the transmitted wave propagating through the polymide layer is completely reflected by the gold substrate. Partial reflected wave propagating to the air are marked as $t_{cro}^{PA}$ and $t_{co}^{PA}$, and the rest reflected into the polymide layer are represented by $r_{cro}^{PA}$ and $r_{co}^{PA}$. The above processes are repeated as multiple reflection and transmission, in which, two additional phase factors ${e^{i2\beta }}$ and ${e^{i\pi }}$ are introduced, where $\beta ={-} \sqrt \varepsilon {k_0}H/\cos \alpha $, ${k_0}$ is the wave number in free space, H is the thickness of the polymide layer, and $\alpha $ is the incident angle. According to multiple interference theory, both the cross-polarized and co-polarized reflection components in each round can be calculated via Eqs. (1–4), in which, m represents the number of the rounds. It is worth noting that $m = 1$ is a special situation with components calculated as $t_{cro}^1 = t_{cro}^{AP}$, $t_{co}^1 = t_{co}^{AP}$, $r_{cro}^1 = r_{cro}^{AP}$ and $r_{co}^1 = r_{cro}^{AP}$, and these reflection and transmission coefficients as $r_{cro}^{AP}$, $r_{co}^{AP}$, $t_{cro}^{AP}$, $t_{co}^{AP}$, $\; r_{cro}^{PA}$, $r_{co}^{PA}$, $t_{cro}^{PA}$ and $t_{co}^{PA}$ can be obtained using different methods such as finite integration technique [25], finite difference time domain method and finite element method in either physical perspective or numerical perspective.

 

Fig. 1. Scheme of multiple interference theory for graphene metamaterial-based tunable broadband THz linear polarization converter design and optimization.

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Afterwards, the overall cross-polarized and co-polarized coefficients ${R_{cro}}$ and ${R_{co}}$ can be respectively computed via Eqs. (5) and (6).

If ${R_{cro}}$ decreases while ${R_{co}}$ increases, polarization conversion can be obtained. It should be noticed that the amplitudes and phases of these parameters are obtained by solving the decoupled system without the gold substrate.

According to multiple interference theory, the process of theoretically computing the overall co-polarized and cross-polarized reflection components can be concluded to following 4 steps.

Step 1: Construct the THz polarization converter structure without the gold substrate.

Step 2: Set the incident wave with a forward propagation from the air layer into the polymide layer, and then extract $\textrm{r}_{\textrm{cro}}^{\textrm{AP}}$, $\textrm{r}_{\textrm{co}}^{\textrm{AP}}$, $\textrm{t}_{\textrm{cro}}^{\textrm{AP}}$ and $\textrm{t}_{\textrm{co}}^{\textrm{AP}}$.

Step 3: Set the incident wave with a backward propagation from the polymide layer into the air layer, and then extract $\textrm{r}_{\textrm{cro}}^{\textrm{PA}}$, $\textrm{r}_{\textrm{co}}^{\textrm{PA}}$, $\textrm{t}_{\textrm{cro}}^{\textrm{PA}}$ and $\textrm{t}_{\textrm{co}}^{\textrm{PA}}$.

Step 4: Calculate the overall co-polarized and cross-polarized reflection components via Eqs. (1–6).

2.2 Graphene metamaterial-based tunable broadband THz linear polarization converter design

In order to test the performance of the multiple interference theory in THz linear polarization converter design and optimization, a THz linear polarization converter model is adopted as shown in Fig. 2(a1). The period structure consists of a graphene monolayer etched with pairs of rectangles, a polymide layer, and a gold substrate to guarantee total reflection of incident THz radiation. The period size of the unit cell is S, the height of the polymide layer is H, and the length and width of the rectangle are L and W, respectively. The conductivity of the gold substrate ${\sigma _{Au}}$ is 4.09×10⁷ S/m [26], the complex relative permittivity of the polymide ${\varepsilon _P}$ is 3.5 + 0.00945i [27], and that of the graphene ${\varepsilon _G}$ can be computed according to Eq. (7), in which ${\varepsilon _0}$ is the free-space permittivity, $\Delta $ is the thickness of the graphene layer set as 1 nm, $\mathrm{\omega }$ is the angular frequency, and ${\sigma _G}$ is the surface conductivity of graphene often computed via Kubo formula [28].

According to the Pauli exclusion principle [29], the inter-band transition can only be excited under the condition of $h\omega > 2{E_f}$, h is the Plank constant, and ${E_f}$ is the graphene chemical potential which can be adjusted via introducing a gate-voltage bias or chemical doping. Whereas in the THz regime, $h\omega \ll 2{E_f}$, therefore the inter-band transition is negligible and ${\sigma _G}$ can be simply computed through Eq. (8).

 

Fig. 2. (a) Design of the graphene metamaterial-based tunable broadband THz linear polarization converter: (a1) Structure, and (a2) Period details; (b), (c) and (d) Period structures of different graphene metamaterial-based tunable broadband THz linear polarization converter designs and their polarization conversion performances: (1) Period structures, (2) $\textrm{Amplitude}\; $ and (3) PCR.

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In Eq. (8), ${k_B}$ is the Boltzmann constant, T is the absolute environment temperature, ${e_0}$ is the electron charge, $\hbar $ is the reduced Plank constant, and $\mathrm{\Gamma }$ is the damping coefficient defined as Eq. (9), in which the Fermi velocity ${v_f}$ is 10⁶ m/s and the electron mobility $\mu $ is 10⁵ cm²·V⁻¹·s⁻¹ [30].

For linearly polarized THz radiation incidence, the relation between the incident field and the reflected field can be expressed by Eq. (10), in which, $E_x^i$ and $E_y^i$ respectively represent the x- and y-axial components of the incident electric field, $E_x^r$ and $E_y^r$ respectively represent the x- and y-axial components of the reflected electric field, R is the reflection coefficient, and the first subscript a of ${R_{ab}}$ denotes the direction of the reflected electric field, while the second subscript b signifies the direction of the incident electric field. Compared to Eqs. (5) and (6), ${R_{xy}}$ (or ${R_{yx}}$) is ${R_{cro}}$, and ${R_{xx}}$ (or ${R_{yy}}$) is ${R_{co}}$.

Due to the proposed THz linear polarization converter is symmetric along 45°, the reflection coefficients are symmetric, such as ${R_{xx}} = {R_{yy}}$ and ${R_{yx}} = {R_{xy}}$. Therefore, in this work, we only study the case under the x-polarized THz radiation incidence.

In order to estimate the performance of the THz linear polarization converter, PCR expressed by Eq. (11) is used according to the overall cross-polarized and co-polarized reflection coefficients. When PCR is 1, the proposed structure obtains the perfect linear polarization conversion.

Besides PCR, the performance of the THz linear polarization converter is also evaluated via polarization azimuth angle $\theta $ and ellipticity $\eta $ respectively describing the polarization direction of the reflected wave and the purity of the linear polarization as shown in Eqs. (12) and (13), in which $\phi = {\varphi _{yx}} - {\varphi _{xx}}$ is the phase difference between y- and x-axial components of the reflected THz radiation. When $|\theta |$ reaches 90° and $\eta $ reaches 0, the proposed structure has high output polarization purity [31, 32].

The graphene metamaterial structures can be fabricated according to following operations. First, gold can be deposited on the substrate using liquid evaporation. Then, polymide can also be deposited on the gold film using chemical vapor deposition. Next, graphene can also be synthesized on the polymide using chemical vapor deposition. Finally, patterns on the graphene can be fabricated using lithography. The fabrication is very similar to the reported works as [35] and [36].

2.3 Multiple interference theoretical model verification

Besides multiple interference theory, $|{{R_{yx}}} |$, $|{{R_{xx}}} |$ and PCR as well as $|\theta |$ and $\eta $ can also be precisely computed using the finite element method. During numerical simulation, the structure was first input into the numerical simulation system. Then, periodic boundary condition was set in the x and y directions and port condition was set in the z direction according to Fig. 2. Finally, free triangular grid was meshed on the input structure for numerically computing the electromagnetic wave fields according to the finite element method as well as extracting a series of parameters including $|{{R_{yx}}} |$, $|{{R_{xx}}} |$, PCR, $|\theta |$ and $\eta $. Here, theoretical computation has been compared to numerical simulation in order to verify the accuracy of the multiple interference theory. The THz linear polarization converter shares the same structure with that in Fig. 2(d). Figure 3(a) lists $|{{R_{yx}}} |$ and $|{{R_{xx}}} |$, Fig. 3(b) plots PCR, Fig. 3(c) reveals $\eta $ and Fig. 3(d) shows $|\theta |$ within the range from 2.4 THz to 4.0 THz obtained using multiple interference theory as theoretical computation and finite element method as numerical simulation. The comparison with almost coincident data clearly illustrates that the adopted multiple interference theory can quantitatively describe the performance of the graphene metamaterial-based THz linear polarization converter verified by classical finite element method, proving that the multiple interference theory can be used for graphene metamaterial-based tunable broadband THz linear polarization converter design and optimization.

 

Fig. 3. (a) $|{{R_{yx}}} |$ and $|{{R_{xx}}} |$; (b) PCR; (c) $\eta $ and (d) $|\theta |$ computed using multiple interference theory and finite element method.

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3. Graphene metamaterial-based tunable broadband THz linear polarization converter optimization, verification and analysis

3.1 Graphene metamaterial-based tunable broadband THz linear polarization converter optimization

After verification on the multiple interference theoretical model, it is next used to seek the optimal graphene metamaterial-based THz linear polarization converter with better polarization conversion performance via optimizing the structural parameters including ${L_{out}}$, ${L_{in}}$, D and H. It should be noticed that other parameters are fixed when one of the above parameters is studied. Figure 4(a1) reveals the theoretically obtained PCR corresponding to different ${L_{out}}$ but fixed S of 10 µm, H of 15 µm, ${L_{in}}$ of 3.2 µm, ${W_{out}}$ of 1 µm, ${W_{in}}$ of 0.5 µm, D of 0.85 µm and ${E_f}$ of 0.59 eV. When ${L_{out}}$ increases from 6.5 µm to 7.1 µm, the polarization conversion band is red-shifted, and the PCR fluctuates. In order to pursue high PCR within the whole polarization conversion band, ${L_{out}}$ of 6.7 µm is a preferred selection, since in this condition, the optimized THz linear polarization converter structure has the broadest polarization conversion band with PCR always higher than 0.97. Figure 4(b1) reveals the theoretically obtained PCR corresponding to different ${L_{in}}$ but fixed S of 10 µm, H of 15 µm, ${L_{out}}$ of 6.7 µm, ${W_{out}}$ of 1 µm, ${W_{in}}$ of 0.5 µm, D of 0.85 µm and ${E_f}$ of 0.59 eV. When ${L_{in}}$ increases from 3.0 µm to 3.3 µm, the polarization conversion band is still red-shifted, and the PCR also fluctuates. Similar to above, ${L_{in}}$ of 3.2 µm is selected according to the same criterion. Figure 4(c1) reveals the theoretically obtained PCR corresponding to different D but fixed S of 10 µm, H of 15 µm, ${L_{out}}$ of 6.7 µm, $\; {L_{in}}$ of 3.2 µm, ${W_{out}}$ of 1 µm, ${W_{in}}$ of 0.5 µm and ${E_f}$ of 0.59 eV, obviously suggesting an optimized D as 0.85 µm to obtain broader polarization conversion band. Figure 4(d1) reveals the theoretically obtained PCR corresponding to different H but fixed S of 10 µm, ${L_{out}}$ of 6.7 µm, $\; {L_{in}}$ of 3.2 µm, ${W_{out}}$ of 1 µm, ${W_{in}}$ of 0.5 µm, D of 0.85 µm and ${E_f}$ of 0.59 eV, demonstrating that H of 15 µm is the best choice to pursue high PCR within the whole polarization conversion band. Therefore, according to the multiple interference theoretical model, the optimal graphene metamaterial-based THz linear polarization converter has the structure as S of 10 µm, H of 15 µm, ${L_{out}}$ of 6.7 µm, $\; {L_{in}}$ of 3.2 µm, ${W_{out}}$ of 1 µm, ${W_{in}}$ of 0.5 µm and D of 0.85 µm. Here, ${E_f}$ is not optimized, but fixed at 0.59 eV, because in this condition, the optimized THz linear polarization converter structure has the broadest polarization conversion band with PCR always higher than 0.97.

 

Fig. 4. Graphene metamaterial-based tunable broadband THz linear polarization converter optimization. (a) Optimization on ${L_{out}}$; (b) Optimization on ${L_{in}}$; (c) Optimization on D; and (c) Optimization on H. (1) Optimization using multiple interference theory; and (2) Optimization using finite element method.

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Additionally, finite element method is also used to calculate PCR with different ${L_{out}}$, ${L_{in}}$, D and H the same as above theoretical optimization, and Figs. 4(a2), 4(b2), 4(c2) and 4(d2) list the results. The numerical simulation not only reveals the coincident PCR distributions compared to those obtained via multiple interference theoretical model, but also provides the same optimal design of the THz linear polarization converter with the structure as S of 10 µm, H of 15 µm, ${L_{out}}$ of 6.7 µm, $\; {L_{in}}$ of 3.2 µm, ${W_{out}}$ of 1 µm, ${W_{in}}$ of 0.5 µm and D of 0.85 µm, both proving the accuracy of the multiple interference theoretical model.

3.2 Graphene metamaterial-based tunable broadband THz linear polarization converter performance verification

In order to test the performance of the optimal graphene metamaterial-based tunable broadband THz linear polarization converter, its $|{{R_{yx}}} |$, $|{{R_{xx}}} |$, PCR, $|\theta |$ and $\eta $ are all computed using both multiple interference theory and finite element method as shown in Fig. 5. Figure 5(a) and 5(b) lists $|{{R_{yx}}} |$ and $|{{R_{xx}}} |$ respectively, Fig. 5(c) reveals PCR, demonstrating that the optimal THz linear polarization converter has a broad polarization conversion band from 2.68 THz to 3.93 THz; moreover, the PCR within such band is no less than 0.97. Furthermore, it should be noticed that the co-polarization amplitude is close to 0 at 2.80 THz, 3.36 THz, 3.68 THz and 3.91 THz, which implicit that there only exists cross-polarized component in the reflected THz radiation and leads to PCR close to 1.

 

Fig. 5. Graphene metamaterial-based tunable broadband THz linear polarization converter performance verification. (a) $|{{R_{yx}}} |$; (b) $|{{R_{xx}}} |$; (c) PCR; (d) $\mathrm{\eta }$; (e)$\; |\theta |$; (f) Central frequency and bandwidth of the frequency conversion band with different ${E_f}$ computed using both multiple interference theory and finite element method. (g) $|{{R_{yx}}} |$, (h) $|{{R_{xx}}} |$ and (i) PCR with different incident angles computed using finite element method. Insert in (d) describes the scheme of central frequency of the polarization conversion band.

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Besides PCR, the performance of the optimal graphene metamaterial-based THz linear polarization converter is also evaluated by $|\theta |$ and $\eta $ to test the output polarization purity. According to Fig. 5(d), $\eta $ is always less than 15° within the polarization conversion band from 2.68 THz to 3.93 THz. Especially, $\eta $ is extremely close to 0 at 2.80 THz, 3.36 THz, 3.68 THz and 3.91 THz. Besides, $|\theta |$ reaches almost 90° in the whole polarization conversion band as shown in Fig. 5(e). Both $|\theta |$ and $\eta $ distributions prove that the optimal graphene metamaterial-based THz linear polarization converter has rather output polarization purity within the polarization conversion band.

More than a broad polarization conversion band, the optimal THz linear polarization converter can also actively shift the polarization conversion band by changing ${E_f}$. Figure 5(f) depicts the linearly fitted relation between the graphene chemical potential and the central frequency of the polarization conversion band, illustrating that the polarization conversion band can be shifted with a rate of 2.63 THz/eV. But the bandwidth is almost independent to the graphene chemical potential different from the band position also exhibited in Fig. 5(f). Besides, it is worth noting that both multiple interference theory and finite element method provide coincident data demonstrating the effectiveness of the multiple interference theoretical model on THz linear polarization converter design and optimization.

Additionally, the influence of incident angle on the optimal graphene metamaterial-based THz linear polarization converter performance is also studied. Figure 5(g) and 5(h) describes the numerically computed $|{{R_{yx}}} |$ and $|{{R_{xx}}} |$ in different incident angles from 0° to 60° within the band from 2.4 THz to 4.0 THz. When the incident angle is below 50°, it has little influence on $|{{R_{yx}}} |$ and $|{{R_{xx}}} |$; while it further increases, $|{{R_{yx}}} |$ decreases while $|{{R_{xx}}} |$ increases, generating significant PCR reduction in Fig. 5(i). These results in Figs. 5(g-i) demonstrate that the optimal graphene metamaterial-based THz linear polarization converter can still manipulate THz radiation polarization in high quality almost insensitive to the incident THz radiation angle when it is below 50°.

According to the above performance verification on the optimal graphene metamaterial-based THz linear polarization converter, it has a broad and tunable polarization conversion band with rather high polarization conversion efficiency, high output polarization purity and almost insensitive to the incident angle, thus providing high-quality performance in THz linear polarization conversion.

3.3 Graphene metamaterial-based tunable broadband THz linear polarization converter analysis

Proved by both theoretical computation and numerical simulation, the optimal THz linear polarization converter has a rather broad polarization conversion band. In order to understand its underlying physics, Fig. 6(a) describes its physical model. The incident electric field can be decomposed into two orthogonal components as shown in the insert of Fig. 6(a4). Here, $|{{R_{uu}}} |$, $|{{R_{vv}}} |$, $|{{R_{uv}}} |$ and $|{{R_{uv}}} |$ represent the amplitudes of reflected coefficients shown in Fig. 6(a1), ${\varphi _{uu}}$ and ${\varphi _{vv}}$ represent the phases revealed in Fig. 6(a2), and there exists a phase difference $\Delta \varphi $ between them, which can be calculated by ${\varphi _{uu}} - {\varphi _{vv}}$. If $|{{R_{uu}}} |= |{{R_{vv}}} |$ and $|{\Delta \varphi } |= \mathrm{\pi }$, a complete 90° polarization rotation can be obtained. According to Fig. 6(a3) plotting $|{|{{R_{vv}}} |- |{{R_{uu}}} |} |$ and Fig. 6(a4) plotting $|{\Delta \varphi } |$, both $|{{R_{uu}}} |\approx |{{R_{vv}}} |$ and $|{\Delta \varphi } |\approx \mathrm{\pi }$ are satisfied in the range from 2.68 THz to 3.93 THz, therefore, the polarization of the reflected THz radiation is along y-direction thus the polarization conversion is obtained.

 

Fig. 6. Graphene metamaterial-based tunable broadband THz linear polarization converter analysis. (a) Amplitude and phase distributions of the reflected coefficients: (a1) $|{{R_{uu}}} |$, $|{{R_{vv}}} |$, $|{{R_{uv}}} |$ and $|{{R_{uv}}} |$, (a2) ${\varphi _{uu}}$ and ${\varphi _{vv}}$, (a3) $|{|{{R_{vv}}} |- |{{R_{uu}}} |} |$, and (a4) $|{\Delta \varphi } |$; (b) ${H_z}$ amplitude, (c) ${H_z}$ direction and (d) ${H_z}$ equivalent vector on the graphene surface at (1) 2.80 THz, (2) 3.36 THz, (3) 3.68 THz and (4) 3.91 THz obtained using finite element method.

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To further study the physical mechanism of the polarization conversion, the magnetic field distributions and the direction of ${H_z}$ on the graphene surface at four distinctive resonant frequencies of 2.80 THz, 3.36 THz, 3.68 THz and 3.91 THz with complete polarization conversion are computed using finite element method. Figure 6(b) shows the magnetic field distributions and Fig. 6(c) reveals the directions of ${H_z}$ at different frequencies, revealing that these polarization conversion modes are completely different. Additionally, the equivalent vectors of the electromagnetic fields in the coordinate system are revealed in Fig. 6(d): the output magnetic field ${H^{out}}$ can be decomposed into two orthogonal directions as $H_x^{out}$ and $H_y^{out}$; however, $H_y^{out}$ cannot induce any cross-polarization THz radiation because it aligns with the input magnetic field $H_y^{in}$; meanwhile, the output component $H_x^{out}$ is parallel with the input electric field $E_x^{in}$, which results in cross-polarization THz radiation because of generating an electric field along the y-axis. It is worth noting that the combined effect of these four resonances enable a broad polarization conversion band.

4. Discussion

Instead of designing and optimizing THz polarization converters empirically via time-consuming and complicated numerical simulations, here we proposed multiple interference theoretical model, which can also quantitatively evaluate the performance of graphene metamaterial-based tunable broadband THz linear polarization converter, fitting well with that obtained from finite element method. Comparing to THz polarization converter design and optimization directly using numerical simulation, our proposed theoretical approach based on multiple interference theory delivers a theoretical model for tunable broadband THz polarization converter design and optimization: with the extracted cross-polarized and co-polarized coefficients, a series of parameters including $|{{R_{yx}}} |$, $|{{R_{xx}}} |$, PCR, $|\theta |$ and $\eta $ can be computed, not only unveiling the underlying physical mechanisms of devices, but also supporting high-quality THz polarization converter design and optimization. More importantly, different from empirical THz polarization converter design and optimization relying on multi-parameter time-consuming numerical simulations, theoretical model obtained using the proposed theoretical approach can rapidly evaluate the THz polarization converter performance through analytical computation, thus significantly reducing the computational load and saving the simulation time. Therefore, different from empirical design and optimization via numerical simulations, theoretical analysis can be used for THz polarization converter design and optimization but still in high accuracy.

Using the multiple interference theoretical model, an optimal graphene metamaterial-based tunable broadband THz linear polarization converter has been obtained, and its polarization conversion parameters are listed in Table 1, which has better performance compared to many other reported ones [37–41]. Moreover, in this design, metamaterial patterns can be fabricated on a continuous graphene surface, therefore, the biasing can be implemented only using a single gate-voltage source. Considering the advantages of the proposed graphene metamaterial-based tunable broadband THz linear polarization converter, this work provides an optimal design offering a way in high-quality manipulation of THz radiation polarization; but more importantly, delivers a theoretical model for THz polarization converter design and optimization. Moreover, since the multiple interference theoretical model can deal with multi-layer metamaterial structures, this work also potentially offers a way to design and optimize other metamaterial-based optical devices even beyond THz bands.

Table 1. Comparisons on graphene-based THz linear polarization converters

View Table

Though the adopted multiple interference theoretical model can successfully provide a series of parameters charactering the performance of the THz polarization converters, such as polarization conversion bandwidth, PCR, polarization azimuth angle, ellipticity and so on, it still cannot provide electromagnetic distribution, which can unveil the underlying physical mechanism. Moreover, in multiple interference theoretical model, the transmission, reflection and even absorption coefficients should be obtained in advance through methods such as finite integration technique, finite difference time domain method and finite element method in either physical perspective or numerical perspective; and most of these methods are still complicated and time-consuming, limiting the efficiency of the multiple interference theoretical model. In order to accelerate its structure design and optimization speed, improved approaches especially those in analytical tactics should be studied which can provide features of metamaterial layer with fast speed and high accuracy to further update the multiple interference theoretical model.

5. Conclusion

In summary, we adopted multiple interference theory to successfully design and optimize a graphene metamaterial-based tunable broadband THz linear polarization converter. Verified by finite element method, the optimal structure achieves PCR over 0.97, polarization azimuth angle of almost ±90° and rather low ellipticity even close to 0 within a broad polarization conversion band of 1.25 THz, which coincide with those directly obtained via the multiple interference theoretical model, suggesting that multiple interference theory can be successfully used for THz polarization converter design and optimization. Additionally, the polarization conversion band can be actively tuned by adjusting the graphene chemical potential and its polarization conversion capability is almost insensitive to the incident THz radiation angle when it is below 50°. Compared to many other reported THz linear polarization converters, the proposed one exhibits a better polarization conversion performance. We believe this work not only delivers a theoretical model for metamaterial-based THz polarization converter design and optimization, but also offers a way to design and optimize other metamaterial-based optical devices even beyond THz bands.