Open Access
Add to BibSonomy
Abstract
In this letter, we propose a dual-band tunable reflective linear-to-circular (LTC) polarization converter, which is composed of a graphene sheet etched with an I-shaped carved-hollow array. In the mid-infrared region, two LTC bands with opposite handedness are simultaneously realized due to the excitation of the three graphene surface plasmon (GSP) modes. The band of line-to-right-circular-polarization (LTRCP) ranges from 9.87 to 11.03THz with ellipticity χ <−0.95, and from 9.69 to 11.36 THz with an axial ratio of less than 3 dB; the band of line-to-left-circular-polarization (LTLCP) ranges from 13.16 to 14.43THz with χ >0.95, and from 12.79 to 14.61 THz with an axial ratio of less than 3 dB. The tunable responses of the reflective polarizer with Fermi energy (Ef) and electron scattering time (τ) are discussed, and especially the perfect LTLCP can be changed to LTRCP with increasing Ef. Also, the influences of geometric parameters, incident angle, and polarization angle on the performances of the dual-band LTC are also investigated, and it is found that our polarizer converter shows angle insensitivity. All simulation results are conducted by the finite element method. Our design enriches the research of tunable LTC polarizers and has potential applications in integrated terahertz systems.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As an emerging and promising technology, terahertz wave manipulation is of great significance and draws huge attention on scientific researches and applications in the field of wireless communication, space exploration, medical imaging and etc. [1–4]. Based on its superior properties, many efforts have been taken to control the propagation of the THz wave, especially in switching or converting the state of the polarization. As one of the inherent properties of the electromagnetic (EM) waves, the polarization defines the vibration characteristics of the light [5]. Effectively controlling and manipulating the state of optical polarization is highly valuable and in urgent demand in high resolution imaging, remote sensing, terahertz communications and other mid-infrared applications, and has attracted large attention form researchers and been widely investigated [6–8]. However, effective functional THz polarization conversion devices are still relatively lacking and remain to be designed. The conventional methods are usually to utilize anisotropic crystal, gases and solutions of chiral molecules to generate phase difference between two orthogonal polarization components to convert polarization of the light [9–10]. However, with the bulky configurations and specific thickness, it’s hard to integrate into nanoscale optoelectronic devices. In this context, metasurface provides a possible way for the miniaturization and integration of the polarizer.
As one kind of artificially designed 2-dimensional(2D) subwavelength composite structures, metasurface boasts exotic properties including ultrathin thickness, lower loss and efficient manipulation. Equipped with above benefits, they could be utilized to control over the amplitude, phase and polarization of electromagnetic waves. Novel chromatic aberration-free meta-devices with broad working ranges enable to modulate both the phase dispersion and reflection amplitude [11]. Through tailoring the geometry of structures with anisotropy by ideal and exquisite design, a variety of polarization conversion devices have been investigated [12–17]. To date, many studies have been reported and a series of novel converters have been realized by using plasmonic metasurface such as rectangle-shape nanorod [18], cross-shaped Ag particle arrays [19], planar metallic arcs in two layers [20], three layer meta-atoms [21] rectangular split-ring resonator [22] and L-shaped metal nanoparticles [23]. However, most of the proposed metasurface are passive because these devices are limitedly functional after being fabricated and cannot be reconfigured flexibly and dynamically. Researchers have turned their attention to active and tunable metasurface. Using feasible strategy by integrating phase-change materials such as black phosphorus [24], liquid crystal [25], VO2 [26], perovskite [27] and graphene [28] with metasurface would provide possible ways for designing tunable optical systems.
Graphene, a novel electrically tunable material, is made of a layer of carbon atoms arranged in a honeycomb lattice. Originating from its massless Dirac electrons with linear dispersion relation, graphene is charactered with outstanding optoelectronic properties especially the ultra-wide band tunability through electrical excitation fields or chemical doping concentration in the mid-infrared region [29–30]. Moreover, good optical transparency, high electron mobility and strong plasmonic response with the relatively loss also provide an opportunity for graphene to develop effective THz devices [31–32]. To date, the combination of graphene with metasurface has been widely investigated in polarization control and many compact functionalities have been demonstrated [33–36]. Specially, Grady et al. proposed an ultrathin and highly effective linear cross-polarization converter in the reflective mode [37]. Zeng et al. designed two types of dual-band reflective tunable and broadband cross-polarization converter based on the U-shaped graphene patch and the U-shaped hollow-carved single graphene layer, respectively [38]. In the meanwhile, line-to-circular (LTC) polarization converters also have been reported, which show the outstanding potential in many fields such as electronic countermeasures and satellite communication [39]. Guo et al. demonstrated a transmitting LTC polarization converter based on a single layer metasurface composed of rectangular graphene patch array, and realized a wide operating frequency range from 4.5 to 5.3 THz [40]. Yao et al. reported a dynamically transmissive LTC polarizer with an elliptical periodic array graphene layer operating from 5.15 to 5.52 THz [41]. Zang et al. designed a reflective broadband LTC polarization converter with a single-layer ultra-thin metasurface [42]. Zeng et al. presented ultra-broadband LTC polarization converter working from 0.92 to 2.28 THz [43]. To the best of our knowledge, dual-band LTC polarizer with opposite handedness based on graphene metasurface has not yet been reported.
In this paper, we propose a novel design of a dual-band tunable reflective LTC polarization converter, which is composed of a single graphene layer etched with periodically I-shaped nano-slots. Excited by the incident THz wave polarized at 45° with respect to x-direction, the polarizer converts linear to left-handed and right-handed circular polarized waves in reflection, simultaneously. The dual-band of LTC originates from the excitation of the three graphene surface plasmons(GSPs) modes. Numerical simulation results indicate that the two bands of line-to-right-circular-polarization and line-to-left-circular-polarization operate in the frequency range of 9.69-11.36THz and 12.79-14.61THz with an axial ratio of less than 3 dB, respectively. The relative bandwidths reach 15.8% and 13.3%, respectively. The conversion efficiency of this broadband polarization converter reaches over 73%. By tuning the Fermi energy and electron scattering time, the tunable responses of double bands of LTC can be realized. Furthermore, the polarizer also presents good angular stability under oblique incidence angles. Besides, the influences of the polarization angle and structural parameters on performances of the converter are also discussed. The proposed polarization converter has promising potential on the terahertz system miniaturization and integration.
2. Design and theories
The schematic of our proposed reflection LTC polarization converter is sketched in Fig. 1(a). The proposed structure is composed of a graphene sheet with an I-shaped carved-hollow array, which is supported by a silica layer. The bottom is Au layer, which acts as the reflective mirror. The top view of the unit cell and the structural parameters are shown in Fig. 1(b), including the lengths l1(=0.58 µm), l2(=0.885 µm), and l3(=1.085 µm) of slots, the width w (=0.09 µm) of the slots, and the distance g (=1.17 µm) between the two horizontal slots. The thickness of the Au layer is hm ( = 1 µm), so the electromagnetic wave is completely reflected. The periods Px and Py are both set to be 1.53 µm. The proposed structure could be obtained through feasible manufacturing processes. The substrate Au layer could be deposited by electron beam evaporation, and the silica dielectric acts as an adhesive layer. After depositing silica with thickness hr( = 4.8µm), one transparent conductive oxide (TCO) layer is covered on the dielectric, and then silica with thickness hx( = 0.2µm) is deposited [44]. Then, a high-quality graphene layer is grown by CVD [45] and could be transferred onto the silica. I-shaped carved-hollow array can be obtained via Helium Ion Beam (HIB) lithography [46]. Finally, a thin TCO layer is also covered at top of the structure so that each cell could be electrically biased through transparent electrodes, as shown in Fig. 1(c).
Fig. 1. (a) Schematic diagram of the proposed dual-band LTC polarization converter. (b)Top view of unit cell of (a). The geometrical parameters are listed as: Px = Py=1.53µm, l1=0.58 µm, l2=0.885 µm, l3=1.085 µm, w = 0.09 µm, g = 1.17 µm. (c) Side view of the converter, and other parameters include hx = 0.2 µm, hr = 4.8µm, and hm=1µm. Bias voltage is applied between the double TCO layers.
In this paper, all the simulation results are obtained by finite element method (FEM) via frequency domain solver in COMSOL Multiphysics. The Floquet boundary condition is employed along the x and y directions, and the perfect matched layer is adopted in the z direction. The optical conductivity of graphene is derived from the Kubo formula [47]. In the mid-infrared region, where ${E_f} \gg {k_B}\textrm{T}$, the surface conductivity of graphene could be calculated approximately as :
Within the formula, ℏ and ${k_B}$ represents the reduced Planck’s constant and Boltzmann constant, respectively. T is the ambient temperature which is regarded as 300K, e is the charge of an electron, ω is the frequency of incident light. Moreover, $\tau$ indicates the electron scattering time, and Ef represents the Fermi energy level of graphene which is defined by the expression of ${E_f} = \hbar {V_f}\sqrt n $ [48]. Here, Vf (=1.1${\times} $106m/s) is the Fermi velocity, while n$({ = |{{n_e} + {n_0}} |} )$ is the total charge carrier concentration and determined by both electrostatic doping (ne) and doping concentration (n0). As for dynamically tuning the Fermi energy, the bias voltage (Vg) is applied to control the electrostatic doping of the patterned graphene following by ${n_e} = {\varepsilon _0}{\varepsilon _r}{V_g}/(e{h_x})$ [49]. Where ${\varepsilon _0}$ and ${\varepsilon _r}$(=2.1) are the permittivity of the vacuum and the relative one of the silica, respectively. The excitation pathways is built by connecting both TCO gates to apply external electrical stimuli. If the large Fermi energy is required, the chemical doping (n0) is employed before electrical stimuli and the targeted Fermi energy is obtained [50]. The permittivity of Au is described by the Drude model, and the typical carrier concentration is set as 4.11× 1027m−3 well as the scattering time of 1ps [51]. The graphene’s effective in-plane permittivity ε is defined as:
Where η(≈377Ω) is the impedance of air, and Dg(=1nm) indicates the thickness of the graphene.
The linearly THz plane wave (i.e. ${\textrm{E}_\textrm{i}}\textrm{ = }{\textrm{e}_\textrm{u}}\textrm{E}_\textrm{u}^\textrm{i}$) is perpendicularly incident, with the polarization angle of 45° respect to the x axis, downward on the top surface of the proposed structure, as shown in Fig. 1. The incident and the reflected electric fields can be combined as follows [52]:
Additionally, ${r_{uu}}$ and ${r_{vu}}$ are the co-polarization and cross-polarization coefficient, ${\varphi _{uu}}$ and ${\varphi _{vu}}$ are the corresponding phases, respectively. Hence, the polarization conversion ratio (PCR) can be described as [54]:
To verify the polarization state of the reflected wave, the Stokes parameters [55] are introduced as follows:
In the LTC frequency range, the relative bandwidth is defined as $({{f_{max}} - {f_{min}}} )/[({f_{max}} + {f_{min}})/2]$ [26].
3. Results and discussions
3.1 Prefect dual-band LTC polarization converter
In this section, we investigate the performance of our proposed dual-band tunable reflective LTC polarizer in the THz range. Here, the Fermi energy (Ef) and the electron scattering time τ of graphene are assumed as 1 eV and 1 ps, respectively. The incident angle is zero, and the polarization angle is 45°. Here, the polarization angle is defined as the angle between the polarization direction and the positive x direction. As shown in Figs. 2(a) and (b), the co-polarization reflection ${\textrm{R}_{\textrm{uu}}}$(=|${\textrm{r}_{\textrm{uu}}}$|2), cross-polarization reflection ${\textrm{R}_{\textrm{vu}}}$(=|${\textrm{r}_{\textrm{vu}}}$|2), ${\varphi _{vu}}$, ${\varphi _{uu}}$ and ${\Delta}\varphi $($= {\varphi _{\textrm{vu}}} - {\varphi _{\textrm{uu}}}$) are plotted in blued dashed line, black dashed line, black dot-dashed line, blue dot-dashed line and red solid line, respectively. ${\textrm{R}_{\textrm{uu}}}$, and ${\textrm{R}_{\textrm{vu}}}$ are equal at 10.44 and 13.90THz, while ${\Delta}\varphi $ is equal to −90° and 90°, respectively. So, the perfect right-hand and left-hand circular polarization are formed at these two frequencies, respectively. Especially, there are three peaks of cross-polarization reflection Rvu located at 9.5, 12.05 and 14.81THz, accompanied by three dips of the co-polarization reflection Ruu at almost the same frequencies. Thus, the double LTC bands with opposite handedness occur between the neighboring peaks of Rvu. Results show that the band of line-to-right-circular-polarization (LTRCP) is obtained at the lower frequency range, and the band of line-to-left-circular-polarization (LTLCP) could be realized at the higher spectrum range.
Fig. 2. (a) Simulation results of the co-polarization reflection (Ruu), cross-polarization reflection (Rvu). (b) Phase of u-polarized(φuu) and v-polarized(φvu) reflected wave together with their phase difference Δφ. (c) Ellipticity and polarization conversion ratio (PCR). (d) The axial ratio and the LTC conversion efficiency. The incident angle is zero, and the polarization angle is 45°.
Besides, the stocks parameters are usually used to characterize the performances of LTC converter. Ellipticity and PCR are calculated and plotted in solid and dashed lines, respectively in Fig. 2(c). It can be found that from 9.87 to 11.03THz (pink region), χ is smaller than −0.95, which indicates that LTRCP is achieved and the relative bandwidth is 11.1%; χ is −1 at 10.44 THz, which indicates that perfect LTRCP is achieved. From 13.16 to 14.43THz (blue region), χ is larger than 0.95, which indicates that LTLCP is achieved and the relative bandwidth is 9.2%; χ is 1 at 13.90 THz, which indicates that perfect LTLCP is achieved. In addition, the PCR peaks’ positions are almost the same with those of Rvu peaks respectively, and the values of the resonant peaks (plotted in the orange dashed line) reach 94.7%, 99.5% and 94.3%, respectively. Further, the axial ratio ($\textrm{ = 10log}|{{\textrm{r}_{\textrm{vu}}}\textrm{/}{\textrm{r}_{\textrm{uu}}}} |$) is also used to describe the performances of LTC and the results are shown in Fig. 2(d). It is noteworthy that from 9.69 to 11.36 THz (the relative bandwidth 15.9%) and 12.79 to 14.61 THz (the relative bandwidth 13.3%), double bands of LTC with 3dB bandwidth have been realized. The bandwidth defined with χ is a little smaller than the one defined with axial ratio. Besides, the three peaks’ positions of the axial ratio are the same with those of PCR peaks. Then, the energy conversion efficiency is also calculated and represented by the blue dashed line. The efficiencies of the two bands of LTC with 3dB bandwidth are both larger than 73%. These characteristics mentioned above make the proposed design a novel and high efficient dual-band polarization converter with opposite handedness.
3.2 Physical mechanisms
To better understand the physical mechanism of the LTC polarization conversion, we tried to find these eigenmodes excited by the u-polarized incident plane wave, which can be divided into two orthogonal polarized components Exi and Eyi. Figure 3(a) shows the co-polarization reflections Rxx, and Ryy under Exi and Eyi incidence in green and blue solid lines, respectively. There is one dip for Rxx at 12.05THz and two dips for Ryy at 9.42 and 14.89THz respectively, corresponding to the three PCR peaks in Fig. 2(c), respectively. The phase difference between Rxx, and Ryy approximately equal to −90° and 90° at 10.44 and 13.90THz, and thus the superimposition of two reflected orthogonal components can produce the perfect right-hand and left-hand circular polarization at these two resonant frequencies, respectively. Thus, the double bands with opposite handedness of LTC occur. The Exi incidence could excite one mode at 12.05THz, and symmetric magnetic field profile about y axis is shown in Fig. 3(c). Eyi incidence excites the other two resonances at 9.42 and 14.89 THz, and the antisymmetric magnetic field profiles about y axis are shown in Figs. 3(b) and (d). All the three modes originate from the excitation of the graphene surface plasmons (GSPs) [56]. The GSPs mode at 12.05THz is excited along x direction, so magnetic field profile is antisymmetric about x axis. The GSPs modes at 9.42 and 14.89 THz are excited along y direction, so magnetic field profile is antisymmetric about y axis. Besides, the two GPSs modes along y axis originate from the coupling between the horizontal slots. In the further way, the two LTC bands with opposite handedness also stem from the three GSPs modes.
Fig. 3. (a) Simulated results of co-polarization reflections Rxx and Ryy with frequency are plotted with green and blue solid lines for the incidence Exi and Eyi respectively. The phase difference is plotted with red dashed line. The magnetic field profiles Hz at three resonant frequencies (b) 9.42THz, (c) 12.05THz and (d) 14.89THz, respectively.
3.3 Tunable dual-band LTC polarization converter with opposite handedness
Next, we investigate the tunable property of our dual-band circular polarizer by varying the Fermi energy from 0.6 to 1eV. The ellipticities (χ), the phase difference between ruu and rvu, and the axial ratio with different Ef and frequency are shown in Fig. 4. The dashed lines in Fig. 4(a) indicate the positions of |χ| equal to 0.95. The dashed lines from left to right in Fig. 4(b) show the positions of −85°, −95°, 95° and 85°, respectively, and the dashed lines in Fig. 4(c) show the positions for the axial ratio equal to ±3. It is obviously the two bands of LTC both blue shift with Ef increasing. The LTC bands can cover a broad range from 8.1 to 14.4THz with |χ|>0.95, and 3dB band from 7.2 to 14.6THz. The blue shift behavior occurs because of the excitation of the GSPs. The wave vector of the GSPs is written as ${\textrm{K}_{\textrm{SPP}}}\textrm{ = (}\hbar {\mathrm{\omega }^\textrm{2}}\textrm{)/(2}{\mathrm{\alpha }_\textrm{0}}\textrm{c}{\textrm{E}_\textrm{f}}\textrm{)}$ [57]. Where ${\mathrm{\alpha }_\textrm{0}} = {\textrm{e}^\textrm{2}}\textrm{/}\hbar \textrm{c}$ represents the fine structure constant. Therefore, the resonant frequency can be defined as follows:
Where LG is the resonant characteristic length proportional to the graphene slots, inverse proportional to the width of slots. Thus, increase of the Fermi energy leads to the blueshift of the resonant frequencies of the three GSPs modes, so does the two bands of LTC. Especially, the simulation demonstrates our proposed structure can achieve the LTLCP changing to LTRCP with increasing Ef. For example, when Ef = 0.6eV and the working frequency is 10.4THz, the perfect line-to-left-circular-polarization is achieved (χ=1, Δφ=90°, and axial ratio is zero); for the Ef=0.98eV and the same working frequency 10.4THz, the perfect line-to-right-circular-polarization is achieved (χ=−1, Δφ=−90°, and axial ratio is zero).
Fig. 4. Calculated (a) ellipticity χ, (b) phase difference Δφ, and (c) the axial ratio of the proposed circular polarization converter as a function of the operation frequency and Fermi energy ranging from 0.6 to 1 eV. Other parameters are the same with those of Fig. 2.
3.4 Influence of scattering time on the LTC polarization converter
We also investigate the influence of the scattering times on the performances of the polarization conversion, and previous studies have shown that the electron scattering time τ can vary within a large range of ps or sub-ps [58,59]. As shown in Fig. 5, the two bands of LTC have no frequency shift as the scattering times varying from 0.4 to 1ps compared with the results of Fig. 2, when other parameters are the same with those of Fig. 2. The perfect right-hand and left-hand circular polarization always happens at 10.44 and 13.90THz, respectively. The bandwidths for the two LTC bands are almost unchanged, and three peaks of axial ratio at 9.42, 12.05 and 14.89THz increase with increasing electron scattering time.
Fig. 5. (a) Simulated (a) ellipticity χ, (b) phase difference Δφ, and (c) the axial ratio of the proposed circular polarization converter with frequency under the different the electron scattering time τ. Other parameters are the same with those of Fig. 2.
3.5 Influence of geometric parameters on the LTC polarization converter
We further explore the influence of different geometric parameters L1, L2, w and g on the performances of the dual-band LTC with opposite handedness, including ellipticity χ, phase difference Δφ, and the axial ratio. As shown in Figs. 6(a)-(c), it is found that the increase of the length of L1 leads to the redshift of the first and third peaks of the axial ratio, which originates from the excitation of two antisymmetrical GSPs modes; and no obvious shift of the second peak of the axial ratio, which originates from the excitation of the symmetrical GSPs mode. It is because the increase of the length of L1 makes Lg of the antisymmetrical GSPs modes increase based on Eq. (9). Thus, the band with |χ|> 0.95 of LTRCP broadens from the frequency range (10.5 to 10.6THz) to one (9.55 to 11.25THz), and the one of LTLCP narrows from frequency range (13 to 14.75THz) to one (13.55 to 14THz), with increasing L1 from 0.54 to 0.62 µm. In a similar way, the band with 3dB bandwidth of LTRCP broadens from frequency range (10.05 to 11.2THz) to one (9.4 to 11.55THz), and the one of LTLCP narrows from frequency range (12.7 to 14.9THz) to one (13 to 14.3 THz), with increasing L1 from 0.54 to 0.62 µm. It can be found that the band of line-to-right-circular-polarization narrows, and the one of line-to-left-circular-polarization broadens with increasing L2, as shown in Figs. 6(d)-(f). It is because that the increase of the length of L2 lead to the redshift of the second peak of the axial ratio, which originates from the excitation of the symmetrical GSPs modes; and the other two peaks of the axial ratio keep unchanged. The redshift of the second peak of the axial ratio originates from the increase of Lg of the symmetrical GSPs modes. Figures 6(g)-(i) show the bands of line-to-right-circular and line-to-left-circular polarization both blue shift, because the excitation frequencies of three GSPs modes all blue shift with increasing w from 0.05 to 0.13 µm. In a similar way, the increase of w leads to decrease of Lg of the three GSPs modes based on Eq. (9). At last, Figs. 6(j)-(l) show the results for the performances of the dual-band LTC under different g, the phenomenon and reason are the same with those of changing the geometric parameters L1.
Fig. 6. Simulated (a), (d), (g), (j) ellipticity χ, (b), (e), (h), (k) phase difference Δφ, and (c), (f), (i), (l) the axial ratio of the proposed circular polarization converter with frequency under different L1, L2, w, and g, respectively. Other parameters are the same with those of Fig. 2.
3.6 Angle insensitivity
To investigate the performance of our dual-band LTC polarization converter with angle insensitivity, we calculate the ellipticity χ and axial ratio under different incident angle from 0° to 60°. As shown Fig. 7(a), the dashed lines represent the positions of |χ|=0.95. The band of LTRCP ranges from 9.87 to 11.03THz when the incident angle is zero, and then this LTC band shrinks to the range from 9.5 to 9.55THz when the incident angle is 60°. The band of LTLCP also shrinks with increasing the incident angle, and the band is from 13.15 to 13.8THz when the incident angle is 60°. In Fig. 7(b), the dashed lines represent the positions of axial ratio equal to ±3. It is found the 3dB band of line-to-right-circular polarization changes a little with increasing the incident angle, and one band split into two bands when the incident angle is 60°. Besides, the 3dB band of line-to-left-circular polarization broadens a little with increasing the incidents angle. So, the dual-band with opposite handedness of LTC is still existent even for the incident angle equal to 60°, which shows the angle insensitivity of our polarizer converter.
Fig. 7. (a) The ellipticity χ and (b) axial ratio of the proposed polarizer with frequency under incident angle θ ranging from 0°to 60°. Other parameters are the same with those of Fig. 2.
Further, we investigate the effect of the polarization angle on performances of the dual-band LTC. It is well known that the polarization conversion stems from the anisotropy of the metasurface and is closely related with the polarization angle of the incident light. Therefore, we vary the polarization angle from 15° to 75° to observe the response of the graphene metasurface. Figure 8(a) shows the ellipticity χ with frequency and polarization angle, and the dashed lines represent the positions of |χ|=0.95. It is found that the two bands with |χ|>0.95 of LTC are always existent with polarization angles increasing from 35° to 55°, and the bandwidths of the bands reach maximum when the polarization angle is 45°. Figure 8(b) shows the axial ratio with frequency and polarization angle, and the dashed lines represent the positions of axial ratio equal to ±3. It is found the two 3dB bands of LTC are always existent with polarization angles varying from 17° to 69°, and the two bands split into two respectively when the polarization angle is out of the range from 17° to 69°.
Fig. 8. The ellipticity χ and (b) axial ratio of the proposed polarizer with frequency under polarization angle ranging from 15°to 75°. Other parameters are the same with those of Fig. 2.
3.7 Comparisons with other polarizers
Finally, we compared this design with other reported graphene-based LTC polarizers to illustrate the innovation and performance of this design, as shown in Table 1. Here, the results of our work are as shown in Fig. 2. The proposed device creatively realizes dual-band LTC polarization conversion with opposite handedness and broad relative bandwidths. Our polarizer provides the opportunity for the dynamical modulation of the state of circular polarization.
Table 1. Comparisons between our proposed design and reported similar works on graphene-based LTC polarization converters
4. Conclusion
In summary, we have proposed a tunable dual-band reflective LTC polarization converter, which is composed of a single graphene layer with periodic I-shaped nano-slots. Due to the excitation of the three GSPs modes under TM-polarized plane wave, the double LTC bands with opposite handedness are obtained which operates in two frequency ranges of 9.69-11.36THz and 12.79-14.61THz with an axial ratio of less than 3 dB, respectively. The LTRCP and LTLCP bands range from 9.87 to 11.03THz, and from 13.16 to 14.43THz with |χ| >0.95, respectively. By varying the Fermi energy, the tunable responses of the dual-band LTC are discussed, and the conversion between LTRCP and LTLCP can be achieved. Moreover, the performances of the dual-band LTC under different geometric parameters, incident angle, and polarization angle are also investigated, and our polarizer shows good angle-independent property. Therefore, our design offers a feasible way of the polarization manipulation in THz field and has shown prospect in a compact THz communication system to effectively control polarization at a subwavelength thickness.
Funding
Jiangsu Provincial Key Research and Development Program (BE2020756); National College Students Innovation and Entrepreneurship Training Program (202010295062); National Natural Science Foundation of China (1148081606193050).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1(1), 26–33 (2002). [CrossRef]
2. F. Zangeneh-Nejad and R. Safian, “A Graphene-Based THz Ring Resonator for Label-Free Sensing,” IEEE Sens. J. 16(11), 4338–4344 (2016). [CrossRef]
3. J. P. Fan and Y. Z. Cheng, “Broadband high-efficiency cross-polarization conversion and multi-functional wavefront manipulation based on chiral structure metasurface for terahertz wave,” J. Phys. D: Appl. Phys. 53(2), 025109 (2020). [CrossRef]
4. W. L. Chan, M. L. Moravec, R. G. Baraniuk, and D. M. Mittleman, “Terahertz imaging with compressed sensing and phase retrieval,” Opt. Lett. 33(9), 974–976 (2008). [CrossRef]
5. T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003). [CrossRef]
6. X. J. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin “guest-host” micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19(6), 5565–5573 (2011). [CrossRef]
7. I. A. Gayduchenko, G. E. Fedorov, M. V. Moskotin, D. I. Yagodkin, S. V. Seliverstov, G. N. Goltsman, A. Yu Kuntsevich, M. G. Rybin, E. D. Obraztsova, V. G. Leiman, M. S. Shur, T. Otsuji, and V. I. Ryzhii, “Manifestation of plasmonic response in the detection of sub-terahertz radiation by graphene-based devices,” Nanotechnology 29(24), 245204 (2018). [CrossRef]
8. C. P. Huang, Q. J. Wang, X. G. Yin, Y. Zhang, J. Q. Li, and Y. Y. Zhu, “Break through the limitation of Malus’ Law with plasmonic polarizers,” Adv. Opt. Mater. 2(8), 723–728 (2014). [CrossRef]
9. V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express 18(18), 19087–19094 (2010). [CrossRef]
10. L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Characterization of birefringent material using polarization-controlled terahertz spectroscopy,” Opt. Express 18(19), 20491–20497 (2010). [CrossRef]
11. T. Cai, S. W. Tang, B. Zheng, G. M. Wang, W. Y. Ji, C. Qian, Z. J. Wang, E. P. Li, and H. S. Chen, “Ultrawideband chromatic aberration-free meta-mirrors,” Adv. Photonics 3(1), 016001 (2020). [CrossRef]
12. Y. Zhao, X. Y. Cao, J. Gao, X. Liu, and S. J. Li, “Jigsaw puzzle metasurface for multiple functions: polarization conversion, anomalous reflection and diffusion,” Opt. Express 24(10), 11208–11217 (2016). [CrossRef]
13. M. I. Khan, Z. Khalid, and F. A. Tahir, “Linear and circular-polarization conversion in X-band using anisotropic metasurface,” Sci. Rep. 9(1), 4552 (2019). [CrossRef]
14. J. H. Shi, Q. C. Shi, Y. X. Li, G. Y. Nie, C. Y. Guan, and T. J. Cui, “Dual-polarity metamaterial circular polarizer based on giant extrinsic chirality,” Sci. Rep. 5(1), 16666 (2015). [CrossRef]
15. T. Cao, C. W. Wei, L. B. Mao, and Y. Li, “Extrinsic 2D chirality: giant circular conversion dichroism from a metal-dielectric-metal- square array,” Sci. Rep. 4(1), 7442 (2015). [CrossRef]
16. K. Song, Y. H. Liu, C. R. Luo, and X. P. Zhao, “High-efficiency broadband and multiband cross-polarization conversion using chiral metamaterial,” J. Phys. D: Appl. Phys. 47(50), 505104 (2014). [CrossRef]
17. Y. Z. Cheng, W. Y. Li, and X. S. Mao, “Triple-band polarization angle independent 90 degrees polarization rotator based on Fermat’s spiral structure planar chiral metamaterial,” Prog. Electromagn. Res. 165, 35–45 (2019). [CrossRef]
18. G. X. Zheng, H. Mühlenbernd, M. Kenney, G. X. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10(4), 308–312 (2015). [CrossRef]
19. T. Li, X. B. Hu, H. M. Chen, C. Zhao, Y. Xu, X. Wei, and G. F. Song, “Metallic metasurfaces for high efficient polarization conversion control in transmission mode,” Opt. Express 25(20), 23597–23604 (2017). [CrossRef]
20. X. L. Ma, C. Huang, M. B. Pu, C. G. Hu, Q. Feng, and X. G. Luo, “Multi-band circular polarizer using planar spiral metamaterial structure,” Opt. Express 20(14), 16050–16058 (2012). [CrossRef]
21. K. Y. Liu, G. M. Wang, T. Cai, and T. Y. Li, “Dual-band transmissive circular polarization generator with high angular stability,” Opt. Express 28(10), 14995–15005 (2020). [CrossRef]
22. M. I. Khan, Q. Fraz, and F. A. Tahir, “Ultra-wideband cross polarization conversion metasurface insensitive to incidence angle,” J. Appl. Phys. 121(4), 045103 (2017). [CrossRef]
23. J. Yang and J. S. Zhang, “Subwavelength quarter-waveplate composed of L-shaped metal nanoparticles,” Plasmonics 6(2), 251–254 (2011). [CrossRef]
24. Y. N. Jiang, H. P. Zhao, L. Wang, J. Wang, W. P. Cao, and Y. Y. Wang, “Broadband linear-to-circular polarization converter based on phosphorene metamaterial,” Opt. Mater. Express 9(5), 2088–2097 (2019). [CrossRef]
25. J. Aplinc, A. Pusovnik, and M. Ravnik, “Designed self-assembly of metamaterial split-ring colloidal particles in nematic liquid crystals,” Soft Matter 15(28), 5585–5595 (2019). [CrossRef]
26. D. X. Yan, M. Meng, J. S. Li, J. N. Li, and X. J. Li, “Vanadium dioxide-assisted broadband absorption and linear-to-circular polarization conversion based on a single metasurface design for the terahertz wave,” Opt. Express 28(20), 29843–29854 (2020). [CrossRef]
27. K. H. Wang and J. S. Li, “Muti-band terahertz modulator based on double metamaterial/perovskite hybrid structure,” Opt. Commun. 447, 1–5 (2019). [CrossRef]
28. S. N. Guan, J. R. Cheng, T. H. Chen, and S. J. Chang, “Widely tunable polarization conversion in low-doped graphene-dielectric metasurfaces based on phase compensation,” Opt. Lett. 45(7), 1742–1745 (2020). [CrossRef]
29. C. H. Gan, H. S. Chu, and E. P. Li, “Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies,” Phys. Rev. B 85(12), 125431 (2012). [CrossRef]
30. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010). [CrossRef]
31. K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012). [CrossRef]
32. D. Wu, M. Wang, H. Feng, Z. X. Xu, Y. P. Liu, F. Xia, K. Zhang, W. J. Kong, L. F. Dong, and M. J. Yun, “Independently tunable perfect absorber based on the plasmonic in double-layer graphene structure,” Carbon 155, 618–623 (2019). [CrossRef]
33. C. Yang, Y. Luo, J. X. Guo, Y. Pu, D. He, Y. D. Jiang, J. M. Xu, and Z. J. Liu, “Wideband tunable mid-infrared cross polarization converter using rectangle-shape perforated graphene,” Opt. Express 24(15), 16913–16922 (2016). [CrossRef]
34. Z. F. Yao, T. T. Wei, Y. K. Wang, M. J. Lu, C. Y. Zhang, and L. L. Zhang, “Tunable multifunctional reflection polarizer based on a graphene metasurface,” Appl. Opt. 58(13), 3570–3574 (2019). [CrossRef]
35. Z. Liu and B. F. Bai, “Ultra-thin and high-efficiency graphene metasurface for tunable terahertz wave manipulation,” Opt. Express 25(8), 8584–8592 (2017). [CrossRef]
36. H. J. Zhang, Y. Liu, Z. Q. Liu, X. S. Liu, G. Q. Liu, G. L. Fu, J. Q. Wang, and Y. Shen, “Multi-functional polarization conversion manipulation via graphene-based metasurface reflectors,” Opt. Express 29(1), 70–81 (2021). [CrossRef]
37. N. K. Grady, J. E. Heyes, D. R. Chowdhury, Y. Zeng, M. T. Reiten, A. K. Azad, A. J. Taylor, D. A. R. Dalvit, and H. T. Chen, “Terahertz metamaterials for linear polarization conversion and anomalous refraction,” Science 340(6138), 1304–1307 (2013). [CrossRef]
38. F. Zeng, L. F. Ye, L. Li, Z. H. Wang, W. Zhao, and Y. Zhang, “Tunable mid-infrared dual-band and broadband cross-polarization converters based on U-shaped graphene metamaterials,” Opt. Express 27(23), 33826–33840 (2019). [CrossRef]
39. D. B. Chen, J. B. Yang, J. Huang, W. Bai, J. J. Zhang, Z. J. Zhang, S. Y. Xu, and W. L. Xie, “The novel graphene metasurfaces based on split-ring resonators for tunable polarization switching and beam steering at terahertz frequencies,” Carbon 154, 350–356 (2019). [CrossRef]
40. T. J. Guo and C. Argyropoulos, “Broadband polarizers based on graphene metasurfaces,” Opt. Lett. 41(23), 5592–5595 (2016). [CrossRef]
41. Z. F. Yao, M. J. Lu, C. Y. Zhang, and Y. K. Wang, “Dynamically tunable and transmissive linear to circular polarizer based on graphene metasurfaces,” J. Opt. Soc. Am. B 36(12), 3302–3306 (2019). [CrossRef]
42. X. F. Zang, S. J. Liu, H. H. Gong, Y. J. Wang, and Y. M. Zhu, “Dual-band superposition induced broadband terahertz linear-to-circular polarization converter,” J. Opt. Soc. Am. B 35(4), 950–957 (2018). [CrossRef]
43. L. Zeng, T. Huang, G. B. Liu, and H. F. Zhang, “A tunable ultra-broadband linear-to-circular polarization converter containing the graphene,” Opt. Commun. 436, 7–13 (2019). [CrossRef]
44. S. N. Guan, J. R. Cheng, T. H. Chen, and S. J. Chang, “Bi-functional polarization conversion in hybrid graphene-dielectric metasurfaces,” Opt. Lett. 44(23), 5683–5686 (2019). [CrossRef]
45. G. Deokar, J. Avila, I. Razado-Colambo, J. L. Codron, C. Boyaval, E. Galopin, M.-C. Asensio, and D. Vignaud, “Towards high quality CVD graphene growth and transfer,” Carbon 89, 82–92 (2015). [CrossRef]
46. A. N. Abbas, G. Liu, B. L. Liu, L. Y. Zhang, H. Liu, D. Ohlberg, W. Wu, and C. W. Zhou, “Patterning, characterization, and chemical sensing applications of graphene nanoribbon arrays down to 5 nm using helium ion beam lithography,” ACS Nano 8(2), 1538–1546 (2014). [CrossRef]
47. G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]
48. T. T. Kim, S. S. Oh, H.-D. Kim, H. S. Park, O. Hess, B. Min, and S. Zhang, “Electrical access to critical coupling of circularly polarized waves in graphene chiral metamaterials,” Sci. Adv. 3(9), e1701377 (2017). [CrossRef]
49. J. S. Gómez-Díaz and J. Perruisseau-Carrier, “Graphene-based plasmonic switches at near infrared frequencies,” Opt. Express 21(13), 15490–15504 (2013). [CrossRef]
50. C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. S. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011). [CrossRef]
51. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. 22(7), 1099–1119 (1983). [CrossRef]
52. C. Menzel, C. Rockstuhl, and F. Lederer, “Advanced Jones calculusfor the classification of periodic metamaterials,” Phys. Rev. A 82(5), 053811 (2010). [CrossRef]
53. J. Ding, B. Arigong, H. Ren, M. Zhou, J. Shao, Y. K. Lin, and H. L. Zhang, “Efficient multiband and broadband cross polarization converters based on slotted L-shaped nanoantennas,” Opt. Express 22(23), 29143–29151 (2014). [CrossRef]
54. J. M. Hao, Y. Yuan, L. X. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef]
55. L. Cong, W. Cao, X. Q. Zhang, Z. Tian, J. Q. Gu, R. J. Singh, J. G. Han, and W. L. Zhang, “A perfect metamaterial polarization rotator,” Appl. Phys. Lett. 103(17), 171107 (2013). [CrossRef]
56. J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012). [CrossRef]
57. F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011). [CrossRef]
58. A. Ghaffar, I. Toqeer, M. Z. Yaqoob, M. A. S. Alkanhal, Y. Khan, and Q. A. Naqvi, “Scattering and absorption characteristics of graphene coated metamaterial cylinder,” Results Phys. 15, 102787 (2019). [CrossRef]
59. P. Neugebauer, M. Orlita, C. Faugeras, A. L. Barra, and M. Potemski, “How perfect can graphene be?” Phys. Rev. Lett. 103(13), 136403 (2009). [CrossRef]
60. W. Zhang, J. L. Jiang, J. Yuan, S. Liang, J. S. Qian, J. Shu, and L. Y. Jiang, “Functionality-switchable terahertz polarization converter based on a graphene-integrated planar metamaterial,” OSA Continuum 1(1), 124–135 (2018). [CrossRef]
