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Abstract
We propose a tunable dual-band reflective cross-polarization converter composed of periodically arranged single layer U-shaped graphene nanostructures in mid-infrared region. The proposed dual-band reflective cross-polarization converter can convert the polarization state of an incident wave from the linear polarization state to its cross polarization state at the operating frequencies of 34.67 and 44.13 THz with the high-efficiency polarization conversion ratio (PCR) approaching 100%. Furthermore, as a complementary structure, a reflective cross-polarization converter with a hollow-carved U-shaped graphene sheet shows a broadband polarization conversion performance with a bandwidth of 1 THz and the PCR over 90%. The bandwidth of this broadband converter can be further extended to 2 THz after certain geometric parameter optimization. More importantly, both the dual-band and broadband cross-polarization converters not only can dynamically tune their PCR peak frequencies and magnitudes by adjusting the chemical potential and relaxation time of graphene without changing the geometric structure but also have good angular stability with high PCR in a wide range of incident angle up to 55°. These polarization converters may have great potential applications in mid-infrared spectroscopy, radiometer, sensor, and other photonic devices.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Polarization converters can manipulate the polarization states of the electromagnetic (EM) waves, which have many applications in imaging, detection and optical communication [1–3]. Because polarization is one of the most important properties of EM waves, controlling the polarization states of EM waves effectively is highly desirable. However, conventional polarization converters are usually achieved based on birefringence effects, dichroic crystal, and optical grating [4–6], which require a long propagation distance to obtain phase accumulation between two orthogonal polarization components and consequently generate bulky size. Therefore, these methods are not suitable for device miniaturization and integration. Investigation and design of compact and lightweight polarization converter have attracted increasing attention in recent years. With some special properties of in-phase reflection, negative refraction indices, and axially frozen modes, metamaterials have been widely applied to the development of ultrathin miniaturized polarization converters to manipulate polarization states. Generally, metamaterial polarization converters have two polarization manipulation modes, the transmission mode and reflection mode. For the transmission mode, the method of realizing polarization conversion mainly relies on the optical activity of chiral metamaterials and the birefringence effect of anisotropic metamaterials [7–10]. For the reflection mode, the approach to achieve polarization conversion mainly depends on the design of converter with single-layer pattern metasurface and topological design based on symmetry-based coding [11–13]. Recently, various metamaterial polarization converters including dual-band, multiband, and broadband converters have been proposed one after another [14–16]. However, because most of the proposed metamaterial converters are made up of conventional metallic and dielectric materials, the polarization manipulation properties are lack of dynamic adjustability once the devices are fabricated.
Graphene is a single layer carbon atom arranged in a hexagonal lattice two-dimensional material with outstanding mechanical, electrical, and optical properties including fast carrier mobility, high optical transparency, and tunability [17], which is a promising tunable material for various electro-optical devices. Taking the advantage of supporting surface plasmon polaritons (SPPs) in the terahertz and infrared ranges [18], graphene has been widely applied in the tunable plasmonic devices including polarization converters [19–21], waveguides [22], modulators [23,24], photodetectors [25–27], and absorbers [28–33]. Compared to conventional metamaterial converters, one of the most significant advantages of graphene-based converters is the dynamic adjustability achieved by changing the chemical potential through external voltage. For example, for the reflection mode, Yang et al. proposed a tunable mid-infrared cross-polarization converter using rectangle-shape perforated graphene [34]. Zhu et al. proposed a broadband tunable terahertz cross-polarization converter based on a sinusoidally-slotted graphene metamaterial [35]. Chen et al. presented a wideband tunable cross polarization converter based on a graphene metasurface with a hollow-carved “H” array [36]. Xu et al. put forward a tunable broadband cross-polarization converter based on $\phi$-shaped graphene pattern [37]. Ding et al. also demonstrated mid-infrared tunable dual-frequency cross polarization converters using graphene-based L-shaped nanoslot array [19]. These graphene polarization converters have a remarkable advantage of dynamical tunability, which provides a new possible application in the tunable polarizers. However, despite the recent progress, to realize an actively tunable graphene converter with dual-band/broadband, high polarization conversion ratio (PCR), wide-angle, and large frequency reconfiguration simultaneously still remains a challenge.
In this paper, we propose a tunable dual-band reflective cross-polarization converter based on periodically arranged single layer U-shaped graphene nanostructures in mid-infrared regions. This tunable dual-band reflective cross-polarization converter operates at frequencies of 34.67 THz and 44.13 THz with the high-efficiency PCR approaching near-unity. Then, we propose a broadband reflective cross-polarization converter by using a hollow-carved U-shaped graphene sheet. And the bandwidth of this broadband polarization converter can be extended to 2 THz after parameter optimization. The results show that the peak frequencies and the magnitudes of PCR for both dual-band and broadband cross-polarization converters can be dynamically tuned by adjusting the chemical potential and relaxation time of graphene without changing the geometric structure. Furthermore, the proposed converters possess angle insensitivity and are capable of working well with high PCR in a wide range of incident angles within 55°. Therefore, the investigation of graphene converters will be of great significance.
2. Design and methods
Figure 1(a) demonstrates the schematic diagrams of the unit cell of the proposed dual-band cross-polarization converter, which is composed of periodically arranged single layer U-shaped graphene nanostructures, a zirconium dioxide (Zro2) dielectric spacer layer, and a metal reflector layer. When a linearly polarized wave illuminates the graphene converter, the polarization state of the reflected wave can be converted. Figure 1(b) depicts the proposed broadband cross-polarization with a complementary hollow-carved U-shaped graphene. In both converters, the U-shaped structures are rotated 45° anticlockwise from x-axis. The thickness of graphene sheet, dielectric spacer, and metal reflector layer are set as h1 = 0 µm, h2 = 1.1 µm, and h3 = 0.1 µm, respectively. The initial values of other geometric parameters are defined as p = 0.095 µm, w = 0.026 µm, g = 0.01 µm, d = 0.028 µm, l = 0.064 µm, as illustrated in Fig. 1. It is worth mentioning that the proposed converters can be produced through state-of-the-art nanoimprint lithography and large-scale graphene synthesis, transfer, and etching techniques [38–40].
Fig. 1. (a) Schematic diagram of the proposed dual-band reflective cross-polarization converter with periodically arranged single layer U-shaped graphene nanostructures. (b) Schematic diagram of the proposed broadband reflective cross-polarization converter with a hollow-carved U-shaped graphene sheet.
In the finite element method (FEM) simulation, periodic boundary conditions are applied along the x-direction and y-direction of the unit cell, and the Floquet ports are assigned in the z-direction. In the mid-infrared range, the surface conductivity of graphene is calculated by Kubo formula as σg = σintra + σinter (Unit: S) [41,42],
3. Results and discussion
3.1 Dual-band cross-polarization converter
To begin with, we investigate the polarization conversion rate (PCR) of the proposed dual-band cross-polarization converter (Fig. 1(a)) under normal incidence. The chemical potential and relaxation time of graphene are initially assumed to be μc = 1.0 eV and τ = 0.8 ps [10,47], respectively, and the temperature (T) is set as 300 K. As illustrated in Fig. 2(a), the simulated co-polarization reflectance (Rxx), cross-polarization reflectance (Ryx), and PCR of the proposed converter as a function of frequency are represented in green (dashed line), blue (dashed line), and red (solid line), respectively. It is found that two reflection peaks are observed in Ryx at 34.67 THz and 44.13 THz corresponding to the dips of near-zero reflection of Rxx. Accordingly, the reflective PCR spectrum demonstrates two peaks of 96.98% and 94.94% located at the frequencies of 34.67 THz and 44.13 THz, respectively. We define the phase difference (Δφ) between the x and y components of the reflected waves as $\Delta \varphi = \arg ({R_{yx}}) - \arg ({R_{xx}})$, indicating all possible polarization states of reflected waves such as circular, linear, and elliptical polarization states, respectively. When the Δφ = nπ, linear polarization waves can convert to its cross polarization waves. When Ryx =Rxx and Δφ = n ± 90°, the linear states can convert to circular polarization states, where Δφ = n + 90° indicates the left circular polarization and Δφ = nπ - 90° for the right circular polarization, respectively. As shown in Fig. 2(b), it is clearly found that the phase difference Δφ between two reflectance components Rxx and Ryx come close to 180° and 0° at the two frequencies of 34.67 THz and 44.13THz, respectively, where the linear polarization waves convert to its cross polarization waves. When the Rxx and of Ryx equal 0.5, as well as the phase difference around nπ ± 90° occurs at the four frequency points of 34.19, 35.21, 43.78, 44.39 THz, respectively, indicating the circular polarization reflected waves are achieved. At other frequencies, the reflected waves are in elliptical polarization states, due to the amplitudes of Rxx and Ryx are different even if the Δφ is nπ ± 90°. Therefore, the proposed dual-band reflective polarization converter with U-shaped graphene nanostructures can achieve perfect polarization transformations from a linear polarization wave to its cross, circular, and elliptical polarization waves at different frequencies. Furthermore, to investigate the physical origin of the proposed converter with U-shaped graphene nanostructure, we display the magnetic field (Hz) profiles cut on graphene plane (z = 0 µm) at frequencies of 34.67 THz and 44.13 THz under x-polarized incidence, as shown in Fig. 3. It is found that the magnetic fields at these frequencies are mainly concentrated on different edges of U-shaped graphene nanostructure, indicating strong surface plasmon polariton (SPP) resonance phenomenon. The coupling of graphene SPP mode with Fabry-Perot resonances results in phase differences and polarization conversion characteristics.
Fig. 2. (a) Simulation results of the reflectance components Rxx, Ryx, and PCR under normal incidence, respectively. (b)The phase difference (Δφ) between reflectance components Rxx and Ryx.
Fig. 3. The magnetic field profiles (Hz) for the normal x-polarized incidence at (a) 34.67 THz and (b) 44.13 THz.
In order to better understand the mechanism of the two resonant modes, we decompose the x-polarized incident wave into two vertical components as $\vec{E}_x^i = \vec{u}E_{xu}^{i}e^{j\phi } + \vec{v}E_{xv}^{i}e^{j\phi }$, as shown in Fig. 4(a). Similarly, the reflected wave can be expressed as $\vec{E}_{x}^r = \vec{u}E_{xu}^{r} + \vec{v}E_{xv}^{r} = \vec{u}{r_u}E_{xu}^{i}{e^{j(\phi + {\varphi _u})}} + \vec{v}{r_v}E_{xv}^{i}{e^{j(\phi + {\varphi _v})}}$, where ru and rv represent the reflected coefficients along the u-axis and v-axis which are + 45° and -45° rotation from the x directions, respectively. The x-polarized incident wave can be decomposed into two orthogonal incident polarization components along the + 45° and -45°. The Ruu and Rvv are the reflection coefficients of + 45° and −45° polarization incidence, respectively. As shown in Fig. 4(b), the components Ruv and Rvu are approaching 0, indicating polarization conversion is negligible. While, two reflection coefficients Ruu and Rvv are plotted in blue and magenta solid lines, respectively. It is found that two resonance modes at 34.67 THz and 44.13 THz is excited by the orthogonal components, respectively. The -45° polarization component excites one LSSP mode resonance at 34.67 THz, and the + 45° polarization component excites the other LSSP mode resonance at 44.13 THz. It should be pointed out that the dips of Ruu and Rvv are shallower than that of Rxx shown in Fig. 2(a), which results from larger impedance mismatching between the converter and the free space under ± 45° polarization incidence than that under 0° polarization incidence. Furthermore, these two modes also exhibit a phase difference ($\Delta \varphi = \arg ({R_{vv}}) - \arg ({R_{uu}})$) of about 180° as shown in Fig. 4(b). A similar conclusion can be drawn from the distribution of magnetic field distributions. As shown in Figs. 4(c) and 4(d), for the -45° polarization incidence, the magnetic fields Hz are concentrated on the edges of the length l of U-shaped at 34.67 THz and there are almost no magnetic fields at 44.13 THz. While for the + 45° polarization incidence, as shown in Figs. 4(e) and 4(f), the magnetic fields are mainly located in the edges of the width w of U-shaped graphene sheet and a small part of fields are concentrated on the length l at 44.13 THz, as well as almost no energy is distributed at 34.67 THz. Therefore, the recombination of the two reflection components also results in cross-polarization in dual bands at 34.67 and 44.13 THz.
Fig. 4. (a) The schematic diagram of the decomposed u- and v- components of different polarizations. (b) Simulated PCR, reflection coefficients (Ruu and Rvv) and the phase difference between Ruu and Rvv for the + 45°and -45° polarized waves under normal incidence. (c)–(f) Simulated magnetic field distributions (Hz) at 34.67 and 44.13 THz under -45°and + 45° polarized incidence, respectively.
We further investigate the influence of geometric parameters on the PCR under normal incidence by varying the size of U-shaped graphene nanostructure. Figure 5(a) indicates the dependence of PCR on the length of l ranging from 62 to 68 nm with a step of 2 nm while maintaining the other geometric parameters fixed. It is clear that the adjustment of length l has an important effect on both frequency bands, and both the dual-band operating frequencies show a clear redshift. The redshift of the first band is more obvious than the second one, which can be expected from the magnetic field profiles in Figs. 3(a) and 3(b). The magnetic field energy is mainly concentrated on the edge of the length l at the first frequency point of 34.67 THz and a small part of the energy is concentrated on the length l at the second frequency of 44.13 THz. Therefore, the adjustment of length l has a greater impact on the first frequency point than the second one. On the other hand, as the width w increases from 22 to 28 nm with a step of 2 nm, the second operating band also presents a large redshift, which is consistent with the magnetic field distributions since the magnetic fields are mainly located in the w for the second resonance frequency. Because the magnetic fields of the first resonance frequency are dominantly concentrated in l-edge but rarely in w-edge, the first operating band is almost unchanged in Fig. 5(b). Therefore, the second band operating frequency band is much more sensitive to the variation of the width w than the length l.
Fig. 5. (a) Simulated PCRs of the proposed converter under normal incidence as a function of the (c) length l and (b) width w of U-shaped graphene sheet.
One of the excellent properties of the proposed dual-band reflective polarization converter is its promising adjustability by tuning the chemical potential (μc) and relaxation time (τ) of graphene. As shown in Fig. 6(a), μc has a significant influence on the dual-band PCR. As the μc increases from 0.8 eV to 1.1 eV, the first peak frequency of PCR increases from 31.1 to 36.17 THz and the second peak frequency of PCR changes from 39.6 to 45.97 THz. The obvious blue shift in the operating frequency can be interpreted by the formula [47]
Fig. 6. (a) Simulated PCRs of the proposed converter under normal incidence with different chemical potential ranging from 0.8 to 1.1 eV. (b) Simulated PCRs of the proposed converter under different relaxation time ranging from 0.1 to 0.8 ps.
Angle independence is another important characteristic of a polarization converter. We also investigate the influence of incident angle and polarization angle on PCR of the proposed dual-band polarization converter. Figure 7(a) illustrates the dependence of PCR spectra on different incident angles. The results clearly indicate that the two resonance frequencies of the PCR spectra are insensitive to the incident angle. The PCR spectra also show good angular stability in a wide range of incident angles between 0 to 75° at 34.67 and 44.13 THz. In addition, the dependence of PCR spectra of dual-band polarization converter on the polarization angle ($\phi$) is shown in Fig. 7(b), where PCR as a function of frequency and polarization angle is presented. It is found that the PCR spectra have a strong dependence on the polarization angle. The PCR was symmetrically distributed with respect to the polarization angle of 45°. The cross-polarization conversion efficiency reaches the maximum at polarization angle of 0 and 90°, while the conversion efficiency is 0 at the polarization angle of 45°. Figure 7(c) depicts the phase difference under the polarization angles of 0, 45, and 90°. Figure 7(d) illustrates the magnitude of the reflectance Rxx, Rxy under the polarization incident angles 0, 45, and 90°. It is found that the highest PCR can be obtained under the polarization angles of 0° and 90° at 34.67 and 44.13 THz, which results from the Rxx is near zero and Rxy reaches its peaks (see the PCR Eq. (5)). However, for the polarization angle of 45°, the PCR is equal to 0 since the value of Rxy is zero.
Fig. 7. (a) The PCR of the proposed converter as a function of incidence angle ranging from 0 °to 70°. (b) The PCR as a function of polarization angle ranging from 0 °to 90°. (c) The phase difference Δφ and (d) reflectance Rxx, Rxy under the 0, 45, and 90° polarization incident angles.
3.2 Broadband reflective cross-polarization converter
We also propose a broadband reflective cross-polarization converter based on the complementary structure of the proposed dual-band converter with a hollow-carved U-shaped graphene sheet, as depicted in Fig. 1(b). In this design, we set the length l2 = 57 nm while with other initial geometric parameters unchanged. As shown in Fig. 8(a), a wideband polarization converter with 1 THz bandwidth is obtained, which results from the two superimposed local surfaces plasmon modes produced by slit resonance. Similarly, the x-polarization incidence can be divided into + 45° and -45° orthogonal components, and then achieve Ruu and Rvv, as shown in Fig. 8(b). It is found near 180° phase difference is obtained between two Ruu and Rvv components, indicating that the linear x-polarization waves are converted to y-direction linear polarization waves. Note that the PCR with above 0.9 illustrates a broad frequency range from 49.7 to 50.7 THz resulting in a broadband cross-polarization response. Figures 8(c)–8(e) depict the magnetic field distributions at 49.61, 49.96, and 50.24 THz in the broadband high PCR region, while Fig. 8(f) depicts the magnetic field distributions at 52.50 THz with PCR close to 0. It is obvious that strong magnetic fields concentrate at different corners (see the dashed circles in Figs. 8(c)–8(e)) of the hollow-carved U-shaped graphene sheet at different operating frequencies in the high PCR region. In contrast, for the operating frequency in the low PCR region, the magnetic fields are very weak, as shown in Fig. 8(f). Furthermore, we also explore the tunable properties of this broadband polarization converter by adjusting the chemical potential and relaxation time of graphene. As shown in Fig. 8(g), the operating frequency band of PCR can be changed by adjusting the chemical potential of graphene while maintaining broadband high PCR over 0.9. Similarly, the amplitude of PCR can also be greatly adjusted by changing the relaxation time of graphene, as shown in Fig. 8(h). In addition, the dependence of the PCR on the angle of incidence of the broadband polarization converter is illustrated in Fig. 8(i). It is found that this broadband converter also has good angular stability, whose PCR spectra remain over 90% when the angle is below 55°.
Fig. 8. (a) Simulation results of the PCR and the phase difference between two components with incident polarizations of -45° and + 45°. (b) Reflectance Ruu and Rvv. (c)–(f) The magnetic field distributions at 45.96, 49.61, 49.96, 50.25 THz, respectively. (g)-(h) are the PCR of the proposed converter with different chemical potential and relaxation time, respectively. (i) The PCR of the proposed converter as a function of incidence angle ranging from 0 °to 85°.
Finally, we optimize the geometric parameters of the broadband converter to obtain even wider bandwidth. It is found that the bandwidth of PCR spectra of the broadband converter can be extended over 2 THz under the period of 65 nm, which is significantly wider than the above-mentioned broadband converter with the bandwidth of 1 THz under the period of 95 nm. As shown in Fig. 9(a), the optimized polarization converter with a period of 65 nm has good frequency reconfiguration. The operating frequency band of PCR can be changed from 45.5 to 50.5 THz while maintaining broadband high PCR over 0.9 by adjusting μc from 0.95 to 1.1 eV. Similarly, Fig. 9(b) shows that the amplitude of PCR can be significantly adjusted by tuning the relaxation time of graphene. If we set relaxation time 0 and 0.8 ps as the “OFF” and “ON” states, respectively, the converter can be applied as a photoelectric polarization switch with over 90% PCR switching property. In addition, the Fabry-Perot cavity defined by the dielectric layer plays an important part in polarization conversion. Figure 9(c) depicts that PCR as a function of different thicknesses (h2) of dielectric layer and frequencies, which illustrates that broadband polarization conversion characteristics maintain as the h2 ranging from 0.8 to 1.3 μm. Figure 9(d) indicates that the dependence of PCR spectra on the angle of incidence ranging from 0 to 70° with a step of 5°. It is clear that the broadband PCR spectra also show excellent angle insensitivity up to 55°. The wide-angle properties are very desirable in many practical applications. Finally, a comparison of the proposed polarization converters and some recently reported graphene-based converters is summarized in Table 1.
Fig. 9. (a) The PCR of the proposed wideband converter with different chemical potential and (b) relaxation time of graphene. (c) PCR as a function of different thicknesses h2 of dielectric layer and frequencies. (d) The PCR of the proposed converter as a function of incidence angle ranging from 0 °to 70°.
Table 1. Comparison of the proposed converters with some recent reported graphene-based converters
4. Conclusion
In conclusion, a tunable dual-band and a broadband mid-infrared reflective cross-polarization graphene converter are numerically designed and demonstrated, which are composed of a periodically arranged single layer U-shaped graphene nanostructures and hollow-carved U-shaped graphene, respectively. The proposed dual-band reflective cross-polarization converter operates at frequencies of 34.67 and 44.13 THz with high-efficiency PCR close to 100%. And the broadband cross-polarization converter with 2 THz bandwidth of 90% PCR is also obtained. The resonant frequencies and the magnitudes of PCR of both the dual-band and broadband graphene reflective polarization converters can be dynamically tuned by adjusting the chemical potential and relaxation time of graphene without changing the geometric construction. The proposed converters also possess angle insensitivity and can work in a wide incident angle range up to 55°. Therefore, these proposed graphene polarization converters may have great applications in mid-infrared spectroscopy, radiometer, and sensor and other optical polarization control devices.
Funding
National Natural Science Foundation of China (61601393); Shenzhen Science and Technology Projects (JCYJ20180306172733197).
Disclosures
The authors declare no conflicts of interest.
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