Research Article Vol. 27, No.

23 / 11 November 2019 / Optics Express 33826

Tunable mid-infrared dual-band and broadband

cross-polarization converters based on
U-shaped graphene metamaterials
FANG Z ENG , 1 L ONGFANG Y E , 1,2,* L I L I , 3 Z HIHUI WANG , 4 W EI
Z HAO, 5 AND YONG Z HANG 6
1 Institute
of Electromagnetics and Acoustics, Fujian Provincial Key Laboratory of Electromagnetic Wave
Science and Detection Technology, Xiamen University, Xiamen 361005, China
2 Shenzhen Research Institute of Xiamen University, Shenzhen 518057, China
3 Microsystem and Terahertz Research Center, China Academy of Engineering Physics, Chengdu, 610200,
China
4 Southwest China Institute of Electronic Technology, Chengdu 610036, China
5 Science and Technology on Electronic Information Control Laboratory, Chengdu 610036, China
6 School of Electronic Science and Engineering, University of Electronic Science and Technology of China,
Chengdu, Sichuan 611731, China
* lfye@xmu.edu.cn

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

#378640 https://doi.org/10.1364/OE.27.033826
Journal © 2019 Received 23 Sep 2019; revised 23 Oct 2019; accepted 23 Oct 2019; published 4 Nov 2019
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33827

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 φ-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
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33828

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 σ g = σ intra + σ inter (Unit: S) [41,42],

je2 ∞ ∂fd (ξ, µc , T) ∂fd (−ξ, µc , T)

 
σintra (ω, µc , Γ, T) = ∫ − ξdξ, (1)
π~2 (ω − j2Γ) 0 ∂ξ ∂ξ

je2 (ω − j2Γ) ∞ fd (ξ, µc , T) − fd (−ξ, µc , T)

σinter (ω, µc , Γ, T) = ∫ dξ, (2)
π~2 0 (ω − j2Γ)2 − 4ξ/~2
where fd (ξ, µc , T) = (e(ξ−µc )/kB T + 1)−1 is the Fermi-Dirac distribution, ω is the radian frequency,
µc is the chemical potential or Fermi level, T is the temperature, Γ is the phenomenological
scattering rate, and Γ = 2τ −1 , τ is the relaxation time, e is the charge of an electron, ξ is energy,
 is the reduced Plank’s constant, and kB is the Boltzmann’s constant. The graphene sheet is
modeled as an infinite-thin layer with the 2D surface impedance Zg = 1/σ g , the permittivity of
the Zro2 layer is set as ε d = 2.1 [43]. The metal layer is assumed as a copper film (Cu) with a
thickness of 0.1 µm and is modeled as a dispersive material using Drude model [44]. As a result,
the transmission is 0 due to the metallic layer is much thicker than the skin depth of the incident
wave. The complex reflection coefficients can be calculated from S parameters for the linear
polarization and cross polarization waves. The relationship between the incident and reflected
electric fields can be expressed as follows [45]:

r i
© Ex ª © Ex ª
­ ® = R­ ®, (3)
E r E i
« y ¬ « y ¬
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33829

where Exr and Eyr denote the electric field magnitudes of reflected waves in the x- and y-directions,
Exi and Eyi indicate the electric field magnitudes of incident waves in the x- and y-directions,
respectively. R represents the general reflection matrix referring to the complex amplitudes of
reflected waves, which can be expressed as [46]:

© Rxx Rxy ª
R=­ ®, (4)
« Ryx Ryy ¬
where Rxy represents the reflected wave in the x direction for the incident wave in the y direction.
Rxx = |Exr /Exi | and Ryx = |Eyr /Exi | are defined as the reflected ratio of x-to-x for the co-polarization
and x-to-y for the cross-polarization, respectively. Where the superscript i and r represent the
incident and reflected waves, the subscripts x and y indicate the polarization states of EM waves.
Due to the symmetry of proposed converter structures, Rxx= Ryy , and Rxy = Ryx . In this study, we
mainly investigated the Rxx and Ryx by assuming the x-polarized incident wave in the incident
port. The performance of the proposed graphene converter can be characterized by polarization
conversion ratio (PCR) denoted as [10]:

|Ryx | 2
PCR = . (5)
|Rxx | 2 + |Ryx | 2

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 (∆ϕ) between the
x and y components of the reflected waves as ∆ϕ = arg(Ryx ) − arg(Rxx ), indicating all possible
polarization states of reflected waves such as circular, linear, and elliptical polarization states,
respectively. When the ∆ϕ = nπ, linear polarization waves can convert to its cross polarization
waves. When Ryx =Rxx and ∆ϕ = n ± 90°, the linear states can convert to circular polarization
states, where ∆ϕ = n + 90° indicates the left circular polarization and ∆ϕ = nπ - 90° for the right
circular polarization, respectively. As shown in Fig. 2(b), it is clearly found that the phase
difference ∆ϕ 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 ∆ϕ 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 (H z ) profiles
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33830

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 (∆ϕ) 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 E ® xi = u®Exu
i ejφ + ® i ejφ , as
vExv
shown in Fig. 4(a). Similarly, the reflected wave can be expressed as E ® x = u®Exu + ®vExv
r r r =
i
u®ru Exu ej(φ+ϕ u + ®
) i
vrv Exv e j(φ+ϕ )
v , where r and r represent the reflected coefficients along the
u v
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°
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33831

polarization incidence than that under 0° polarization incidence. Furthermore, these two modes
also exhibit a phase difference (∆ϕ = arg(Rvv ) − arg(Ruu )) 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 H z 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.
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

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 (H z ) at 34.67 and 44.13 THz under
-45°and + 45° polarized incidence, respectively.
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33832

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]

ω α0 cµc
r
f = ∝ (6)
2π 2π 2 ~Lg
2
where α0 = ~c e
is the fine structure constant, Lg is the resonant characteristic length of the
U-shaped graphene (mainly proportional to the length l and width w for the first and second
resonance modes respectively). Furthermore, Fig. 6(b) plots the relationship between the PCR
and τ with the fixed chemical potential of 1.0 eV under normal incidence. It is found that the
peak of PCR dramatically decreases as τ decreases. In particular, τ has a much greater impact
on the first peak of PCR than the second one. When τ is more than 0.6 ps, both bands of PCR
rapidly increase to over 90% peak values. It is worth to point out that the operating frequency
and the amplitude of the PCR of the dual-band polarization converter can be flexibly adjusted by
graphene chemical potential and relaxation time, respectively, without changing the geometric
parameters. The excellent characteristics may provide many potential applications in polarization
switches and tunable polarizers.
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
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33833

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.

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
(φ) 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.

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
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33834

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 ∆ϕ and (d) reflectance Rxx , Rxy under the 0, 45, and 90° polarization
incident angles.

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°.
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.
Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33835

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°.
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33836

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
Absolute
bandwidth for
Unit cell PCR > 0.9,
graphene except otherwise Angular
References structure specified (THz) stability Frequency reconfiguration of PCR
[34] rectangle-shape 2.17 (PCR > 0.5) >50° 30 to 50 THz with PCR ranging from
0.4 to 0.95 as µ c increases from 0.5
to 1.0 eV
[35] Sinusoidal slot 0.8 (PCR > 0.8) >50° 1.2 to 2.2 THz with PCR over 0.75 as
µc increases from 0.3 to 0.5 eV
[36] H-array 3.53 >50° 26 to 38 THz with PCR over 0.8 as µc
increases from 0.6 to 1 eV
[37] φ-shape 1.81 >40° 3.5 to 9.5 THz with PCR over 0.6 as
µc increases from 0.4 eV to 1 eV
[48] L-shape 1.57 (@31.4 THz); >40° 27.5 to 38.75 THz for the first band
1.239 (@41.3 THz) and 36.25 to 43.75 THz for the
second band with PCR over 0.9 as
µc varies from 0.7 eV to 1.0 eV
U-shape 0.30 (@34.67 THz); >75° 31.1 to 36.17 THz for the first band
This work (dual-band) 0.175(@44.13 THz) and 39.6 to 45.97 THz for the
second band with PCR over 0.9 as
µc increases from 0.8 eV to 1.1 eV
Hollow U-shape 2 >55° 45.5 to 50.5 THz with PCR over 0.9 as
(broadband) µc increases from 0.95 eV to 1.1 eV
 Research Article Vol. 27, No. 23 / 11 November 2019 / Optics Express 33837

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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