Research Article Vol. 63, No.

12 / 20 April 2024 / Applied Optics 3099

Multifunction and switchable hybrid metasurface

based on graphene and gold
Muhammad Sajjad,* Xiangkun Kong, Shaobin Liu, AND Muhammad Irshad Khan
Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, College of Electronic and Information Engineering,
Nanjing University of Aeronautics and Astronautics (NUAA), Nanjing 211106, China
*sajjadwazir@nuaa.edu.cn

Received 13 February 2024; revised 18 March 2024; accepted 19 March 2024; posted 20 March 2024; published 11 April 2024

This paper presents the design and numerical investigation of a graphene-based switchable terahertz (THz) meta-
surface for ultrawideband absorption and multiband cross polarization conversion. The device’s operational mode
can be altered to absorption or reflection by using the electrostatic capabilities exhibited by graphene. The numeri-
cal calculations yield results indicating that in absorption mode, it maintains a bandwidth ratio of 152% within the
frequency range of 1.04–7.74 THz. In polarization conversion mode, the design demonstrates the ability to convert
linearly polarized and circularly polarized waves to their respective cross-polarization states within the frequency
ranges of 1.8–2.5 THz, 3.5–4.1 THz, and 5.6 THz. Moreover, calculated results indicate that linear-to-circular
conversion can be realized at 2.64, 3.45, and 5.4 THz frequencies. In addition, the absorption and polarization
conversion ratio parameters were analyzed using the multiple reflection theory, which demonstrated significant
agreement with the simulation results. The designed metasurface exhibits significant potential in the field of tera-
hertz devices, including stealth technology, smart switches, and other related applications. © 2024 Optica Publishing
Group

https://doi.org/10.1364/AO.521333

1. INTRODUCTION Such aspects offer a high degree of flexibility in their design,

Terahertz technology has gained significant attention in recent especially as a response to particular external influences. This
decades owing to its vital potential in numerous fields [1–3]. approach enables researchers to attain dynamic control over
The main challenge hindering the real-world implementation EM wave polarization [10], reflection [11], and absorption
of THz technology is the absence of efficient devices that exhibit [12,13]. The practical applications of merging broadband and
exceptional performance. The reason for this is the lack of bifunction within a single metasurface have been highlighted in
natural materials that are capable of dealing with THz waves. various research studies. Hence, certain multifunctional meta-
The creation of devices using metamaterials has facilitated surfaces that integrate polarization conversion and absorption
the development of terahertz technology. Metamaterials typi- have garnered the attention of scholars [14–19]. For example,
cally comprise metals or dielectric materials with significantly the metasurface proposed by Hassan et al. and Huang et al.
smaller dimensions compared to the operating wavelength, incorporates diodes in order to facilitate the seamless transition
which enables the manipulation of electromagnetic (EM) waves between two key functionalities: absorption and polarization
through subwavelength microstructures. They have the ability conversion (PC) [14,15]. Niu et al. and Peng et al. independ-
to manipulate EM waves across a range of frequencies, including ently developed distinct bifunctional metasurfaces that exhibit
optical, THz, and microwave regions. Nevertheless, altering the broadband absorption and PC functions. These metasurfaces
behavior of conventional metamaterials after production is not have been developed based on the insulating-to-metallic state
a straightforward task. This significantly hampers their ability transition of VO2 [16,17]. The hybrid graphene-metal metasur-
to be used in a wide variety of optoelectronic devices. Therefore, face proposed by Zhang et al. and Wang et al. demonstrates the
there is a significant demand for the development of adjustable capability to transition between a broadband quarter-wave plate
metasurfaces that can effectively combine multiple diverse func- and a half-wave plate. This transition is achieved by tuning the
tionalities and simultaneously adjust various functionalities in Fermi energy level of graphene [18,19].
an efficient way. One effective approach for achieving dynamic One potential strategy involves integrating the metasurface
manipulation of EM waves across various wavelength bands with graphene in the design of the device. This allows for the
involves integrating tunable materials like diodes [4], dirac manipulation of the device’s performance by the application
semimetal [5], vanadium dioxide (VO2 ) [6,7], graphene [8], of external stimulation. Graphene is a newly discovered two-
and photosensitive silicon [9] with the standard metasurface. dimensional material that is composed of a single layer of a

1559-128X/24/123099-09 Journal © 2024 Optica Publishing Group

 3100 Vol. 63, No. 12 / 20 April 2024 / Applied Optics Research Article

hexagonal lattice structure made of carbon atoms. Graphene is

a very popular active material for making tunable devices. This
is because it has unique properties, such as good optical trans-
parency, changeable EM properties, and high electron mobility
[20]. Changing the properties of graphene is realized by chang-
ing its Fermi level and electron relaxation time by applying a
bias voltage. Consequently, graphene based metasurfaces can be
controlled by means of an external bias voltage. Nevertheless,
the previously discussed metasurface achieved bifunctionality in
terms of interchanging between absorption and linear polariza-
tion conversion (LPC), or between LPC and cross polarization
conversion (CPC). However, there are still areas that could ben-
efit from improvement, including a more simplified structure,
increased absorptivity, and enhanced bandwidth quality.
This work creates a multifunctional switchable hybrid
metasurface (MFSHM) using graphene and gold for an ultra-
wideband absorption and multiband polarization conversion
in the THz region. The notable enhancement in the concep-
tual framework or methodology for the provided MFSHM is
as follows: (1) The concept uses two metasurfaces formed of Fig. 1. (a) Unit cell structure of the MFSHM; (b) geometry
of the graphene pattern; (c) geometry of the top resonator with
resonant unit cells with distinct simple patterns. (2) The use of
L4 = L3 = 16.3 µm, and R1 and R2 are 5 µm and 16.3 µm,
a double layer of graphene in resonant unit cells is advantageous respectively.
in attaining a broader operational bandwidth. (3) The presence
of C4 symmetry in the graphene unit cells results in polarization
independent absorption, while the C2 symmetry of the gold Fig. 1(a). A layer of ion-gel with a thickness of H4 and a refrac-
resonant unit cells adds the features of polarization conver- tive index value of 1.83 is added at the top of each graphene
sion. (4) The integration of simple structures is able to fulfill layer. The graphene films are deposited on the spacer (sili-
its objective of attaining various functions. (5) The operation con dioxide). The substrate material utilized in this design is
mode of the design can be switched to absorption or reflection composed of silicon dioxide (SiO2 ), possessing a refractive
mode by utilizing the electrostatic properties of the graphene index value of 3.9. A layer of gold metal, possessing a con-
layer. The polarization conversion mode is turned on when ductivity of 4.56 × 107 S/m and a thickness Tm of 1 µm, is
employed beneath the structure for the purpose of preventing
the chemical potential (µc ) is switched to 0 eV. In this mode,
the transmission of EM waves from the opposite side. The other
MFSHM is capable of converting x/y-polarized waves to their
parameters are as follows: Px = Py = 40.3 µm, L1 = 39.8 µm,
corresponding y/x-polarized waves, as well as left-handed/right-
L2 = 12.4 µm, W1 = 5 µm, H1 = 3 µm, H3 = 7.65 µm,
handed circular polarized (CP) waves to their corresponding
Tr = 3 µm, and H2 = H4 = 30 nm.
right-handed/left-handed CP waves, operating within the same
The fast-evolving micro- and nanoprocess technology offers
frequency band. Moreover, the MFSHM demonstrated the
techniques for creating the proposed structures. Initially, a
ability to convert a linear polarized (LP) wave into a CP wave at
silicon substrate has been used as a mechanical support, and
three specific frequencies: 2.64 THz, 3.45 THz, and 5.4 THz. the bottom gold layer is created using electron beam evapo-
The utilization of electric field distribution, impedance match- ration (EBE). Next, the SiO2 dielectric layer (H1) is applied
ing theory, and interference theory is employed to elucidate the to the bottom gold layer using spin coating and curing. After
phenomenon of PC and ultra-wideband (UWB) absorption by that, a smooth, high-quality layer of graphene is grown, and
the MFSHM. This metasurface offers the benefits of switchable then chemical vapor deposition (CVD) is used to move it onto
multifunctions in a wide operating bandwidth and a remarkably SiO2 dielectric layer 1. The graphene layer 1 is then patterned
thin profile, making it a promising candidate for tunable devices using electron beam lithography and the reactive ion etch-
in THz communications. ing technique. After following the steps outlined above, the
SiO2 dielectric layer (H3) and graphene layer 2 are prepared.
2. STRUCTURE DESIGN AND MATERIAL Furthermore, a layer of ion gel is deposited onto the array of
graphene layers using thermal evaporation. The dielectric ion
THEORY
gel is deposited onto the array of graphene resonators using
Figure 1(a) shows a perspective three-dimensional view of thermal evaporation. Finally, the incurved top metal is produced
the unit cell of a graphene-gold integrated THz metasurface. using photolithography and metallization techniques. The sum
Figure 1(b) depicts the structure of the graphene pattern. At of interband and intraband components can represent the
the top layer, the incurved resonator made of gold metal with surface conductivity of graphene within the THz range. The
a thickness of Tr is placed diagonally on the structure, as pre- dominant factor influencing the conductivity of graphene in
sented in Fig. 1(c). The proposed design includes two layers the THz frequency band is mainly due to the intraband elec-
of graphene. Both graphene patterns have the same structure tron transitions. This can be expressed by a Drude-like model
but with 180◦ rotation with respect to each other, as shown in [21,22],
 Research Article Vol. 63, No. 12 / 20 April 2024 / Applied Optics 3101

ie 2 E F under consideration displays two discrete absorption peaks

σg = . (1)
π ~2 (ω + iτ −1 ) at frequencies of 2.7 THz and 7.2 THz, exhibiting absorptiv-
ity levels of 92.7% and 95.4%, respectively. The subsequent
In the aforementioned equation, the symbol ~ denotes the
sections will employ these two absorption peaks to examine
reduced Planck’s constant, while e, τ , and ω represent the
the absorption operation. Furthermore, the µc of the two
electron charge, relaxation time, and angular frequency of
graphene layers has been established at 0.8 eV, rendering it a
the incident wave, respectively. The surface conductivity of
more feasible option for experimental implementation. The
graphene can be modulated by regulating its chemical potential.
absorption level was improved through the utilization of the
The approximate relationship between µc and bias voltage Vg
slotted square graphene patches in the double layer, as shown
can be stated as follows:
s in Fig. 1(a). And each of the two graphene layers exhibits an
π εr εo Vg identical structure, only with a rotation of 180◦ . The inclusion
E F = µc ≈ ~ν f . (2) of a second layer of graphene with 180◦ rotation in the design
e Ts
ensured the preservation of its four-fold symmetry, thereby
The VF and Vg represent the Fermi velocity and external bias resulting in comparable performance under both TE- and
voltage, respectively. The relative permittivity of a substrate is transverse magnetic (TM)-polarization. The effective medium
represented by the symbol εr , and the permittivity of a vacuum theory gives a possible explanation for the UWB absorbance
is commonly represented by εo . As per Eq. (2), the Fermi energy event seen in the proposed design. According to the effec-
level of graphene can be modulated by varying the bias voltage. tive medium theory, the relative impedance of the proposed
The achievement of tuning can be carried out through the regu- metamaterial absorber can be determined r using S parameters
lation of the gate voltage via an ion-gel top configuration [23]. q
µ (1+S )2 −S 2 1+R
[24,25] as follows: Zeff = ε eff = (1−S11 )2 −S21 2 = 1−R .
This phenomenon alters the surface impedance of the patterned eff 11 21
graphene. Consequently, it is possible to design an absorber that The variable R represents the reflectance. The absorption
can be adjusted. The former method is more commonly utilized coefficient, denoted as A, can be determined through the
due to its simplicity and common usage. At a value of µc equal following calculation: A = 1 − R = 1 − Z−1
Z+1
2
= Z+1 =
to 0 eV, graphene can be considered as a thin dielectric layer for 2[Re(Z)+1] 2im(Z)
− i [Re(Z)+1]2 +im(Z)2 . In general, the con-
EM waves. The increase in the Fermi level in graphene results [Re(Z)+1]2 +im(Z)2
dition for achieving perfect absorption is characterized by the
in a corresponding increase in surface conductivity, ultimately
equality of the real portion of impedance, denoted as Re(Z),
leading to the attainment of a metallic state. The numerical
to a value of 1, while the imaginary component of impedance,
simulation is conducted using the CST Microwave Studio.
The frequency domain approach was employed to simulate the denoted as Im(Z), is simultaneously equal to 0 [26,27]. This
structure and calculate its associated reflection (R) and transmis- specifies that the impedance of the absorber is precisely aligned
sion (T) coefficients. In addition, the THz wave that is incident with the impedance in free space (Z0 ≈ 377), leading to
has been set up as a y-polarized transverse electric (TE) mode. maximum absorption. From Fig. 2(b), we can find that in the
Within the context of CST, unit cells are established for both the frequency range of 1.03–7.74 THz, the effective impedance has
x and y directions, while open boundaries are implemented for a real component that approximates 1 and an imaginary compo-
the z direction. nent that approximates 0. The impedance values at peak I and
peak II are 1.07 − 0.52i and 0.79 + 0.35i, respectively. These
results provide substantial evidence that the absorber effectively
3. RESULTS AND DISCUSSION absorbs at both peaks with high efficiency. In order to better
When graphene is in a metallic state, the MFSHM undergoes a describe the mechanism of the wideband absorption mode
transition to function as a THz absorber. The absorption level of the absorber, the absorption spectra of a single-layer and a
is an essential factor that characterizes the performance of an multi-layered structure are provided in Fig. 3(a). Two graphene
absorber. The equation employed for computing the absorp- layers with varying orientations exhibit two unique absorption
tance is of great importance. The calculation of absorption levels above 85%. The absorption bandwidth over 85% with
(A) is performed as A = 1 − T − R = 1 − |S21 |2 − |S11 |2 , a single layer of patterned graphene is relatively limited. The
where T = |S21 |2 and R = |S11 |2 , which represent the trans- simultaneous interaction of two layers of patterned graphene
mission coefficient and reflection coefficient, respectively, are results in a noticeable expansion of the bandwidth, as shown in
generated by the incident wave that impinges on the absorber. Fig. 3(a). The findings from the simulation demonstrate that
When the thickness of the base gold sheet exceeds its skin depth the use of a multilayer structure has the potential to enhance the
to a significant level, the transmission coefficient (S21 ) of the absorption range of the absorber. Furthermore, the absorption
absorber exhibits a near-zero value, thereby allowing S21 to be spectrum of the MFSHM design is also illustrated for the pur-
technically reduced to zero. When the graphene Fermi level is pose of comparison, as shown in Fig. 3(b). When comparing
0.8 eV and τ = 0.05ps, the proposed design switches to a THz the absorption characteristics of the proposed design with and
absorber. As illustrated in Fig. 2(a), the results indicate that without the top (reflector) layer, it is observed that the absorp-
in the absorption mode, the design can absorb about a mini- tivity of the MFSHM with the top layer is slightly decreased
mum of 85% of the THZ wave while maintaining a bandwidth for low frequencies, but it exhibits an improvement in high
ratio of 152.6% across the frequency band of 1.04–7.74 THz. frequencies in comparison with the structure without the top
This range is notably wider than that of the majority of pre- layer, as depicted in Fig. 3(b). The observed phenomenon could
viously bifunctional THz absorbers. The proposed design potentially be attributed to the presence of the gold resonator
 3102 Vol. 63, No. 12 / 20 April 2024 / Applied Optics Research Article

Fig. 2. Magnitude of reflection and absorption curve under the incidence of the x-y polarized wave of the proposed MFSHM; (b) relative imped-
ance.

Fig. 3. (a) Absorption curves for distinct components of the absorber: red line for two layers, green for the top layer, and blue for the second layer;
(b) absorption spectrum with and without integration of the top reflector layer.

positioned at the top of the structure. These resonators serve to Within the aforementioned ranges of the structural parameters,
amplify the surface plasmons of the graphene material, thereby the proposed MFSHM exhibits a bandwidth variation that is
leading to an augmentation in the carrier concentration [28]. less than 10%. The results prove the physical significance and
Throughout the fabrication process of the metamaterials, utility of the proposed structure.
inaccuracies may arise as a result of the constraints of fabrication Designing absorbers with polarization insensitivity and tol-
technology. Thus, we observed the impact of the structural erance across a wide incident angle range is crucial. This section
parameters of the suggested MFSHM by analyzing the vari- illustrates the absorption insensitivity of the proposed absorber
ations in the bandwidth for various parameters as shown in for the variation of incident and polarization angles through
Table 1. The following parameters include the period of the contour maps. Figure 4(a) illustrates the absorption spectra
structure (P), graphene disk width (W), dielectric thickness for different polarization angles under normal incidence. The
(H1 and H3), permittivity of the substrate, and graphene relax- absorption bandwidth of the proposed MFSHM is consistently
ation time. It is important to consider that when we modify stable when the polarization angles vary from 0◦ to 90◦ , with a
one specific parameter, the other parameters remain constant. step width of 10◦ . When the incident THz wave polarization
The data presented in Table 1 are calculated using the following shifts from TE to TM mode, the proposed design demonstrates
method: Determine the deviation by applying the formula: polarization independence due to the symmetry of the unit
Bdeviation = (Bsimulated − Bbased )Bbased × 100%. In this con- cell. The absorption spectra for a TE- and TM-polarized wave
text, “Bbased ” refers to the bandwidth obtained with desired at various incidence angles are shown in Figs. 4(b) and 4(c).
parameters, “Bsimulated ” represents the simulated bandwidth It can be noticed that the absorption spectra remain above
obtained with different parameters, and “Bdeviation ” denotes 85% for the entire bandwidth, for the incident angle variation
the percentage difference between the corresponding and from 0◦ to 40◦ for both TM and TE modes. As illustrated in
simulated bandwidths. Calculations are made for bandwidth Fig. 4(b), the efficacy of the absorption band will reduce for
deviations of the proposed MFSHM within specific ranges: incident angles higher than 40◦ , specifically in the lower fre-
H1(2.0−4.0) µm, H3(6.5−8.5) µm, W(4.0−6.0) µm, quency range. Consequently, for TE mode, the magnetic flux
P(39.9−40.7) µm, ε(3.7–4.1), and τ (0.03–0.07) ps. The between the ground plane and the graphene layer decreases as
structural characteristics exhibit excellent resilience within the angle of incidence increases whereas the high absorption
the ranges of 2.0−4.0 µm, 6.5−8.5 µm, 4.0−6.0 µm, of the MFSHM remains effective up to 70◦ for TM mode as
39.9−40.7 µm, 3.7–4.1, and 0.03–0.07 ps, respectively. depicted in Fig. 4(c). Subsequently, at a higher incidence angle,
 Research Article Vol. 63, No. 12 / 20 April 2024 / Applied Optics 3103

a
Table 1. Bandwidth Variations of the Proposed MFSHM for Probable Material Impurities and Structural Defects
Structural Parameter H2(µm) W1(µm)
6.5 7.0 8.0 8.5 4.0 4.5 5.5 6.0
Bandwidth deviation (%) −0.29 −0.59 +0.89 +4.77 −2.53 −1.94 +10.44 +14.02
Structural Parameter H1(µm) τ (ps)
2 2.5 3.5 4 .03 .04 .06 .07
Bandwidth deviation (%) −1.94 −1.34 +0.14 +1.79 +7.76 +2.38 −4.92 −9.10
Structural Parameter Permittivity P(µm)
3.7 3.8 4.0 4.1 39.9 40.1 40.5 40.7
Bandwidth deviation (%) +0.59 −0.14 −0.44 −0.59 +1.34 +2.9 −4.98 −5.82
a
A negative sign (−) indicates a decrease in the bandwidth, where as a positive sign (+) indicates an increase in the bandwidth.

Fig. 4. Influence of polarization and incident angle on the absorption spectrum of the proposed MFSHM in absorption mode (a) influence of
polarization angle; (b) influence of incident angle on TE wave; (c) and TM waves.

Fig. 5. (a) Absorption curve of the MFSHM at various Fermi levels of the graphene; (b) absorption (black line), and polarization conversion ratio
(PCR) spectrum (red line).

the magnetic flux between the graphene layer and the ground valuable in encouraging more robust plasma oscillation and
layer remains unchanged for the TM mode. Therefore, it can augmenting absorption efficacy [29]. The realization of a Fermi
be concluded that the MFSHM maintains absorption stability level of µc = 0.8 eV in graphene results in the realization of
across different incident angles for both TE and TM modes. UWB absorption. The bandwidth and relative bandwidth of
To investigate the electrically tunable properties of the this absorption are 6.7 THz and 152.6%, respectively. When
MFSHM, Fig. 5(a) displays the absorptivity curves of the the absorption rate exceeds 80%, it can be accomplished to get a
MFSHM at various Fermi levels of graphene. The blue shift bandwidth of 8.4 THz and a relative bandwidth of 190%.
of the absorption peak is observed, accompanied by a grad-
ual increase in both absorptivity and bandwidth, as the µc of
graphene is elevated from 0.5 to 0.8 eV, as depicted in Fig. 5(a). 4. WORKING AS A MULTIBAND POLARIZATION
This suggests that the absorption of the MFSHM can be modi- CONVERTER
fied in a dynamic manner through the manipulation of the µc The manipulation of the Fermi level can result in significant
levels of the graphene layer. The improved absorption could changes to the surface conductivity of graphene. At a value of
be attributed to the enhanced inherent loss of the MFSHM µc equal to 0 eV, graphene can be interpreted as a thin dielec-
in conjunction with a higher level of µc . This phenomenon is tric layer that interacts with EM waves, with the MFSHM
 3104 Vol. 63, No. 12 / 20 April 2024 / Applied Optics Research Article

Fig. 6. (a) Amplitude of reflection coefficients under normal incidence of LP wave of the proposed MFSHM under PC mode; (b) phase and phase
difference.

Fig. 7. PCR calculation when the proposed device works as a polarization converter: (a) PCR at linear polarized wave incidence; (b) PMR at circu-
lar polarized wave incidence.

switched to PC mode. As the µc increases, the surface conduc- When an incident wave is left-hand circular polarization
tivity of graphene rises, leading to the behavior of a metallic (LHCP), the interchange of “+” and “−” occurs in Eq. (4).
region. Hence, through the manipulation of the Fermi level in Figure 6 displays the simulated reflection coefficients for the
graphene, the device’s operation mode can be switched to an cross-polarization and PCR when subjected to normal inci-
absorption or reflection mode, as illustrated in Fig. 5(b). The dence of a y-polarized wave with Fermi level (µc = 0 eV and
metallic strip resonators located on the top layer can be consid- τ = 2 ps). The graphical representation in Fig. 6(a) illustrates
ered equivalent to the diagonal metal strip resonators, which that the magnitudes R xy and R yy of the reflected wave are close
to 1 and 0, respectively, in the frequency bands of 1.8–2.5 THz,
possess the capability of polarization conversion [30]. The
3.5–4.1 THz, and 5.6 THz. The findings depicted in Fig. 7(a)
polarization conversion mode is turned on when the graphene
demonstrate that the metasurface design is highly effective, with
µc is switched to 0 eV. In this mode, the MFSHM is capable of
a PCR exceeding 95% within the above frequency range, except
converting incident x/y co-polarized waves to their correspond- 3.84–4.1, which is above 80%. Moreover, the PCR reaches
ing y/x cross-polarized waves, as well as incident left-handed or its peak value near 1 at the resonant frequencies of 2.01–2.37
right-handed EM waves to their corresponding right-handed or and 3.7 THz. Subsequently, we also conducted a simulation
left-handed reflected wave [31]. The calculation of the PCR for of the polarization converter under circularly polarized wave
the y-polarized incident wave is as follows: incidence. The simulation results are presented in Fig. 7(b).
Notably, the magnitudes of the co-polarized reflection coeffi-
|R xy |2 cients, in conjunction with the PMRs, at both RCP and LCP
PCR = . (3)
|R xy |2 + |R yy |2 incidences are nearly identical to those observed at LP incidence
in the same frequency ranges. This observation suggests that a
In Eq. (3), the interchange of y and x occurs for x polarization. tri-band reflection-type CPC has been accomplished within the
The metasurface’s capacity to maintain polarization for the same frequency band. Furthermore, it can be inferred from the
CP wave is ascertained by the polarization-maintaining ratio simulated results that |R ++ | = |R −− | = |R xy |. Furthermore,
(PMR). The definition of the PMR for right-hand circular it is illustrated in Fig. 6(a) that the reflection coefficients for
polarization (RHCP) incident waves is as follows: R yy and R xy of the reflected wave exhibit similar magnitudes,
with |R yy | = |R xy | ≈ 0.65 at the frequencies of 2.64, 3.44, and
|R ++ |2 5.41 THz. Meanwhile, their corresponding phase and phase dif-
PMR = . (4) ference reaches −271◦ , −86◦ , and 90◦ , respectively, as depicted
|R −+ |2 + |R ++ |2
 Research Article Vol. 63, No. 12 / 20 April 2024 / Applied Optics 3105

Fig. 8. Influence of the polarization and incident angle on the PCR of the proposed MFSHM in PC mode: (a) polarization angle; (b) y-polarized
incident angle, and (c) x-polarized incident angle.

in Fig. 6(b). This indicates that an LP incident wave will be they remain constant and larger than 90% for incidence angles
reflected as a CP wave in these bands. of 60◦ .
Additionally, an examination of the impact of the polari-
zation angle and incidence angle on the PCR spectrum is 5. PHYSICAL MECHANISM OF THE
conducted for PC mode. As depicted in Fig. 8(a), with an POLARIZATION STATE
increase in the polarization angle of the incident wave to 18◦ , the
PCR remains almost constant. When the angle of polarization The investigation into the underlying physical mechanism
of the incoming wave rises, the PCR of the three operational responsible for PC is a significant matter, as it corresponds to the
bands starts to decline. At an increase in the polarization angle influence of electric and magnetic resonance. In order to obtain
to 27◦ , the PCR drops below 0.8. The multifunctional polari- a deeper understanding of the underlying physics principles
governing the designed structure, simulations are conducted
zation converter has a diagonal symmetric design, which is
to analyze the surface current distributions on the MFSHM
noteworthy. When the polarization angle surpasses 45◦ , the
structure. These simulations are performed at frequencies cor-
PCR is completely opposite to the way it functions before 45◦ .
responding to the two resonance peaks. Figure 9 illustrates the
The PCR curves for both y- and x-polarized incidences at vari- surface current distributions on both the top as well as bottom
ous angles are plotted in Fig. 8(b) and Fig. 8(c), respectively. layers when subjected to a y-polarized incident wave at two
It can be observed that the higher edge of the PCR spectrum resonance frequencies, 2.2 THz and 3.7 THz. As depicted in
undergoes a little downward shift in frequency as the incidence Fig. 9(a), it is evident that at a frequency of 2.2 THz, the surface
angle increases for both x- and y-polarized waves. For the sug- current flowing through the top resonator is in the opposite
gested design, the response has been noticed to be nearly stable direction compared to the current flowing through the bot-
up to 30◦ . When the angle of incidence is greater than 30◦ , tom layer. The current flow between two layers can be seen as
a higher frequency peak of polarization conversion is seen, a closed current ring, creating an induced magnetic field H1 .
which could mean that a higher-order mode response is present In the context of polarization conversion, it is observed that
[32], while in the lower frequency ranges of 1.9–2.3 THz, the y-component of the induced magnetic field, denoted as

Fig. 9. Surface current distributions along the top resonator and bottom gold plane under the normal incidence of a y-polarized wave with a Fermi
level of 0 eV and their corresponding eigenmode decomposition of the y-polarized wave. (a) First row 2.2 THz; (b) second row 3.7 THz.
 3106 Vol. 63, No. 12 / 20 April 2024 / Applied Optics Research Article

1 1
H1y , aligns and appears parallel to the direction of the incident (a) (b)
electric field, denoted as Ei. This alignment has significance as 0.8 0.8

it facilitates the generation of cross-polarization coupling, par-

Absorption
0.6 0.6

PCR
ticularly at low frequencies. In contrast, as depicted in Fig. 9(b),
0.4 0.4
it can be seen that the current directions on the upper and lower
layers are identical. The existing electrical movement between 0.2 Theoretical calculation
0.2
Simulation Theoretical calculation
two layers can be described as an electric dipole, leading to the Simulation
0 0
occurrence of an induced electric field E. The perpendicularity 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6
Frequency (THz) Frequency (THz)
between the component E 1x of the induced electric field E in the
x-direction and the incident electric field Ei facilitates the gen- Fig. 10. Absorption and PCR spectrum obtained from simulation
eration of cross-polarization coupling at high frequency. This and theoretical calculations. (a) Absorption; (b) PCR.
enables the occurrence of cross-polarization, thereby facilitating
the conversion of y-polarized waves into x-polarized waves. The these coefficients, the above equation was used to determine the
reason for this phenomenon is that magnetic dipoles generate resulting reflected wave. The first component r˜12 is the direct
circular currents, whereas electrical dipoles generate directional reflection originating from the top layer. Conversely, the second
currents. The phase modulation of incident waves and the term, which has a negative sign, denotes the collective reflection
subsequent PC process can be determined by both magnetic and resulting from superposition. Figure 10(a) shows a comparison
electric dipole moments. between the theoretically calculated absorption spectrum and
the simulated absorption spectrum, demonstrating that the sim-
ulated spectrum is largely similar to the theoretically calculated
6. INTERFERENCE THEORY one. Figures 10(a) and 10(b) present a comparison between
Finally, in order to further investigate the physical mechanism the simulated and calculated absorption and PCR curves of
of the MFSHM, we use the interference theory model [33,34]. the proposed MFSHM. It is shown that both plots are in good
The reflected wave resulting from the interference theory, as agreement with each other.
explained in Ref. [35], can be mathematically represented by
Eq. (5),
7. CONCLUSION
t12 t21 e i2βd We have proposed a graphene-based switchable metasurface
R = r 12 − . (5)
1 + r 21 e i2βd (MFSHM). The operational modes, namely linear polarization,
circular polarization, and absorption modes of the MFSHM,
The phase that has accumulated as p a result of reflection at can be switched by manipulating the chemical potentials asso-
the bottom layer can be written as β̃ = ε̃sio 2 k◦ d . In the given ciated with the graphene metasurface. In absorption mode,
context, k◦ represents the wave number in free space, whereas the proposed MFSHM can achieve UWB absorption in the
d denotes the height of the dielectric layer. In the context of range of 1.04–7.74 THz with a relative bandwidth of 152%.
polarization conversion mode, it is essential to take into account In polarization conversion mode, the MFSHM can convert an
both the co-polarized and cross-polarized components when x/y-polarized wave into a y/x-polarized wave or an LCP/RCP
the input wave is y-polarized. After that, we can write an expres- wave into an RCP/LCP wave at 1.8–2.5 THz, 3.5–4.1 THz,
sion for the combined co- (y-y) and cross-polarization (y-x) and 5.6 THz. Additionally, the metasurface converts LP waves
reflection coefficients as [36,37] to CP waves at 2.64, 3.45, and 5.4 THz. Interference theory was
used as a theoretical framework to investigate the underlying
t˜12 t˜21 R xy e i2β t˜
R̃ xy = r˜12 − , (6) mechanism of the two functions. The suggested MFSHM offers
1 + r˜21 R xy e i2β t˜ a novel approach to the construction of adjustable multifunc-
tional devices operating in the THz band. The anticipated
t˜12 t˜21 R yy e i2β t˜ use of this technology is within the domain of wireless com-
R̃ yy = r˜12 − . (7)
1 + r˜21 R yy e i2β t˜ munication. These characteristics render it highly suitable
for prospective applications in THz absorption, polarization
The reflection coefficient, denoted as r˜12 = r 12 e iϕ12 , repre- conversion, modulation, and imaging.
sents the proportion of the incident wave that is partly reflected Funding. National Natural Science Foundation of China (62071227);
back into the air. On the other hand, the transmission coeffi- Open Research Program in China’s State Key Laboratory of Millimeter Wave
cient, denoted as t˜12 = t12 e iϕ12 , represents the proportion of (K202323); Aeronautical Science Foundation of China (20220018052002).
the incident wave that is transmitted into the dielectric layer. Disclosures. The authors declare no conflicts of interest.
Similarly, the reflection and transmission coefficients resulting
from partial reflection and transmission between the top layer Data availability. No data were generated or analyzed in the presented
research.
and air can be represented as r˜21 = r 21 e iϕ21 and t˜21 = t21 e iϕ21 ,
respectively. Simulation results are used to calculate interference
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