RESEARCH ARTICLE
www.advtheorysimul.com
Easy-to-Implement Ultra-Thin, Wide-Band, and
Multi-Functional Polarization Converter for K and Ka Band
Applications
Aykut Coskun,* Ugur Cem Hasar, Ahmet Ozmen, and Mehmet Ertugrul
This article presents an ultrathin, broadband, and multipurpose polarization
converter design utilizing an anisotropic metasurface for K and Ka band. The
proposed polarization converter, which has a single layer F4B as a substrate
material with hexagonal-shaped metallic solid structure along with hexagonal
ring with diagonal splits on its front surface and a background (a completely
metallic surface) on its back, works as not only a circular polarization
converter but also a linear polarization to circular polarization (LP to CP)
converter. Its polarization conversion rate (PCR) is more than 90% in the
frequency range from 17.87 to 43.15 GHz, covering all of the K and Ka bands
with a relative bandwidth of 83% under normal incidence case. For incidence
angles up to 40°, PCR is observed to be greater than 75% in almost all of the K
and Ka bands (except for the frequency range between 24.72 and 27.11 GHz).
Furthermore, the proposed design has LP to CP in two different frequency
bands, 16.23–16.74 GHz and 48.6–48.8 GHz. The proposed polarization
converter, as advantages, is low cost, ultra thin, broadband, and facile, which
can be useful in linear cross polarization conversion in K and Ka band
applications.
A. Coskun
Department of Electronics and Automation
Bayburt University
Bayburt 69000, Turkey
E-mail: aykutcoskun@bayburt.edu.tr
U. C. Hasar
Department of Electrical and Electronics Engineering
Gaziantep University
Gaziantep 27310, Turkey
A. Ozmen
Department of Electronics and Automation
Agri Ibrahim Cecen University
Agri 4100, Turkey
M. Ertugrul
Department of Electrical and Electronics Engineering
Ataturk University
Erzurum 25240, Turkey
M. Ertugrul
Department of Electrical and Electronics Engineering
Universiti Putra Malaysia
UPM Serdang, Selangor 43400, Malaysia
M. Ertugrul
Department of Electric and Electronics Engineering
Kyrgyz Turkish Manas University
56 Chyngyz Aitmatov Avenue, Bishkek Kyrgyz Republic
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adts.202100543
DOI: 10.1002/adts.202100543
Adv. Theory Simul. 2022, 2100543
1. Introduction
Metamaterials have superior properties
such as controlling and manipulating the
phase, amplitude, and polarization of an
electromagnetic wave.[1–4] The manipulation of electromagnetic wave polarization
is gaining importance due to its applications such as remote sensing, imaging, and
communication.[5,6] Polarization converters
utilizing the Faraday effect and the optical
activity of crystals have disadvantages such
as high sensitivity to incidence angle, bulky
volume, and narrowband.[7] To eliminate
these disadvantages, metasurface-based polarization converters, which are gaining
popularity in recent years, could be applied.
These converters allow easy control of the
polarization of the incidence electromagnetic wave in reflection mode or transmission mode.
Polarization converters operating in the
transmission mode usually have multilayer
structures.[8] Therefore, their production is costly, timeconsuming, and difficult. It should be noted that there are
some polarization converter designs in the transmission mode
with one single layer in the literature.[9,10] On the other hand,
polarization converters operating in the reflection mode can be
implemented on one single layer through metal-dielectric-metal
structure. In addition, polarization converters operating in the
reflection mode have a higher bandwidth than the polarization
converters operating in the transmission mode, which is an
important property in the design of the polarization converters.
Therefore, polarization converters operating in the reflection
mode are more popular than polarization converters operating
in the transmission mode for manipulating and controlling the
polarization of electromagnetic wave.
In recent years, polarization converters operating in the reflection mode with versatile polarization conversion operations such
as from circular to circular, linear to circular, and linear to linear
have received great attention.[11–16] These converters can be constructed by various resonators including W shape,[17] U shape,[18]
L shape,[19,20] H shape,[21] V shape,[22] and split ring with center disc.[23] By designing resonance peaks of these converters sequentially positioned in a frequency band, it is possible to implement a broadband polarization converter. Although these polarization converters have broadband and high polarization conversion rate (PCR), their bandwidths decrease as the incidence
2100543 (1 of 8)
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Figure 1. Proposed polarization converter. a) Top view. b) Top view including dimension parameters. c) Side view.
angle increases.[17,21–23] Therefore, they are sensitive to the incidence angle.
In this work, we propose a new ultra-thin (single-layer), multifunctional and broadband polarization converter. While its PCR
efficiency is more than 90% in the frequency range from 17.87 to
43.15 GHz (covering all of the K and Ka band with a RB of 83%
under normal incidence), it is more than 75% in almost all K and
Ka band (except for the frequency range between 24.72 and 27.11
GHz) up to 40° angle stability. Moreover, an ultra-thin polarization converter is presented for the K and Ka band with a thickness
of 0.07𝜆0 .
2. Materials and Method
2.1. Metasurface Design and Unit Cell Configuration
Dimensions of the cell of the designed polarization converter are
seen in Figure 1. It involves a hexagonal-shaped metallic solid
structure along with hexagonal ring with diagonal splits. Its bottom and top layers are made of copper with a thickness (t) of 35
𝜇m and an electrical conductivity (𝜎) of 5.96 × 107 S m-1 . Its substrate is assumed to be made of F4B with a thickness (h) of 1.18
mm, a loss tangent (tan𝛿) value of 0.001, and a relative dielectric constant (𝜀r ) of 2.65. The values of the proposed polarization
converter parameters are summarized in Table 1.
2.2. Reflection Coefficients
If the incidence electric field Ei is y-polarized Eiy , the reflection
coefficients of the reflected field Er for co- and cross-polarized
Adv. Theory Simul. 2022, 2100543
Table 1. Dimensions of the proposed polarization converter (mm).
R1
1.45
R2
r
g
P
h
t
1.63
0.84
0.19
3.37
1.18
0.035
components can be expressed as, Rxy = |Erx |∕|Eiy | and Ryy =
|Ery |∕|Eiy |, respectively. Similarly, if the incidence electric field
Ei is x-polarized Eix , the reflection coefficients of the reflected
field Er for co- and cross-polarized components can be written
as, Ryx = |Ery |∕|Eix | and Rxx = |Erx |∕|Eix |, respectively.
Horizontal and vertical linear polarizations are denoted by x
and y labels, while right-handed circular polarization (RHCP) and
left handed circular polarization (LHCP) are designated by “+”
and ”-”, respectively.[1] In mathematical form, the Jones reflection coefficient matrix on a Cartesian basis is expressed by R in
Equation (1).
[
R
R = xx
Ryx
Rxy
Ryy
]
(1)
The relation between linear and circular polarization in incident and reflected EM wave is expressed as in Equation (2) on
a Cartesian basis with the Jones reflection coefficient matrix for
the mathematical analysis of co- and cross-polarization. The reflection coefficients Rlm for circular polarization (l and m correspond to + and/or -) and the reflection coefficients Rst for linear
polarization (s and t correspond to x and/or y) are related by the
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following equation:
[
]
R++ R+−
R−+ R−−
[
]
1 (Rxx − Ryy ) − i(Rxy + Ryx ) (Rxx + Ryy ) + i(Rxy − Ryx )
=
2 (Rxx + Ryy ) − i(Rxy − Ryx ) (Rxx − Ryy ) + i(Rxy + Ryx )
RCP =
(2)
PCR can be used to interpret the polarization conversion efficiency or performance of a linear polarization converter. If the
polarization of the incidence electric field is assumed to be along
the y−axis, the PCR is calculated according to the following equation:
| |2
|Rxy |
| |
PCR =
| |2 | |2
|Rxy | + |Ryy |
| |
| |
(3)
Besides, if the polarization of the incidence electric field is assumed to be along the x−axis, the PCR is calculated using Equation (3), after interchanging the x−axis with the y−axis.
On the other hand, in circular polarization converters, the ability of the metasurface to maintain polarization is evaluated by the
polarization maintenance ratio (PMR).[6] The PMR for RHCP incident waves is expressed by
PMR =
|R++ |2
|
|
|R−+ |2 + |R++ |2
|
|
|
|
(4)
Similarly, if the incident wave is the LHCP, + and − are interchanged in Equation (4).
Finally, normalized ellipticity (e), which shows how well the reflected wave is circular polarized, for the incident wave polarized
in the y-direction can be calculated from
e=2
| || |
|Rxy ||Ryy |
| || | sin Δ𝜙
1
| |2 | |2
|Rxy | + |Ryy |
| |
| |
(5)
where Δ𝜙1 = 𝜙yy − 𝜙xy is the phase difference, and 𝜙yy and 𝜙xy
denote the phases of Ryy and Rxy , respectively. If the reflected
wave is RHCP, then |Rxy | = |Ryy | and Δ𝜙1 = 90◦ + 2k𝜋, yielding
e = +1. Here, k is an integer number. On the other hand, if the
reflected wave is LHCP, Rxy = Ryy and Δ𝜙1 = −90◦ + 2k𝜋, producing e = −1.
3. Results
3.1. Simulation Results
Simulations for the proposed polarization converter were performed by a full 3D electromagnetic simulation program—
Computer Simulation Technology (CST) Microwave Studio (CST
2020)—to analyze its PCR performance versus incidence angle.
Tetrahedral mesh type analysis was performed in the frequency
domain. The number of meshes per unit wavelength was selected automatically.
Adv. Theory Simul. 2022, 2100543
Figures 2a and 2b illustrate, respectively, magnitude and phase
variations of Rxy and Ryy (and Δ𝜙1 ), while Figures 2c and 2d
demonstrate, respectively, frequency variations of the ratio of the
magnitude of the co-polarized electric field Eco to the magnitude
of the cross-polarized electric field Ecross and ellipticity e. It is
noted that the dependencies |Rxx |, |Ryx |, 𝜙xx , and 𝜙yx are not
demonstrated in Figure 2 because Ryx = Rxy and Rxx = Ryy due to
symmetry of the structure in Figure 1 for normal incidence case.
The following points are noted from the results in Figure 2a–d.
First, as seen in Figure 2a, the magnitude of the co-polarization
coefficient |Ryy | is less than 0.3 in the frequency range from 17.85
to 43.15 GHz, while the magnitude of the cross-polarization coefficient |Rxy | is higher than 0.94 in the same frequency range.
Second, it is also noted from the same figure that |Ryy | and |Rxy |
attain equal magnitudes of approximately 0.7 at 16.48 and 48.74
GHz, resulting in a PCR value of 0.5 as seen from Equation (3).
Third, as seen from Figure 2b, 𝜙xy has a slower frequency variation in comparison with the frequency variation of 𝜙yy , which
means that the proposed polarization converter design has different Δ𝜙1 values over frequency. Fourth, |Eco |∕|Ecross |, which could
be considered as the ratio of |Ryy | to |Rxy |, gets values of unity
at 16.48 and 48.74 GHz (please see the insets) at which e goes
to sinΔ𝜙1 , as noted from Equation (5). Finally, as observed from
Figure 2d, e attains unity value at 16.48 and 48.74 GHz, meaning
that the proposed polarization converter operates as a RHCP at
those frequencies.
3.2. Eigen-Polarization and Eigenvalue
The polarization transformation phenomenon can be better examined by analyzing the eigen-polarizations and eigenvalues of
the proposed polarization converter. Equation (7) is used to obtain eigen-polarizations and eigenvectors:
RX − mX = 0
(6)
Here, the eigenvector and the eigenvalue are represented by X
and m, respectively. In this equation, the cross polarized reflections are neglected, and the ideal condition is assumed.
According to the results in Figure 2a, it can be observed that
|Ryy | = |Rxx | ≈ 1 and |Rxy | = |Ryx | ≈ 0 at 18.96, 28.54, 40.8, and
47.9 GHz resonance frequencies. When the approximate values
are written in the reflection coefficient matrix in Equation (1), the
following equation is obtained:
R=
[
]
0 1
1 0
(7)
While the linearly independent eigenvectors for the R matrix
T
T
are u = [1 1] and v = [−1 1] , the linearly independent eigeni0
values for the R matrix are e = 1 ei𝜋 = −1, respectively.
To better interpret polarization concept, orthogonal components of the proposed polarization converter, as shown in Figure 3, could be determined. It can be seen in Figure 3 that the linearly polarized field striking along the u- and v-axes oriented ±45o
with respect to the the x-axis or y-axis is reflected back without any
transformation. The two orthogonal components of the incident
electromagnetic wave Ei in the u and v directions are shown in
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Figure 2. Dependencies of a) |Rxy | and |Ryy |, b) 𝜙xy , 𝜙yy , and Δ𝜙1 , c) |Eco |∕|Ecross |, and d) ellipticity (e) of the proposed polarization converter in the xand y-direction.
Here, û and v̂ are unit vectors and ru and rv are complex reflection coefficients in the u axis and v axis, respectively. Khan et al.
2019 propose following equation:
̂ uu Eiu ei𝜙uu + Ruv Eiv ei𝜙uv ) + v̂ (Rvv Eiv ei𝜙vv + Rvu Eiu ei𝜙vu ) (10)
Er = u(R
Figures 4a and 4b illustrate, respectively, the magnitude and
phase variations of Ruu and Rvv (and Δ𝜙2 ). The following points
are observed from the results in Figure 4a,b. First, it is noted that
the magnitudes of the co-polarized reflection coefficients |Ruu |
and |Rvv | have magnitudes larger than 0.9 over the entire frequency band. Second, it is observed that the magnitudes of the
cross-polarized reflection coefficients |Ruv | and |Rvu | are almost
zero, not shown here for simplicity. Third, 𝜙uu and 𝜙vv have different frequency variations, indicating that the proposed polarization converter design has varying Δ𝜙2 values over frequency
where Δ𝜙2 = 𝜙uu − 𝜙vv .
3.3. Polarization Converter Rate Value
Figure 3. Orthogonal components of the proposed polarization converter
in the u and v directions.
Figure 3 to analyze the working principle of the designed polarization converter. The incident and reflected waves for polarization converter can be given in the following expressions[1] :
̂ iu + v̂ Eiv
Ei = ŷ Ei = uE
(8)
̂ ru + v̂ Erv = ur
̂ u Eiu + v̂ rv Eiv
Er = uE
(9)
Adv. Theory Simul. 2022, 2100543
It is observed from Figure 5 that PCR is greater than 0.9 over
the entire K and Ka bands and over the lower frequency part of
the V band for the normal incidence case. This means that the
designed polarization converter works efficiently for the purpose
of circular polarization converter in the whole K and Ka bands.
It is also noted from Figure 5 that PCR reaches unity around the
discrete frequencies 18.96, 28.62, 40.8, and 47.9 GHz, meaning
that the efficiency of the proposed converter could be improved
if the converter is operated around these frequency ranges. We
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Figure 4. Dependencies of a) |Ruu | and |Rvv | and b) 𝜙uu , 𝜙vv , and Δ𝜙2 of the proposed polarization converter in the u- and v-directions.
with a decrease in R1 and R2 values. Analysis of surface current,
which will be discussed in next subsection, further validates our
deduction. Except for a sharp decrease over a narrower frequency
band, the performance of the proposed converter could be conTM
TE
and 𝜃in
. Besides, as
sidered as to be nearly independent of 𝜃in
observed from Figure 6a,e, it is possible to eliminate the sharp
decrease over the frequency region of interest by using different
R1 and R2 values.
3.4. Surface Current
Figure 5. Frequency variation of the PCR value of the proposed polarization converter (normal incidence case).
have carried out additional analysis to examine the performance
of the proposed converter for oblique incidence case.
We also carried out additional analysis to examine the performance of the proposed converter for oblique incidence case.
While Figure 6a,b illustrates the frequency dependence of this
TE
), Figconverter for different incidence angles of the TE mode (𝜃in
ure 6c,d illustrates the frequency dependence of this converter for
TM
). It is seen from
different incidence angles of the TM mode (𝜃in
Figure 6a–d that the performance of the proposed polarization
TM
TE
or 𝜃in
up to 40o almost
converter does not change much with 𝜃in
over the entire K and Ka bands (almost 75% of the these bands)
except for the frequency range between 24.72 and 27.11 GHz. It
is noted that a sharp reduction of the PCR value around this frequency range is attributed to the resonance effect of the pentagon
ring with gaps. To validate this, we performed additional simulations for the pentagon ring having different R1 and R2 values.
For example, Figure 6e,f shows the frequency dependence of our
proposed converter when R1 = 1.25 mm and R2 = 1.43 mm for
TE
. It is seen from Figure 6e,f that the PCR value of
different 𝜃in
the modified polarization converter design has a sharp decrease
around 27.8 GHz, shifting upward (toward higher frequencies)
Adv. Theory Simul. 2022, 2100543
We made additional analysis to further examine the performance
and efficacy of the proposed polarization converter. For this
end, we investigated the current distribution over the resonating
metallic structure for all resonance frequencies.[11] The incoming
electromagnetic wave induces surface currents at the junction of
the metasurface due to the anisotropy of its front surface. The
following equation shows the relation between electric and magnetic current densities and electric and magnetic fields through
the polarization effect:
[ ]
[
J
𝛼
= i𝜔 ee
𝛼me
M
𝛼em
𝛼mm
][ ]
E
H
(11)
Here, J = [Jx , Jy ]T and M = [Mx , My ]T are electric and magnetic
current densities, respectively[1,2,11] ; 𝛼ee , 𝛼mm , 𝛼em , and 𝛼me are the
self and coupled electric and magnetic polarizations; and 𝜔 is the
angular frequency.
𝜇(𝜔) =
Z(𝜔)
𝜀(𝜔)
(12)
where, the surface impedance of the metasurface is denoted by
Z(𝜔). Also, magnetic permeability and electrical permeability are
denoted by 𝜇(𝜔) and 𝜀(𝜔), respectively. These parameters change
depending on the frequency.[1,2,11] The reflection coefficient (R)
at normal incidence is expressed by the following equation:
R(𝜔) =
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Z(𝜔) − Z0
Z(𝜔) + Z0
(13)
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TE ), c,d) for different incidence angles of the TM mode (𝜃 TM ) of the proposed
Figure 6. PCR values a,b) for different incidence angles of the TE mode (𝜃in
in
TE ) of the modified polarization
polarization converter design (R1 = 1.45 mm and R2 = 1.63 mm), and e,f) for different incidence angles of the TE mode (𝜃in
converter design (R1 = 1.25 mm and R2 = 1.43 mm).
In the above equation, R(𝜔) is the complex reflection coefficient with both real and imaginary parts. Also, Z0 the impedance
of free space at 377 Ω.[1,2,11]
Figure 7a–h illustrates surface current distributions over the
ground and resonator at resonance frequencies, that is, 18.96,
28.62, 40.8, and 47.9 GHz. When the current distributions in Figure 7a–h are examined, it is noted that the currents at the ground
and the resonator are in opposite directions, meaning that the
proposed converter design has magnetic resonance at all three
resonance frequencies f = 18.96, 28.62, 40.8, and 47.9 GHz.
Table 2. Comparison of the performance of the proposed polarization converter with some polarization converters in reflection mode in the literature.
Ref no.
LP to CP band [GHz]
CPC band [GHz]
Thickness [mm]
[1]
7.5 − 7.7 and 11.5 − 11.9
8 − 11
0.04𝜆0
[3]
N/A
12 − 18
0.06𝜆0
[7]
N/A
8.77 − 24.71
0.09𝜆0
[13]
N/A
13.8 − 40.7
0.09𝜆0
[23]
N/A
5.7 − 10.3
0.06𝜆0
16.23 − 16.74 and 48.6 − 48.8
17.87 − 43.15
0.07𝜆0
This work
3.5. Analysis of the Performance of the Proposed Converter
In order to examine the performance of our polarized converter
design, we compared its polarization characteristics with those
Adv. Theory Simul. 2022, 2100543
of the other converters in the literature.[1,3,7,13,23] The comparison
is presented in Table 2 in terms of the frequency band for lin-
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Figure 7. Surface current distributions over the ground and resonator at all resonant frequencies: a,e) 18.96 GHz, b,f) 28.62 GHz, c,g) 40.8 GHz, and
d,h) 47.9 GHz.
ear to circular polarization conversion and for circular polarization conversion (CPC) and thickness of the converter. It is noted
from Table 2 that our polarization converter design and the converter design in the study[1] have linear polarization to circular
polarization characteristics at two different frequencies, in comparison with the converter in the studies.[3,7,13,23] Besides, it is observed that our converter design and the converter design in the
study[13] have the largest frequency bands (wideband property)
to operate the converter in circular polarization mode. However,
the thickness of our converter design (0.07𝜆0 ) is smaller than the
thickness of the converter design (0.09𝜆0 ) in this study,[13] indicating that our design is thinner than the converter design in the
study.[13]
We also compared the efficiency of our proposed polarization
converter with those of the polarization converters in the transmission mode.[9,10] When our proposed polarized converter is
compared with those in the studies,[9,10] it is noted that our proposed method has both LP to CP conversion and CPC conversion,
while the polarization converters in the studies[9,10] have only LP
to CP conversion. Besides, our proposed polarization converter
design has a very broad frequency band (between 17.87 and 43.15
GHz) over which its PCR value is above 90%.
Finally, it should be mentioned that in our study we utilized a
hexagonal-shaped metallic solid structure along with hexagonal
ring with diagonal splits for concentrating electromagnetic signals around the ring and for improving angle-independence of
our design for different oblique angles with TE or TM mode incident waves. Other geometries such as hexagonal-shaped metallic solid structure along with pentagon ring with diagonal splits
could as well be considered for the polarization converter analysis, which will be undertaken as a future study.
as a circular polarization converter in the entire K and Ka band
frequency bands and a linear circular polarization converter in a
part of the Ku and V bands. The designed polarization converter
has a polarization conversion rate of over 90% as a circular
polarization converter with a relative bandwidth of 83% from
17.87 to 43.15 GHz. The polarization conversion ratio is often
above 75% for a wide angle of incidence up to 40° in the K and
Ka bands. Moreover, the LP to CP conversion in the proposed
design is in the frequency ranges 16.23–16.75 GHz (part of the
Ku band) and 48.6–48.8 GHz (part of the V band).
Acknowledgements
This work was supported by TUBITAK under the project number 218M341.
Conflict of Interest
The authors declare no conflict of interest.
Data Availability Statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Keywords
circular polarization conversion, K band, Ka band, linear polarization to
circular polarization, metasurface, polarization conversion rate, polarization converter
4. Conclusion
An easy-to-implement, ultra-thin, wide-band, and multifunctional circular polarization converter has been designed
Adv. Theory Simul. 2022, 2100543
2100543 (7 of 8)
Received: November 20, 2021
Revised: January 21, 2022
Published online:
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[1] M. I. Khan, Z. Khalid, F. A. Tahir, Sci. Rep. 2019, 9, 4552.
[2] F. Ahmed, M. I. Khan, F. A. Tahir, IEEE Antennas Wireless Propag. Lett.
2021, 20, 2186.
[3] T. Q. H. Nguyen, T. K. T. Nguyen, T. Q. M. Nguyen, T. N. Cao, H. L.
Phan, N. M. Luong, D. T. Le, X. K. Bui, C. L. Truong, D. L. Vu, Opt.
Commun. 2021, 486, 126773.
[4] H. O. Ali, A. M. Al-Hindawi, J. Eng. 2021, 27, 1.
[5] D. Yang, H. Lin, X. Huang, Prog. Electromagnet. Res. Lett. 2016, 61,
71.
[6] T. K. T. Nguyen, T. M. Nguyen, H. Q. Nguyen, T. N. Cao, D. T. Le, X. K.
Bui, S. T. Bui, C. L. Truong, D. L. Vu, T. Q. H. Nguyen, Sci. Rep. 2021,
11, 2032.
[7] B. Lin, J. Guo, L. Lv, J. Wu, Y. Ma, B. Liu, Z. Wang, Appl. Phys. A 2019,
125, 76.
[8] P. Naseri, S. A. Matos, J. R. Costa, C. A. Fernandes, N. J. G. Fonseca,
IEEE Trans. Antennas Propag. 2018, 66, 7128.
[9] A. K. Fahad, C. Ruan, R. Nazir, M. Saleem, T. U. Haq, S. Ullah, W. He,
IEEE Access 2020, 8, 163244.
[10] Z. Y. Li, S. J. Li, B. W. Han, G. S. Huang, Z. X. Guo, X. Y. Cao, Adv.
Theor. Simul. 2021, 4, 2100117.
Adv. Theory Simul. 2022, 2100543
[11] C. Mao, Y. Yang, X. He, J. Zheng, C. Zhou, Appl. Phys. A 2017, 123,
767.
[12] J. Xu, R. Li, S. Wang, T. Han, Opt. Express 2018, 26, 26235.
[13] M. M. Couto, M. W. B. Silva, A. L. P. S. Campos, J. Electromagn. Waves
Appl. 2021, 35, 1652.
[14] B. Lin, L. Lv, J. Guo, Z. Liu, X. Ji, J. Wu, IEEE Access 2020, 8, 82732.
[15] F. Li, H. Chen, L. Zhang, Y. Zhou, J. Xie, L. Deng, V. G. Harris, IEEE
Trans. Microwave Theory Tech. 2019, 67, 606.
[16] L. Zhang, P. Zhou, H. Lu, H. Chen, J. Xie, L. Deng, IEEE Antennas
Wirel. Propag. Lett. 2015, 14, 1157.
[17] Y. Zhao, B. Qi, T. Niu, Z. Mei, L. Qiao, Y. Zhao, AIP Adv. 2019, 9,
085013.
[18] Z. L. Mei, X. M. Ma, C. Lu, Y. D. Zhao, AIP Adv. 2017, 7, 125323.
[19] M. F. Zafar, U. Masud, A. Rashid, M. Murtaza, T. Ullah, Waves in Random Complex Media 2021, 31, 1.
[20] B. Kamal, J. Chen, Y. Yingzeng, J. Ren, S. Ullah, W. U. R. Khan, Opt.
Mater. Express 2021, 11, 1343.
[21] J. Xu, R. Li, S. Wang, T. Han, Opt. Express 2018, 26, 26235.
[22] X. Gao, X. Han, W.-P. Cao, H. O. Li, H. F. Ma, T. J. Cui, IEEE Trans.
Antennas Propag. 2015, 63, 3522.
[23] J. Zhao, Y. Cheng, Appl. Phys. B 2016, 122, 255.
2100543 (8 of 8)
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