Graphene-based double-loaded complementary split ring resonator (CSRR) slotted MIMO patch antenna for spectroscopy and imaging THz applications

Abstract

Wireless data transmission has surged at an exponential rate and researchers are now looking at radio frequency bands that can accommodate these ever-increasing needs of cellular data users. Wireless infrastructure must be developed and utilized to meet the growing capacity and connectivity requirements. To fulfil the requirement of high-speed data transmission in wireless devices and applications, Terahertz (THz) frequency range (0.1-10) THz is considered to be the crucial step and has aroused the curiosity of the research community. Antennas are the critical part of any THz communication system and require a great deal of expertise for the designing part. The design and construction of a miniaturized THz antenna employing a complementary split ring and a modified ground structure are given in this article. The planned antenna comprises a complementary split ring formed by two slots etched on a patch, one substrate layer, and a common ground plane that is changed to achieve the appropriate resonance frequency. The designed multi-input multi-output (MIMO) antenna shows a wide fractional bandwidth of 85.81% from 2.5 to 11 THz by making exhibits a wide impedance bandwidth of 85.81% (2.5-11 THz) due to the derived changes in the MIMO configuration. The proposed design has a maximum gain of 49 decibels. The developed MIMO antenna is effective for Wireless Body Area Network (WBAN) applications, health care, aerospace, and biomedical imaging in the THz frequency range because of better gain, wider bandwidth, and good isolation.

Full text

Vol.:(0123456789)
1 3
Applied Physics A (2022) 128:656
https://doi.org/10.1007/s00339-022-05820-6
Graphene‑based double‑loaded complementary split ring resonator
(CSRR) slotted MIMO patch antenna forspectroscopy andimaging THz
applications
KavanDave1· VishalSorathiya2· SunilP.Lavadiya1· ShobhitK.Patel3· UtsavDhankecha4· DeviprasadSwain1·
OsamaS.Faragallah5· MahmoudM.A.Eid6· AhmedNabihZakiRashed7
Received: 13 February 2022 / Accepted: 24 June 2022
© The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2022
Abstract
Wireless data transmission has surged at an exponential rate and researchers are now looking at radio frequency bands that
can accommodate these ever-increasing needs of cellular data users. Wireless infrastructure must be developed and utilized
to meet the growing capacity and connectivity requirements. To fulfil the requirement of high-speed data transmission in
wireless devices and applications, Terahertz (THz) frequency range (0.1–10) THz is considered to be the crucial step and
has aroused the curiosity of the research community. Antennas are the critical part of any THz communication system and
require a great deal of expertise for the designing part. The design and construction of a miniaturized THz antenna employ-
ing a complementary split ring and a modified ground structure are given in this article. The planned antenna comprises
a complementary split ring formed by two slots etched on a patch, one substrate layer, and a common ground plane that is
changed to achieve the appropriate resonance frequency. The designed multi-input multi-output (MIMO) antenna shows a
wide fractional bandwidth of 85.81% from 2.5 to 11 THz by making exhibits a wide impedance bandwidth of 85.81% (2.5–11
THz) due to the derived changes in the MIMO configuration. The proposed design has a maximum gain of 49 decibels. The
developed MIMO antenna is effective for Wireless Body Area Network (WBAN) applications, health care, aerospace, and
biomedical imaging in the THz frequency range because of better gain, wider bandwidth, and good isolation.
Keywords Terahertz (THz)· Graphene· MIMO· Reflectance coefficient· Gain
* Ahmed Nabih Zaki Rashed
ahmed_733@yahoo.com
Kavan Dave
kavan.dave@marwadieducation.edu.in
Vishal Sorathiya
vishal.sorathiya9@gmail.com
Sunil P. Lavadiya
sunil.lavadiya@marwadieducation.edu.in
Shobhit K. Patel
shobhitkumar.patel@marwadieducation.edu.in
Utsav Dhankecha
utsav.dhankecha105245@marwadiuniversity.ac.in
Deviprasad Swain
deviprashad.swain108247@marwadiuniversity.ac.in
Osama S. Faragallah
o.salah@tu.edu.sa
Mahmoud M. A. Eid
m.elfateh@tu.edu.sa
1 Information andCommunication Engineering Department,
Marwadi University, Rajkot360003, India
2 Faculty ofEngineering andTechnology, Parul Institute
ofEngineering andTechnology, Parul University, Waghodia
Road, Vadodara391760, Gujarat, India
3 Department ofComputer Engineering, Marwadi University,
Rajkot360003, India
4 Electronics andCommunication Engineering Department,
Marwadi University, Rajkot360003, India
5 Department ofInformation Technology, College
ofComputers andInformation Technology, Taif University,
P.O. Box11099, Taif21944, SaudiArabia
6 Department ofElectrical Engineering, College
ofEngineering, Taif University, P.O. Box11099, Taif21944,
SaudiArabia
7 Electronics andElectrical Communications Engineering
Department, Faculty ofElectronic Engineering, Menoufia
University, Menouf32951, Egypt

K.Dave et al.
1 3
656 Page 2 of 12
1 Introduction
Since the dawn of the twenty-first century, the number of
people using wireless technology has grown significantly
due to the development of online apps on social networks.
Several organizations are working to assist the wireless
traffic growth, like 3GPP long-term evolution (LTE), wire-
less personal area network (WPAN, WiHD, IEEE 802.15,
and IEEE 802.11 WLAN) [1]. As a result, the frequency
spectrum utilized progressively grew to meet the enor-
mous needs for immediate information for each of these
standards. Edholm’s Bandwidth Law [2] predicts that the
wireless data rate will reach 100Gbps by 2030 to meet
various demands in telecommunication services. The
bandwidth available in the sub-6GHz and millimetre-wave
(mm-Wave) bands will become insufficient to serve numer-
ous bandwidth-hungry applications in the future, such as
virtual reality, augmented reality, and so on because of this
massive increase. Therefore, there has been a lot of inter-
est in the terahertz (THz) spectrum as a viable solution
for these needs. Thus, terahertz (THz) spectrum is being
looked at as a possible answer to these demands.
In comparison to the millimetre-wave (mm-Wave)
band, the THz band can provide larger bandwidth (0.1–10
THz), high-speed data (in thousands of Gbps), and reduced
latency (in microseconds). Therefore, It has recently arisen
as an attractive solution to deal with the aforementioned
"bandwidth problem" by moving present frequency bands
to the under-exploited and extensive range of 0.1–10 THz
[3]. This band is suggested to represent an extension of
microwave and millimetre-wave frequencies. In compari-
son to other frequency ranges, it has a higher transmis-
sion capacity. More secure in spread spectrum technol-
ogy than microwaves, THz is less affected by fog than the
infrared region [4]. The large bandwidth is one of the key
advantages. Therefore, after the successful establishment
of millimetre-wave (mm-Wave) communications in fifth-
generation (5G) networks, THz communications are now
a progressing research on possible sixth-generation (6G)
wireless communications. Significantly facilitating ubiqui-
tous wireless communications is communication between
microwave and optical bands above 100GHz and below
10 THz.
Due to its abundance of physical and chemical pro-
cesses, the far-infrared region is critical. Unfortunately,
scientists and academics have ignored this band for a pro-
longed time due to the lack of dependable hardware such
as transceivers, sources, and detectors. As a result, it has
been labelled the "terahertz bandgap" [5]. Semiconductor
technology has evolved rapidly over the past 2decades,
and its impact on electromagnetic spectrum studies has
also been noted. Various uses of the terahertz spectrum
in science and technology have been noticed as terahertz
research continues to advance [6]. There is, nevertheless, a
requirement for an examination of the different THz wire-
less communication system components as operating fre-
quencies grow. With its unique location between the two
already well-studied regimes of the spectrum, the terahertz
spectrum may be accessed via both electrical and photonic
routes. Electrical and photonic methods are used to inves-
tigate these components in the near microwave and far-
infrared THz regions. Advances in photonics, electrical,
and plasmonic graphene-based technologies have helped
close the THz gap in recent years providing higher data
rates and high output power, respectively [7].
Terahertz research is making steady progress, which has
led to a growing list of possible uses for this spectrum in
health [8, 9], information processing in imaging [10–15],
THz-TDS [16], military applications [17], space research
and space instruments [18, 19] are all examples of terahertz
spectrum utilization. Agribusiness, semiconductor wafer
inspection, environmental monitoring, basic sciences,
pharmaceuticals, and many more will benefit from THz
advancements [20]. For scientific and industrial uses, the
terahertz frequency of the radio waves in the EM spectrum
is an attractive option because of the distinctive and remark-
able radiation characteristics [21] like the low ionization
effect because of low power levels in the biological tissues; it
passes through different materials through different levels of
attenuation, better image resolution then microwave region
as the wavelength has been decreased, low scattering than
the light region as the wavelength has been decreased, col-
limation of THz wave is better than the microwave, several
solid as well as condensed gases materials reveals THz sig-
nature in 0.5 to 3 THz band and hereby making the detection
easier. Although the THz band has many tempting features,
it is not an easy task to build a dependable transmission link
at THz frequencies. The RF link becomes sporadic because
of significant free space losses and atmospheric attenuation
in the THz band, and also the linkages are usually inter-
rupted since the LoS connection is particularly subject to
blocking effects in the THz range [22]. As a result of the
short wavelength, THz communications have two main
drawbacks, namely, severe signal attenuation and poor dif-
fraction, which make the THz signals extremely vulnerable
to barriers and hence severely restrict their reach [23]. Due
to the drawbacks mentioned above, the range of THz com-
munication systems may be significantly reduced. It may be
possible to circumvent the constraints of THz communica-
tions by deploying massive MIMO and intelligent reflective
surface (IRS) in systems and thus providinguninterrupted
wireless connectivity.
The free space path loss quadruples as the carrier fre-
quency rises, according to Friis' law, assuming constant

Graphene‑based double‑loaded complementary split ring resonator (CSRR) slotted MIMO patch…
1 3
Page 3 of 12 656
antenna gains. In contrast, antenna components may be
densely packed into a small form factor at sub-THz fre-
quencies because of the decreasing wavelength. A quad-
ratic decrease in the free space path loss is predicted if the
antenna array's physical size (effective aperture) is main-
tained constantly on the receiver as well as transmitter side.
One of the most common THz creation and detection com-
ponents is the antenna. Ultra-short excitation laser pulses
can cause transient photocurrents, with which THz pulses
in devices are generated and detected. Only by raising the
modulation size or the frequency spectrum employed can
the data rate be increased in a single-antenna system, result-
ing in complexities and difficulties. Multi-antenna systems'
capacity grows in perfect sync with the number of transmit-
ting antennas, well above Shannon's theoretical limit [24,
25]. This reference paper demonstrates that multi-antenna
systems can sustain fainting and interference [26]. To keep
up with the proliferating demand for capacity, the combina-
tion of THz and MIMO technologies might further simplify
things [27]. As an alternative, a phased array (also known
as an array of antennas) is a set of two or more antenna
components fed from a single frequency source. To improve
the all-around performance of the system, they integrate the
signals from each of the individual antennas. Using these
insights, concepts of MIMO's were developed. It is possible
to pack more antenna components into an antenna array with
half-wavelength spacing because of the tiny wavelength in
the THz frequency range. This allows for greater distance
and data rate expansion using massive MIMO in THz com-
munications. MIMO transmissions use multiple antennas
to transmit the same data over a single channel in multiple
ways. Using numerous antennas to boost an RF link's signal
strength and quality is a form of antenna diversification. To
receive the data, another MIMO radio with the same number
of antennas is used to split the data into numerous streams
and recombine them. When receiving signals, the receiver
compensates for various factors, including the short lag time
between transmissions, extra noise or interference, and even
dropped communications. MIMO radios add redundancy to
data transmission that isn't possible with traditional single-
antenna configurations (SISO: Single In, Single Out).
An effective antenna design also includes the difficult
challenge of selecting a material with low propagation
losses. There are many advantages to using copper for
antenna manufacturing. However, copper metal's skin depth
and conductivity diminish at THz frequencies, reducing the
radiation effects of the antenna elements [28]. In addition,
Ohmic-resistance significantly influences copper's surface
impedance at lower THz frequencies, such as the 6.45 THz
resonance frequency, making it challenging to build anten-
nas utilizing copper as a material. Even though copper is
regarded as an excellent material for constructing low RF
band antennas, it has substantial negative consequences for
the THz antenna development. Researchers have looked into
different options to get around these limitations. For exam-
ple, THz antennas may be made using Graphene and Carbon
nanotubes (CNT), better alternatives to copper [28].
Countless different forms and sizes are possible for THz
antennas. Graphene and photoconductive antennas, as well
as bow-tie dipoles and angle reflector arrays, are a few of the
many possible designs for THz antennas. In addition, THz
antennas can be classified as dielectric, metallic, or modern
material antennas based on the amount of processing they
include. There is a considerable quantity of research acces-
sible to comprehend and validate the notion of MIMO THz
antenna configuration. Graphene-based nano-patch antennas
are used to create a reconfigurable THz MIMO antenna for
wireless communication [29] by tweaking its characteris-
tics. Using a MIMO design, the authors in [29] demonstrate
increased throughput capacity, while picking the optimum
channel state. High bandwidth and more data rates are dis-
cussed in [30] concerning the THz band. In [30], Massive
MIMO antennas have been used to address and resolve
the difficulties of low power and short THz transmission.
Pattern diversity is used to divide a 2 × 2 MIMO antenna
tuned to the THz band, guaranteeing a high coupling level
for MIMO applications. The graphene patch is used in this
design, because it allows for fine-tuning of the antenna char-
acteristics. This was achieved in [31].
For spectroscopy and imaging applications, penetration
through the material is the key element. Now, compared to
microwave and infrared, THz waves can easily penetrate
through the materials because of their unique radiation
characteristics. Therefore, it is natural to switch it to THz
frequency in spectroscopy and imaging but because of the
THz gap, it is very much difficult to find the necessary hard-
ware for the generation and detection of THz radiation. In
spectroscopy for laser gated THz detection, antenna design
is one of the most important system components. Antenna
design with wide bandwidth, large gain and multiple reso-
nant characteristics is preferred for sensing applications [32].
For imaging applications, THz technology is targeted for its
non-ionizing nature. To make the communication possible,
antenna design is one of the most important design param-
eters because of its power source and impedance matching
characteristics in imaging applications. THz antennas with
comparatively improved bandwidth and gain are proven
useful for various directional imaging/sensing applications
[33–35].
2 Antenna design andmodeling
This paper has designed a 2 × 2 microstrip patch antenna
slotted with a square complementary split ring resonator.
In addition, a complementary split ring resonator has been

K.Dave et al.
1 3
656 Page 4 of 12
etched out of the top part of the patch antenna. This step was
taken, because using a double-loaded split ring, slot ring, or
notches can improve the problem of spurious radiations in
the patch antenna. This designed microstrip patch antenna
consists of CSRR, often used as a radiating element. This
antenna is designed with RT/Duroid5880 substrate with
16µm thickness.
Figure1a shows the antenna geometry of a 2 × 2 MIMO
antenna. Figure1b shows the Top View, and Fig.1c shows
the Bottom View. All the dimensions are shown in detail
in Table1. Over the substrate, the CSRR element is etched
out from the conventional microstrip patch, and on the
backside modified ground plane is etched out. A horizon-
tal conductive strip and an etched out CSRRmake up the
electrical stab. The antenna's conducting component (patch
and ground) is shown in perspective with the substrate's
thickness of 1.6mm. Several phases are performed to design
the suggested 2 × 2 MIMO dual complementary split ring
antenna, as illustrated in Fig.2. Initially, a single rectangular
slotted patch element was taken with no electrical stubs. In
the next phase, two rectangular slotted patch elements were
taken with one electrical stub in between making a 1 × 2
MIMO structure. The third phase includes a 2 × 1 MIMO
element with one electrical stub in between. At last, 2 × 2
MIMO of double-loaded CSRR rectangular patches are pro-
posed with one electrical stub in between with the hope of
providing good isolation. As a result, better isolation and
gain were achieved at the THz frequency.
On an RT/Duroid substrate, the designed slotted rectan-
gular microstrip patch antenna has a fragmented ground
plane (εr = 2.2 and tangent loss = 0.02) of the size of
(T × U × h), where T, U and h are length, width and height
Fig. 1 a Proposed design structure, b upper view of the proposed design, c bottom view of the proposed design
Table 1 Design dimensions of
the proposed MIMO antenna
structure
A—9 B—9 C—10 D—2.5 E—2.5 F—4.1 G—4.1 H—0.6 I—2
J—0.3 K—5 L—3.2 M—1.8 N—2 O—1 P—0.4 Q—0.5 R—3
S—0.5 T—38 U—50 V—12.5 W—5 X—2 Y —4 Z—1

Graphene‑based double‑loaded complementary split ring resonator (CSRR) slotted MIMO patch…
1 3
Page 5 of 12 656
of substrate, respectively. The antenna’s total dimension
is 38µm × 50m × 1.6µm. A 50-microstrip line with a feed
length FL = 9µm and a feed width FW = 1.8µm feeds the
patch. The top layer of the substrate has been etched with
CSRR. The rectangular CSRR is composed of two rectan-
gular C-shaped slots. The bigger C slot has been etched
out from the top by keeping a 2.5µm distance from both
sides with a width of 0.6µm. The complementary short
rectangular C slot has been etched by keeping a 0.3µm
distance from the bigger slot. All four patches have simi-
lar CSRR structures. On the substrate's bottom surface,
a partial ground plane of 5 × 4µm is etched. For better
results from that patch, some part has also been etched.
All the ground patches have similar etched out structures.
Equations1–4 from the reference [36] was used to com-
pute the Microstrip patch parameters. The width of the
structure is computed by:
In the above equation, the width of the patch is deter-
mined by W,
fr
is the proposed antennas’ resonance fre-
quency, C0 is its light speed, and r is the substrate’s dielec-
tric constant. Microstrip patch antenna design relies heavily
on the patch's effective dielectric constant (Ɛeff), which is
a critical design parameter. The air and the substrate are
used to carry radio signals from the patch to the ground
(1)
W
=C0
2fr
√
2
𝜀
r
+1
.
Fig. 2 The evolution of the proposed MIMO antenna in four phases.
a Top and bottom view of single rectangular slotted patch element.
b Top and bottom view of 1 × 2 MIMO element with one electrical
stub. c Top and bottom view of 2 × 1 MIMO element with one electri-
cal stub. d Top and bottom view of 2 × 2 proposed MIMO antenna

K.Dave et al.
1 3
656 Page 6 of 12
(called fringing). Because the substrate's and air's dielectric
constants differ, we must figure out the effective dielectric
constant for the device. It is possible to measure the effective
dielectric constant using the following Eq.2.
Electrically, the antenna's size increases by (ΔL) due to
fringing. Therefore, the patch's increased length (ΔL) may
be determined using the following Eq.3.
where h is the substrate’s height, using the following Eq.4,
the preciselength of the patch can now be measured.
For a conductor, we have taken graphene, because there
are significant differences in the electrical and thermal con-
ductivity of graphene in comparison with silver and cop-
per. Faster electrical conductivity can be achieved using
graphene because the electrons pass through the graphene
material with less resistance as it has high charge carrier
mobility. Compared to traditional metal-based antennas, the
property assists in the development of distinct electromag-
netic radiation in the THz frequency band.
To use this property to our advantage, one should be
familiar with the surface conductivity parameter. Radian
frequency (ω), Temperature (T), bias magnetostatic field
(B0), bias and scattering rate (Γ = 1/τ), and chemical poten-
tial (μc), all affect graphene's surface conductivity value. As
a result of the applied electrostatic field, the chemical poten-
tial can be represented. Hall conductivity of the graphene
is zero when the magnetostatic field is zero. Therefore, the
only field component affecting the component of 'σg' is E0,
known as the diagonal conductivity where ‘σg’ is the con-
ductivity of graphene. Graphene’s diagonal conductivity is
the sum of the conductivities of both intraband and interband
transitions. According to [37], the real interband conductiv-
ity at lower frequencies is still insignificant. 'σg' is acquired
only from the intraband contribution in our planned MIMO
structure operating in the terahertz frequency range. Using
Drude's form representation, graphene's intraband conduc-
tivity may be expressed as in Eq.5 [38].
(2)
𝜀
eff =
𝜀r+1
2
+
𝜀r−1
2[
1+12 h
w]−0.5
.
(3)
Δ
L
h=0.412
(𝜀eff +0.3)
(
w
h+0.264
)
(𝜀eff −0.258)
(
w
h+0.8
),
(4)
L
=
1
2fr
√
𝜀eff𝜇0𝜀0
−2Δ
.
(5)

σg𝜔,𝜇c,Γ,T

=−je
2
KBT
𝜋h2
(
𝜔
−
j2
Γ)
×

𝜇c
K
B
T+2ln

e
−𝜇c
KBT+1
.
Boltzmann's constant (kB), the electron's charge (e), and
Planck's constant (h) are all used in this equation.
Even though there are various advantages of graphene
material, issues like material uniformity and consistency are
the concerns which cannot be ignored. Fabrication of gra-
phene is yet to be proved easily plausible but some novel and
cardinal works have been done to synthesize graphene. A
few of the popular methods are chemical vapour deposition
(CVD), reduced graphene oxide, and melting of metal–car-
bon alloys. Higher uniformity of the graphene film has been
observed in [39] because of using a flat ceramic plate instead
of the ceramic boat during the CVD growth of graphene.
Synthesis of graphene using reduction of graphene oxide
via spin coating method is getting better results in terms of
uniformity [40, 41]
3 Results anddiscussion
This section discusses the results of a 2 × 2 double-loaded
split patch antenna with electrical stab and modified ground
plane. In four subsections, the results are summarised and
presented. The reflection coefficient (S11, dB) parameter and
voltage standing wave ratio (VSWR) features of the devel-
oped antennas are discussed in the first part. The antenna's
performance was determined by the gain and radiation effi-
ciency parameters in the second part. The far-field radiation
pattern and directivity are discussed in the third part. Finally,
compatibility of the designed MIMO antenna in various
applications is determined by analyzing diverse THz MIMO
parameters like total active reflection coefficient (TARC),
diversity gain (DG), channel capacity loss (CCL), mean
effective gain (MEG), the envelope correlation coefficient
(ECC) in the last section.
When it comes to analyzing the behaviour of MIMO
antenna systems, the correlation between signals is a
resource. "Signal correlation" is the phrase used to deter-
mine the correlation between two complex signals [42] [43].
A scattering matrix is formed by the scattering characteris-
tics of reflection and transmission coefficients, which influ-
ences the Equation that produces the correlation coefficient
for MIMO antennas. In terms of the correlation coefficient,
the scattering matrix is taken from the references [44, 45]. A
direct correlation between antenna performance and system
capacity may be seen from the Eq.6.
For the dual-port MIMO antenna's simulated S-param-
eters, see the diagrams in Fig.3. Figure3a describes the S
parameters of Design 1, Fig.3b describes the S parameters
(6)
𝜌
s=
−
(
S∗
11S12 +S∗
21S22
)
√
1−
|
|
S11
|
|
2−
|
|
S21
|
|
21−
|
|
S22
|
|
2−
|
|
S21
|
|
2
.

Graphene‑based double‑loaded complementary split ring resonator (CSRR) slotted MIMO patch…
1 3
Page 7 of 12 656
of Design 2, Fig.3c describes the S parameters of Design
3 and Fig.3d describes the s parameters of Design 4. In
Design 1, multiple bands are observed throughout the
operational band. The reflection coefficient at 3.125 THz is
− 22.515dB which is the first band, next one is at 7.5 THz
with − 15.426dB as the reflection coefficient. − 13.26dB
reflection coefficient is achieved at 15.06 THz. The
fourth band is at 20.825 THz at − 11.006dB as reflection
coefficient. In designs 2 and 3, multiple bands are achieved
at 7.25 THz and 15.05 THz with reflection coefficients of
− 15.01dB and − 13.914dB, respectively. For Design 4,
the resonant frequency is 15.08 THz at all 4 ports with
S11 = − 12.27dB, S22 = − 10.0793dB, S33 = − 12.33dB and
S44 = − 11.04dB. In Design 4, the dual-port MIMO sys-
tem's reflection coefficients (S11 = S22 = S33 = S44) are identi-
cal because of the antenna structure's symmetry. For S11
Fig. 3 Scattering parameters of the proposed MIMO antenna struc-
ture. a Multiple bands of reflection coefficient are achieved maximum
being at 3.125 THz giving − 22.515 dB, b maximum reflection coef-
ficient is achieved at 7.25 THz giving − 15.01dB, c maximum reflec-
tion coefficient is achieved at 7.25 THz giving − 15.01dB, d maxi-
mum reflection coefficient is achieved at resonant frequency 15.08
THz giving S33 = − 12.33dB

K.Dave et al.
1 3
656 Page 8 of 12
10dB (S11 is equal to or below 10dB for the frequency
range), fractional bandwidth of 85.81% is calculated from
the formula 2((fmax
− fmin)/(fmax + fmin)) × 100, where fmax and
fmin are decided by keeping the reference of S11 equal to or
below 10dB. Spanning the whole working spectrum, i.e.
from 1 to 25 THz, a transmission coefficient (S21) less than
10dB is maintained by the suggested MIMO architecture.
At 13 THz, a maximum transmission coefficient of around
− 40dB or below − 40dB is achieved between all four ports.
A good MIMO antenna design necessitates a high isolation
level between the antenna parts.
Antenna performance is heavily influenced by the imped-
ance match between the transmission line and the antenna.
Due to the mismatch in impedance between antenna and
source, the signal reflected back to the source can be defined
as the voltage standing wave ratio (VSWR). Good imped-
ance matching demands a VSWR less than 2. Standing wave
voltage builds up in the feed line due to the reflected signal,
degrading the antenna's performance. A VSWR of 1 indi-
cates that 100% of the power is received, and there is zero
reflection.
Figure4 shows the peak gain plot of the antenna of all
four designs. The gain of the proposed antenna between 1 to
25 THz is more than 10dB. As the frequency is significantly
high, the gain will be relatively low compared to the lower
frequencies but this achieved gain value is more than appro-
priate and we will get a strong signal in this frequency range.
This is advantageous for the THz application. In terms of
antenna performance as a function of space, the radiation
pattern, also known as the antenna pattern is a graphical
representation of the antenna radiating properties. That is,
the antenna's design illustrates how the antenna sends energy
into space. As an antenna transfers energy to all directions,
at least to some extent; the antenna pattern thus has a 3D
shape. The basic plane patterns are two planar patterns that
are commonly used to depict this 3D design. Cutting two
cuts across the 3D pattern at the pattern's maximum value
or direct measurement can be used to construct these pri-
mary plane patterns. Antenna patterns are the names given
to these primary plane geometries.
Figure5 shows the 3D total gain plot of all the designs.
Total gain of different designs-1,2,3 and 4 are, respectively,
4.84dB, 5.08dB, 4.86dB and 5.027dB. Maximum total
gain attained in the 4 × 4 MIMO structure. Here, the radia-
tion patterns of each design are shown in Fig.6. The 3D
radiation pattern is doughnut-shaped, and the 2D radiation
pattern is more like a pea-shaped pattern.
The above diagram shows the radiation patterns of an
antenna. Now, if one out of the two antennas is radiating
upwards and the other one is radiating downwards, then the
ECC of these two antennas is 0. As the number of ECC
nodes rises, so does the quality of the isolation between indi-
vidual antenna nodes, resulting in a more effective MIMO
antenna system. The ideal MIMO antenna ECC value is less
than or equal to 0.5. It is possible to estimate the envelope
correlation (ECC) by using the scattering parameters given
in Eq.7 [46].
Diversity gain (DG) refers to the increase in the signal-
to-noise ratio (SNR) that numerous antenna systems achieve
over a single-antenna system whose ideal value is 10. The
following Eq.8 is used for the calculation of DG.
In a situation where the power received by a diversity
antenna is less than the power received by an isotropic
antenna, it is considered to be fading which can be quantified
using mean effective gain. Equation9 contains the formula
[17] for calculating MEG.
(7)
ECC =
|
|
|
S∗
11S12 +S∗
21S22 |
|
|
2
(
1−
(|
|
S11
|
|
2+
|
|
S21
|
|
2
))(
1−
(|
|
S22
|
|
2+
|
|
S12
|
|
2
)).
(8)
DG =
10
√
1
−�ECC�
2
.
(9)
MEG
1=0.5
[
1−|S11|
2
−|S12|
2]
MEG2=0.5
[
1−|S12|
2
−|S22|
2]
MEG = MEG
1
∕MEG
2.
Fig. 4 The peak gain plot over the 1 THz to 25 THz of all four pro-
posed designs. a Peak gain of 21dB is achieved at 3.125 THz, b max-
imum peak gain of 14.5 dB is achieved at 17.05 THz, c maximum
peak gain of 14.5dB is achieved at 17.05 THz, d maximum peak gain
of 39dB is achieved at 18.2 THz

Graphene‑based double‑loaded complementary split ring resonator (CSRR) slotted MIMO patch…
1 3
Page 9 of 12 656
A decent MIMO system should have a gain of less than
3dB [46]. MEG indicates that the antenna has improved
diversity performance. When utilizing many ports, the opti-
mum measure to characterize frequency and radiation per-
formance is the Total Active Reflection Coefficient (TARC)
[46]. In a MIMO system, TARC can be computed by taking
the square root of the ratio of total reflected power and total
incident power. Using TARC, randomized signal combina-
tions between ports are taken into account, as well as mutual
coupling. Equation10 uses reflected and incident waves to
express it. It may be estimated using Eq.11 in terms of S
parameters, as described in [47].
Fig. 5 3D total gain plot of proposed four designs
Fig. 6 2D radiation patterns of all the designs

K.Dave et al.
1 3
656 Page 10 of 12
where aj stands for incident waves and bj stands for reflected
waves. Here, θ represents the phase of the input signal.
Another significant characteristic to consider while evalu-
ating the MIMO performance of the proposed THz antenna
is Channel Capacity Loss (CCL). Channel capacity loss
defines the maximum pace at which information may be
sent without significant degradation. As a result, for lossless
data transfer, a well-designed MIMO system should oper-
ate at 0.5 bits/s/Hz. In short, CCL informs the user of the
maximum limit beforewhich communication can be carried
out safely and without loss. The following Equation can be
used to calculate it.
(10)
Γ
t
a=
√
ΣM
j|||bj|||
2
√
ΣM
j
|||
aj
|||
2
,
(11)
Γ
t
a=
√||
S11 +S12ej𝜃
||
2+
||
S21 +S22ej𝜃
||
2
2
,
(12)
CCL = −log2
Det
(
∅
R)
where Table3 clarifies the comparison for all four phases,
which can assist us in determining which design is best for
a particular wireless communication application. Table4
illustrates the comparison between the proposed design with
other previous designs.
4 Conclusion
This research paper proposes a graphene-based microstrip
patch antenna with double-loaded CSRR etched out for
wideband Terahertz wireless communication. This pro-
posed design was choreographed in four phases to achiev-
ing a better gain. Furthermore, the suggested design's per-
formance has been examined and addressed in terms of its
numerous antenna characteristics factors such as surface
current distribution, impedance bandwidth, gain, reflec-
tion coefficient, efficiency, and radiation characteristics.
The fractional bandwidth of 85.81% is achieved for the
(13)
∅
R=
[
∅11∅12 ∅21∅22
]
∅11 =1−
(
|
|S11|
|
2+|
|S21|
|
2
)
∅12 =S∗
11S12 +S∗
21S22 ∅21 =S∗
22S21 +S∗
12S11
∅22 =1−
(|
|
S22
|
|
2+
|
|
S12
|
|
2
)
,
Table 3 Compares all four phases, which can assist us in determining which design is best for a particular wireless communication application
Sr. No Operating band for
(S11 > = − 10dB)
Peak gain Isolation (S21) Return loss (S11)
Design 1 1 to 7 THz 21dB at approx. 7 THz NA − 10dB or below for operating band
Design 2 1 to 7 THz 11dB at approx. 17 THz Below − 20dB for operating band − 10dB or below for operating band
Design 3 1 to 7 THz 11dB at approx. 17 THz Below − 20dB for operating band − 10dB or below for operating band
Design 4 2.5 to 11 THz 39dB at approx. 17 THz Below − 10dB for operating band − 10dB or below for operating band
Table 4 Comparative table of
presented design with other
designs
Structure Substrate Size (µm2) Peak gain (dB) Bandwidth (THz)
Proposed Roger RT Duroid 5880 9 × 10 39 7
[48] RT/Duroid 6006 600 × 700 9.7 0.15
[49] Triethylamine 400 × 400 9.70 0.119
[50] Photonic crystal 500 × 500 10.7 –
[51] RT/Duroid 6006 1000 × 1000 10.43 0.155
[52] Polyimide 600 × 800 8 0.0364
[53] Rogers RT/Duroid 5880 500 × 450 16 30.05
[54] Polyimide 300 × 300 5.7 0.269
[55] Pyrex 500 × 500 7.3 Very Narrow
[56] Polyimide 433.2 × 208.98 5.09 0.05
[57] RT/Duroid 6006 1000 × 1000 3.09 0.15
[58] Tetra flouroethylene 109.76 × 150.93 – 0.13
[59] Polyimide 600 × 600 9.19 0.2

Graphene‑based double‑loaded complementary split ring resonator (CSRR) slotted MIMO patch…
1 3
Page 11 of 12 656
band where S11 is equal to or below 10dB. In addition,
the suggested antenna maintains isolation of 10dB across
all ports over the whole operational range.
Acknowledgements This study was funded by the Deanship of Scien-
tific Research, Taif University Researchers Supporting Project number
(TURSP-2020/08), Taif University, Taif, Saudi Arabia.
Declarations
Conflict of interest The authors declare no conflicts of interest.
References
1. B. Ning, Z. Tian, Z. Chen, C. Han, J. Yuan, S. Li, Prospective
Beamforming Technologies for Ultra-Massive MIMO in Terahertz
Communications: A Tutorial. pp. 1–32 (2021).
2. S. Cherry, Edholm’s law of bandwidth. IEEE Spectr. 41(7), 58–60
(2003). https:// doi. org/ 10. 1109/ MSPEC. 2004. 13098 10
3. A. Liao etal., Terahertz ultra-massive MIMO-based aeronautical
communications in space-air-ground integrated networks. IEEE
J. Sel. Areas Commun. 39(6), 1741–1767 (2021). https:// doi. org/
10. 1109/ JSAC. 2021. 30718 34
4. J. Federici, L. Moeller, Review of terahertz and subterahertz wire-
less communications. J. Appl. Phys. 107(11), 111101 (2010).
https:// doi. org/ 10. 1063/1. 33864 13
5. K.R. Jha, G. Singh, Terahertz planar antennas for future wireless
communication: a technical review. Infrared Phys. Technol. 60,
71–80 (2013). https:// doi. org/ 10. 1016/j. infra red. 2013. 03. 009
6. A. Redo-Sanchez, X.C. Zhang, Terahertz science and technol-
ogy trends. IEEE J. Sel. Top. Quantum Electron. 14(2), 260–269
(2008). https:// doi. org/ 10. 1109/ JSTQE. 2007. 913959
7. H. Sarieddeen, A. Abdallah, M.M. Mansour, M.-S. Alouini, T.Y.
Al-Naffouri, Terahertz-band MIMO-NOMA: adaptive superposi-
tion coding and subspace detection. IEEE Open J. Commun. Soc.
2, 2628–2644 (2021). https:// doi. org/ 10. 1109/ ojcoms. 2021. 31317
69
8. P.H. Siegel, Terahertz technology in biology and medicine. IEEE
Trans. Microw. Theory Tech. 52(10), 2438–2447 (2004). https://
doi. org/ 10. 1109/ TMTT. 2004. 835916
9. A.J. Fitzgerald, E. Berry, N.N. Zinovev, G.C. Walker, M.A. Smith,
J.M. Chamberlain, An introduction to medical imaging with
coherent terahertz frequency radiation. Phys. Med. Biol. (2002).
https:// doi. org/ 10. 1088/ 0031- 9155/ 47/7/ 201
10. K. Kawase, Y. Ogawa, Y. Watanabe, H. Inoue, Non-destructive
terahertz imaging of illicit drugs using spectral fingerprints. Opt.
Express 11(20), 2549 (2003). https:// doi. org/ 10. 1364/ oe. 11.
002549
11. M.K. Choi etal., Potential for detection of explosive and biologi-
cal hazards with electronic terahertz systems. Philos. Trans. R.
Soc. A Math. Phys. Eng. Sci. 362(1815), 337–349 (2004). https://
doi. org/ 10. 1098/ rsta. 2003. 1319
12. H. Zhong, A. Redo-Sanchez, X.-C. Zhang, Identification and clas-
sification of chemicals using terahertz reflective spectroscopic
focal-plane imaging system. Opt. Express 14(20), 9130 (2006).
https:// doi. org/ 10. 1364/ oe. 14. 009130
13. T. Yasuda, T. Yasui, T. Araki, E. Abraham, Real-time two-dimen-
sional terahertz tomography of moving objects. Opt. Commun.
267(1), 128–136 (2006). https:// doi. org/ 10. 1016/j. optcom. 2006.
05. 063
14. S. Galoda, G. Singh, Fighting terrorism with terahertz. IEEE
Potentials 26(6), 24–29 (2007). https:// doi. org/ 10. 1109/ MPOT.
2007. 906117
15. M.K. Choi, K. Tayloir, A. Bettermann, D.W. van der Weide,
Broadband 10–300 GHz stimulus-response sensing for chemi-
cal and biological entities. Phys. Med. Biol. 47(21), 3777–3787
(2002). https:// doi. org/ 10. 1088/ 0031- 9155/ 47/ 21/ 316
16. P.H. Seigel, Terahertz technology. IEEE Trans. Microw. Theory
Tech. 50(3), 910–928 (2022)
17. M. S. S. (Eds.). D.L. Woolard, J.O. Jensen, R.J. Hwu, Terahertz
Science and Technology for Military and Security Applications.
2007.
18. R.E. Cofield, P.C. Stek, Design and field-of-view calibration of
114–660-GHz optics of the Earth Observing System Microwave
Limb Sounder. IEEE Trans. Geosci. Remote Sens. 44(5), 1166–
1181 (2006). https:// doi. org/ 10. 1109/ TGRS. 2006. 873234
19. P.H. Siegel, THz instruments for space. IEEE Trans. Antennas
Propag. 55(11 I), 2957–2965 (2007). https:// doi. org/ 10. 1109/ TAP.
2007. 908557
20. L. Engineering, Cutting-edge terahertz technology. Nat. Photonics
1, 97–105 (2002)
21. D.L. Woolard, E.R. Brown, M. Pepper, M. Kemp, Terahertz fre-
quency sensing and imaging: a time of reckoning future applica-
tions? Proc. IEEE 93(10), 1722–1743 (2005). https:// doi. org/ 10.
1109/ JPROC. 2005. 853539
22. H. Do, S. Cho, J. Park, H.-J. Song, N. Lee, A. Lozano, Terahertz
line-of-sight MIMO communication: theory and practical chal-
lenges. IEEE Commun. Mag. 59(3), 104–109 (2021). https:// doi.
org/ 10. 1109/ mcom. 001. 20007 14
23. Z. Wan, Z. Gao, F. Gao, M. Di Renzo, M.S. Alouini, Terahertz
massive MIMO with holographic reconfigurable intelligent sur-
faces. IEEE Trans. Commun. 69(7), 4732–4750 (2021). https://
doi. org/ 10. 1109/ TCOMM. 2021. 30649 49
24. S. Park, H.S. Lee, J.G. Yook, Orthogonal code-based transmitted
radiation pattern measurement method for 5G massive MIMO
antenna systems. IEEE Trans. Antennas Propag. 68(5), 4007–
4013 (2020). https:// doi. org/ 10. 1109/ TAP. 2019. 29632 07
25. J.Y. Guo, F. Liu, G.D. Jing, L.Y. Zhao, Y.Z. Yin, G.L. Huang,
Mutual coupling reduction of multiple antenna systems. Front.
Inf. Technol. Electron. Eng. 21(3), 366–376 (2020). https:// doi.
org/ 10. 1631/ FITEE. 19004 90
26. M. El Ghzaoui, A. Hmamou, J. Foshi, J. Mestoui, Compensation
of non-linear distortion effects in MIMO-OFDM systems using
constant envelope OFDM for 5G applications. J. Circuits Syst.
Comput. 29(16), 1–21 (2020). https:// doi. org/ 10. 1142/ S0218
12662 05025 76
27. A. Faisal, H. Sarieddeen, H. Dahrouj, T.Y. Al-Naffouri, M.S.
Alouini, Ultramassive MIMO systems at terahertz bands: pros-
pects and challenges. IEEE Veh. Technol. Mag. 15(4), 33–42
(2020). https:// doi. org/ 10. 1109/ MVT. 2020. 30229 98
28. S. Dash, A. Patnaik, Material selection for THz antennas. Microw.
Opt. Technol. Lett. 60(5), 1183–1187 (2018). https:// doi. org/ 10.
1002/ mop. 31127
29. J.B.Z. Xu, X. Dong, Design of a reconfigurable mimo system for
thz communications based on graphene antennas. IEEE Trans.
Terahertz Sci. Technol. 4(5), 609–617 (2014)
30. I. F. Akyildiz, J. Miquel, Realizing Ultra-Massive MIMO
(1024x1024) Communication (2016).
31. G. Varshney, S. Gotra, V.S. Pandey, R.S. Yaduvanshi, Proximity-
coupled two-port multi-input-multi-output graphene antenna with
pattern diversity for THz applications. Nano Commun. Netw.
(2019). https:// doi. org/ 10. 1016/j. nancom. 2019. 05. 003
32. S. Poorgholam-Khanjari, F.B. Zarrabi, Reconfigurable Vivaldi
THz antenna based on graphene load as hyperbolic metamaterial

K.Dave et al.
1 3
656 Page 12 of 12
for skin cancer spectroscopy. Opt. Commun. (2021). https:// doi.
org/ 10. 1016/j. optcom. 2020. 126482
33. D. M. Kumar, A. Professor, A review of design and analysis for
various shaped antenna in terahertz and sub-terahertz applications
(2021)
34. U. Raj, M. Kumar Sharma, V. Singh, S. Javed, A. Sharma, Eas-
ily extendable four port MIMO antenna with improved isolation
and wide bandwidth for THz applications. Optik (Stuttg) (2021).
https:// doi. org/ 10. 1016/j. ijleo. 2021. 167910
35. H. Sarieddeen, N. Saeed, T.Y. Al-Naffouri, M.S. Alouini, Next
generation terahertz communications: a rendezvous of sensing,
imaging, and localization. IEEE Commun. Mag. 58(5), 69–75
(2020). https:// doi. org/ 10. 1109/ MCOM. 001. 19006 98
36. V. K. Srivastava, G. Saini, A Dual Wide-Band Slotted Rectangular
Patch Antenna for 2.4/5 GHz WLAN Applications. http:// www.
ijert. org
37. K. V. Babu, A Micro-Scaled Graphene Based Tree-Shaped Wide-
band Printed MIMO Antenna For Terahertz Applications (2021)
38. R. Bala, A. Marwaha, Characterization of graphene for per-
formance enhancement of patch antenna in THz region. Optik
(Stuttg) 127(4), 2089–2093 (2016). https:// doi. org/ 10. 1016/j. ijleo.
2015. 11. 029
39. Y. Sheng, Y. Rong, Z. He, Y. Fan, J.H. Warner, Uniformity of
large-area bilayer graphene grown by chemical vapor deposition.
Nanotechnology (2015). https:// doi. org/ 10. 1088/ 0957- 4484/ 26/
39/ 395601
40. C. Reiner-Rozman etal., The top performer: towards optimized
parameters for reduced graphene oxide uniformity by spin coating.
Micro Nano Lett 16(8), 436–442 (2021). https:// doi. org/ 10. 1049/
mna2. 12070
41. N.S. Struchkov, E.V. Alexandrov, A.V. Romashkin, G.O. Silakov,
M.K. Rabchinskii, Uniform graphene oxide films fabrication via
spray-coating for sensing application. Fullerenes Nanotub. Carbon
Nanostruct 28(3), 214–220 (2020). https:// doi. org/ 10. 1080/ 15363
83X. 2019. 16866 23
42. T. Svantesson, Correlation and channel capacity of MIMO sys-
tems employing multimode antennas. IEEE Trans. Veh. Technol.
51(6), 1304–1312 (2002). https:// doi. org/ 10. 1109/ TVT. 2002.
804856
43. P.S. Kildal, K. Rosengren, Correlation and capacity of MIMO
systems and mutual coupling, radiation efficiency, and diversity
gain of their antennas: simulations and measurements in a rever-
beration chamber. IEEE Commun. Mag. 42(12), 104–112 (2004).
https:// doi. org/ 10. 1109/ MCOM. 2004. 13675 62
44. X. Chen, P.S. Kildal, J. Carlsson, J. Yang, Comparison of ergodic
capacities from wideband MIMO antenna measurements in rever-
beration chamber and anechoic chamber. IEEE Antennas Wirel.
Propag. Lett. 10(2), 446–449 (2011). https:// doi. org/ 10. 1109/
LAWP. 2011. 21523 60
45. S. Lu, H.T. Hui, M. Bialkowski, Optimizing MIMO channel
capacities under the influence of antenna mutual coupling. IEEE
Antennas Wirel. Propag. Lett. 7, 287–290 (2008). https:// doi. org/
10. 1109/ LAWP. 2008. 928474
46. D.G. Kang, J. Tak, J. Choi, MIMO antenna with high isolation for
WBAN applications. Int. J. Antennas Propag. (2015). https:// doi.
org/ 10. 1155/ 2015/ 370763
47. M. S.-I. A. and propagation Magazine and undefined 2013,
“Printed multi-band MIMO antenna systems and their perfor-
mance metrics,” ieeexplore.ieee.org. [Online]. https:// ieeex plore.
ieee. org/ abstr act/ docum ent/ 67355 22/. Accessed 3 Feb 2022
48. R.H. Mahmud, Terahertz microstrip patch antennas for the surveil-
lance applications. Kurdistan J. Appl. Res. 5(1), 16–27 (2020).
https:// doi. org/ 10. 24017/ scien ce. 2020.1.2
49. A. Sharma, V. K. Dwivedi, G. Singh, THz rectangular microstrip
patch antenna on multilayered substrate for advance wireless com-
munication systems, in Progress in Electromagnetics Research
Symposium, 2009, vol. 1, pp. 617–621. [Online]. https:// www.
resea rchga te. net/ profi le/ Vivek- Dwive di-5/ publi cation/ 26648
5005_ THz_ Recta ngular_ Micro strip_ Patch_ Anten na_ on_ Multi
layer ed_ Subst rate_ f or_ Advan ce_ Wirel ess_ Commu nicat ion_ Syste
ms/ links/ 601e8 17229 9bf1c c26a7 520a/ THz- Recta ngular- Micro
strip- Patch- Antenn. Accessed 11 Jul 2021
50. K.R. Jha, G. Singh, Dual-band rectangular microstrip patch
antenna at terahertz frequency for surveillance system. J. Com-
put. Electron. 9(1), 31–41 (2010). https:// doi. org/ 10. 1007/
s10825- 009- 0297-8
51. M. Younssi, a Jaoujal, Y. Diallo, a El Moussaoui, and N. Aknin,
Study of a microstrip antenna with and without superstrate for ter-
ahertz frequency. Int. J. Innov. Appl. Stud. 2(4), 369–371 (2013).
https:// cites eerx. ist. psu. edu/ viewd oc/ downl oad? doi= 10.1. 1. 299.
7838& rep= rep1& type= pdf. Accessed 11 Jul 2021
52. R.K. Kushwaha, P. Karuppanan, L.D. Malviya, Design and analy-
sis of novel microstrip patch antenna on photonic crystal in THz.
Phys. B Condens. Matter 545, 107–112 (2018). https:// doi. org/ 10.
1016/j. physb. 2018. 05. 045
53. C.M. Krishna, S. Das, S. Lakrit, S. Lavadiya, B.T.P. Madhav, V.
Sorathiya, Design and analysis of a super wideband (0.09 – 30.14
THz) graphene based log periodic dipole array antenna for tera-
hertz applications. Optik (Stuttg) 247, 167991 (2021). https:// doi.
org/ 10. 1016/j. ijleo. 2021. 167991
54. C.M. Krishna, S. Das, A. Nella, S. Lakrit, B.T.P. Madhav, A
micro-sized rhombus-shaped THz antenna for high-speed short-
range wireless communication applications. Plasmonics 16(6),
2167–2177 (2021). https:// doi. org/ 10. 1007/ s11468- 021- 01472-z
55. A. Nejati, R.A. Sadeghzadeh, F. Geran, Effect of photonic crystal
and frequency selective surface implementation on gain enhance-
ment in the microstrip patch antenna at terahertz frequency. Phys.
B Condens. Matter 449, 113–120 (2014). https:// doi. org/ 10.
1016/j. physb. 2014. 05. 014
56. S. Anand, D.S. Kumar, R.J. Wu, M. Chavali, Graphene nanorib-
bon based terahertz antenna on polyimide substrate. Optik (Stuttg)
125(19), 5546–5549 (2014). https:// doi. org/ 10. 1016/j. ijleo. 2014.
06. 085
57. A. Sharma, G. Singh, Rectangular microstirp patch antenna design
at THz frequency for short distance wireless communication sys-
tems. J. Infrared Millimeter Terahertz Waves 30(1), 1–7 (2009).
https:// doi. org/ 10. 1007/ s10762- 008- 9416-z
58. A. Azarbar, M. S. Masouleh, A. K. Behbahani, A new terahertz
microstrip rectangular patch array antenna. academia.edu 4(1),
25–29 (2014). https:// www. acade mia. edu/ downl oad/ 66929 175/
10. 5923.j. ijea. 20140 401. 03. pdf. Accessed 11 Jul 2021
59. A. Hocini, M.N. Temmar, D. Khedrouche, M. Zamani, Novel
approach for the design and analysis of a terahertz microstrip
patch antenna based on photonic crystals. Photonics Nanostruct.
Fundam. Appl. (2019). https:// doi. org/ 10. 1016/j. photo nics. 2019.
100723
Publisher's Note Springer Nature remains neutral with regard to
jurisdictional claims in published maps and institutional affiliations.