# Fast and Highly Sensitive Ionic Polymer Gated WS2-Graphene Photodetectors

Jake D. Mehew  Centre for Graphene Science, College of Engineering,
Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QL, UK
EPSRC Centre for Doctoral Training in Metamaterials, College of Engineering,
Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QL, UK
Both authors contributed equally to this work  Selim Unal  Centre for Graphene
Science, College of Engineering, Mathematics and Physical Sciences, University
of Exeter, Exeter, EX4 4QL, UK  Both authors contributed equally to this work
Elias Torres Alonso  Centre for Graphene Science, College of Engineering,
Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QL, UK
Gareth F. Jones  Centre for Graphene Science, College of Engineering,
Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QL, UK
Saad Fadhil Ramadhan  Centre for Graphene Science, College of Engineering,
Mathematics and Physical Sciences, University of Exeter, Exeter, EX4 4QL, UK
Department of Physics, College of Science, University of Duhok, Duhok, 42001
Kurdistan Region, Iraq  Monica F. Craciun  Centre for Graphene Science,
College of Engineering, Mathematics and Physical Sciences, University of
Exeter, Exeter, EX4 4QL, UK  Saverio Russo  Centre for Graphene Science,
College of Engineering, Mathematics and Physical Sciences, University of
Exeter, Exeter, EX4 4QL, UK  Email<EMAIL_ADDRESS>
###### Abstract

The combination of graphene with semiconductor materials in heterostructure
photodetectors, has enabled amplified detection of femtowatt light signals
using micron-scale electronic devices. Presently, the speed of such detectors
is limited by long-lived charge traps and impractical strategies, e.g. the use
of large gate voltage pulses, have been employed to achieve bandwidths
suitable for applications, such as video-frame-rate imaging. Here, we report
atomically thin graphene-WS2 heterostructure photodetectors encapsulated in an
ionic polymer, which are uniquely able to operate at bandwidths up to 1.5 kHz,
whilst maintaining internal gain as large as $10^{6}$. Highly mobile ions and
a nanometre scale Debye length of the ionic polymer are used to screen charge
traps and tune the Fermi level of graphene over an unprecedented range at the
interface with WS2. We observe a responsivity $R=10^{6}$ A W-1 and detectivity
$D^{*}=3.8\times 10^{11}$ Jones, approaching that of single photon counters.
The combination of both high responsivity and fast response times makes these
photodetectors suitable for video-frame-rate imaging applications.

Keywords. graphene, WS2, van der Waals heterostructures, photodetectors,
ionic-polymer gating

The use of two-dimensional (2D) materials in optoelectronic devices has the
potential to supersede current state-of-the-art technology1 by added
functionalities, such as mechanical flexibility and ease of integration onto
textile fibres, enabling the development of new wearable electronic
applications.2 Graphene transistors have been shown to operate as high-speed
photodetectors3 with response times comparable to conventional silicon-based
devices, but the absence of a band gap and lack of significant gain mechanism
limits its use for ultra-sensitive light detection. Hybrid structures of
graphene with semiconductor materials such as quantum dots,4, 5, 6 chlorophyll
molecules,7 and MoS28, 9, 10 have been shown to enhance light absorption and
provide an internal gain mechanism. However, these implementations typically
have a limited operational bandwidth of less than 10 Hz which hampers their
use in real world applications.

Slow response times in these systems are produced by the long-lived trapping
of charges, often manifested as hysteresis in gate voltage sweeps. This has
been observed in organic, carbon nanotubes, graphene, and more recently in
transition metal dichalcogenide (TMD) field-effect transistors, and is
typically attributed to unavoidable intrinsic and/or extrinsic charge traps,
e.g. SiO2 surface states11, 12, 13, 14 and atmospheric contamination. 15, 12,
13, 16, 17 To reduce the impact of such traps, various solutions have been
explored including gate voltage pulses,11, 18, 19 vacuum annealing,20, 21 and
ionic liquid gating.22, 23 Although ionic liquid gating has been utilised in
WS2 phototransistors24 and MoTe2-graphene photodetectors25, the beneficial
effect of polymer gating on the performance of photodetectors consisting of
atomically thin heterostructures has not yet been explored.

In this work, we report the first study of WS2-graphene heterostructure
photodetectors with an ionic polymer gate. We demonstrate a gate tunable
responsivity up to $10^{6}$ A W-1, which is comparable with other
heterostructure devices,4, 5, 9, 7, 10, 6 and surpasses that of graphene or
TMD photodetectors by at least 4 orders of magnitude. Our devices reach a -3
dB bandwidth of 1.5 kHz, without the need for any gate pulse, leading to sub-
millisecond rise and fall times. The observed $10^{3}$ fold increase of
photodetection bandwidth, when compared to other heterostructure
photodetectors, is enabled by the enhanced screening properties of the mobile
ions in our ionic polymer top gate, which act to compensate the charge traps
limiting the speed of previous devices. Our devices have a detectivity
$D^{*}=3.8\times 10^{11}$ Jones, which is approaching that of single photon
counters, and are able to operate on a broad spectral range (400 - 700 nm).
These properties make ionic polymer gated WS2-graphene photodetectors highly
suitable for video-frame-rate imaging applications unlike previously developed
graphene-based heterostructure photodetectors.4, 5, 7, 8, 9, 10

Figure 1:  Device schematic and Raman spectrum of the WS2-graphene field-
effect transistor. (a) Device schematic with electrical connections included.
A voltage ($V_{gs}$) is applied to the transparent polymer (PEO + LiClO4)
using a gate electrode in close vicinity to the WS2-graphene photodetector.
Raman spectra of the WS2-graphene stack are shown for ranges of wavenumber
relevant to (b) WS2 and (c) graphene. Peaks labelled $*$ are resonant second
order processes. Inset in (c) shows the spectrum before baseline subtraction.

Hybrid WS2-graphene photodetectors have been fabricated onto p-Si/SiO2 (300
nm) substrates, where the doped Si serves as a global back gate. Few-layer WS2
was mechanically exfoliated from natural crystals and transferred onto the
SiO2 substrate by means of adhesive tape. High quality graphene grown by
chemical vapour deposition was then transferred onto the WS2, see Supporting
Information.26 Electrical contacts were defined by standard electron beam
lithography, electron beam deposition of Au (20 nm) and lift-off in acetone.
Subsequently, conductive graphene channels of widths ranging from 3 to 10
$\mu$m and lengths 1 to 12 $\mu$m were defined by means of O2 plasma etching.
The WS2-graphene devices were covered by a transparent ionic polymer, lithium
perchlorate/poly(ethylene oxide) (LiClO4/PEO, 8:1 in methanol), which serves
as a top gate, see Figure 1a.

Raman spectroscopy is used for the characterization of WS2 and graphene
heterostructures and reveals peaks in two well-separated regions, 200
cm${}^{-1}\leq\omega\leq$ 450 cm-1 and 1200 cm${}^{-1}\leq\omega\leq$ 3000
cm-1 respectively. Lorentzian fits of the spectra reveal the presence of
several peaks, which originate from the E2g, 2LA (second-order longitudinal
acoustic) and A1g modes of WS2 (see Figure 1b).27 The E2g phonon mode is an
in-plane displacement of both sulphur and tungsten atoms, whereas, the A1g
mode is an out-of-plane displacement of the sulphur atoms. The position of
both modes shifts with increasing numbers of layers, and their wavenumber
difference changes with layer number.28, 29, 30, 31 For the spectra in Figure
1c, a peak separation of 68.7 cm-1 is indicative of a trilayer WS2 flake. The
2LA peak is a disorder activated overtone of the LA mode, which is the in-
plane collective motions of atoms in the lattice.29 Resonant enhancement of
this mode is observed because the photon energy used in acquiring the Raman
spectra lies close to the B exciton energy of WS2.32 This is consistent with
the broad photoluminescence peak located at $\sim$3100 cm-1, attributed to the
direct electronic transition of WS2. After subtracting this photoluminescence
peak from the Raman spectrum, we identify the D, G, and 2D peaks of graphene
(Figure 1c).33 As we have reported elsewhere these films are monolayer
graphene.26 At the same time, the observed low D/G peak intensity ratio ($\sim
0.2$) indicates a low defect density.26 Finally, the fact that the measured
Raman spectrum on the WS2-graphene heterointerface simply is the sum of the
individual spectrum for isolated WS2 and graphene confirms the formation of a
van der Waals interface.

Figure 2: Characterisation of optoelectronic response and charge transfer
mechanism. (a) Channel resistance ($R_{s}$) as a function of gate voltage
($V_{gs}$). Insets show schematics of Fermi level position. Scanning
photocurrent maps of a large area device in short circuit configuration,
($V_{ds}=0$ mV), (b) and under a source drain bias, ($V_{ds}=5$ mV), (c). (d)
Photocurrent ($I_{pc}$) versus top gate voltage ($V_{gs}$). Inset shows
optical micrograph of device. Scale bar is 16 $\mu$m. (e) Drain current
($I_{ds}$) versus $V_{gs}$ in dark and under illumination. (f) Schematic of
charge transfer at WS2/graphene interface.

Figure 2a shows the typical ambipolar electrical transport of graphene. Upon
applying a bias to the ionic polymer a stable electric double layer is formed
at the interface with graphene without the occurrence of chemical reactions
within the electrochemical stability window, -2 V $<V_{gs}<$ 2 V. An extremely
large gate capacitance easily attained in ionic gated transistors ($\geq
2\,\times\,10^{-6}$ F cm-2) allows us to probe the properties of graphene at
record high charge carrier densities $\geq 10^{14}$ cm-2.34, 35 Most
importantly, the ions in the polymer are highly mobile and provide a
significant additional screening mechanism of charge impurities.36

To determine the photo-responsive region of the fabricated WS2-graphene hybrid
structures we use Scanning Photocurrent Microscopy (SPCM) which employs a
focussed laser beam, see Experimental Section.37 Figure 2b shows that in the
short circuit configuration ($V_{ds}=0$ V) photocurrent generation is
localised to the lateral interfaces of the device, such as the edges of Au
contacts and the WS2 flake, and changes in polarity across the photo-
responsive region. Upon applying a finite source-drain bias, a uniform
photocurrent is generated over the entire vertical WS2-graphene interface, see
Figure 2c.

To gain insight in the microscopic origin of the measured photocurrent and
understand the role played by the ionic polymer gate on device performance, we
characterize the photoresponse of these structures in a vacuum chamber at
finite source-drain bias and under illumination with collimated light (see
Experimental Section). Figure 2d shows that upon increasing top gate voltage
($V_{gs}$) $I_{pc}$ increases until $V_{gs}=-2$ V, at which point $I_{pc}$
reaches a peak value of $-18$ nA. For $V_{gs}\leq-2$ V no further increase in
$I_{pc}$ is observed. To explain the increased photocurrent under a gate bias
we examine the transfer curves (Vds = 10 mV) taken in both dark and light (600
nm, 200 $\mu$W cm-2) conditions as seen in Figure 2e. Under illumination a
reduction in the current ($\Delta I_{ds}$) is observed and this increases for
more negative gate biases. This is expected when the photocurrent generation
mechanism is the photogating effect1 where absorption of photons in WS2
creates electron-hole pairs, which can be split at the interface between
graphene and WS2, with one charge carrier transferred to graphene and the
other remaining in WS2, as shown schematically in Figure 2f. The in-built
fields at the interface enable this separation and arise from the work
function difference between graphene and WS2. For $V_{gs}<V_{dirac}$
illumination of the heterostructure results in an increase in resistance due
to the recombination between electrons, generated in WS2 and subsequently
transferred to graphene, and electrostatically induced holes present in
graphene. This manifests as a shift in the charge neutrality point ($\Delta
V_{gs}$) to negative values, indicating n-type doping. Photogenerated holes
remain trapped in WS2 and could be considered as a light induced gating
potential.

Figure 3: Characterisation of the spectral response of WS2-graphene
heterostructures. (a) Measured responsivity (black dots) versus incident
photon energy for $\text{V}_{ds}=10\text{ mV}$ and $\text{V}_{gs}=0\text{ V}$.
A, B and C exciton peaks, as well as the direct gap transition ($E_{g}$), are
fit with Gaussian functions with the cumulative fit described by the yellow
continuous line. (b) Schematic of electronic transitions responsible for each
peak fitted in the spectral responsivity of WS2/graphene interface.

These devices display an energy dependent responsivity ($R$) when illuminated
by monochromatic light, see Figure 3a. More specifically, a photoresponse is
only observed for incident photons of energy greater than 1.8 eV, with the
spectral profile of responsivity consisting of four Gaussian peaks centred at
1.92 eV, 2.06 eV and 2.36 eV, with a broader peak at 2.97 eV also present. All
of these peaks relate to different electronic transitions in WS2, as
illustrated in Figure 3b. The peak at 2.06 eV is the single particle band gap,
Eg, and at 1.92 eV we also observe the peak arising from the A exciton.38 This
exciton corresponds to the electronic transition from the upper branch of the
split valence band to the conduction band, and subsequent formation of a bound
state between an electron and hole.

In most semiconductors excitons can be described using a Wannier-Mott 2D
hydrogen model.39 Although the applicability of this model to 2D systems can
be questioned because of the increased exciton confinement and reduced
electric field screening,39 in this case we find that it serves as a
reasonable approximation. From the model we can extract the binding energy,
$\beta$, using $E_{A}=E_{g}-\beta$ which gives $\beta=140$ meV which is a
value between that of bulk ($\sim 50$ meV)38 and monolayer ($\sim 300-800$
meV)39, 40 WS2. Such a high binding energy inhibits the contribution of
excitons to the measured photocurrent unless they can dissociate into an
unbound electron-hole pair and be transferred to the graphene charge transport
layer.41 This dissociation can occur as long as the binding energy can be
overcome which typically requires large electric fields. The in-built field at
the interface, arising from the work function mismatch ($\Delta\phi$) between
graphene and WS2 could encourage this dissociation, although our estimate of
$\Delta\phi\sim 100$ meV indicates that this alone would not be sufficient.
Applying a non-zero value of $V_{gs}$ creates large electric fields at the
surface of graphene which can contribute to the exciton dissociation in WS2 as
the fields are not completely screened by graphene.42 This has been verified
by taking spectral scans at different top gate biases (see Figure S1).

Finally, the peak at 2.36 eV is due to the exciton formed from the electronic
transition originating in the lower branch of the valence band. The difference
in energy between this B exciton and the A exciton allows us to extract a
spin-orbit splitting energy of $440$ meV, which is in good agreement with both
theoretical 43 and other experimental 44 works. The broad peak at 2.97 eV,
Figure 3a, can be attributed to transitions between regions of high density of
states in the valence and conduction bands which give these materials their
strong light-matter interaction.45 The joint density of states (JDoS) exhibits
this in a clearer fashion and has a prominent peak around this energy, see
Figure 3b.

Figure 4: Photodetector performance of WS2-graphene heterostructures. (a)
Photocurrent ($|I_{pc}|$) and (b) responsivity (R) as a function of incident
optical power (P) at $V_{ds}=100$ mV. (c) Temporal response of the device at
$V_{ds}=100$ mV and $V_{gs}=-1.5$ V. (d) Normalised photoresponse as a
function of light modulation frequency. Inset shows eye diagram acquired at
2.9 kbit s-1. Scale bar is 150 $\mu$s.

Hence, in our devices the whole WS2-graphene interface is photoactive and its
photosensitivity extends across the spectral range 400 - 700 nm. To fully
characterise the device performance we have illuminated the device with
monochromatic light ($\lambda=625$ nm) of varying intensity and the
photocurrent was recorded. Figure 4a shows the photocurrent as a function of
incident optical power at zero and finite negative bias applied to the polymer
gate. A maximum photocurrent of 339 nA is recorded for an incident power
density of approximately 15 W m-2, which reduces to 2.55 nA at the lowest
detectable illumination levels (Vgs = -1.5 V, Vds = 100 mV. For both gate
voltages the photocurrent decreases with reducing optical power, transitioning
from a sub-linear power dependence to a linear one below $0.1$ W/m2. In the
linear regime, indicated by the straight line fits, photogenerated charge
carriers are split, with one charge type being transferred to the graphene
channel whilst the other remains trapped in the WS2. Upon increasing the
illumination intensity, the large number of photogenerated charge carriers
reduces the electric field at the heterointerface, resulting in a sub-linear
power dependence.4, 9 Application of a bias to the polymer gate allows for
more efficient exciton splitting within WS2 leading to an increase in
$I_{pc}$, as seen previously in Figure 2d.

In Figure 4b we plot the responsivity as a function of incident optical power
for both $V_{gs}=0$ V and $V_{gs}=-1.5$ V. The responsivity has been
calculated using $R=I_{pc}/P$, where $I_{pc}$ is the photocurrent and $P$ the
incident optical power, and follows a non-linear power dependence. This can be
well fit using a function of the form $R=a/(b+P^{n})$, where $a$, $b$ and $n$
are fitting parameters. The power exponent $n\sim 2/3$ is indicative of non-
radiative Auger recombination,46 previously observed in other indirect
semiconductors such as Ge and Si.47 In our devices the responsivities reach a
maximal value of $1\times 10^{6}$ A W-1 at $V_{gs}=-1.5$ V for $V_{ds}=100$
mV, an order of magnitude higher than that without a bias applied to the top
gate, corresponding to an external quantum efficiency of 2.0$\times 10^{6}$.
The high responsivities observed in these devices can be explained in terms of
a gain mechanism arising from the aforementioned photogating effect; to
maintain charge conservation the removal of one electron at a contact requires
the injection of one at the opposite contact. This electron circulation exists
as long as the holes remain trapped in the WS2 resulting in a net gain.1 The
gain ($G$) in our devices can be theoretically calculated considering the
change in carrier density ($\Delta n$) from a known photon flux ($\phi$), see
Supporting Information. This gives a value of $G_{th}=3.4\times 10^{6}$, which
is in excellent agreement with our experimental measurement of responsivity,
Figure 4b.

The temporal response of a polymer gated WS2-graphene device is shown in
Figure 4c at $V_{ds}=100$ mV and $V_{gs}=-1.5$ V whilst the incident light is
modulated at 140 Hz. The rise and fall times are defined as the time period
taken for $\Delta I_{pc}$ to change from 10 % (90 %) to 90 % (10 %) of its
maximum value respectively. Analysing multiple iterations of this square wave
signal, we find to high precision that the transient response of the
WS2-graphene photodetectors takes place over sub-millisecond timescales with
$\tau_{\text{rise}}=130$ $\mu$s and $\tau_{\text{fall}}=440$ $\mu$s. Prior to
encapsulation in the ionic polymer our devices typically had rise and fall
times >1 s (see Figure S2), often with the decay of the photocurrent signal
persisting well beyond the time frame of the experiment. After deposition of
the ionic polymer the response times of our devices improved by at least four
orders of magnitude, resulting in sub-millisecond rise and fall times, as seen
in Figure 4c.

These response times are $10^{4}$ faster than previously reported
heterostructure photodetectors which utilise TMDs9, 10 or QDs4, 5 as a light
absorbing layer, typically operating over time scales of seconds or greater,
owing to long lived charge trapping present in these devices. Typically, a
large gate pulse is applied to reduce the potential barrier between graphene
and the semiconductor, thereby accelerating the recombination rate of
photogenerated electrons and holes, allowing a swift transition back to dark
conditions. Indeed, hysteresis in current-gate sweeps of carbon nanotubes,
attributed to atmospheric contamination and oxide charge traps, can be
resolved through gate pulsing strategies.18 However, for graphene-QDs these
gate-pulses have been found to be device specific.4 Our devices exhibit rise
and fall times that are up to five orders of magnitude faster than these
previous works, without the need to apply large electrical pulses. This
surprising finding is the result of the ability of mobile ions in the polymer
electrolyte to efficiently screen charge traps responsible for the
localization of charge carriers in monolayer TMDs.14 To date the screening
properties of polymer electrolytes have been widely demonstrated in electrical
transport measurements.34 Here, we harvest this aspect of fundamental physics
to reduce the role of long-lived trap states in atomically thin
photodetectors, demonstrating an unprecedented fast time response without the
need for any gate voltage pulsing strategies

In Figure 4d, we verify these response times by ascertaining the -3 dB
bandwidth of polymer gated WS2-graphene photodetectors by measuring the
decline in photocurrent magnitude as an incident light signal is modulated
with increasing frequency, using an optical chopper wheel. A similar trend is
shown for the situation with and without a bias applied to the polymer gate,
where photocurrent signals are normalised to the maximum, which occurs at low
modulation frequencies. The normalised signal reduces when increasing
frequency, as one would expect when the period of modulation begins to impinge
upon the rise and fall times of the device. The -3 dB bandwidth, a common
figure of merit for photodetectors, is the point at which the signal has
dropped to 70% of its initial value, which for our devices are 1.3 kHz
($V_{gs}=0$ V) and 1.5 kHz ($V_{gs}=-1.5$ V). From this we can extract a rise
time using $\tau_{rise}\approx 0.35/f_{-3dB}$ of 220 $\mu$s, in good agreement
with the data extracted from Figure 4c.

This -3 dB bandwidth of 1.5 kHz, coupled with extremely sensitive
photodetection across a broad spectral range, means that WS2-graphene
heterostructures are highly suitable for video-frame-rate imaging
applications, thanks to the unique screening properties of the ionic polymer
top gate. To demonstrate the feasibility of this claim we constructed a home-
built optical data link, with a pseudo-random bit sequence generator used to
modulate the 625 nm light of a light-emitting diode. This light was focussed
onto the WS2-graphene heterostructure maintained at $V_{ds}=100\text{ mV}$ and
$V_{gs}=-1.5\text{ V}$ and the output data stream amplified and delivered into
an oscilloscope to obtain an eye diagram. The inset in Figure 4d shows such an
eye diagram, with the open eye at 2.9 kbit s-1 demonstrating that these
heterostructures can truly be used in video-frame-rate imaging applications.
Our polymer electrolyte encapsulated photodetectors exhibit a gain-bandwidth
product of 7.2 GHz which is comparable to established technology based on
III-V phototransistors, see Supporting Information.48

Finally, in order to compare the performance of WS2-graphene heterostructures
to that of other photodetectors, we use the specific detectivity ($D^{*}$).
This can be calculated using the responsivity ($R$) and the noise density
($S_{n}$, see Figure S3) using $D^{*}=R\sqrt{A}/S_{n}$ where A is the device
area. Taking the responsivity at $V_{gs}=-1.5$ V and noise value extracted at
150 Hz, we calculate a $D^{*}=3.8\times 10^{11}$ Jones which is comparable to
other graphene hybrid photodetectors.4, 5, 9, 7, 10, 6, 49

To summarise, we have characterised the optoelectronic properties of ionic
polymer gated WS2-graphene heterostructure photodetectors across a broad
spectral range. The photogating effect has been found to be the dominant
photocurrent generation mechanism, with a high gain process resulting in
responsivities of $1\times 10^{6}$ A W-1. Furthermore, we demonstrate sub-
millisecond response times of our devices through both rise and fall time
estimates as well as by measuring a -3 dB bandwidth of 1.5 kHz. The high gain
and fast response found in our devices arises from the ability to compensate
charge traps with the ionic polymer, which is a limiting factor in similar
photodetectors. Our study demonstrates that both high gain and sub-millisecond
response times can be achieved in two-dimensional heterostructure
photodetectors. A calculated detectivity of $3.8\times 10^{11}$ Jones brings
the realisation of high frame-rate video-imaging applications with 2D
materials ever closer.

## Experimental Section

Optoelectronic measurements. Raman spectra were acquired using a 532 nm laser
source with a spot size of $\sim 1$ $\mu$m and an incident laser beam power
<40 $\mu$W to avoid overheating and damage to WS2-graphene. Photocurrent maps
were recorded at room temperature in ambient conditions in a custom built set-
up on an upright BX51 Olympus microscope described and characterised
extensively in reference.37 The external quantum efficiency, spectral
responsivity, and transient response measurements were performed in a custom
built vacuum chamber (10-3 mbar) using a Xenon Lamp, monochromator and
collimating optics (Oriel TLS-300X), to provide a spectrally tunable incident
light source. Neutral density filters and a motorized chopper wheel were used
to attenuate and modulate the incident signal respectively. Power calibrations
were performed with a ThorLabs PM320E power meter equipped with a S130VC
sensor.

## Supporting Information

Supporting Information is available from http://doi.org/10.1002/adma.201700222
or from the author.

## Acknowledgements

J.D.M. and S.U. contributed equally to this work. The authors thank Adolfo De
Sanctis for assistance in obtaining the photocurrent maps and useful
discussions. J.D.M. acknowledges financial support from the Engineering and
Physical Sciences Research Council (EPSRC) of the United Kingdom, via the
EPSRC Centre for Doctoral Training in Metamaterials (Grant No. EP/L015331/1 ).
S.F.R acknowledges financial support from the Higher Committee for Education
Development in Iraq (HCED). S.R. and M.F.C. acknowledge financial support from
EPSRC (Grant No. EP/J000396/1, EP/K017160/1, EP/K010050/1, EP/ G036101/1,
EP/M001024/1, and EP/M002438/1) and from Royal Society International Exchanges
Scheme 2016/R1.

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