arXiv:1008.3362v1 [physics.optics] 19 Aug 2010
Customised broadband metamaterial
absorbers for arbitrary polarisation
Hiroki Wakatsuchi∗, Stephen Greedy,
Christos Christopoulos∗, and John Paul
George Green Institute for Electromagnetics Research, School of Electrical and Electronic
Engineering, University of Nottingham, Tower Building, University Park, Nottingham,
NG7 2RD, U.K.
electromagnetic waves having arbitrary polarisation is possible by use of
lossy cut–wire (CW) metamaterials. These useful features are confirmed by
numerical simulations in which different lengths of CW pairs are combined
as one periodic metamaterial unit and placed near to a perfect electric
conductor (PEC). So far metamaterial absorbers have exhibited some
interesting features, which are not available from conventional absorbers,
e.g. straightforward adjustment of electromagnetic properties and size
reduction. The paper shows how with proper design a broad range of
absorber characteristics may be obtained.
This paper shows that customised broadband absorption of
© 2010 Optical Society of America
OCIS codes: (160.3918) Metamaterials; (50.6624) Subwavelength structures; (260.5740) Res-
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Recently the use of metamaterials as wave absorbers has been attracting the interest of many
researchers from the viewpoint of feasible metamaterial applications using current technology.
Since the first experimental metamaterial work was reported by Smith et al. , various meta-
materials have been proposed to realise their exotic properties, such as negative permittivity,
negative permeability and negative refractive index (NRI), from the microwave region to the
optical region [2, 3, 4]. At the same time many metamaterial applications have also been sug-
gested; the superlens , invisible cloaking [6, 7] and optical transformation  to name but a
few. However, there are obstacles in the realisation of these schemes. Most metamaterial appli-
cations rely on the negative properties described above. At high frequencies, such as terahertz
and optical bands, the properties have non–zero imaginary parts of refractive index and wave
impedance mainly due to the conductiveloss of the metal components,making the applications
less attractive or sometimes unrealistic. For this reason the conductive loss issue is recognised
as a problem to be solved  and many researchers are trying to address this matter, for ex-
ample, by the use of gain mediums  or by optical transformation designs that include the
conductive loss . In this paper we seek to exploit these losses for efficient absorber design.
In metamaterial absorbers the use of the conductive loss can be taken into account as part of
the absorber design to achieve strong levels of absorptance. Thus the practical use of metama-
terials as wave absorbers is becoming popular for applications in areas such as EMC, crosstalk
So far metamaterial absorbers have exhibited attractive features which are not available from
conventional wave absorbers. One example is in the manipulation of the electromagnetic prop-
erties. In conventionalabsorbers design options are limited by substrate properties and mixture
ratios to realise desired permittivity and permeability values. This is not easy to accomplish. In
this paper we aim at systematic design techniques for metamaterial absorbers to enable us to
modify their electromagnetic properties with relative ease (e.g. changes in metallisation length
and geometry). More importantly the use of metamaterials makes the absorber substrate thick-
nesses significantly smaller. In the conventional absorbers the total thickness of the structures
need to be comparable to a quarter wavelength λ0of the operating frequency. However, the
λ0/4 thickness can limit the range of application, for example, where available working space
is restricted. This issue has successfully been solved by use of thin metamaterials, which al-
lowed us to relax the limitation of the physical size remarkably (e.g. in  1 mm thickness at
design options became possible.
An outstanding issue is the limitation of the absorption band width. In most cases absorption
is concentrated in a narrow frequency band. Although narrow band absorbers may be useful in
some applications, the real need is for broadband absorbers with customised characteristics to
meet specific user needs.
This papershowsthat highlycustomisablebroadbandabsorptionis possibleusingmetamate-
rials as wave absorber. Different lengths of conductive and lossy cut–wires (CW) (see insets of
Figs. 1 (a)and(b) as examplesof CWs) are deployedas a singleperiodicmetamaterialabsorber
unit. Highly customisable absorption is achieved by independent conductive loss optimisation
in each CW. In addition, this absorption can be obtained for arbitrary polarisations without any
serious absorptance reduction when other pairs of CWs are introduced. Furthermore, it is also
demonstrated that not only enhancing the absorptance but also reducing it is possible by use
of additional CWs. These results indicate that the CWs make it possible to design very flexi-
ble absorptance characteristics. Before the customisable absorber configurations are explained
in detail, this paper introduces characteristics of lossless CW metamaterials in section 2 then
examines the basic properties of CW metamaterials in sections 3. In section 4 the customised
broadband absorber designs are introduced and conclusion is made in section 5. Previous work
is described in  which was done using limited numerical resolution. This work is extended
here to develop customised absorbers.
2. Calculation models
This paper uses a thin rectangular metal form, the so–called CW, as a base metal geometry for
the following reasons. Firstly, the CW metamaterials are very simple structures and the peri-
odic unit is composed of only a dielectric substrate and a single or paired CW. Due to their
simplicity, CW metamaterials can be transformed into other types of metamaterials [14, 15],
so they play an important role in basic metamaterial research. Secondly, the CW metamaterials
do not require any extra metal components to yield a NRI. For example, the first metamaterial
 is composed of split–ring resonators, yielding a negative value of permeability, and long
metal strips, yielding a negative value of permittivity, and hence two types of metal structures
are necessary to produce a NRI. However, the CW metamaterials can exhibit both negative
permittivity and permeability through a simply paired CW. Thirdly, CW structures are suit-
able for introducing stronger losses. As is reported in , compared to fishnet structures 
which have some similar properties with those CW metamaterials have, the CW metamaterials
can exhibit greater losses, which although undesirable in most metamaterial applications they
are needed in absorber applications. Moreover, from a fabrication viewpoint, the CW form is
straightforward to manufacture due to its simple geometry. Finally, CWs with conductive loss
easily produce multi–absorptance peaks as will be demonstrated in this paper.
In absorber applications described in this paper conductive loss is used instead of dielectric
loss which is assumed to be a primary resource in most metamaterial absorbers (e.g. ). One
of the reasons is that materials with suitable conductive losses are readily available through
recently developed technologies, e.g. conductive inks . Also, independent optimisation of
the metal resistances gives us more flexible options for absorption characteristic designs, e.g.
multi–peak broadband absorption, as will be demonstrated in section 4.
The default structures of the simulated CW metamaterials are illustrated in the insets of
Figs. 1 (a) and (b) for single and paired CWs and the simulations were performed by using
the transmission line modelling (TLM) method . To simplify the situation and consider the
absorption effect due only to the conductive loss of the CW metals, the relative permittivity εr
of the substrate was set εr= 1 and all other loss mechanisms were removed. The CW structure
had a width of 0.3 mm along the y axis (H–field) and a length of 5.1 mm along the x axis
(E–field). The dimension of the unit cell was Ax= Ay= 6.3 mm. This structure was modelled
using cubical TLM unit cells having edge lengths of ∆l = 0.075 mm. The sheet resistance R
(Ω2−1) used to quantify the conductive loss was allocated so that the scattering coefficients
from the metal are determined by
and T =
where Γ and T respectively represent reflection coefficient and transmission coefficient both
multiplied by the incident voltage (the incident wave) in each TLM unit cell, Z0 is the
impedancein vacuumand R0=RZ0/(R+Z0). The scattering parameters were calculated using
observation planes 15 mm away from the absorber surface and a Gaussian pulse was excited
on a plane one cell above the observation plane for the reflection coefficient. Since periodic
boundarieswere applied for the xz and yz plane boundaries,the CW metamaterial absorberunit
modelled was assumed to belong to infinite array on the bottom xy plane.
The simulated paired CW metamaterials are generally known to exhibit two types of reso-
nances: electric resonances and magnetic resonances . These resonances are explained in
Fig. 1 where the reflection coefficient, the electric fields and the conduction currents of the CW
metamaterials all calculated by TLM method are illustrated. When an incident wave is excited
with the electric field parallel to the direction of the CW metals, the conductioncurrents flow in
opposite directions in each CW at the magnetic resonance (see Fig. 1 (d)). This is the minimum
|S11| at 24.89 GHz in Fig. 1 (b). In this case the electric field is anti–parallel at the two edges of
the CW metamaterial, Fig. 1 (c), and a magnetic field concentrated within the area bounded by
the paired CW is generated. This magnetic field plays the role of an artificial magnetic dipole
and can lead to a negative value of permeability. On the other hand, at the electric resonance
found at around an |S11| peak (26.71 GHz in Fig. 1 (b)), conduction currents in the CWs be-
come dominant, resulting in a strong unidirectional electric field at the edges of the CWs, Figs.
1 (e) and (f). Similarly with the magnetic resonance this electric field behaves as an artificial
electric dipole so as to produce a negative value of permittivity. A similar electric resonance is
found in the |S11| peak of the single CW metamaterial (26.65 GHz of Fig. 1 (a)) as well. The
positions of the two types of the resonances can be manipulated [14, 20] and in subsection 3.2
the influence of the resonant frequency positions on the absorptance peak will be discussed.
3.Absorptances of single CW metamaterials and paired CW metamaterials
3.1.Absorptances of single CW metamaterials
This subsection investigates basic absorptance characteristics of single CW metamaterial ab-
sorbers. The default size of the periodic structure is illustrated in Fig. 2 (a). First of all, con-
ductive loss is distributed in one of three ways: allocations to all the metal part, both of the
edges (0.9 mm for each edge and 1.8 mm in total) and one of the edges (1.8 mm or 1.2 mm).
Secondly, the absorptances of different CW lengths are investigated and they are combined as
one metamaterial unit to achieve broadband absorption. In all the simulations the value of the
sheet resistance, R, is constant.
In Fig. 2 (b) the absorptance A of the single CW composed of only lossy metal is shown for
various sheet resistance values. The absorptance was calculated from A = 1−|S11|2−|S21|2.
It is found from Fig. 2 (b) that the positions of the maximum absorptance are fixed at around
26.59 GHz, which is close to the resonant frequency found in Fig. 1 (a). In addition it turns
out that the absorptance peak curve reaches the maximum values with a sheet resistance R =
6.0 Ω2−1, the inset of Fig. 2 (b). This absorptance peak dependence can be easily explained
with the equivalent circuit drawn in the inset of Fig. 2 (c). At the resonant frequency the circuit
Fig. 1. Default structures of simulated CW metamaterials and their properties. |S11| of (a)
lossless single CW and (b) lossless paired CW. (c) Electric field and (d) conduction current
of the magnetic resonance frequency (24.89 GHz). (e) Electric field and (f) conduction
current of the electric resonance frequency (26.71 GHz).
impedancebecomesZ =R.IntermsoftheconductioncurrentI, numericalsimulationsrevealed
its dependence on R as the curve with closed circles shown in Fig. 2 (c). Therefore, the power
dissipated in the circuit, P (= I2R), as illustrated by the curve with open squares in Fig. 2 (c),
well corresponds to the result in the inset of Fig. 2 (b).
Similar maximum absorptance peaks were obtained when the conductive loss area was re-
stricted to one or both of the edges of the CW metal (see Figs. 2 (d) to (f)). However, further
increase of the loss amount exhibited different absorptance peaks at higher frequencies. These
absorption positions were expected to correspond to resonances of CWs shortened by the lossy
metal part(s), since the conductive losses were too high causing a highly distorted current dis-
tribution. Numerical simulations confirmed that the 3.3 mm–length CW, whose length corre-
spond to the lossless parts of Figs. 2 (d) and (e), has resonant frequency at 38.06 GHz, which
is in the vicinity of the absorptance peaks at the higher frequencies in Figs. 2 (d) and (e). Sim-
ilarly the 3.9 mm–length CW, whose metal length is same with the lossless part of Fig. 2 (f),
was found to have resonant frequencyat 33.55 GHz, which is also close to another absorptance
peak of Fig. 2 (f). Although the absorptance effect obtained from these structures is weak, one
point noticed from Figs. 2 (e) and (f) is that the decrease of the absorptance at the frequency
range between the two peaks can be reduced by restricting the lossy metal part to the narrow
Secondly, the absorptances of different CW lengths were calculated. The calculation results
are summarised in Fig. 3 (a) where the simulated CWs had lengths of 3.3 to 5.1 mm by 0.6
mm steps. It is found from Fig. 3 (a) that the absorptance peak depends on the CW length.
Next several of the CWs used in Fig. 3 (a) were combined as one metamaterial unit and the
resultant absorptance curves are illustrated in Fig. 3 (b). The inset in Fig. 3 (b) describes a
structure consisting of four CWs. In this structure the distance between the CWs was 0.3 mm
and one end of the CWs were positionedat a same x axis position (0.3 mm from one of xz plane
boundaries). In the other structures only those lengths noted were included. Compared to the
results in Fig. 3 (a), the results in Fig. 3 (b) illustrate broadband behaviour.
3.2. Absorptances of paired CW metamaterials
This subsection examines absorptance characteristics of paired CW metamaterials. As was ex-
plained in section 2, the paired CW metamaterials have two types of resonance: electric reso-
nance and magnetic resonance. These resonant frequency positions can be manipulated and in
, for example, one of the CW pairs is shifted a distance dx(see Fig. 4 (a)). In this case the
magnetic resonance frequency is increased, while the electric resonance frequency is reduced.
This effect is shown in Fig. 4 (b) where the dependence of the reflection coefficient curves on
the various offset lengths dxare shown. It is known that, when the magnetic resonance fre-
quency is greater than the electric resonance frequency, a NRI is obtained in the paired CW
metamaterial due to overlap of the negative permeability with the negative permittivity .
This paper utilises the geometrical asymmetry introducedin  to change the resonance posi-
tions and implement loss in the structure so that the absorption characteristics in the paired CW
metamaterial absorber are investigated in more detail.
Before the asymmetricallypairedCW is simulated, the absorptioncharacteristics ofthe sym-
metrically paired CWs are investigated. The calculation results are summarised in Fig. 4 (c) in
which various sheet resistance values, R, are applied equally to the front and back CWs. In Fig.
4 (c) we have marked the electric and magnetic resonant frequencies (feand fm) of the sym-
metrically paired CW shown in Fig. 4 (b) and it is seen that the absorptance peak shifts from
fmto feas R increases. It is also found that the symmetrically paired CW shows the stronger
absorption (A ≃ 0.696) than that of the single CWs (A ≃ 0.500 in Fig. 2).
Next, the absorptance of the paired CW metamaterial absorber with various values of dxwas
Fig. 2. Absorptances of single CW having constant resistance values. (a) Details of the
simulated single CW metamaterial. (b) Absorptance of the single CW composed of only
lossy metal. In the inset the absorptance dependence on R at 26.59 GHz is illustrated. (c)
The conduction current I and the dissipated power P (=IR2) in the CW with various values
of R.(d)–(f)Absorptances of thesingleCWcomposed ofboth losslessmetal part andlossy
metal part. The lossy metal parts were restricted to both edges (0.9 mm per each edge and
1.8 mm in total) in (d) and one edge in (e) (1.8 mm) and in (f) (1.2 mm).
Fig. 3. Absorptance of different lengths of single CWs (a) and absorptance of structure
composed of part or all of the CWs (b). The lengths and the resistances in the legends
represent the CW length and R, respectively.
optimised. The calculation results are summarised in Table 1 and Fig. 4 (d). Again, the same
resistance values were applied for both front CW and back CW. It turns out in this case that
the maximum absorptance of the symmetrically paired CW is increased by nearly 10 % for
dx= 1.8 mm.
Moreover the absorptance of the paired CW was further enhanced by using different sheet
resistance values for the front CW and the back CW. In Figs. 4 (e), (f) and (g) the absorptances
for dx= 0.0mm, 1.2mm and 2.4mm are illustrated. Each distributionwas calculatedat the fre-
quency corresponding to each absorptance peak; 26.35, 26.23 and 27.20 GHz, respectively. In
these figures, the sheet resistance values were varied from 0 to 12 Ω2−1in 2 Ω2−1steps. The
intermediate values between the calculated results were estimated using spline interpolation.
Despite the coarse resolution the simulations confirm that the absorptance is further increased
in each case by the use of different sheet resistance values. In addition the distribution of the
absorptance depends on the offset length dx. Although the absorptance of the symmetrically
paired CW metamaterial was enhanced by the manipulation of the resonant frequency posi-
tions and by use of different resistance values, the maximum value was still far from perfect
absorption (i.e. A ∼ 1.0). In the next section the absorptance of the CW metamaterial absorber
is significantlyimprovedandapproachesperfectabsorptionbyplacinga singleCW ona perfect
electric conductor (PEC) wall.
Table 1. Absorptance peaks of paired CW with various x axis offset dx.
dx[mm] AbsorptanceFrequency [GHz]
Fig. 4. Characteristics of paired CW. Geometrical asymmetry was introduced as is de-
scribed in (a). (b) |S11| of the lossless paired CW having the various geometrical offset
length dx. (c) Absorptance of the symmetrically paired CW with various R. (d) Absorp-
tances of the paired CW with various dx. From (b) to (d) dxis expressed in each legend.
In these figures same values of R are used for the front CW and the back CW. In (e) to (g)
various combinations of R are applied for both CWs. (e), (f) and (g) show the absorptances
of no offset at 26.35 GHz, 1.2 mm offset at 26.23 GHz and 2.4 mm offset at 27.20 GHz,
respectively. The dots in the figures represent the calculated sheet resistance patterns and
the intermediate values were estimated by using spline interpolation.
4.Absorptances of single CW metamaterials placed on PEC
This section introduces CW metamaterial structures which exhibit very effective absorption
characteristics. In addition, it is shown that broadband absorption is achieved when different
lengths of CWs are combined in one periodic metamaterial absorber unit. Strong absorptances
were observed when single CW metamaterial was placed on a PEC surface, as illustrated in
the inset of Fig. 5 (a). In these simulations the CW positions are the same with those used
in the inset of Fig. 3 (b), while the resistance values were optimised to extract the maximum
absorptances. The calculation results are shown in Fig. 5 (a) and the strong absorptances of
A ∼ 1.0 are seen.
Consideringthe results obtained,the case of the CW with the metal backinggivesthe highest
absorptance (A ∼ 1.0) followed by two CWs without the metal backing (A ∼ 0.75). Finally a
single CW gives the lowest absorption (A ∼ 0.5). We note that the conduction currents in each
case are different as shown in Fig. 1 (d).
Next the same pattern of CWs was deployed along the y axis to reduce polarisation depen-
dence. The calculation results are shown in Fig. 5 (b), where the sheet resistance of each CW
were again optimised. The inset of Fig. 5 (b) describes the simulated structure. As a result of
the comparison with Fig. 5 (a), strong absorptance of A ∼ 1.0 is still maintained despite the
use of another orthogonalCW. Accordingto , straight conductorsorthogonalto the electric
field do not react with the external field significantly so that the electromagnetic properties of
the whole structure are not significantly affected.
To obtainbroadbandbehavioursomeor all ofthe pairs ofthe CWs usedin Fig. 5(b)are com-
bined as one metamaterial unit. The inset of Fig. 5 (c) illustrates the structure. The calculation
results are shown in Fig. 5 (c). The results in this figure indicate that the absorptance properties
in the high frequency region are improved by use of additional lossy pairs of CW. The addition
of extra CWs introduces additional absorption peaks, as shown in Fig. 5 (d) where two CW
pairs of 5.1 and 3.3 mm show two absorptance peaks corresponding to those of the individual
CWs. Although such behaviour has been recently reported [22, 23], the advantage of using the
lossy CWs introducedhere is to easily customise the absorptancecharacteristics for both polar-
isations. Furthermore, as is explained below, it is also easy to realise several absorptance peaks
by adding extra pairs of CW.
The absorption characteristics may be further enhanced by optimising the sheet resistance
values. This is shown in Fig. 5 (e) in which the three CW pairs of 5.1, 3.9 and 3.3 mm are
deployed. In this figure the sheet resistance value of only the 3.3 mm CW is varied, while the
values of the other CWs are the same as those of Fig. 5 (b). It is found from Fig. 5 (e) that
the absorption characteristics are improved by use of adjusted resistance values, leading to a
triple absorptance peak (0.993 at 24.28 GHz, 0.975 at 31.17 GHz and 0.981 at 36.29 GHz).
Again, this structure will interact with both polarisations, compared with that of [22, 23] and
is an important advantage of the lossy CW metamaterial absorber. Although only the triple
absorptance peak is illustrated, further absorptance peaks are possible by using extra CW pairs.
Use of additionalpairs of CW enables us not onlyto increase absorption,but also to decrease
it. In Fig. 5 (f), the absorptance of the CW metamaterial absorber composed of 5.1 and 3.9 mm
CW pairs with the sheet resistance values used in Fig. 5 (b) is illustrated. This absorptance
peaks can be enhanced by use of optimised sheet resistance values as is described in the figure.
In addition to these two CW pairs, when the lossless CW pair of 3.9 mm is deployed (see the
inset of Fig. 5 (f)), the absorptance magnitude between the two absorption peaks is markedly
reduced due to the resonance of the 3.9 mm CW pair (where the sheet resistance values of 5.1
and 3.9 mm CWs were modified again). As expected, the centre of the absorptance reduction
is close to the resonant frequency of the 3.9 mm CW (c.f. Fig. 5 (b)). This allows for a fully
customised absorptance characteristic.
Fig. 5. Absorptance of single CW metamaterial placed on a PEC wall. (a) shows absorp-
tances of different lengths of CWs. The inset describes the simulated situation. In (b) an-
other pair of the CW used in (a) is placed orthogonally to the first, as is illustrated in the
inset. In (c) part or all of the CW pairs are combined as one metamaterial unit. The inset
shows the structure having all the CW pairs. (d) shows that use of two CW exhibits a dou-
ble absorptance peak close to the individual peaks. (e) illustrates absorptance of three CW
pairs (5.1, 3.9 and 3.3 mm). Modification of the resistance value used for the 3.3 mm CW
leads to atriple absorptance peak. The resistance values used for the 3.3 mm CW are shown
in the legend. The other resistance values are the same as those of (b). In (f) absorptance of
two CW pairs of 5.1 and 3.9 mm is improved by use of adjusted resistance values. In addi-
tion, the use of a lossless 4.5 mm CW pair exhibits a strong reduction of the absorptance at
about 30 GHz.
This paper demonstrated by numerical simulation that highly customisable broadband absorp-
tion for arbitrary polarisation is possible by use of conductively lossy CWs as metamaterial
absorbers. To begin with, the basic properties of the conductively lossy CW metamaterial ab-
sorbers were investigated. A dependence of absorptance peak on the conductive loss was ex-
plained with a simple equivalent circuit. In paired CW metamaterials, absorptance peaks were
improved by manipulating the two resonance frequency positions and by using independent
sheet resistance values for the front and back CWs. The absorptance of the conductively lossy
CW metamaterial was further improved,when single CW metamaterials were placed on a PEC
wall. Moreover,whendifferentlengthsofCWs werecombinedas onemetamaterialunit,broad-
band absorption was exhibited. The deployment of orthogonal pairs of CWs showed that the
structuresimulated hereworks for bothpolarisations.Dueto the flexibleabsorptancecharacter-
istics, the ideaofusingconductivelylossyCW pairs addsadditionaladvantagestometamaterial
absorbers and opens up a new area for metamaterial applications. The interesting properties of
CW metamaterials may be further improved, when the structures are designed to absorb off–
normal incident waves. This may be possible by using multiple CWs whose lengths and sheet
resistance values are suitably optimised.