Sharp dark-mode resonances in planar metamaterials with broken
  structural symmetry
Sharp dark-mode resonances in planar metamaterials with broken structural
symmetry
V. A. Fedotov,1, ∗ M. Rose,1 S. L. Prosvirnin,2 N. Papasimakis,1 and N. I. Zheludev1, †
Optoelectronics Research Centre, University of Southampton, SO17 1BJ, UK
Institute of Radio Astronomy, National Academy of Sciences of Ukraine, Kharkov, 61002, Ukraine
(Dated: October 29, 2018)
We report that resonant response with a very high quality factor can be achieved in a planar
metamaterial by introducing symmetry breaking in the shape of its structural elements, which
enables excitation of dark modes, i.e. modes that are weakly coupled to free space.
PACS numbers: 78.67.-n, 42.70.-a, 42.25.Bs
Metamaterials research has attracted tremendous
amount of attention in the recent years. The interest is
mainly driven by the opportunity of achieving new elec-
tromagnetic properties, some with no analog in naturally
available materials. Extraordinary transmission [1], ar-
tificial magnetism and negative refraction [2], invisible
metal [3], magnetic mirror [4], asymmetric transmission
[5] and cloaking [6] are just few examples of the new
phenomena emerged from the development of artificially
structured matter.
The exotic and often dramatic physics predicted for
metamaterials is underpinned by the resonant nature of
their response and therefore achieving resonances with
high quality factors is essential in order to make metama-
terials’ performance efficient. However, resonance quality
factors (that is the resonant frequency over width of the
resonance) demonstrated by conventional metamaterials
are often limited to rather small values. This comes from
the fact that resonating structural elements of metama-
terials are strongly coupled to free-space and therefore
suffer significant losses due to radiation. Furthermore,
conventional metamaterials are often composed of sub-
wavelength particles that are simply unable to provide
large-volume confinement of electromagnetic field neces-
sary to support high-Q resonances. As recent theoretical
analysis showed, high-Q resonances involving dark (or
closed) modes are nevertheless possible in metamaterials
if certain small asymmetries are introduced in the shape
of their structural elements [7].
In this Letter we report the observation of exception-
ally narrow resonant responses in transmission and reflec-
tion of planar metamaterial achieved through introduc-
ing asymmetry into its structural elements. The appear-
ance of narrow resonances is attributed to the excitation
of otherwise forbidden anti-symmetric modes, that are
weakly coupled to free-space (”dark modes”).
Metamaterials that were used in our experiments con-
sisted of identical sub-wavelength metallic ”inclusions”
structured in the form of asymmetrically split rings
(ASR), which were arranged in a periodic array and
placed on a thin dielectric substrate (see Fig. 1). ASR-
patterns were etched from 35 µm copper cladding cov-
ering IS620 PCB substrate of 1.5 mm thickness. Each
copper split ring had the radius of 6 mm and width
of 0.8 mm and occupied a square translation cell of
15×15mm (see Fig. 1). Such periodic structure does not
diffract normal incident electromagnetic radiation for fre-
quencies lower than 20 GHz. The overall size of the sam-
ples used were approximately 220× 220 mm. Transmis-
sion and reflection of a single sheet of this meta-material
were measured in an anechoic chamber under normal in-
cidence conditions using broadband horn antennas.
FIG. 1: (Color online) Fragments of planar metamaterials
with asymmetrically split copper rings. The dashed boxes
indicate elementary translation cells of the structures.
We studied structures with two different types of asym-
metry designated as type A and B in Fig. 1. The rings of
type A had two equal splits dividing them into pairs of
arcs of different length corresponding to 140 and 160 deg
(see Fig. 1A). The rings of type B were split along their
diameter into two equal parts but had splits of different
length corresponding to 10 and 30 deg (see Fig. 1B).
http://arxiv.org/abs/0704.1577v1
Transmission and reflection properties of structures of
both types depended strongly on the polarization state
of incident electromagnetic waves. The most dramatic
spectral selectivity was observed for electrical field being
perpendicular to the mirror line of the asymmetrically
split rings, which corresponded to x-polarization in the
case of structure A and y-polarization for structure B
(as defined in Fig. 1). For the orthogonal polarizations
the ASR-structures did not show any spectral features
originating from asymmetrical structuring.
FIG. 2: (Color online) (a) Normal incidence reflection and
transmission spectra of A-type metamaterial (presented in
Fig. 1A) for x-polarization: solid line - experiment, filled cir-
cles - theory (method of moments), empty circles - theory
for reference structure with symmetrically split rings. (b) x-
Component of the instantaneous current distribution in the
asymmetrically split rings corresponding to resonant features
I, II and III as marked in section (a). Arrows indicate in-
stantaneous directions of the current flow, while their length
corresponds to the current strength.
The results of reflection and transmission measure-
ments of metamaterial A obtained for x-polarization are
presented in Fig. 2a. The reflection spectrum reveals an
ultra-sharp resonance near 6 GHz (marked as II), where
reflectivity losses exceed -10 dB. It is accompanied by
two much weaker resonances (marked as I and III) cor-
responding to reflection peaks at about 5.5 and 7.0 GHz
respectively. The sharp spectral response in reflection
is matched by a very narrow transmission peak reaching
-3 dB and having the width of only 0.27 GHz as mea-
sured at 3 dB below the maximum. The quality factor
Q of such response is 20, which is larger than that of the
most metamaterials based on lossy PCB substrates by at
least one order of magnitude. On both sides of the peak
the transmission decreases resonantly to about -35 dB at
frequencies corresponding to reflection maxima.
Fig. 3a presents transmission and reflection spectra
of B-type metamaterial measured for y-polarization. A
very narrow resonant transmission dip can be seen near
5.5 GHz, where transmission drops to about -5 dB.
The corresponding reflection spectrum shows an usually
sharp roll-off (I-II) between -4 and -14 dB spanning only
0.13 GHz at around the same frequency. At the fre-
quency of about 11.5 GHz the ASR-structure exhibits its
fundamental reflection resonance (marked as III) where
the wavelength of excitation becomes equal to the length
of the arcs.
To understand the resonst nature of the response, the
ASR-structures were modelled using the method of mo-
ments. It is a well established numerical method, which
involves solving the integral equation for the surface cur-
rent induced in the metal pattern by the field of the in-
cident wave. This is followed by calculations of scattered
fields as a superposition of partial spatial waves. The
metal pattern is treated as a perfect conductor, while
the substrate is assumed to be a lossy dielectric. For
both transmission and reflection the theoretical calcula-
tions show a very good agreement with the experimental
results assuming ǫ = 4.07+ i ·0.05 (see Fig. 2 and 3, filled
circles). For comparison we also modelled metamaterial
composed of split rings with no structural asymmetry,
i.e. equally split along their diameter. Our calculations
indicate that for both polarizations the response of such
structure is free form sharp high-Q resonant feature (see
Fig. 2 and 3, open circles).
The origin of the unusually strong and narrow spec-
tral responses of the ASR-structures can be traced to
so-called ”dark modes”, i.e. electromagnetic modes that
are weakly coupled to free-space. It is this property of the
dark modes that allows in principal to achieve high qual-
ity resonances in very thin structures [7]. These modes
are usually forbidden but can be excited in a planar meta-
material if, for example, its particles have certain struc-
tural asymmetry.
Our calculations showed that in the case of structure A
an anti-symmetric current mode can dominate the usual
symmetric one: at the high-Q transmission resonance, as
shown in Fig. 2b (II), two parts of the ring are excited
in anti-phase while currents have almost the same ampli-
tude. The scattered electromagnetic fields produced by
such current configuration are very weak, which dramat-
ically reduces coupling to free-space and therefore radia-
FIG. 3: (Color online) (a) Normal incidence reflection and
transmission spectra of B-type metamaterial (presented in
Fig. 1B) for y-polarization: solid line - experiment, filled cir-
cles - theory (method of moments), empty circles - theory
for reference structure with symmetrically split rings. (b) y-
Component of the instantaneous current distribution in the
asymmetrically split rings corresponding to resonant features
I, II and III as marked in section (a). Arrows indicate in-
stantaneous directions of the current flow, while their length
corresponds to the current strength.
tion losses. As a consequence, the strength of the induced
currents can reach very high values and therefore ensures
high quality factor of the response. At the reflection res-
onances, in contrast to the ”dark mode” regime, currents
in both sections of the asymmetrically split ring oscillate
in phase but excitation of one of the sections dominates
the other (see Fig. 2b (I and III)). Importantly, the ampli-
tudes of the currents in this case are significantly smaller
than in ”dark mode” resonance, which yields lower Q-
factors for this type of the response. If the structural
asymmetry is removed the anti-symmetric current mode
becomes forbidden while two reflection resonances de-
generate to a single low-Q resonance state where both
parts of the ring are excited equally. Thus introduction
of asymmetry in the split-ring structure effectively allows
to create a very narrow pass-band inside its transmission
stop-band. This effect is somewhat analogous to appear-
ance of an allowed state in the bandgap of photonic crys-
tals due to structural defects.
Interpretation of the results obtained for structure B
appears to be slightly more elaborate. From the symme-
try of the split rings it follows that for y-polarized excita-
tion at any frequency current distribution in the opposite
sections of the ring should have equal y-components os-
cillating in phase and equal x-components oscillating in
anti-phase. The net current in the ring has therefore al-
ways zero x-component, while its y-component can not
be fully compensated due to the structural asymmetry.
At low frequencies the net y-component is small but it
increases significantly as the frequency of excitation ap-
proaches 5.5 GHz. At this frequency the wavelength
becomes equal to circumference of the split ring and, as
shown in Fig. 3b (I), the right side of the ring dominates
its left side oscillating in anti-phase. The later results
in a resonant increase of the metamaterial reflection (see
Fig. 3a). Immediately above this resonance contributions
of both sides of the ASR-particle are still in anti-phase
but become nearly identical (see Fig. 3b (II)) making the
y-component of the induced net current almost zero and
therefore dramatically reducing radiation losses (reflec-
tion). Further increase of the excitation frequency leads
to rise of the reflection until the fundamental resonance
of the ASR-structure is reached where the correspond-
ing wavelength is equal to the length of the arcs. In this
case both sides of the ASR-particle oscillate in phase and
equally contribute to electromagnetic field scattering (see
Fig. 3b (III)).
The quality factor of the dark-mode resonances will in-
crease on reducing the degree of asymmetry of metama-
terial particles and in case of low dissipative losses can be
made exceptionally high. In the microwave region met-
als are almost perfect conductors and the main source of
dissipative losses is the substrate material (dielectrics).
Therefore significantly higher resonance quality factors
can be achieved for a free-standing thin metal film, which
is patterned complimentary to ASR-structure, i.e. pe-
riodically perforated with ASR-openings. In the visi-
ble and IR spectral ranges, however, losses in metals
dominate and therefore nano-scaled versions of the orig-
inal metal-dielectric ASR-structures would perform bet-
ter. According to our estimates Q-factor of such ASR-
nanostructures in the near-IR can be as high as 6.
In summary, we experimentally and theoretically
showed that a new type of planar metamaterials com-
posed of asymmetrically split rings exhibit unusually
strong high-Q resonances and provide for extremely nar-
row transmission and reflection pass- and stop-bands.
The metamaterials’ response has a quality factor of about
20, which is one order of magnitude larger than the typ-
ical value for many conventional metamaterials. This is
achieved via weak coupling between ”dark modes” in the
resonant inclusions of the ASR-metamaterial and free-
space, while weak symmetry breaking enables excitation
of so-called ”dark modes”. Achieving the ”dark mode”
resonances will be especially important for metamate-
rials in the optical part of the spectrum, where losses
are significant and unavoidable. In a certain way such
symmetry-breaking resonances in meta-materials resem-
bles the recently identified spectral lines of plasmon ab-
sorbtion of shell nanoparticle appearing due to asymme-
try [8].
The authors would like to acknowledge the financial
support of the EPSRC (UK) and Metamorphose NoE.
∗ Electronic address: n.i.zheludev@soton.ac.uk
† URL: www.nanophotonics.org.uk
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mailto:n.i.zheludev@soton.ac.uk
www.nanophotonics.org.uk
