© 2013 Science Wise Publishing &
DOI 10.1515/nanoph-2013-0009
Nanophotonics 2013; 2(4): 247–264
Review article
Alexander B. Khanikaev, Chihhui Wu and Gennady Shvets*
Fano-resonant metamaterials and their applications
Abstract: New developments in the field of Fano-resonant
plasmonic metamaterials are reviewed. The emphasis
is on the applications of such artificial electromagnetic
materials to a variety of technologically important areas:
solar energy harvesting and conversion, sensing/identification of ultra-small molecular contents, and extreme
molding of the flow of light. Most recent theoretical tools
for describing Fano-resonant metamaterials are reviewed.
Both fully three-dimensional metamaterials and planar
meta-surfaces are discussed, and their future prospects
for applications are critically evaluated.
Keywords: Fano resonance; metamaterials; plasmonics.
*Corresponding author: Gennady Shvets, Department of Physics
and Center for Nano and Molecular Science and Technology,
The University of Texas at Austin, Austin, TX 78712, USA,
e-mail: gena@physics.utexas.edu
Alexander B. Khanikaev: Department of Physics and Center for Nano
and Molecular Science and Technology, The University of Texas
at Austin, Austin, TX 78712, USA; Department of Physics, Queens
College of The City University of New York, Flushing, New York
11367, USA; and The Graduate Center of The City University of New
York, New York, New York 10016, USA
Chihhui Wu: Department of Physics and Center for Nano and
Molecular Science and Technology, The University of Texas at Austin,
Austin, TX 78712, USA; and Department of Mechanical Engineering,
University of California at Berkeley, Berkeley, CA 94720
Edited by Pierre Berini
1 I ntroduction and basics: the
physics of Fano resonances
Metamaterials and meta-surfaces [1–5] have greatly
expanded the range of electromagnetic properties exhibited by naturally occurring materials. In so doing, metamaterials have challenged our intuition by enabling such
unusual phenomena as optical magnetism [6–8], negative
refraction [1, 2, 9–11] and bi-anisotropy [12–14]. Numerous
applications of metamaterials include super-lenses [1, 15],
transformation optics and invisibility cloaks [16–20], and
novel biosensors [21–25]. Because metamaterials are produced by structuring their unit cells (“meta-molecules”)
on a spatial scale d which is smaller than the relevant radiation wavelength λ, they occupy a unique niche between
photonic crystals (structured on a scale of λ) and regular
materials (structured on the atomic scale). Therefore,
metamaterials can be viewed as mesoscopic materials
exhibiting a number of unique and unusual properties in
addition to those shared with the regular materials. At the
same time, metamaterials have been shown to emulate a
number of basic optical phenomena observed in the naturally occurring atomic/molecular media. Among such
familiar phenomena are electromagnetically induced
transparency (EIT) [26–36], slow light (SL) [37], and even
topological insulators [38]. One of the most interesting
and rich in applications phenomena successfully emulated by optical metamaterials is the so-called Fano resonance [39], which is the subject of this Review.
Fano resonances were originally discovered in
quantum physics [39] to describe asymmetrically shaped
ionization spectral lines of atoms and molecules. Specifically, it has been shown that ionization of an atom
by a high-energy photon (or a fast passing electron) can
proceed in two distinct ways: (i) through direct excitation
of an electron from its bound state into an unbound (continuum) state, or (ii) through indirect excitation of two
electrons into an intermediate bound state, followed by an
Auger-like process of electron ejection. The first process
is non-resonant, i.e., electron ejection occurs as long as
the photon’s energy exceeds the ionization threshold. It
can also be described within the framework of singleparticle ionization. On the other hand, the second process
is inherently resonant because the two electrons must be
excited into a well-defined auto-ionizing state. Moreover, electron-electron interactions are responsible for the
excitation and subsequent auto-ionization. The quantummechanical interference between these two ionization
pathways results in highly asymmetric [39] dependence
of the ionization cross-section on the photon energy.
Of course, wave interference is not specific to quantum
mechanics, and a great number of classical systems exhibiting Fano resonance have since been identified. Most
recently the concept of Fano resonances was introduced to
the field of photonics [40] and then metamaterials [26]. By
analogy with the original atomic system, a photonic structure must possess two resonances generally classified as
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A.B. Khanikaev et al.: Fano-resonant metamaterials
“bright” (i.e., exhibiting strong coupling to incident light
and short radiative lifetime) and “dark” (exhibiting weak
radiative coupling and long lifetime). Typically (although
not always) the near-field interaction between the two
resonances is analogous to electron-electron interaction
in an atom. Another analogy of metamaterials and atomic
systems is that Fano resonances generally originate from
the response of isolated meta-atoms whose periodic
arrangement plays no crucial role.
Several comprehensive reviews of various manifestations of Fano resonances in nanostructures and metamaterials [41, 42] have recently appeared. A number of recent
developments motivate the present Review. First, the
improved experimental diagnostic tools such as EELS [43]
and near-field optical microscopy [36] enabled much more
direct look at Fano interferences and resonances. Second,
the improved theoretical understanding of the phenomenon [37, 44–47] enabled the design and intuitive analytic/
semi-analytic treatment of novel two and three-dimensional metamaterial structures in which Fano resonance
is an important feature. Finally, Fano-resonant metamaterials and meta-surfaces started featuring prominently in
a variety of applications. These applications include solar
energy harvesting and conversion [48], refractive index
sensing (especially for bio-sensing applications) [21, 23,
49–52], and broadband manipulation of light propagation
[37]. Another recent important development in the field is
the realization of the possibility of coupling the internal
molecular degrees of freedom, such as infrared molecular
vibrations, to electromagnetic metamaterial resonances
[21, 23], with the resulting Fano-like interferences.
The rest of the review is organized as follows. The
basic analytic theory of Fano-resonant metamaterials is
introduced in Section 2. The most important properties of
Fano-resonant structures, such as the large field enhancement at the dark resonance’s frequency, the asymmetric
and spectrally steep line shapes of the reflection/transmission spectral profiles, and the connection between Fano
resonance and EIT, are derived. Optical properties of the
single-layer metamaterials (also known as meta-surfaces)
are described in Section 3. Fano-resonant meta-surfaces
are the most common and most amenable to large-area
fabrication examples of meta-materials. For that reason,
practical applications based on meta-surfaces, such as
sensing, are presently the most mature. Section 4 discusses meta-surfaces with a ground plate, which is a specific class of meta-materials that falls between single-layer
meta-surfaces and fully three-dimensional metamaterials. The least explored at the moment three-dimensional
(multi-layer) Fano-resonant metamaterials are discussed
in Section 5. Applications of 3D metamaterials to molding
© 2013 Science Wise Publishing &
light propagation, including “slow” light structures, are
also reviewed. The approaches to dynamic tuning of metasurfaces are discussed in Section 6. Section 7 discusses
the opportunities for refractive index sensing and molecular fingerprinting using FRAMs. The Summary and Future
Outlook are presented in Section 8.
2 M
athematical description of
Fano-resonant optical structures
The basic mathematics of Fano resonances in photonic
systems can be best developed within the framework of
temporal coupled mode theory [53–55] describing the
interaction of two coupled photonic resonators with light.
We further assume that only the first (“bright”) resonator
with natural frequency ωb is directly coupled to incident
light, while the second (“dark”) resonator with natural
frequency ωd interacts with the light indirectly due to its
coupling to the first resonators. A conceptual schematic
of such a system is shown in Figure 1, where it is assumed
that only a single channel of light reflection/transmission is active. Such situation would correspond to a
sub-wavelength photonic meta-surface which does not
produce higher diffractive orders of light in either transmission or reflection. Near-field interactions between
meta-­
molecules comprising the meta-surface could be
responsible for the coupling between the two resonances.
Because the two resonances are differently coupled to farfield radiation, they can have very different radiative lifetimes τb«τd justifying their designation as bright and dark.
The dynamics of such two-resonant system can be
described by the equations of the temporal coupled mode
theory [53, 55]:
Sin
St
ωb, τb
Sr
κ
ωd, τb
Figure 1 Schematics of the simplest Fano resonant system described
by Eq. (1). The two resonators (“bright” and “dark”) are coupled to
each other, and the bright resonator is coupled to an input/output
port that represents incident, reflected, and transmitted light.
d
where b and d are the field amplitudes in the bright and
dark resonators, respectively, αb is coupling strength of
the bright resonator to the wave in the waveguide, Sin and
ω are amplitude and frequency of the incident light wave,
respectively, and κ is a real number determining coupling
strength between the resonators [53]. In Eq.(1) the amplitudes b, d and Sin are normalized such that |b|2 and |d|2 is
the energy stored by the resonators and |Sin|2 is the incident power.
Note that while the simple single-input/single-output
port theory of Fano interference described by this model
captures most of the phenomena described in this Review,
it falls short of describing polarization conversion and
manipulation that occurs in double-continuum Fano
(DCF) systems that are described in Section 5. Polarization of light represents a second set of input/output ports
that can be resonantly coupled to each other through an
asymmetric Fano-resonant metamaterial. Multiple input/
output ports can also represent multiple waveguides
coupled to Fano resonant cavities [40] or multiple diffracted waves in periodic systems with the Fano resonance [56].
Assuming that the system is symmetric with respect to
the transmission and reflection channels, the amplitudes
of the scattered waves can be expressed [53, 55] in terms of
the modal amplitude of the bright mode b as S r = α*bb and
S t = S in + α*bb, giving rise to the following expressions for
the complex reflection/transmission coefficients:
r=
-| αb | j( ω-ωd -j τ )
S
S
=
, t = in = 1+ r .
S in ( ω-ωb -j τ-1b )( ω-ωd -j τ )-κ 2
S
r
2
-1
d
-1
d
t
(2)
In general, when Ohmic losses are present in the system in
addition to the radiative losses, the total lifetime τ of the
modes of the system is expressed through the Ohmic τo and
radiative τR lifetimes as τ = [ 1/ τ o + 1/ τ R ] -1 . In the absence of
the Ohmic losses, energy conservation condition (1 = |r|2+|t|2)
imposes a relation between the radiative lifetime of the
bright mode τ bR and its radiative coupling parameter
αb. By calculating the decay rate of the total stored energy
in the absence of the excitation (Sin = 0), we find that
R
d
d
d
W = (| d | 2 + | b | 2 ) = -2| b | 2 / τ b = | b | 2 , where it was
dt
dt
dt
assumed that the dark mode has infinite radiative lifetime
(1/ τ
R
d
=0
)
in the absence of resonator coupling (κ = 0). On
the other hand, in the lossless case the energy can only be
d
W = -2| b | 2 / τ bR =| S r | 2 + | S t | 2 = -2| αb | 2 | b | 2 ,
dt
thereby providing the sought after relationship:
radiated out:
1/ τ bR =| αb | 2 .
Typical transmission/reflection spectra of the model
Fano system described by Eqs. (2) are plotted in Figure 2
for different values of the spectral detuning δ = ωb-ωd
between the dark and bright resonances assuming that
ωb is fixed and Ohmic losses are negligible. The spectra
reveal a broad reflection peak centered at ωb and a sharp
spectral feature in the proximity of the dark frequency
ωd. The strong asymmetry of the reflection/transmission
spectra for (ωb≠ωd) are characteristic of the Fano interference between the two modes. Both the sharpness and the
amplitude of the Fano feature are reduced by finite nonradiative (Ohmic) losses.
One particular case of the Fano interference corresponding to spectrally matched resonances, ωb = ωd, is
referred to as electromagnetically induced transparency
(EIT). A number of EIT implementations based on planar
meta-surfaces (including the complementary ones) [26–36,
51, 57] and, more recently, on three-dimensional [37] metamaterials have been proposed. The physical manifestation of EIT shown in Figure 2 (green line) is the emergence
of a narrow transmission peak due to Fano interference
between the bright and dark states. Only a broad transmission dip due to the excitation of the bright resonance is
observed in the absence (κ = 0) of such interference.
1.0
Reflectance |r|2
d
(1)
0.8
0.6
0.4
0.2
δ=-0.1ωb
1.0
Transmittance |t|2
b -j(ωb +j τ-1b ) b + jκ d = αb S ine jωt ,
d -j( ω + j τ-1 ) d + jκ b = 0,
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A.B. Khanikaev et al.: Fano-resonant metamaterials
© 2013 Science Wise Publishing &
δ=0
δ=0.1ωb
0.8
0.6
0.4
0.2
0
0.80
0.85
0.90
0.95 1.00 1.05
Frequency (ω/ωb)
1.10
1.15
1.20
Figure 2 Transmission and reflection spectra of the Fano-resonant system described by Eqs. (1,2) with finite Ohmic losses.
The three curves correspond to the cases of Fano resonance with
δ = (ωd-ωb) = ± 0.1 ωb (red and blue curves) and electromagnetically
induced transparency ωd = ωb (green curve). Parameters: τRb =10/ωb ,
τob = τod = 500/ωb and κ = 0.05ωb.
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A.B. Khanikaev et al.: Fano-resonant metamaterials
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Another important feature of the Fano resonance is the
enhanced optical energy stored by a Fano-resonant structure when illuminated by light with the frequency ω coincident with that of the dark resonance’s ωd [45]. Figure 3
illustrates the point by plotting the energy W = |d|2+|b|2
stored by the system described by the Eqs. (1, 2). The
stored energy can reach very high values near ω = ωd when
the dark mode is excited. The resulting enhancement of
the optical near-field is the main enabler of the metamaterials-based sensing of minute analyte quantities: protein
monolayers [21–23, 58, 59], trace amounts of hydrogen
gas [60], or single-layer graphene [61–63] to name just a
few. The field enhancement peak manifests itself as the
absorption peak shown in Figure 3 (right), thereby giving
rise to the recently proposed [55] electromagnetically
induced absorption. It is worth noting that the absorption peak does not exactly coincide with either minimum
or maximum of the reflectivity as has been recently noted
[21, 46].
The highly simplified bi-resonant Fano model
expressed by Eqs. (1, 2) has another important utility: it
provides simple analytic expressions for transmission/
reflection coefficients that can be used for analytic multiparameter fitting of the experimentally obtained data.
Such fitting enables numerical extraction of the most
important parameters of the analytical model such as the
modes’ lifetimes and spectral positions. In particular, it
has been shown that the Fano model based on four-parameter fits of the results of the electromagnetic simulation
[44–46] accurately reproduce the spectra of a Fano-resonant meta-molecule. The bi-resonant Fano model has also
been used to precisely describe experimentally observed
r( ω ) =
A1
A
+ 2 ,
1 ω-ω
2
ω-ω
(3)
where the complex amplitudes A1,2 and frequen 1,2 , respectively, are related to the origicies ω
nal parameters of the Fano model through:
ω
ω
-ω

-ω

and
A2 = j | αb | 2  2 d  ,
A1 = - j | αb | 2  1 d  ,
1 -ω
2
1 -ω
2
ω
ω
1
1,2 = [( ω
b +ω
d )± ( ω
b -ω
d ) 2 + 4 κ 2 ], where the complex
ω
2
b = ωb + j τ-1b and ω
d = ωd + j τ-1d .
frequencies are defined as ω
In the approximation of weak coupling corresponding
to the case of high quality Fano resonance ( | κ | | δ| /2,
b -ω
d ≡ ( ωb -ωd ) + j( τ-1b -τ-1d ) is the complex-valwhere δ = ω
ued mode detuning) a simpler and more instructive ansatz
can be used. In this approximation the radicals in Eq. (3)
are expanded up to second order in the small parameter
2 κ / δ which gives the double Lorenzian expression of the
form:
B
1.0
200
0.5
1.0
0.3
0.5
0.2
Transmittance |t|2
0.5
100
Absorbance 1-|t|2-|r|2
0.4
Reflectance |r|2
Total energy stored by the resonators |b|2+|d|2
A
sharp Fano and EIT-like features of microwave metamaterials [35]. Even more importantly from the applications
standpoint, the bi-resonant fits can be used for spectroscopic characterization of small amounts of analyte added
to metamaterials. For example, spectral shifts and lifetime
modifications can be used for characterizing the complex
conductivity of single layer graphene [63].
It follows from Eq. (3) that the Fano expression for
the reflectivity can be exactly represented in the form of
the double Lorenzian under the assumption that the coupling strength κ between the dark and bright resonances
is frequency-independent:
0.1
0
0.80
0.85
0.90
0.95
1.0
Frequency (ω/ωb)
1.05
0
1.10
0
0.80
0.85
0.90
0.95
1.0
Frequency (ω/ωb)
1.05
0
1.10
Figure 3 (A) Energy of the dark mode W = |d|2+|b|2 (red line) superimposed with the reflectivity (green line) spectrum. Note that the field
enhancement peak falls between the peak and dip of the reflectance spectrum. (B) Enhanced absorbance (blue line) at the Fano resonance
superimposed with the transmittance (green line). Parameters used are: ωd = 0.9ωb, τRb = 10/ωb , τob = τod = 500/ωb , and κ = 0.02ωb.
ˆ
iφ
b
ˆ d | 2e
-j| α
ˆ
iφ
d
+
,
ˆ b ) + jˆτ-1b ( ω-ω
ˆ d ) + jˆτ-1d
( ω-ω
0.8
ˆ b/ d and lifewhere the renormalized frequencies ω
times ˆτ b/ d of the “dressed” bright and dark modes are
κ 
1 ) ≈ ωb + Re   ,
ˆ b = Re( ω
ω
 δ 
2
κ 
2 ) ≈ ωd -Re   ,
ˆ d = Re( ω
ω
 δ 
2
κ 
κ 
2 ) ≈ τ-1d -Im   ,
ˆτ-1b = Im( ω
1 ) ≈ τ-1b + Im   , and ˆτ-1d = Im( ω
 δ 
 δ 
2
2
while the effective radiative coupling parameters of the
κ2
δ 2 + κ 2
ˆ d | 2 = | αb | 2 2
|α
.
ˆ b | = | αb | 2
modes are | α
and
δ + 2 κ 2
δ + 2 κ 2
2
1.0
(4)
2
The expression (4) has simple physical meaning of the
scattering of light by two independent short-living superradiant and long-living sub-radiant modes formed by the
hybridization of the original bright and dark modes. It is
important to note that in addition to the corrections to
the frequencies and the lifetimes due to the interaction
of the modes and modification of their radiative coupling
caused by their hybridization, there is also a relative phase
ˆ =φ
ˆ -φ
ˆ , where
between the new “dressed” modes δφ
b
d
2
 κ

 δ 2 + κ 2 
ˆ = arg 
ˆ = arg 
. This addiφ
and φ
d
b
 δ 2 + 2 κ 2 
 δ 2 + 2 κ 2 
ˆ is crucial for reproducing strongly
tional phase shift δφ
asymmetric features seen in the experimental spectra of
the Fano-resonant systems. To illustrate that Eq. (4) is
indeed a good approximation to the Fano model, the calculation results obtained with the use of the exact expression for |r|2 of Eq. (2) and the approximate expression Eq.
(4) are plotted alongside in Figure 4. Examples of using
Eqs. (3, 4) for multi-parameter fitting of experimental
spectra are given in Section 6 in the context of investigating the modification of the reflectivity spectrum by adding
a thin conductive or dielectric layer to a meta-surface. In
ˆ d and ω
ˆ b are shifted and
that case resonant frequencies ω
ˆ
ˆ
modes lifetimes τ d and τ b are modified by the amount
determined by physical properties and thickness of the
perturbing layers.
3 Single-layer Fano-resonant
metamaterials
Planar (two-dimensional) meta-surfaces are the most
common and most thoroughly studied Fano-resonant
structures because of their fabrication simplicity and historical connection to frequency selective surfaces well
known in the microwave field. Such meta-surfaces can be
Reflectance |r|2
r( ω ) ≈
ˆ b | 2e
-j| α
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A.B. Khanikaev et al.: Fano-resonant metamaterials
© 2013 Science Wise Publishing &
0.6
0.4
Exact Fano result Eq.(2)
Double Lorenzian Eq.(4)
0.2
0
0.70
0.75
0.80
0.85 0.90 0.95
Frequency (ω/ωb)
1.00
1.05
1.10
Figure 4 Comparison of the reflectivities calculated with (a) the
exact Fano expression Eq. (2) with the parameters ωd = 0.75ωb,
τRb = 6.25/ωb , τob = τod = 300/ωb , and κ = 0.05ωb, and an approximate double Lorenzian Eq. (4) with the renormalized parameters
ˆ b |2 = 0.158,
ˆ b = 1.0071 ωb , τˆ Rb = 6.2942/ωb , τˆ ob = 300/ωb , | α
ω
ˆ = 1.4231deg., ω
ˆ d = 0.7429ωb , ˆτR = 127.0029/ω , ˆτo = 300/ω ,
φ
b
d
b
d
b
ˆ = -62.3567deg.
ˆ d |2 = 0.0044, and φ
|α
d
either periodic or aperiodic [5, 64–67]. The first studies of
planar systems showing asymmetric Fano-like response
date back to fundamental works of Wood and Rayleigh
[68, 69] who studied metallic diffraction gratings. Resonant phenomena in such gratings stem from periodic
pattern on the metal surface which gives rise to Bragg
diffraction. Resonances appear at the frequencies and
critical angles corresponding to the onset of a particular
diffraction orders manifesting in reflectivity spectra as
sharp asymmetric spectral features. It is interesting that
Fano himself has contributed to study of diffraction gratings and developed rigorous theory of light scattering by
these structures [56].
While metallic diffraction gratings and frequency
selective surfaces in general were among common tools
for optical and microwave engineers for many years, it was
not until the discovery of the extraordinary optical transmission (EOT) [70] that these systems gained interest from
the broad community of physicists working in photonics.
In 1998 Ebbesen and coauthors experimentally observed
the EOT of visible light through perforated silver film
and attributed the effect to the excitation of the surface
plasmon polaritons (SPPs). Spectrally, the EOT takes place
close to the frequency corresponding to the SPP’s folded
dispersion curve, suggesting that the excitation of the
SPPs (or similar waves) facilitates light tunneling through
sub-wavelength sized holes. The asymmetric shape of the
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transmission peaks encouraged the attribution of the EOT
to Fano-type interference [71, 72] between broad featureless transmission through the holes and narrowband excitation of the “dark” SPPs by the periodic structure. Similar
Fano-shaped reflection spectra are also observed in periodic arrays of plasmonic particles [73–75]. Detailed analysis of the EOT is beyond the scope of this Review, and in
what follows we concentrate on meta-surfaces whose unit
cell is comprised of one or more meta-molecules supporting bright and dark resonances. Frequencies and lifetimes
of such resonances can be engineered through meta-molecules’ design.
3.1 E
ngineering of constituent
meta-molecules
Spatial symmetry of the constituent meta-molecules
plays the key role in lifetime engineering of Fano resonances as was first demonstrated in the microwave
spectral range for meta-surfaces comprised of a periodic
array of asymmetrically split rings [26] shown in Figure 5.
Near-field interaction between the two halves of the ring
results in two modes: bright symmetric (current flowing
in the same direction in both ring halves) and dark antisymmetric (currents flowing in opposite directions in
both ring halves). The lifetime of the dark mode responsible for transmission dip is controlled by two factors:
the degree of asymmetry γ (responsible for the radiative lifetime) and substrate loss tangent ε (responsible
for the non-radiative lifetime). For small degree of symmetry breaking (γ ≤ 0.1), strong Fano features are shown
in the inset of Figure 5A for the horizontally polarized
electric field. The same design was later used to engineer sharp Fano resonances in the THz range [30], and
similar (but complementary) design of asymmetric slits
in plasmonic surface was used at visible frequencies
[76]. Conceptually similar mirror symmetry breaking
of a bi-layer [29] and single-layer plasmonic meta-surfaces shown in Figure 5B, C and a single-dolmen [32]
meta-molecule shown in Figure 5C were also shown to
produce characteristic Fano spectra in the optical part
of the spectrum. In all cases shown in Figure 5 the electric field polarization is orthogonal to the remaining
mirror symmetry plane.
A number of other planar Fano systems with resonant
responses controllable by symmetry breaking of metamolecules have been recently proposed, including those
based on metallic truncated nanoshells [77], plasmonic
Fano resonances in nano-crosses [78] and disk-ring plasmonic nanostructures with record values of quality factors
© 2013 Science Wise Publishing &
[79, 80]. Asymmetry can also be introduced by employing
different materials (e.g., Au and Ag) for making different
segments of an otherwise geometrically symmetric structure [81, 82]. In this case the degree of asymmetry is controlled by the mismatch in the materials’ properties (e.g.,
their dielectric permittivities). Combining nanoparticles
of different shapes (i.e., nanospheres, core-shell particles,
etc.) into heterodimers [83] was also shown to result in
Fano intereferences and asymmetric scattering. Although
even single nanoparticles can exhibit Fano resonance
[84], by controlling arrangement of multiple nanoparticles in oligomers enables unprecedented control of their
resonant response.
In the structures with two elements (sometimes
referred to as dimers [83, 85–89]) comprising the metamolecules, such as the ones shown in Figure 5A, the
Fano resonance stems from the interaction between
individual modes of these elements. Spectral repulsion
between the modes necessitates that the frequencies of
the hybrid bright and dark modes are mismatched. More
complex meta-molecules containing more elements and
resonances enables independent control of the frequencies of the bright and dark resonances. When the two frequencies are spectrally matched, EIT-like response can be
obtained [27, 28] as shown in Figure 5B. By appropriately
choosing the length of the horizontal antenna, its bright
electric dipolar resonance can be spectrally matched to
the electric quadrupolar resonance of the two vertical
antennas, which is dark for normally incident light. When
incident light excites the dipole resonance of the horizontal antenna, the antenna’s near field excites the vertical
antennas’ quadrupolar resonance. These two antennas,
in turn, depolarize the horizontal antenna causing the
reflectivity to drop, thereby giving rise to the EIT of the
meta-surface. The details of the optical response of the
meta-surface (including the quality factor of the EIT resonance and the depth of the reflectivity dip) are determined
by the degree of near-field coupling [κ-coefficient in the
Eq.(1)] between the bright dipolar and dark quadrupolar
modes controlled by the antenna’s displacement s defined
in Figure 5B.
The dark (sub-radiant) character of the electric multipole and magnetic dipole resonances of meta-­molecules
comprising the meta-surface is predicated on their
forming a regular periodic lattice which prevents sidescattering. Depending on the exact structure of constituent meta-molecules, long-range interaction may be either
suppressed (incoherent meta-surfaces), or enhanced
(coherent meta-surfaces) [64, 90]. Coherent effects in
Fano-resonant meta-surfaces are reviewed below. Even
more sophisticated meta-molecules comprised of clusters
A.B. Khanikaev et al.: Fano-resonant metamaterials
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40
-40
20
8
6
Frequency (GHz)
4
ε′′=0.05
γ=0.33
γ=0.23
-20
γ=0.11
60
γ=0.06
Transmission (dB)
ε′′=0
80
Quality factor (Q)
B
0
10
Transmittance/ reflectance
A 100
0
0
0.1
253
0.2
Asymmetry (γ)
0.3
0.4
0.8
0.6
0.4
0.2
0
C
s=50 nm
120 140
160 180 200 220
Frequency (THz)
Extinction (1-T)
0.2
0.1
0
800
1000
1200
Wavelength (nm)
1400
Figure 5 Lifetime engineering of Fano resonances by breaking one of the mirror symmetries of the constituent meta-molecules. (A) Microwave and (B) optical meta-surfaces with gradually reduced spatial symmetries. (C) Single-dolmen meta-molecule with only one remaining
mirror symmetry. In all three cases Fano features are observed for the electric field orthogonal to the remaining mirror symmetry plane.
Reproduced by permission from Ref. [26] (A), Ref.[29] (B), and Ref.[32].
of plasmonic nanoparticles (sometimes referred to as
plasmonic oligomers) have been used to design Fano resonant meta-surfaces with electric [33, 36, 50, 91–101] and
magnetic [102] subradiant modes. Plasmonic oligomers
have been fabricated using both bottom-up assembly [94]
or, more commonly, top-down fabrication.
In addition to plasmonic systems, recently there was a
surge of interest in so called “all-dielectric” metamaterials
made of high-index dielectric nanostructures [103, 104].
Such systems can be especially promising in the near IR
and visible frequency ranges were the lifetimes and quality
factors of the Fano resonances are limited by strong losses
in metals. In their recent work [105] Miroshnichenko and
Kivshar have theoretically shown that light scattering by
all-dielectric oligomers exhibits well-pronounced Fano
resonances originating from the optically induced magnetic dipole modes of individual high-dielectric nanoparticles. By comparing all-dielectric structures to their
plasmonic counterparts they have shown that Fano resonances in all-dielectric oligomers are also less sensitive to
structural variations thus offering a more practical alternative for many nanophotonic applications.
3.2 I maging of Fano-resonant meta-­
molecules in the near field
Although spectroscopic signatures of Fano interference
have been conventionally observed in far-field measurements of transmission, reflection, or extinction, recent
advances in near-field imaging enable direct characterization of the charge density distributions on the
meta-surface. Such characterization of multi-resonant
meta-surfaces yields a more complete signature of the
Fano interference than its far-field counterpart because
the same scattering pattern can be caused by different
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© 2013 Science Wise Publishing &
charge distributions. To unambiguously demonstrate the
root cause of Fano resonance one has to be able to spatially resolve the charge redistribution between different portions of the Fano-resonant meta-molecules. Two
near-field imaging techniques have recently emerged. The
first technique is the Electron Energy Loss Spectroscopy
(EELS) [106] that enables direct mapping of the spatial
distribution of all optical resonances of any structure,
including plasmonic [107, 108] or dielectric-based nanostructures (see [43] for a comprehensive review and additional references). Because electrons enter the near-field
of a nanostructure, EELS can be used for mapping either
bright or dark resonances. The resolution of EELS is fundamentally limited the de Broglie wavelength of an electron which is typically much smaller that the diffraction
limit of light. One potential limitation of EELS is that its
relationship to the local optical density of states (LDOS),
which is of primary interest in determining optical properties of nanoparticles, is clearly established [43] only for
two-dimensional nanostructures. The advantage of EELS
over near-field optical microscopy outlined below is that
it can potentially probe the completely dark resonances
Si tip
Interferometric
detection
Ein
Ep
Polarizer
C
1.5
Einc
Normalized reflectivity
A
of symmetric meta-molecules that are totally decoupled
from the far-field optical excitation.
The second technique illustrated by Figure 6 is
the interferometric scattering-type near-field scanning
optical microscopy (s-NSOM) [109]. It has been recently
[36] applied to two infrared Fano-resonant meta-surfaces
fabricated using top-down electron beam lithography
comprised of (a) highly symmetric heptamer structures
comprised of plasmonic disks shown in Figure 6A, and (b)
asymmetric π-shaped nanorod antennas shown in Figure
6B. While the far-field signature of the Fano interference
is a conventional asymmetric reflectivity spectrum shown
in Figure 6C, its near-field signature is more interesting.
Figure 6D indicates that the Fano interferences results
in the phenomenon of intensity toggling: strong spatial
redistribution of the high-field areas inside the metamolecules upon crossing the “dark” resonance. This toggling
represents a direct experimental evidence of interfering
electromagnetic eigenmodes of plasmonic metamolecules
responsible for the phenomenon of the Fano resonance.
As near-field tools such as s-NSOM become more widely
available, we anticipate that more research will be done
Q
C
1.0
0.5
D
Einc
B
0
1 µm
B
Si tip
Ep
Polarizer
A
8
9
10
Wavelength (µm)
11
12
Interferometric
detection
D
|Ez|
A
B
C
D
Ein
Figure 6 NSOM images of Fano interference and intensity toggling in infrared meta-surfaces. (A, B) Spatially-symmetric plasmonic heptamers (A) and asymmetric pi-structures (B) are imaged using tunable CO2 laser. (C) Polarized reflectivity from the π–structures. Vertical
polarization reveals far-field Fano interference around λ≈10 μm. (D) Fano interference manifests in the near-field as intensity toggling: the
left antenna is bright at the spectral point A and dark at the spectral point D. From Ref.[ 36].
on detailed mapping of charge distributions on the metasurfaces. Thus obtained information will enable detailed
comparisons with numerical simulations which, so far,
have been the only reliable source of information about
electric and magnetic field enhancements and charge distributions on Fano-resonant meta-surfaces.
4 Meta-surfaces with a ground plate
A special class of Fano-resonant metamaterials involves
planar meta-surfaces separated by a dielectric spacer
from a metallic ground plate shown in Figure 7A, B. The
ground plate blocks the transmission and provides an
ultra-broadband reflection background. In addition, the
background reflection interferes with the resonances of
the top meta-surface, resulting in reduced total reflection
and therefore enhanced absorption. Such meta-surfaces
with a ground plate have been widely used for designing
C
A
p
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A.B. Khanikaev et al.: Fano-resonant metamaterials
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“perfect” (zero-reflectivity) plasmonic absorbers in the
terahertz and mid-infrared frequency ranges [110–116]. A
wide variety of resonator geometries, including circular
disks [110], square and rectangular patches[114], Swiss
crosses [115], split-ring resonators [112] and straight plasmonic strips [60, 111, 113, 117–119] among others have
been demonstrated to achieve nearly perfect absorption.
Figure 7C and D show the disk on ground plate design
from Ref. [110] that exhibits more than 90% absorption in
both TE and TM polarizations over a wide range of incident angles. The property of “perfect” spectrally-selective
wide-angle infrared absorption has been proposed for
several practical applications, including ultra-sensitive
refractive index sensing [60, 110] and highly efficient
thermal photovoltaics [48, 115] spectrally matched to the
bandgap of a photovoltaic cell.
For meta-surfaces with a ground plate perfect absorption implies vanishing reflection. That has been interpreted in the past [120, 121] as the condition for matching
the complex effective dielectric permittivity εeff(ω) and
D
TE polarization
TM polarization
p
E
H
E
H
E
E
H
80
80
70
H
60
E
p
m
m
p
E
p
Angle (°)
E
p
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
50
40
30
20
10
0
140
160
180 200 220
Frequency (THz)
240
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
70
60
Angle (°)
B
50
40
30
20
10
0
140
160
180 200 220
Frequency (THz)
240
Figure 7 Ground plate based meta-surfaces used for designing “perfect” absorbers, narrow-band infrared emitters, and ultra-sensitive
refractive index sensors (from [110] and [111]). (A) When the resonators are far from the ground plate, incoming radiation is mostly reflected
by the excitation of plasmonic resonances. (B) When the resonators are close to the ground plate, induced image currents in the ground
plate reduce the far-field radiation from the resonators, resulting in lower radiative damping rates. (C) and (D), the plasmonic absorber
design and simulated angular dispersions of the absorbance peak for both TE and TM polarizations taken from Ref. [110].
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A.B. Khanikaev et al.: Fano-resonant metamaterials
magnetic permeability μeff(ω) of the resulting layer so that
reflectivity vanishes for some unique frequency ωa that satisfies the impedance-matching condition εeff(ωa) = μeff(ωa).
However, the assignment of effective bulk parameters
to a metal-terminated layer is ambiguous. For example,
the bi-anisotropic response of such surface is inherently
neglected. The assignment of a single quantity, frequencydependent surface impedance z(ω) [111], circumvents
this problem. Under a single-resonance model [111], the
surface impedance of the ground plate terminated metasurface can be expressed using the coupled mode theory
γR
as z ( ω ) =
, where ωa is the resonant frequency
i( ω-ωa ) + γQ
of the eigenmode, and γR and γQ are the radiative and
resistive damping rates, respectively. While the resistive
damping rate is intrinsic to the choice of materials, the
radiative damping rate can be controlled by changing the
intermediate spacer thickness. When resistive and radiative damping rates of the resonant mode are equal (γR = γQ),
the impedance matching with vacuum (z = 1) is achieved
resulting in 100% absorption at the resonant frequency
ω = ωa. Note that γR is controlled by the spacing between
the meta-surface and the ground plate because the radiative damping rate of the resonant mode is reduced by the
image current induced in the ground plate as illustrated in
Figure 7A and B.
The capability of absorbing all of the incoming light
with an ultra-thin plasmonic layer indicates strong nearfield enhancement at the plasmonic resonance. Recent
experimental estimates [111] of the propagation length of
the surface plasmon responsible for absorption confirmed
its classification as a localized surface plasmon resonance
(LSRP). The strongly sub-wavelength nature of the LSRP
makes the absorber’s performance virtually independent of the incidence angle as shown in Figure 7C and D.
Another important consequence of the sub-wavelength
nature of ground plate based absorbers is that multiple
absorbing meta-molecules can be placed within the same
macro-cell, thereby expanding the absorber’s spectral
bandwidth [68, 115, 118, 122].
5 Three-dimensional metamaterials
While single-layer and few-layer [29, 97, 123, 124] metamaterials (of which meta-surfaces with a ground plate is just
one example) are relatively straightforward to fabricate,
considerable challenges remain to fabricating genuine
three-dimensional metamaterials. Several three-dimensional metamaterials, including a negative index metamaterial [125] and a 3D chiral polarizer [126] have been recently
© 2013 Science Wise Publishing &
fabricated, but the task of demonstrating 3D metamaterials exhibiting Fano resonances still appears challenging
with the exception of lower (microwave) frequencies [27].
Experimental challenges have not deterred theoretical
explorations of such metamaterials because using the
third dimension enables novel applications unattainable
in planar geometries. One such application is slow light
(SL): the phenomenon first realized in three-level atomic
systems that relies on EIT to generate extremely sharp
frequency dependence of the refractive index n(ω). The
resulting group velocity v g ( ω ) = c / n + ( ωdn / d ω ) in the
media comprised of atoms exhibiting the EIT can then be
made much smaller than the speed of light c in vacuum.
As was discussed in Section 3, Fano-resonant metasurfaces have been shown to emulate EIT. Therefore, a stack
of such meta-surfaces constitutes a three-dimensional
metamaterial that can be employed for SL applications.
Because the reduction in group velocity is accompanied
by pulse compression and energy density increase, SL promotes stronger light-matter interactions and finds numerous applications in various linear and nonlinear devices
[127]. One limitation of the EIT approach is that the bandwidth of the resulting slow light is rather limited. Recent
microwave experiments [27] have demonstrated that the
SL’s bandwidth is not improved by stacking Fano-resonant
microwave meta-surfaces with different resonant frequencies. The EIT approach to producing slow light suffers from
yet another serious limitation: a rather moderate value of
the product of the time delay Tdel in the medium and the
bandwidth of the delayed in the medium pulse δωdel. While
increasing the length of the delay medium Ldel increases
Tdel, it also decreases δωdel in the same proportion because
of the frequency-dependence of vg(ω), thereby keeping the
product (δωdel Tdel) independent of Ldel. Three-dimensional
Fano-resonant metamaterials may provide a surprising
platform for engineering the bandwidth-delay product
which is directly proportional to the metamaterial’s length.
This is accomplished by utilizing the so-called doublecontinuum Fano (DCF) resonance described in the original
Ugo Fano’s paper [39]. It was recently demonstrated [37]
that DCF enables broad-band SL.
A typical meta-molecule comprising a DCF metasurface shown in Figure 8C possesses no mirror reflection symmetries, thereby coupling the dark (quadrupolar)
resonance to both (x- and y-polarized) in-plane dipoles.
Thus, the dark (discrete) resonance of a DCF meta-surface
is coupled to two electromagnetic continua, x- and y-polarized electromagnetic waves propagating in the z-direction, thus justifying its designation. A stack of identical
DCF meta-surfaces supports a propagating mode which is
spectrally broad, yet possesses a “flat” ( v g =∂ω / ∂k c )
A
B
2500
2000
ω0+∆ω
In
|E|2/|E|2
DCF of the last layer
∆ω
Out
ω0
ω0
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A.B. Khanikaev et al.: Fano-resonant metamaterials
© 2013 Science Wise Publishing &
ω0−∆ω
DCF of the first layer
18 THz
18.3 THz
18.6 THz
Gap
Sy
L2
1500
g
w
1000
500
y-Polarized fast light band
ω
0
Slow light band
0
70
140
x-Polarized fast light band
kz
C 1.0
280
D 1.0
2
|Ty|
Loss
|T|2
Vg/C
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
17
210
z (µm)
18
19
20
Frequency (THz)
0
18
Loss
19
Vg/C
20
Frequency (THz)
Figure 8 Double-continuum Fano (DCF) approach to making slow-light metamaterials. (A) Photonic band structures of three sequentially
stacked DCF meta-surfaces. (B) Different frequency components of the wave packet are slowed down inside different meta-surfaces. Inset
shows unit cell of the metamaterial with red dot indicating position of the field intensity probe. (C) Spectrally-flat profiles of transmission,
loss, and group velocity. (D) Same, but for a stack of meta-surfaces supporting EIT. From Ref. [37].
segment as schematically shown in Figure 8A [37]. The
low group velocity spectral region occurs for ω≈ωQ, where
ωQ is the frequency of the dark resonance. By stacking N
meta-surfaces with adiabatically varying Fano resonance
frequencies ω(Qj=1⋅⋅⋅N ) ≡ ωQ ( z ), as shown in Figure 8A, one
can ensure that different spectral components of the
wave-packet are slowed down at different locations inside
the 3D meta-material, as illustrated in Figure 8B.
The result of such adiabatic dispersion engineering
is that a propagating wave packet can be slowed down
over a broad frequency range with spectrally uniform
group velocity and transmission coefficients as shown in
Figure 8C. Therefore, by stacking more meta-surfaces one
can enhance the spectral bandwidth ω0-Δω < ω < ω0+Δω
over which the pulse can be uniformly slowed down,
thereby indefinitely increasing the bandwidth-delay
product (δωdel Tdel). Note that such increase is impossible
to accomplish with EIT by increasing the number of identical stacked meta-surfaces because the dependence of
vg(ω) and |T|2(ω) on the frequency shown in Figure 8D
reduces the bandwidth.
6 D
ynamic tuning of Fano-resonant
metamaterials and meta-surfaces
Although Fano-resonant metamaterials can strongly
enhance light-matter interactions, this comes at the
expense of broadband response that may be desirable
for some applications that require broad spectral range.
To circumvent this limitation, large arrays of Fano-resonant “pixels” with different spectral responses can be
utilized. For example, arrays of individual pixels tuned
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A.B. Khanikaev et al.: Fano-resonant metamaterials
© 2013 Science Wise Publishing &
to various vibrational (fingerprint) resonances of biological molecules have been utilized for fingerprinting and
orientation-sensing of protein monolayers [21]. However,
for many other applications real-time control of Fano resonances is desirable, and several avenues for such dynamic
tuning recently suggested for various (not necessarily
Fano-resonant) metamaterials and meta-surfaces include
using phase-change media [128, 129], liquid crystals [130–
132], carrier manipulation in semiconductor substrates
[133], electrical modulation with graphene [134–136], and
electromechnical reconfiguration [137]. Some of these
and other approaches are now applied to Fano-resonant
structures. For example, one approach to dynamic tuning
relies on controlling the symmetry of Fano-resonant metamolecules embedded into elastic materials. It has been
suggested that mechanically tunable plasmonic nanostructures can serve as a platform for dynamically tunable
nanophotonic devices such as tunable filters and sensors.
Gold heptamers have been embedded into a flexible matrix
[138] to show that the reduction of the spatial symmetry
of these plasmonic molecules caused by the mechanical
stress can control the strength of the Fano interference.
Another promising approach is to utilize the optical
response of single-layer graphene (SLG) for dynamic
tuning. In particular, due to its controllable optical
response, graphene was shown to allow modulation of
the spectral position and quality factors of the Fano resonances. Strong optical absorption of SLG due to interband
transitions was used to experimentally demonstrate the
red-shifting and lifetime modification of Fano resonances
[61] in the near-infrared part of the spectrum. Graphene is
A
also attractive for tuning the response of THz metamaterials. SLG’s response at THz frequencies is predominantly
resistive, and the resulting Ohmic loss was shown to be
broadly tunable by electrostatic doping of graphene. Substantial gate-induced switching and linear modulation of
terahertz waves can thus be achieved in Fano-resonant
meta-surfaces at the room temperature [62].
In contrast to resistive THz response, in the mid-IR
spectral range graphene has a distinct plasmonic response
which enables its application for spectral tuning of the
Fano resonances as opposed to amplitude tuning in THz.
Indeed, it has been recently shown [63] that inductive
coupling of Fano resonant meta-surface with graphene
enables a unique blue-shift tunability of the Fano resonances. It was experimentally shown that just by placing
graphene on top of a meta-surface as shown in Figure 9,
the Fano resonance can be blue-shifted as much as 30 cm-1
and reflectivity changed by more than 10%. Dynamic tunability can be achieved by electrostatic gating of graphene
in a slightly different geometry [136].
Hybridization between Fano-resonant metamaterials and graphene has an additional appealing
application: infrared spectroscopy of graphene. Specifically, by using Eq.(3) for the reflectivity coefficient
from the meta-surface and realizing that the addition
of graphene to the meta-surface results in the spectral
1,2 to
shift of the complex reflectivity poles from ω = ω
ω = ω1,2 + ∆ω1,2 , we can use the complex-valued spectral
shifts Δω1,2 to estimate the ratio of the imaginary and real
parts of graphene’s conductivity. Specifically, it can be
shown that for small spectral shift the following relation
B 0.8
No Graphene
EF=0.2 eV
0.7
EF=0.4 eV
Reflection
0.6
Quadrupole
resonance
EF=0.6 eV
0.5
0.4
0.3
0.2
Dipole
resonance
0.1
0
1400
1600
1800
2000
2200
2400
2600
ω (cm-1)
Figure 9 Single-layer graphene can be used to tune metamaterial resonances. (A) SLG laid on top of a Fano-resonant metamaterial. (B) Blue
shifting of the metamaterial resonance by increasing the Fermi level EF of the SLG. From Ref. [62].
© 2013 Science Wise Publishing &
holds: Re( ∆ω1,2 ) / Im( ∆ω1,2 ) = Im( σ g ) / Re( σ g ), where the
complex conductivity of graphene σg is evaluated at the
corresponding frequency of the first (bright) or second
(dark) resonance. Graphene can be characterized as
being low-loss, and its response as primarily inductive
whenever Im(σg)>>Re(σg). Such spectral shift is illustrated in Figure 9. Note that by using several metamaterial pixels tuned to different resonant frequencies it is
possible to optically characterize graphene’s parameters
(such as the Fermi level energy EF) at mid-infrared frequencies [63]. The importance of Fano-resonant metamaterial for such infrared spectroscopy of graphene is
underlined by generally weak response of graphene to
mid-IR radiation. Strong optical field enhancement in
close proximity of the meta-surface is responsible for
considerable spectral shift of metamaterial’s resonance
due to graphene’s conductivity.
7 Applications of Fano-resonant
meta-surfaces to biological
sciences
Fano-resonant metamaterials enable strong spectrallyselective enhancement of electromagnetic fields in their
immediate vicinity, thereby considerably boosting the
interaction of light with matter placed in close proximity
of (or in direct contact with) the meta-surface. Therefore,
even weak perturbation in the electromagnetic environment of the metamaterial can significantly alter its scattering characteristics [79]. Small changes of the refractive
index are particularly easy to detect optically using metamaterials. One of the most common applications the Fano
resonant plasmonic metamaterials is, therefore, refractive
index sensing [22, 31, 49–51, 139, 140]. Such sensors can be
used for determining bulk concentrations of the analyte
which contains chemically or biochemically relevant molecules, such as glucose or proteins. The main consequence
of altered dielectric environment on the Fano spectra is
spectral shifts of the resonant peaks and change in their
intensity. Absolute values of spectral shift can be directly
related to mass accumulation of an analyte in the vicinity of the metamaterial. At the same time, for the case of
absorptive media, strong field enhancement can result in
broadening and decrease of the amplitude of sharp spectral features associated with Fano resonances. Analyzing
this information enables the quantitative characterization
of the analyte.
If the optical fields are localized within a distance
Lloc from metamaterial’s surface, it can be used as an
A.B. Khanikaev et al.: Fano-resonant metamaterials
259
attractive biosensor [23, 37, 141] which is particularly sensitive to binding events involving small molecules such
as, for example, proteins. Moreover, spectral selectivity of Fano-resonant meta-surfaces enables researchers
to match the spectral positions of the “dark” resonances
with those of the vibrational fingerprints of various biomolecules such as proteins, DNA/RNA, and others. Using
a diversity of Fano-resonant “pixels”, some of them tuned
to molecular fingerprint, it is possible [37] to carry out
in-depth characterization of the bio-molecules attached
to metamaterial-based sensors. This is done by measuring sensor reflectivities |rbare|2(ω) and |rprot|2(ω) without/
with the protein, followed by the analysis of the difference
spectrum ΔR(ω) = |rbare|2-|rprot|2. In general, ΔR(ω) peaks at
the frequency of the dark resonance ω≈ωQ. However, the
spectral shape of ΔR(ω) can become considerably more
complex whenever a vibrational resonance occurs at the
frequency ωi close to ωQ. The difference spectrum contains
detailed information Such measurement can be carried
out either with completed mono and bi-layers of proteins
[37], or even in real time during the buildup of protein
monolayers. The resulting difference spectra are sensitive
not only to the mass density of the protein, but also to proteins’ orientation on the surface of the sensor. Obtaining
the information on protein’s orientation is important for
designing high capacity biosensors that rely on the specific orientation of antibodies and attachment proteins for
capturing the antigens.
A typical example of such biosensor based on an array
of Fano-resonant asymmetric metamaterials (FRAMMs) is
shown in Figure 10. Spectral positions of Fano resonances
are varied by scaling the dimensions of the individual
meta-molecules inside each pixel. The FRAMM-based
biosensor was applied to studying the sequential attachment of two protein monolayers. The first fusion protein
A/G was used as an attachment monolayer for the second
monolayer of antibodies (IgG) as shown in Figure 10. The
resulting difference spectra ΔR(ω) for one (dashed lines)
and two (solid lines) monolayers are shown in Figure 10 for
three characteristic pixels. One of the pixels (green line)
is tuned to the so-called Amide-I (C = O vibration of the
protein backbone) resonance while the other two pixels
are detuned from all vibrational resonances. By comparing
the maximum values of ΔR for the detuned pixels to theoretical predictions, the thicknesses of the monolayer and
bi-layer were shown to be h1≈2.7 nm and H≡h1+h2≈7.9 nm,
respectively. Owing to the enhanced interaction of light
with the protein at the meta-surface, < 3 nm thick protein
A/G monolayer causes easily detectable 4% reflectivity
changes, indicating that molecular monolayer thickness
can be reliably measured with nm-scale accuracy.
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A.B. Khanikaev et al.: Fano-resonant metamaterials
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× 1.98
0.15
(ε2)
h2
IgG
× 2.93
× 3.38
(ε1)
h1
∆R/RQ
0.10
Protein
A/G
0.05
ωII
ωI
0
-0.05
1300
1400
1500
1600
1700
1800
1900
2000
Wavenumber (cm-1)
Figure 10 Schematic representations of proteins’ mono- and bilayers binding to the metal surface and the equivalent dielectric model
(left panel). Experimental spectra before (dashed lines) and after (solid lines) binding of IgG antibodies to three different FRAMM substrates immobilized by the protein A/G (right panel). Indicated reflectivity ratios vary with the spectral position of the FRAMMs’ resonant
frequencies.
Further information about proteins’ orientation
on the surface can be obtained by analyzing the ratios
( bi )
( mono )
T ( ωQ ) =∆Rmax
/ ∆Rmax
of the peak reflectivities for a bilayer and a monolayer. Using the detailed information
about the proteins’ structure from the protein data bank
[37], it is possible to demonstrate that the attachment
protein A/G is connected to the FRAMM with its helical
axis almost normal to the FRAMM’s surface. This orientation of the attachment protein is indeed conducive to
high-capacitance antigen sensing because the Y-shaped
antibody attaches its stem (the Fc region) to protein A/G
while leaving its Fab region available for antigen binding.
Such detailed information about binding and orientation
of proteins can be used for studying real-time dynamics
and buildup of protein monolayers. Because FRAMMbased biosensing and fingerprinting provides more specific information about attached biomolecules than the
more common surface plasmon resonance (SPR) sensor,
we can speculate that metamaterials-based biosensor will
eventually become commonplace tools for biochemistry
and biosensing.
8 Future outlook
Tremendous advances in theoretical understanding,
experimental characterization, and sheer variety of Fanoresonant metamaterials and meta-surfaces that occurred
during this decade transformed these electromagnetic
structures from objects of curiosity into powerful exploratory tools. Two properties of Fano resonances, their sharp
spectral features and strong field enhancements, have
made them ideally suited for developing novel spectroscopic and sensing tools. In the next few years we will
most likely witness the expansion of Fano-resonant media
into the nonlinear regime, where these two properties
will be essential for enhancing light-matter interactions.
Heterogeneous integration of Fano metamaterials with
nanoscale objects such as quantum dots, quantum wells,
graphene, and bio-molecules will be used for developing
new active and switchable devices as well as for characterizing these inherently quantum structures. Experimental
demonstrations of introducing gain media into metamaterials will result in low-threshold lasers. And so the history
will make a full circle: the phenomenon that originated
in the quantum mechanical world and was most recently
adopted by classical physicists will be used for enhancing
and modifying quantum phenomena
Acknowledgements: The authors would like to acknowledge the support of the grant from the Office of Naval
Research and the National Science Foundation.
Received April 5, 2013; accepted July 23, 2013; previously published
online September 21, 2013
A.B. Khanikaev et al.: Fano-resonant metamaterials
© 2013 Science Wise Publishing &
261
References
[1] Pendry JB. Negative refraction makes a perfect lens. Phys Rev
Lett 2000;85:3966–9.
[2] Smith DR, Pendry JB, Wiltshire MCK. Metamaterials and
negative refractive index. Science 2004;305:788–92.
[3] Engheta N, Ziolkowski RW. Metamaterials: physics and
engineering explorations. Hoboken, NJ, USA: Wiley & Sons, 2006.
[4] Cai W, Shalaev V. Optical Metamaterials: Fundamentals and
Applications. New York: Springer, 2009.
[5] Holloway CL, Kuester EF, Gordon JA, O′Hara J, Booth J,
Smith DR. An overview of the theory and applications of
metasurfaces: the two-dimensional equivalents of metamaterials. IEEE Antennas Propag 2012;54(2):10–35.
[6] Pendry JB, Holden AJ, Robbins DJ, Stewart WJ. Magnetism from
conductors, and enhanced non-linear phenomena. Microwave
Theory Tech 1999;47(11): 2075–84.
[7] Linden S, Enkrich C, Wegener M, Zhou J, Koschny T,
Soukoulis CM. Magnetic response of metamaterials at 100
Terahertz. Science 2004;306(5700):1351–3.
[8] Yen TJ, Padilla WJ, Fang N, Vier DC, Smith DR, Pendry JB,
Basov DN, Zhang X. Terahertz magnetic response from artificial
materials. Science 2004;303(5663):1494–6.
[9] Smith DR, Padilla WJ, Vier DC, Nemat-Nasser SC, Schultz S.
Composite medium with simultaneously negative permeability
and permittivity. Phys Rev Lett 2000;84:4184–7.
[10] Veselago VG. The electrodynamics of substances with simultaneously negative values of permittivity and permeability.
Soviet Physics Uspekhi 1968;10(4):509–14.
[11] Shelby RA, Smith DR, Schultz S. Experimental verification of a
negative index of refraction. Science 2001;292(5514):77–9.
[12] Saadoun MMI, Engheta N. A reciprocal phase shifter using
novel pseudochiral or omega medium. Microw Opt Techn Let
1992;5(4):184–8.
[13] Marqués R, Medina F, Rafii-El-Idrissi R. Role of bianisotropy in
negative permeability and left-handed metamaterials. Phys
Rev B 2002;65:144440.
[14] Serdyukov AN, Semchenko IV, Tretyakov SA, Sihvola A.
Electromagnetics of bi-anisotropic materials: Theory and
applications. Amsterdam: Gordon and Breach Science
Publishers, 2001.
[15] Fang N, Lee H, Sun C, Zhang X. Sub–diffraction-limited optical
imaging with a silver superlens. Science 2005;308:534–7.
[16] Ulf L. Optical conformal mapping. Science
2006;312(5781):1777–80.
[17] Pendry JB, Schurig D, Smith DR. Controlling electromagnetic
fields. Science 2006;312(5514):1780–2.
[18] Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF,
Smith DR. Metamaterial electromagnetic cloak at microwave
frequencies. Science 2006;314:977–80.
[19] Liu R, Ji C, Mock JJ, Chin JY, Cui TJ, Smith DR. Broadband
ground-plane cloak. Science 2009;323(5912):366–9.
[20] Chen H, Chan CT, Sheng P. Transformation optics and metamaterials. Nat Mater 2010;9:387–96.
[21] Wu C, Khanikaev AB, Adato R, Arju N, Yanik AA, Altug H,
Shvets G. Fano-resonant asymmetric metamaterials for
ultrasensitive spectroscopy and identification of molecular
monolayers. Nat Mater 2012;11:69–75.
[22] Adato R, Yanik AA, Amsden JJ, Kaplan DL, Omenetto FG, Hong MK,
Erramilli S, Altug H. Ultra-sensitive vibrational spectroscopy of
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
protein monolayers with plasmonic nanoantenna arrays. Proc
Natl Acad Sci USA 2009;106:19227–32.
Cubukcu E, Zhang S, Park Y-S, Bartal G, Zhang X. Split ring
resonator sensors for infrared detection of single molecular
monolayers. Appl Phys Lett 2009;95:043113.
Çetin AE, Yanik AA, Yilmaz C, Somu S, Busnaina A, Altug H.
Monopole antenna arrays for optical trapping, spectroscopy,
and sensing. Appl Phys Lett 2011;98:111110:1–3.
Kabashin AV, Evans P, Pastkovsky S, Hendren W, Wurtz GA,
Atkinson R, Pollard R, Podolskiy VA, Zayats AV. Plasmonic nanorod
metamaterials for biosensing. Nat Mater 2009;8:867–71.
Fedotov VA, Rose M, Prosvirnin SL, Papasimakis N, Zheludev
NI. Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry. Phys Rev Lett
2007;99:147401.
Papasimakis N, Fedotov VA, Zheludev NI, Prosvirnin SL.
Metamaterial analog of electromagnetically induced
transparency. Phys Rev Lett 2008;101:253903:1–4.
Zhang S, Genov DA, Wang Y, Liu M, Zhang X. Plasmon-induced
transparency in metamaterials. Phys Rev Lett 2008;101:047401.
Liu N, Langguth L, Weiss T, Kästel J, Fleischhauer M, Pfau T,
Giessen H. Plasmonic analogue of electromagnetically
induced transparency at the Drude damping limit. Nat Mater
2009;8:758–62.
Singh R, Al-Naib IAI, Koch M, Zhang W. Sharp Fano resonances
in THz metamaterials. Opt Express 2011;19:6312–9.
Hao F, Sonnefraud Y, Van Dorpe P, Maier SA, Halas NJ,
Nordlander P. Symmetry breaking in plasmonic nanocavities:
subradiant LSPR sensing and a tunable Fano resonance. Nano
Lett 2008;8(11):3983–8.
Verellen N, Sonnefraud Y, Sobhani H, Hao F, Moshchalkov VV,
Van Dorpe P, Nordlander P, Maier SA. Fano resonances in
individual coherent plasmonic nanocavities. Nano Lett
2009;9(4):1663–7.
Bao K, Mirin NA, Nordlander P. Fano resonances in planar silver
nanosphere clusters. Appl Phys A 2010;100: 333–9.
Kurter C, Tassin P, Zhang L, Koschny T, Zhuravel AP,
Ustinov AV, Anlage SM, Soukoulis CM.Classical analogue
of electromagnetically induced transparency with a
metal-superconductor hybrid metamaterial. Phys Rev Lett
2011;107:043901:1–4.
Tassin P, Zhang L, Zhao R, Jain A, Koschny T, Soukoulis CM.
Electromagnetically induced transparency and absorption
in metamaterials: the radiating two-oscillator model and its
experimental confirmation. Phys Rev Lett 2012;109:187401.
Alonso-Gonzalez P, Schnell M, Sarriugarte P, Sobhani H,
Wu C, Arju N, Khanikaev A, Golmar F, Albella P, Arzubiaga L,
Casanova F, Hueso LE, Nordlander P, Shvets G, Hillenbrand R.
Real-space mapping of Fano interference in plasmonic
metamolecules. Nano Lett 2011;11(9):3922–6.
Wu C, Khanikaev AB, Shvets G. Broadband Slow light
metamaterial based on a double-continuum Fano resonance.
Phys Rev Lett 2011;106:107403.
Khanikaev AB, Mousavi SH, Tse W-K, Kargarian M,
MacDonald AH, Shvets G. Photonic topological insulators.
Nat Mater 2013;12:233.
Fano U. Effects of configuration interaction on intensities and
phase shifts. Phys Rev 1961;124:1866.
262
A.B. Khanikaev et al.: Fano-resonant metamaterials
[40] Fan S, Joannopoulos JD. Analysis of guided resonances in
photonic crystal slabs. Phys Rev B 2002;65:235112.
[41] Miroshnichenko AE, Flach S, Kivshar YS. Fano resonances in
nanoscale structures. Rev Mod Phys 2010;82:2257–98.
[42] Luk’yanchuk B, Zheludev NI, Maier SA, Halas NJ, Nordlander P,
Giessen H, Chong CT. The Fano resonance in plasmonic
nanostructures and metamaterials. Nat Mater 2010;9:707–15.
[43] Garcia de Abajo FJ. Optical excitations in electron microscopy.
Rev Mod Phys 2010;82:209–75.
[44] Gallinet B, Martin OJF. Ab initio theory of Fano resonances
in plasmonic nanostructures and metamaterials. Phys Rev B
2011;83:235427.
[45] Gallinet B, Martin OJF. Influence of electromagnetic
interactions on the line shape of plasmonic Fano resonances.
ACS Nano 2011;5:8999–9008.
[46] Gallinet B, Martin OJF. Relation between near–field and
far–field properties of plasmonic Fano resonances. Opt Exp
2011;19:22167.
[47] Giannini V, Francescato Y, Amrania H, Phillips CC, Maier SA.
Fano resonances in nanoscale plasmonic systems: a
parameter-free modeling approach. Nano Lett 2011;11(7):
2835–40.
[48] Wu C, Neuner B, John J, Milder A, Zollars B, Savoy S, Shvets G.
Metamaterial-based integrated plasmonic absorber/emitter for
solar thermo-photovoltaic systems. J Opt 2012;14:024005.
[49] Lahiri B, Khokhar AZ, De La Rue RM, McMeekin SG, Johnson NP.
Asymmetric split ring resonators for optical sensing of organic
materials. Opt Express 2009;17:1107.
[50] Lassiter JB, Sobhani H, Fan JA, Kundu J, Capasso F,
Nordlander P, Halas NJ. Fano resonances in plasmonic
nanoclusters: geometrical and chemical tunability. Nano Lett
2010;10:3184–9.
[51] Liu N, Weiss T, Mesch M, Langguth L, Eigenthaler U,
Hirscher M, Sönnichsen C, Giessen H. Planar metamaterial
analogue of electromagnetically induced transparency for
plasmonic sensing. Nano Lett 2010;10(4):1103–7.
[52] Liu N, Tang ML, Hentschel M, Giessen H, Alivisatos AP.
Nanoantenna-enhanced gas sensing in a single tailored
nanofocus. Nat Mater 2011;10:631–6.
[53] Haus H. Waves and Fields in Optoelectronics. Englewood Cliffs,
NJ: Prentice-Hall, 1984.
[54] Ruan Z, Fan S. Temporal coupled-mode theory for fano
resonance in light scattering by a single obstacle. J Phys Chem
C 2010;114:7324–9.
[55] Fan S, Suh W, Joannopoulos JD. Temporal coupled-mode theory
for the Fano resonance in optical resonator. J Opt Soc Am A
2003;20:569–72.
[56] Fano U. Some theoretical considerations on anomalous
diffraction gratings. Phys Rev 1936;50:573.
[57] Taubert R, Hentschel M, Kästel J, Giessen H. Classical analog
of electromagnetically induced absorption in plasmonics.
Nano Lett 2012;12(3):1367–71.
[58] Enders D, Rupp S, Kuller A, Pucci A. Surface enhanced infrared
absorption on au nanoparticle films deposited on sio2/si for
optical biosensing: detection of the antibody-antigen reaction.
Surf Sci 2006;600:L305–8.
[59] Neubrech F, Pucci A, Cornelius TW, Karim S, García-Etxarri A,
Aizpurua J. Resonant plasmonic and vibrational coupling in
a tailored nanoantenna for infrared detection. Phys Rev Lett
2009;101:157403.
© 2013 Science Wise Publishing &
[60] Tittl A, Mai P, Taubert R, Dregely D, Liu N, Giessen H. Palladiumbased plasmonic perfect absorber in the visible wavelength
range and its application to hydrogen sensing. Nano Lett
2011;11:4366.
[61] Papasimakis N, Luo Z, Shen ZX, De Angelis F, Di Fabrizio E,
Nikolaenko AE, Zheludev NI. Graphene in a photonic
metamaterial. Opt Express 2010;18:8353–9.
[62] Lee SH, Choi M, Kim T-T, Lee S, Liu M, Yin X, Choi HK, Lee SS,
Choi C-G, Choi S-Y, Zhang X, Min B. Switching terahertz waves
with gate-controlled active graphene metamaterials. Nat Mater
2012;11:936–41.
[63] Mousavi SH, Kholmanov I, Alici KB, Purtseladze D, Arju N,
Tatar K, Fozdar DY, Suk JW, Hao Y, Khanikaev AB, Ruoff RS,
Shvets G. Inductive tuning of Fano-resonant metasurfaces
using plasmonic response of graphene in the mid-infrared.
Nano Lett 2013;13(3):1111–7.
[64] Papasimakis N, Fedotov VA, Fu YH, Tsai DP, Zheludev NI.
Coherent and incoherent metamaterials and order-disorder
transitions. Phys Rev B 2009;80:041102.
[65] Zhao Y, Alù A. Manipulating light polarization with
ultrathin plasmonic metasurfaces. Phys Rev B
2011;84:205428:1–6.
[66] Adato R, Yanik AA, Wu C-H, Shvets G, Altug H. Radiative
engineering of plasmon lifetimes in embedded nanoantenna
array. Opt Express 2010;18:4526–37.
[67] Maradudin AA. ed. Structured Surfaces as Optical Metamaterials. Cambridge, UK: Cambridge University Press, 2011.
[68] Wood RW. On a remarkable case of uneven distribution
of light in a diffraction grating spectrum. Philos Mag
1902;4:396–408.
[69] Rayleigh L. On the dynamical theory of gratings. Proc R Soc
London 1907;79:399–416.
[70] Ebbesen TW, Lezec HJ, Ghaemi HF, Thio T, Wolff PA.
Extraordinary optical transmission through sub-wavelength
hole arrays. Nature 1998;391:667–9.
[71] Sarrazin M, Vigneron J-P, Vigoureux J-M. Role of wood
anomalies in optical properties of thin metallic films with
a bidimensional array of subwavelength holes. Phys Rev B
2003;67:085415.
[72] Genet C, vanExter MP, Woerdman JP. Fanotype interpretation of
red shifts and red tails in hole array transmission spectra. Opt
Commun 2003;225:331–6.
[73] Chang S-H, Gray SK, Schatz GC. Surface plasmon
generation and light transmission by isolated nanoholes
and arrays of nanoholes in thin metal films. Opt Express
2005;13:3150–65.
[74] Auguié B, Barnes WL. Collective resonances in gold
nanoparticle arrays. Phys Rev Lett 2008;101:143902.
[75] Garcia de Abajo FJ. Light scattering by particle and hole arrays.
Rev Mod Phys 2007;79:1267–90.
[76] Nikolaenko AE, De Angelis F, Boden SA, Papasimakis N,
Ashburn P, Di Fabrizio E, Zheludev NI. Carbon nanotubes in
a photonic metamaterial. Phys Rev Lett 2010;104:153902.
[77] Wang Q, Tang C, Chen J, Zhan P, Wang Z. Effect of symmetry
breaking on localized and delocalized surface plasmons
in monolayer hexagonal-close-packed metallic truncated
nanoshells. Opt Express 2011;19:23889–900.
[78] Verellen N, VanDorpe P, Vercruysse D, Vandenbosch GAE,
Moshchalkov VV. Dark and bright localized surface plasmons
in nanocrosses. Opt Express 2011;12:11034–51.
© 2013 Science Wise Publishing &
[79] Hao F, Nordlander P, Sonnefraud Y, Van Dorpe P, Maier SA.
Tunability of subradiant dipolar and fano-type plasmon
resonances in metallic ring/disk cavities: implications for
nanoscale optical sensing. ACS Nano 2009;3(3):643–52.
[80] Fu YH, Zhang JB, Yu YF, Luk′yanchuk B. Generating and
manipulating higher order fano resonances in dual-disk ring
plasmonic nanostructures. ACS Nano 2012;6:5130–7.
[81] Bachelier G, Russier-Antoine I, Benichou E, Jonin C, Del Fatti N,
Vallée F, Brevet P-F. Fano profiles induced by near-field
coupling in heterogeneous dimers of gold and silver
nanoparticles. Phys Rev Lett 2008;101:197401.
[82] Yang Z-J, Zhang Z-S, Zhang W, Hao Z-H, Wang Q-Q. Twinned
Fano interferences induced by hybridized plasmons in Au–Ag
nanorod heterodimers. Appl Phys Lett 2010;96:131113.
[83] Brown LV, Sobhani H, Lassiter JB, Nordlander P, Halas
NJ. Heterodimers: plasmonic properties of mismatched
nanoparticle pairs. ACS Nano 2010;4:819.
[84] López-Tejeira F, Paniagua-Domínguez R, ­Rodríguez-Oliveros R,
Sánchez-Gil JA, Fano-like interference of plasmon resonances at
a single rod-shaped nanoantenna. New J Phys 2012;14:023035.
[85] Nordlander P, Oubre C, Prodan E, Li K, Stockman MI.
Plasmon hybridization in nanoparticle dimers. Nano Lett
2004;4:899.
[86] Willingham B, Brandl DW, Nordlander P. Plasmon hybridization
in nanorod dimers. Appl Phys B 2008;93:209–16.
[87] Slaughter LS, Wu YP, Willingham B, Nordlander P, Link S. Effects
of symmetry breaking and conductive contact on the plasmon
coupling in gold nanorod dimers. ACS Nano 2010;4(8):4657–66.
[88] Reed JM, Wang H, Hu W, Zou S. Shape of Fano resonance
line spectra calculated for silver nanorods. Optics Lett
2011;36(22):4386–8.
[89] Shafiei F, Wu C, Wu Y, Khanikaev AB, Putzke P, Singh A, Li X,
Shvets G. Plasmonic nano-protractor based on polarization
spectro-tomography. Nat Photonics 2013;7:367–2.
[90] Mousavi SH, Khanikaev AB, Neuner B 3rd, Fozdar DY,
Corrigan TD, Kolb PW, Drew HD, Phaneuf RJ, Alù A, Shvets G.
Suppression of long-range collective effects in meta-surfaces
formed by plasmonic antenna pairs. Optics Express
2011;19(22):22142–55.
[91] Prodan E, Radloff C, Halas NJ, Nordlander P. A Hybridization
model for the plasmon response of complex nanostructures.
Science 2003;302:419–22.
[92] Urzhumov YA, Shvets G, Fan JA, Capasso F, Brandl D,
Nordlander P. Plasmonic nanoclusters: a path toward negativeindex metafluids. Opt Express 2007;15:14129.
[93] Hentschel M, Saliba M, Vogelgesang R, Giessen H,
Alivisatos AP, Liu N. Transition from isolated to collective
modes in plasmonic oligomers. Nano Lett 2010;10:2721–6.
[94] Fan JA, Wu C, Bao K, Bao J, Bardhan R, Halas NJ, Manoharan VN,
Nordlander P, Shvets G, Capasso F. Self-assembled plasmonic
nanoparticle clusters. Science 2010;328:1135–8.
[95] Fan JA, He Y, Bao K, Wu C, Bao J, Schade NB, Manoharan VN,
Shvets G, Nordlander P, Liu DR, Capasso F. DNA enabled
self-assembly of plasmonic nanoclusters. Nano Lett
2011;11:4859–64.
[96] Hentschel M, Dregely D, Vogelgesang R, Giessen H, Liu N.
Plasmonic oligomers: the role of individual particles in
collective behavior. ACS Nano 2011;5(3):2042–50.
[97] Hentschel M, Schäferling M, Weiss T, Liu N, Giessen H. Threedimmensional chiral oligomers. Nano Lett 2012;12(5):2542–7.
A.B. Khanikaev et al.: Fano-resonant metamaterials
263
[98] Fan JA, Bao K, Wu C, Bao J, Bardhan R, Halas NJ,
Manoharan VN, Shvets G, Nordlander P, Federico C. Fano-like
interference in self-assembled plasmonic quadrumer
clusters. Nano Lett 2010;10:4680–5.
[99] Artar A, Yanik AA, Altug H. Directional double fano resonances
in plasmonic hetero-oligomers. Nano Lett 2011;11:3694–700.
[100] Rahmani M, Lukiyanchuk B, Ng B, Tavakkoli KGA, Liew YF,
Hong MH. Generation of pronounced Fano resonances
and tuning of subwavelength spatial light distribution in
plasmonic pentamers. Opt Express 2011;19(6):4949–56.
[101] Rahmani M, Lei DY, Giannini V, Lukiyanchuk B, Ranjbar M,
Liew TY, Hong M, Maier SA. Subgroup decomposition of
plasmonic resonances in hybrid oligomers: modeling the
resonance lineshape. Nano Lett 2012;12(4):2101–6.
[102] Shafiei F, Monticone F, Le KQ, Liu XX, Hartsfield T, Alù A, Li X.
A subwavelength plasmonic metamolecule exhibiting magneticbased optical Fano resonance. Nat Mater 2013;8:95–9.
[103] Ginn JC, Brener I. Realizing optical magnetism from dielectric
metamaterials. Phys Rev Lett 2012;108:097402.
[104] Neuner B III, Wu C, Eyck GT, Sinclair M, Brener I, Shvets G.
Efficient infrared thermal emitters based on low-albedo
polaritonic meta-surfaces. Appl Phys Lett 2013;102:211111.
[105] Miroshnichenko AE, Kivshar YS. Fano Resonances in
all-dielectric oligomers. Nano Lett 2012;12(12):6459–63.
[106] Hillier J, Baker RF. Microanalysis by means of electrons. J Appl
Phys 1944;15:663–75.
[107] Nelayah J. Kociak M, Stéphan O, García de Abajo FJ, Tencé M,
Henrard L, Taverna D, Pastoriza-Santos I, Liz-Marzán LM,
Colliex C. Mapping surface plasmons on single metallic
nanoparticle. Nat Phys 2007;3:348–53.
[108] Koh AL, Fernandez-Domínguez AI, McComb DW, Maier SA,
Yang JKW. High-resolution mapping of electron-­beamexcited plasmon modes in lithographically defined gold
nanostructures. Nano Lett 2011;11:1323–30.
[109] Schnell M, García-Etxarri A, Huber AJ, Crozier K, Aizpurua J,
Hillenbrand R. Controlling the near-field oscillations of loaded
plasmonic nanoantennas. Nat Photonics 2009;3(5):287–91.
[110] Liu N, Mesch M, Weiss T, Hentschel M, Giessen H. Infrared
perfect absorber and its application as plasmonic sensor.
Nano Lett 2010;10:2342.
[111] Wu C, Neuner B III, ShvetsGY, John J, Milder A, Zollars B,
Savoy S. Large-area wide-angle spectrally selective plasmonic
absorber. Physl Rev B 2011;84:075102.
[112] Tao H, Bingham CM, Strikwerda AC, Pilon D, Shrekenhamer D,
Landy NI, Fan K, Zhang X, Padilla WJ, Averitt RD. Highly
flexible wide angle of incidence terahertz metamaterial
absorber: design, fabrication, and characterization. Phys Rev
B 2008;78:241103 (R).
[113] Diem M, Koschny T, Soukoulis CM. Wide-angle perfect
absorber/thermal emitter in the terahertz regime. Phys Rev B
2009;79:033101.
[114] Hao J, Wang J, Liu X, Padilla WJ, Zhou L, Qiu M. High
performance optical absorber based on a plasmonic
metamaterial. Appl Phys Lett 2010;96:251104.
[115] Liu X, Tyler T, Starr T, Starr AF, Jokerst NM, Padilla WJ.
Taming the blackbody with infrared ­metamaterials
as selective thermal emitters. Physl Rev Lett
2011;107:045901.
[116] Aydin K, Ferry VE, Briggs RM, Atwater HA. Broadband
polarization-independent resonant light absorption
264
[117]
[118]
[119]
[120]
[121]
[122]
[123]
[124]
[125]
[126]
[127]
[128]
[129]
A.B. Khanikaev et al.: Fano-resonant metamaterials
using ultrathin plasmonic super absorbers. Nat Commun
2011;2:517.
Wu C, Avitzour Y, Shvets G. Ultra-thin, wide-angle
perfect absorber for infrared frwequencies. Proc SPIE
2008;7029:70290W.
Cui Y, Xu J, Fung KH, Jin Y, Kumar A, He S, Fang NX. A thin film
broadband absorber based on multi-sized nanoantennas.
Appl Phys Lett 2011;99:253101.
Mason JA, Smith S, Wasserman D. Strong absorption and
selective thermal emission from a midinfrared metamaterial.
Appl Phys Lett 2011;98:241105.
Avitzour Y, Urzhumov YA, Shvets G. Wide-angle infrared
absorber based on a negative-index plasmonic metamaterial.
Phys Rev B 2009;79:045131.
Liu X, Starr T, Starr AF, Padilla WJ. Infrared spatial and
frequency selective metamaterial with near-unity absorbance.
Phys Rev lett 2010;104:207403.
Wu C, Shvets G. Design of metamaterial surfaces with
broadband absorbance. Optics Lett 2012;37:308–10.
Liu N, Liu H, Zhu S, Giessen H. Stereometamaterials. Nat
Photonics 2009;3:157–62.
Zhao Y, Belkin MA, Alù A. Twisted optical metamaterials
for planarized ultrathin broadband circular polarizers. Nat
Commun 2012;3:Article no 870.
Valentine J, Zhang S, Zentgraf T, Ulin-Avila E, Genov DA, Bartal
G, Zhang X. Three-dimensional optical metamaterial with a
negative refractive index. Nature 2008;455:376–9.
Gansel JK, Thiel M, Rill MS, Decker M, Bade K, Saile V,
von Freymann G, Linden S, Wegener M. Gold helix photonic
metamaterial as broadband circular polarizer. Science
2009;325:1513–5.
Krauss TF. Why do we need slow light? Nat Photonics
2008;2:448–50.
Driscoll T, Kim H-T, Chae B-G, Kim B-J, Lee Y-W, Jokerst NM,
Palit S, Smith DR, Di Ventra M, Basov DN. Memory Metamaterials. Science 2003;325:1518.
Samson ZL, MacDonald KF, De Angelis F, Gholipour B,
Knight K, Huang CC, Di Fabrizio E, Hewak DW, Zheludev NI.
Metamaterial electrooptic switch of nanoscale thickness.
Appl Phys Lett 2010;96:143105.
© 2013 Science Wise Publishing &
[130] Zhao Q, Kang L, Du B, Li B, Zhou J, Tang H, Liang X, Zhang B.
Electrically tunable negative permeability metamaterials based
on nematic liquid crystals. Appl Phys Lett 2007;90:011112.
[131] Wang X, Kwon D-H, Werner DH, Khoo I-C, Kildishev AV, Shalaev
VM. Tunable optical negative-index metamaterials employing
anisotropic liquid crystals. Appl Phys Lett 2007;91:143122.
[132] Khatua S, Chang W-S, Swanglap P, Olson J, Link S. Active
modulation of nanorod plasmons. Nano Lett 2011;11(9):
3797–802.
[133] Chen HT, Padilla WJ, Zide JMO, Gossard AC, Taylor AJ,
Averitt RD. Active terahertz metamaterial devices. Nature
2006;444:597–600.
[134] Liu M, Yin X, Ulin-Avila E, Geng B, Zentgraf T, Ju L, Wang F,
Zhang X. A graphene-based broadband optical modulator.
Nature 2011;474:64–7.
[135] Emani NK, Chung T-F, Ni X, Kildishev AV, Chen YP,
Boltasseva A. Electrically tunable damping of plasmonic
resonances with Graphene. Nano Lett 2012;12(10):
5202–6.
[136] Yao Y, Kats MA, Genevet P, Yu N, Song Y, Kong J, Capasso F.
Broad electrical tuning of graphene-loaded plasmonic
antennas. Nano Lett 2013;13(3):1257–1264.
[137] Ou J-Y, Plum E, Zhang J, Zheludev NI. An electromechanically
reconfigurable plasmonic metamaterial operating in the
near-infrared. Nat Nanotechnol 2013;8:252–255.
[138] Cui Y, Zhou J, Tamma VA, Park W. Dynamic tuning and
symmetry lowering of fano resonance in plasmonic
nanostructure. ACS Nano 2012;6:2385–93.
[139] Zhang S, Bao K, Halas NJ, Xu H, Nordlander P. Substrateinduced fano resonances of a plasmonic nanocube: a route
to increased-sensitivity localized surface plasmon resonance
sensors revealed. Nano Lett 2011;11(4):1657–63.
[140] López-Tejeira F, Paniagua-Domínguez R, Sánchez-Gil JA.
High-performance nanosensors based on plasmonic fano-like
interference: probing refractive index with individual nanorice
and nanobelts. ACS Nano 2012;6(10):8989–96.
[141] Yanik AA, Cetin AE, Huang M, Artar A, Mousavic SH,
Khanikaev A, Connord JH, Shvets G, Altug H. Seeing protein
monolayers with naked eye through plasmonic Fano
resonances. Proc Natl Acad Sci USA 2011;108(29):11784–9.