rXXXX American Chemical Society
dx.doi.org/10.1021/nl200197j|Nano Lett. XXXX, XXX, 000–000
Multispectral Plasmon Induced Transparency in Coupled Meta-Atoms
Alp Artar,†Ahmet A. Yanik,†and Hatice Altug*
Electrical and Computer Engineering Department, Boston University, Boston, Massachusetts 02215, United States
S Supporting Information
extreme dispersion, results from quantum interference of multi-
resonances.1Within this spectral window, dramatically slowed
down photons and orders of magnitude enhanced nonlinearities
can enable manipulation of light at few-photon power levels.2
Historically, EIT has been implemented in laser-driven atomic
requirements to preserve the coherence of excitation pathways in
atomic systems have significantly constrained the use of EIT
Recent studies have revealed that EIT-like optical re-
sponses can be obtained classically using on-chip plasmonic
and photonic nanoresonators.4?20Much of the research effort
so far focused on isolated meta-atoms (either photonic or
plasmonic) showing EIT-like effect at a single resonance. On the
other hand, metamaterial systems supporting EIT-like optical
responses at multiple-spectral windows can simultaneously en-
hance multicolored photon?photon interactions and open up
new possibilities in nonlinear optics and optical information
In this Letter, we propose and demonstrate a novel approach
based on coupled meta-atoms to construct a homogeneous and
scalable medium supporting multispectral EIT-like effect
(plasmon induced transparency). The proposed structure con-
sists of a two slot antenna based complementary metamaterial
near-field interaction in between. Each planar metamaterial layer
has bright (radiant) and dark (subradiant) plasmonic modes
coupled through the structural asymmetry (s 6¼ 0) in an analogy
to transition-allowed and -forbidden atomic orbitals coupled
lectromagnetically induced transparency (EIT), a spectrally
narrow optical transmission window accompanied with
short and long-lived
through a common excited state.6As shown in Figure 1b (blue
curve), isolated meta-atoms on a single-layer metamaterial
exhibit an EIT-like reflection10with spectral features that are
controlled by the artificial atomic orbitals (plasmonic modes).
Once stacked in a multilayered structure (Figure 1b, black
curve), presence of strong near-field coupling between the
meta-atoms causes splitting of the EIT resonances and leads
to multispectral EIT-like behavior. The underlying physical
principles for this phenomenon are related to plasmonic
hybridization effects24and dark-bright mode couplings of the
in-phase and out-phase hybridized states. To explain these
novel spectral features, we introduce a perturbative model
we experimentally demonstrate the proposed scheme by
developing a lift-off free fabrication scheme that can simulta-
neously register multiple metamaterial layers in the third
structures. For the double layered metamaterial, a total Hamil-
tonian can be defined as
HT¼~ H0þ~ H0
0þ~ K þ Σ~
Here,~ H0and~ H00are the 2 ? 2 unperturbed Hamiltonians of
the isolated metamaterial layers defined in a basis set consist-
ing of decoupled bright (dipolar) and dark (quadrupole)
modes in the absence of a structural asymmetry (s 6¼ 0).
The weak interactions between the bright and the dark modes
January 18, 2011
March 4, 2011
of a scalable metamaterial media supporting multispectral
plasmon induced transparency. The composite multilayered
media consist of coupled meta-atoms with radiant and sub-
radiant hybridized plasmonic modes interacting through the
structural asymmetry. A perturbative model incorporating
hybridization and mode coupling is introduced to explain the observed novel spectral features. The proposed scheme is
demonstrated experimentally by developing a lift-off-free fabrication scheme that can automatically register multiple metamaterial
layers in the transverse plane. This metamaterial which can simultaneously enhance nonlinear processes at multiple frequency
domains could open up new possibilities in optical information processing.
KEYWORDS: Metamaterials, electromagnetically induced transparency, plasmons, plasmon hybridization, Fano resonances,
dx.doi.org/10.1021/nl200197j |Nano Lett. XXXX, XXX, 000–000
are incorporated with the perturbative Hamiltonian~ K, when a
structural asymmetry is introduced (s 6¼ 0). Interactions
between the two metamaterial layers are included through
the strong near-field coupling Hamiltonian Σ~. Accord-
ingly, the total Hamiltonian for the coupled meta-atoms is
HT¼~ H0þ~ H0
0þ~ K þ~Σ ¼
where |1æ and |2æ represent the top and bottom metamaterial
layers, respectively. The eigenvalues of the bright (|D0æ) and the
dark (|Q0æ) modes of the isolated metamaterials are defined as
layer are denoted with primes, even for structurally symmetric
dark and bright modes in each layer. τinter,Dand τinter,Qare the
strong interlayer coupling terms for the bright and dark modes,
respectively. χ and χ0are the cross couplings among the bright
and dark modes of different layers (interlayer). An important
consideration in our analysis is that χ and χ0, the cross couplings
Validity of this assumption will be justified in the following by
benchmarking our analytical relations with numerical simula-
tions and experimental measurements. For a metamaterial
system where the individual layers have identical structural
characteristics, the Hamiltonian terms for both layers are iden-
tical (κ = κ0, τinter,D/Q= τinter,D0/Q0, ED0/Q0= ED00/Q00). After
a simple rearrangement of the matrix elements and a unitary
transformation, the total Hamiltonian can be rewritten as in
ED0þ ΔD? εD
0EQ0þ ΔQþ εQ
hyb¼^ U½HT?^ U?¼
ED0þ ΔDþ εD
0EQ0þ ΔQ? εQ
in an orthogonal basis set consisting of
p ½jD0æ ( jD00æ?ð3aÞ
p ½jQ0æ ( jQ00æ?ð3bÞ
Figure 1. (a) Geometry of the multilayered metamaterial. Structure
consists of two Au layers (30 nm thickness) that are separated by a
quadrupole slot antenna (all slot antennas have 700 nm length,
100 nm width). The small in-plane separation between the dipolar
and quadrupolar antennas is 50 nm on both sides and periods are
of the dipolar antenna from the geometrical center of the structure.
Blue arrows show the configuration of the incident light. (b) Simu-
lated reflection spectra for asymmetric (s 6¼ 0) single- and double-
layered structures are shown (with an offset for clarity). Multispectral
EIT-like response (in-phase and out-of-phase) is observable with
Figure 2. (a) Hybridization scheme for the dipolar mode. (b) Tuning of
the spectra with the dielectric layer thickness is shown for the symmetric
blue dashed curve. Splitting energies (2εD) are 202, 260, 297 meV and
energy offsets (ΔD) are 60, 68, 78 meV for gap sizes (dielectric layer
charge distribution is acquired from in-phase state |Dþæ of the multilayered
structure; however the out-of-phase state |D?æ and also the single-layered
dipolar state |D0æ have the exact same charge distribution (not shown). (d)
Charge distributions of the hybrid dipolar modes acquired from a multi-
layered structure with a dielectric layer thickness of 50 nm (cross-sectional
view) are shown at a position marked with the red dashed line in (c).
dx.doi.org/10.1021/nl200197j |Nano Lett. XXXX, XXX, 000–000
diagonalizing the Hamiltonian Hs=0
the system is symmetric s = 0) in the strong coupling regime
eigenstate pairs are in-phase (þ) and out-of phase (?) super-
multilayer system (s = 0). The associated energies of the dipolar
hybrid modes are, ED
ΔD= ÆD0|τinter,D|D0æ and the splitting term is εD= ÆD0|τinter,D|D00æ
(a similar set can be obtained for quadrupole modes). Since off
diagonal terms in the transformed Hamiltonian Hhyb
weaker than the diagonal terms, the off-diagonal matrix elements κ
and κ0are treated as the elements of the perturbative Hamiltonian
introduced by the structural asymmetry (s 6¼ 0). Using the trans-
formed Hamiltonian Hhyb
relations can be derived in an analogy to atomistic EIT resonances.
(þ) and out-of phase (?) superpositions of the isolated layer eigen-
modes is shown in Figure 2 for the structurally symmetric multilayer
analysis. For a single-layered metamaterial, only the resonance dip
corresponding to the excitation of the dipolar bright mode is observ-
able in the reflection spectrum (Figure 2(b), dashed blue curve). For
the double layered metamaterial, two resonance dips appear corre-
sponding to in-phase and out-of-phase hybridized modes due to the
mode energies and the splitting in between are controlled by the
strength of the interlayer coupling of the metamaterial layers. As
thicknesses) lead to larger energy splittings as this coupling becomes
cross-sectional charge distributions of the dipolar modes (Figure 2d).
The in-phase hybrid mode is radiant as a result of its overall dipolar
character. The radiant out-of-phase mode is harder to excite with
respect to the in-phase mode, due to the partial cancellation of the
corresponding to the out-of-phase mode is still observable due to the
retardation effects (Figure 2b, solid curves). In Figure 2b, resonances
due to hybridized quadrupolar modes are not observable, since any
structures is also subradiant. Structural symmetry must be broken for
the excitation of these quadrupolar hybridized modes.
Breaking the symmetry of the multilayered structure (s 6¼ 0)
leads to near-field coupling between the dark and bright modes
(κ 6¼ 0) and results in the excitation of the dark modes with the
perpendicularly incident light. Indirect excitation of these hybrid
(Figure 3 black curve). Charge distribution of the out-of-phase
(OP) EIT resonance at the top surface (Figure 3a inset),
indicates strong coupling of the external driving field to this
mode. A similar charge distribution is also observed for the in-
phase (IP) EIT resonance (not shown). Cross sectional charge
distributions of the quadrupolar modes (Figure 3b) confirm the
in-phase and out-of-phase mode characters. Full spectral re-
= ~ H0þ ~ H00þ Σ~(when
(= ED0þ ΔD( εD, where the offset term is
T, a set of coupled Lorentzian oscillator
our perturbative Hamiltonian approach. Here, a coupled Lor-
entzian oscillator model is derived from the transformed Hamil-
in a similar way to the EIT concepts in atomic
physics. In our analysis, the following three observations are
in weak near-field coupling of the hybridized dark and bright
Hamiltonian (s = 0) with the perturbative terms κ and κ0. (ii)
hybrid modes, due to the large energy difference in between (D(
satisfied. Here ω(are the resonant frequencies of the in-phase and
out-of-phase hybrid pairs (ω(= ED
of linear equations is obtained for the coupled Lorentzian oscillators
(/p ≈ EQ
ω ? ωþþ iγþ
ω ? ωþ? δþþ iγþ
ω ? ω?þ iγ?
ω ? ω?? δ?þ iγ?
Figure 3. (a) Asymmetric (s = 150 nm) and symmetric (s = 0 nm)
double-layer EIT-like spectra. Two dips seen in the symmetric structure’s
spectrum corresponds to hybrid dipolar modes as in Figure 2b. Asym-
layered structure (red dashed curve with κ?= 12 THz, κþ= 23 THz),25
which traces the calculated spectra very well. A genetic search algorithm
is implemented to extract the parameters using a least-squares sum fit.
= 16, ng
terms κ(. Inset shows the top view charge distribution at the air/metal
interface for the out-of-phase EIT peak (in-phase EIT peak also shows
the same distribution). Stronger excitation of the quadrupolar mode is
shown. (b) Cross-sectional charge distributions of the quadrupolar
antennas are shown at a position marked with the red dashed line in
the inset. Hybridization of the quadrupolar resonance is shown.
?= 9.3. These values can be optimized by adjusting the coupling
dx.doi.org/10.1021/nl200197j |Nano Lett. XXXX, XXX, 000–000
Here κ(values are the coupling parameters of the perturbative
term for the in-phase and out-of-phase hybrid pairs, which are
determined by the structural offset “s”. δ(values are the small
detuning of the frequencies of in-phase and out-of-phase hybrid
mode pairs (δ(= (ED
modes (D() to the external field. Equation 4 represents two
coupled Lorentzian oscillator pairs corresponding to in-phase
and out-of-phase hybridized modes of the whole structure. The
external field (E0) drives the bright modes in each meta-atom,
which are subsequently coupled to the dark modes (through κ().
With these equations the amplitudes of the dipolar hybrid states
(D() can be derived as
()/p). g(values are the geometrical
?g(~E0ðω? ω(? δ(þ iγ(
ðω ? ω(þiγ(
DÞðω ?ω(? δ(þ iγ(
The complex amplitudes of the corresponding modes (given
in eq 5) are directly proportional to the polarizability of the
modes, which governs the spectral characteristics of the plasmo-
nic structure. The overall spectral response is given by the
this analytical derivation and the FDTD analysis confirms the
validity of our perturbative model as shown in Figure 3a (dashed
curve). The physical principles leading to multispectral EIT-like
behavior can be equivalently observed in other structures. As an
example, we implemented our approach with multilayered dol-
men structures,6and obtained a clear multispectral EIT-like
behavior (see Supporting Information).
Equation 5 is in close analogy to atomic physics, where the
investigated atomic absorption cross section are given with a
EIT phenomena in our composite structure with five-level state
diagram as shown in Figure 4. It is important to note that these
eigenstates are strongly correlated, since they are a linear
combination of the same basis sets (D0,Q0) as shown in the
hybridization diagram in Figure 2a.
Experimental verification of this novel phenomenon is demon-
strated using a lift-off free fabrication method that results in
simultaneous patterning of multilayered slot antennas.26In our
fabricationscheme,westartwitha free-standing membrane,which
etching.27,28Subsequent metal deposition on both sides with a
are automatically registered with respect to each other in the xy-
plane. Similarly, this fabrication scheme can be extended to
fabricate devices with an even larger number of layers.29Cross-
sectional scanning electron microscope (SEM) image of the final
structure shows negligible metal covering at the inner side walls
(inset to Figure 5d). Spectral data collection is done with a Bruker
IFS 66/s Fourier transform infrared (FTIR) spectrometer with a
Hyperion 1000 IR microscope in reflection mode. In measure-
ments obtained from the single-layered structure, a clear EIT-like
spectral response is observed at a single frequency (∼100 THz,
Figure 5c). On the other hand, experimental measurements
obtained from the double-layered structure reveal two EIT peaks
as predicted by the analytical relations (Figure 5d). The length of
the dipolar slot antenna is 700 nm, and its width is 125 nm. The
quadrupolar antenna lengths are 900 nm with a same width of
quadrupolar antenna is 60 nm. The thicknesses of the deposited
between. A structural asymmetry (s) of 135 nm is introduced to
enable the excitation of hybrid quadrupolar modes.
In conclusion, we presented a method to extend the EIT-like
Figure 4. Coupled three-level system model for multispectral plasmon
induced transparency. Coupled meta-atoms havefour states whichform
a five-level system with the continuum.
Figure 5. (a) Illustration of the double-layered structure fabrication on a free-standing membrane. (b) SEM image of an array is shown. Reflection
spectra of the symmetric (s = 0) and asymmetric (s 6¼ 0) for (c) single-layered and (d) double-layered structures are shown. A model fit based on
Lorentzian harmonic oscillators is shown for the double-layered asymmetric structure’s spectrum (red dashed curve with κ?= 9.7 THz, κþ= 27.4
THz).30The dipolar slot antenna length is 700 nm and the quadrupolar antenna lengths are 900 nm, all antenna widths are kept at 125 nm. The gap
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dx.doi.org/10.1021/nl200197j |Nano Lett. XXXX, XXX, 000–000
coupling of meta-atoms in a multilayered metamaterial system. In
particular, two near-field interaction mechanisms make this phe-
nomena possible; (i) hybridization of plasmonic resonances (Σ~)
and(ii) interactionbetweenthebrightanddarkantennas(~ K).The
method is demonstrated experimentally and theoretically with
planar slot antenna based multilayered metamaterial systems. For
experimental demonstration, a lift-off free fabrication scheme that
can simultaneously register multiple metamaterial layers is intro-
duced. The provided analytical investigations are kept general.
Therefore, our method can be easily extended to other antenna
geometries31(see Supporting Information) as well as scaled to a
larger number of metamaterial layers.
ing electric field distributions and enhancements at plasmon
induced reflection peaks and multispectral plasmon induced
transparency with nanoparticles. This material is available free
of charge via the Internet at http://pubs.acs.org.
†These authors contributed equally
This work is supported in part by NSF CAREER Award
(ECCS-0954790), ONR Young Investigator Award, Massachu-
setts Life Science Center New Investigator Award, NSF Engi-
neering Research Center on Smart Lighting (EEC-0812056),
Boston University Photonics Center, and Army Research
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