Giant nonlinearity of carbon nanotubes in a photonic metamaterial

Abstract

Metamaterials, artificial media structured on the subwavelength scale offer a rich paradigm for developing unique photonic functionalities ranging from negative index of refraction and directionally asymmetric transmission to slowing light. Here we demonstrate that a combination of carbon nanotubes with a photonic metamaterial offers a new paradigm for the development of nonlinear media with exceptionally strong ultrafast nonlinear response invaluable in photonic applications. It is underpinned by strong coupling between weakly radiating Fano-type resonant plasmonic modes and the excitonic response of single-walled semiconductor carbon nanotubes. Using a "combinatorial" approach to material discovery we show that the optical response of such a composite system can be tailored and optimized by metamaterial design. Comment: 5 pages, 5 figures

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Giant nonlinearity of carbon nanotubes in a photonic metamaterial
Andrey E. Nikolaenko,1Francesco De Angelis,2Stuart A. Boden,3Nikitas
Papasimakis,1Peter Ashburn,3Enzo Di Fabrizio,2and Nikolay I. Zheludev1
1Optoelectronics Research Centre, University of Southampton, Southampton SO17 1BJ, United Kingdom
2Italian Institute of Technology, 16163 Genova and the University of Magna Graecia, 88100 Catanzaro, Italy
3School of Electronics and Computer Science, University of Southampton, Southampton SO17 1BJ, United Kingdom
(Dated: December 3, 2009)
Metamaterials, artificial media structured on the subwavelength scale offer a rich paradigm for
developing unique photonic functionalities ranging from negative index of refraction and direction-
ally asymmetric transmission to slowing light. Here we demonstrate that a combination of carbon
nanotubes with a photonic metamaterial offers a new paradigm for the development of nonlinear
media with exceptionally strong ultrafast nonlinear response invaluable in photonic applications. It
is underpinned by strong coupling between weakly radiating Fano-type resonant plasmonic modes
and the excitonic response of single-walled semiconductor carbon nanotubes. Using a ”combinato-
rial” approach to material discovery we show that the optical response of such a composite system
can be tailored and optimized by metamaterial design.
Carbon nanotubes (CNTs) are nearly ideal one-
dimensional systems, with diameter of only a few
nanometers and length on the micron scale. Single walled
CNTs rolled from a graphene sheet to create spiral ar-
rangements of atoms along the tube are of particular in-
terest to photonics. Such nanotubes are direct gap semi-
conductors with absorbtion spectra dominated by exci-
ton lines [1]. Their possible technological uses include
nanometre-scale light sources, photodetectors and photo-
voltaic devices. CNTs also possess unique nonlinear opti-
cal properties [2] as they exhibit high third-order suscep-
tibility with sub-picosecond recovery time [3, 4] lending
to applications in ultrafast lasers [5, 6, 7, 8, 9]. CNTs ex-
hibit significant advantages over other materials as non-
linear media: they offer much simpler and cheaper fabri-
cation than conventional semiconductor nonlinear optical
components, they are robust and they can be easily in-
tegrated into optical-fibre and waveguide environments.
The main source of optical nonlinearity in semiconduc-
tor CNTs is the saturation of the resonant exciton line.
Combining CNTs as nonlinearity agents with metamate-
rial structures provides the opportunity to link the plas-
monic resonances of metamaterials with the excitonic res-
onances of nanotubes. In fact, we demonstrate here that
engaging the strong local fields in the vicinity of the meta-
material leads to an enhanced response of the nonlinear
agent. For that matter selecting an appropriate meta-
material structure is crucially important. In our experi-
ments we used a planar structure that belongs to the class
of metamaterials supporting dark mode plasmonic exci-
tations [10]. In such metamaterials weak coupling of the
excitation mode to the free-space radiation modes cre-
ates narrow reflection, transmission and absorption reso-
nances with asymmetric, Fano-like dispersion. The first
example of such a metamaterial was a double-periodic ar-
ray of metallic asymmetrically split ring wire resonators
that has found numerous applications in cases where
sharp spectral features are required [11, 12, 13, 14]. Here
we used a structure complementary to the split ring wire
metamaterial: a double periodic array of asymmetrically
split ring slits in a metal film (see Fig. 1).
The metamaterial structures were fabricated by fo-
cused ion beam milling through a 65 nm thick gold film
evaporated on a 102 nm thick Si3N4membrane. Gold
film roughness of less than 5 nm was obtained with low
pressure (10−8mbar) thermal evaporation. On a sin-
gle membrane we manufactured five metamaterial arrays
with overall sizes 22 × 22 µm2and different unit cell size
D varying from to 731 nm to 839 nm. This allowed us
to follow a combinatorial approach for materials discov-
ery, where a rapid search for the optimal composition is
achieved by parallel screening of a number of different
but structurally related samples [15]. Here the spectral
position of the plasmonic resonance λp depends on the
size of the unit cell. The available range of metamate-
rial structures with different unit cell size D allowed the
study of the linear and nonlinear response for varying
spectral separation of the main excitonic resonance of
CNTs at λ11from the plasmonic resonance of the meta-
material at λp, providing thus control over δpe= λ11−λp.
For wavelengths longer than the unit cell such periodic
nanostructures do not cause diffraction of infrared op-
tical radiation. In the spectral range of the CNT ex-
citonic absorption lines they are true metamaterials as
far as their far-field electromagnetic properties are con-
cerned and may be fully characterized by their absorp-
tion, transmission and reflection. Characteristic spectra
of the metamaterial are presented on Fig. 2a for an array
with D = 731 nm. Fig. 3d shows the dependence of the
peak of the metamaterial plasmon absorption line λpon
the unit cell size.
The Au@Si3N4 metamaterial structures were func-
tionalized with single walled semiconductor carbon nan-
otubes with a characteristic diameter of 1.4 nm. A thin
layer of nanotubes was formed on the metamaterial sur-
arXiv:0912.0680v1 [physics.optics] 3 Dec 2009

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FIG. 1: Carbon Nanotube Metamaterial imaged under a scan-
ning helium ion microscope. The combinatorial sample con-
sists of five different structurally related metamaterial designs
with different unit cell sizes D and an empty area annotated as
”Si3N4 window” on the same substrate (a). The metamate-
rial structure is a two-dimensional nanoscale array of slits in a
gold film supported on a silicon-nitride mebrane (b). Carbon
nanotubes deposited on the surface of the metal nanostruc-
ture form a layer of ”nanoscale feutre” (c). Plates (d) and (e)
show unit cells of the metamaterial before and after deposi-
tion of nanotubes. On plate (e) note the arrow pointing at
a single nanotube crossing the slit. Plate (f) shows a milled
slit manufactured to study the morphology of the structure,
which is presented in plate (g).
face by spraying a sonificated water suspension of nan-
otubes and heating to 1000C resulting in the rapid evap-
oration of the water component. When deposited on a
bare Si3N4membrane, the nanotube layer shows a char-
acteristic absorption spectrum dominated by λ11and λ22
excitonic lines, as presented in Fig. 3b. Figure 1 shows
microscope images of the metamaterial before and af-
ter functionalization with CNTs. The images were taken
with a scanning helium ion microscope. This novel imag-
ing technique [16] is very well suited for imaging car-
bon nanotubes on metamaterials as it benefits from large
depth of field, small interaction volume of ions with the
medium and high contrast of the image ensuring excellent
FIG. 2: Spectral response of the Carbon Nanotube Metama-
terial: Transmission (T), Reflection (R) and Absorption (A)
for a metamaterial array with a D = 731 nm unit cell size (a)
and for the same metamaterial fuctionalized with CNTs (b).
Note the red shift of the plasmon absorption resonance in the
CNT-fuctionalized metamaterial.
surface detail. CNTs seem to form a strongly interlinked
network, a layer of ”nanoscale feutre” where individual
nanotubes are bunched in thicker thread-like structures.
On a few occasions single nanotubes bridging the gaps
of the metal nanostructure are also seen (see Fig. 1e).
We investigated the morphology of the carbon nanotube
metamaterial by observing its cross-section in a trench
cut through the sample by a focused ion beam (Fig. 1f).
For this matter, a section of the sample was covered by
a thin protective layer of tungsten. The layer of carbon
nanotubes had a thickness between 20 nm and 70 nm
across the sample as can be seen on Fig. 1g. It creates
negligible scattering at optical frequencies as it is struc-
tured at a deep sub-wavelength scale.
We observed substantial changes in the metamaterial’s
optical properties resulting from the CNT functionaliza-
tion.All resonance features exhibited an anticipated
”red shift” ∆ = λ∗
sulting from the reduction of the plasmon frequency due
to the presence of the highly polarizable carbon nan-
otubes (compare Fig. 2a and Fig. 2b). After functional-
ization the metamaterial’s reflection decreased, whereas
the spectrum of absorption accrued a background asso-
ciated with the interband and exciton transition in the
p− λp of the plasmon resonance re-

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FIG. 3: Electronic Density of States (DOS) in a semiconduc-
tor single walled carbon nanotube (a); Plasmonic absorption
resonance in a metamaterial without CNTs and excitonic res-
onances in a CNT film on a silicon nitride substrate (b); cal-
culated color coded field map showing the total magnitude of
the electric field of the light wave in the immediate proxim-
ity of the metamaterial plane at the plasmonic resonance λp
(c); and the dependence of the metamaterial absorption res-
onance spectral position on the unit cell size before and after
functionalization with CNTs (d).
nanotubes. Additional losses introduced by the CNTs
damped the metamaterial plasmonic resonance, hence its
quality factor decreased. Hidden in the stronger spectral
features of the metal nanostructure, the λ11excitonic line
is not identifiable on the absorption spectrum of the func-
tionalized metamaterial. The red-shifted positions of the
trapped mode resonance in the metamaterial-CNT sys-
tem are presented in Fig. 3d for different sizes of the unit
cell D.
The nonlinear response of the metamaterial was in-
vestigated with a broadband ultrafast super-continuum
fiber source generating a continuous train of pulses with
a repetition rate of 20 MHz. The source was equipped
with a computer-controllable, tunable, 10 nm bandwidth,
spectral filter. The sample was placed at the focal point
of a dispersion-free reflective parabolic concentrator to
achieve a spot size of about 20 µm in diameter (full
width at half maximum).
super-continuum generation process the pulse duration
was a function of wavelength and within the investigated
spectral interval varied from a few ps to a few hundred
femtoseconds; thus it is instructive to present results of
nonlinearity measurements in terms of fluence of the light
excitation. The measurements (see Fig. 4b) were taken
by increasing fluence from about 3 µJ/cm2to the level
of 40 µJ/cm2corresponding to the average power level
Through the nature of the
on the sample of only about 2.4 mW. The spectra of
the nonlinear response are presented on Fig. 4. Here the
nonlinear response is normalized to the fluence level of
40 µJ/cm2across the entire spectrum. At resonance the
light induced transmitted intensity variation of the car-
bon nanotube metamaterial is about 10 percent. In good
agreement with previous works [8, 9], we detected a much
weaker nonlinear response of CNTs on the unstructured
dielectric substrate (Fig. 4a).
FIG. 4: Light-induced change of transmission of the CNT-
functionalized metamaterial for different unit cell sizes (a).
Light-induced transmission change for different levels of inten-
sity for a CNT-functionalized metamaterial with unit cell size
D = 839 nm (b). The nonlinear response of CNTs on a sili-
con nitride membrane (magnified by a factor of 10) is shown
for comparison on panel (b) and also on panel (a) (without
magnification).
The nonlinear response of the metamaterial has a com-
plex frequency dispersion that could be decomposed on
two main components derived from the analysis of the
response in structures with different unit cell sizes. The
first component that is practically independent of the
unit cell size is relevant to the bleaching of the carbon
nanotube excitonic resonance. Here increase of the light
intensity leads to an increase of transmission. On Fig. 4b
this component of the response is illustrated by a dashed
bell-shaped line with amplitude A1 that is centered at
the CNT’s exciton absorbtion peak at 1950 nm and has a
width of about 310 nm. This bleaching response is super-
imposed to a much sharper ”negative” peak of reduced
transmission. For a metamaterial with D = 839 nm this
peak, indicated as A2, has a width of about 120 nm. We
argue that this ”negative” component is linked to the
reduced damping of the plasmon mode through exciton-
plasmon coupling.Indeed under strong resonant cou-
pling, the lower excitonic damping results in the plas-
mon absorption peak becoming more intense and par-
tially recovering the low transmission levels characteris-
tic of the ”CNT-free” metamaterial. This interpretation
is very well supported by the fact that the negative peak
migrates towards higher frequencies in structures with
a smaller unit cell size, i.e. with the reduction of the
plasmon resonant wavelength. This mechanism will be

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illustrated below using a classical oscillator model.
However, as the nonlinear effect here has a transient
nature, and also involves nonlinear refraction, it takes
the form of dynamic resonance pulling, where the ap-
parent resonance frequency of the ”negative” response is
somewhere in between the excitonic line position and the
plasmonic resonance in the structure. When the plasmon
and exciton resonances nearly coincide, as in the case
presented in Fig. 4b, the ”negative” effect is most pro-
nounced. Here the nonlinear response may be compared
with that of CNTs deposited on a bare Si3N4membrane:
one can see that the CNT’s response on the unstructured
substrate (peak A3) is about 12 times smaller than the
overall ”negative” response of the CNTs on the metama-
terial (peak A2). One can also argue that the positive
response on the CNTs (peak A3) is a factor of 13 smaller
than that of the positive component of the CNT’s re-
sponse in the metamaterial (peak A1) while the overall
negative response (peak A1plus peak A2) is a factor of
25 smaller than that of the CNTs alone. From a slightly
different prospective, the enhanced non-linear response
of the composite metamaterial-carbon nanotube system
is due to the resonant increase of the plasmon fields in the
vicinity of the slits in the metal film through which light
penetrates the metamaterial. This is illustrated in Figs.
3c, where we present the results of full three-dimensional
Maxwell calculations of the electric field magnitude just
above the metamaterial surface. At the plasmon reso-
nance λpthe field just above the split-ring slits is up to
20 times stronger than the electric field of the incident
wave, ensuring a strongly intensity-dependent response.
The main features of the mechanism underlying the
nonlinear optical response of the coupled plasmon-
exciton system in the carbon nanotube metamaterial can
be understood in terms of a simple mechanical model
consisting of coupled Hooke oscillators (mass on elastic
spring) driven by an external harmonic force F (see Fig.
5a) [17]. Here the plasmon resonance is represented by
the harmonic oscillation of two masses, M1and M2, elas-
tically coupled through a third mass, M3. The oscillators
represent excitations in the Π-shaped and straight slit of
the unit cell of the metamaterial and hence have different
masses, while friction Γ stands for the plasmonic losses.
The mass M3linking the two oscillators is also damped
to account for the radiation losses γr. At the plasmonic
dark-mode resonance the larger masses oscillate with op-
posite phases leaving the middle mass still. Hence radia-
tion losses are at minimum (since the mass M3does not
move), all the energy is stored in high-amplitude oscilla-
tions of the large masses M1and M2leading to a sharp
absorption peak associated with friction Γ as seen in the
corresponding dissipation spectrum of Fig. 5b. To ac-
count for the carbon nanotube layer we introduce two ad-
ditional nonlinear oscillators containing masses M4and
M5. They are responsible for the formation of the exci-
ton absorption line (see Fig. 5b). The saturation of the
FIG. 5: (a) Illustrative model of the carbon nanotube meta-
material and the plasmon-exciton nonlinearity. The metama-
terial’s plasmon response is represented by harmonic oscilla-
tors with masses M1 and M2 linked to mass M3. The carbon
nanotube’s excitonic response is represented by the nonlinear
oscillators M4 and M5. Plate (b) separately shows the lin-
ear dissipation losses of the uncoupled plasmon (red line) and
exciton (blue line) systems. Plate (c) shows the dissipation
losses of the linked plasmon-exciton system at different levels
of excitation. Note that the higher excitation level leads to
an increase in the overall losses in spite of bleaching of the
exciton absorption.
excitonic absorption in the carbon nanotubes is intro-
duced assuming that the oscillators are subject to non-
linear dissipation (β). The plasmon-exciton coupling is
represented by elastic springs of constant Kc. The model
reproduces all the essential features observed in the non-
linear response of the carbon nanotube metamaterial:
When measured separately, the plasmon resonance ap-
pears at a frequency slightly higher then the carbon nan-
otube excitonic resonance and is sharper (see Fig. 5b).
For a small amplitude of the driving force F, correspond-
ing to low light intensity, the dark mode resonance ex-
periences strong damping as a result of the plasmon-
exciton coupling. For a high level of excitation, corre-
sponding to high levels of light intensity, the excitonic
absorption saturates and hence the plasmonic peak, now
subject to lower losses, partially recovers, increasing in
amplitude and becoming narrower (see Fig. 5b). This il-
lustrates our experimental observation that in the strong
exciton-plasmon coupling regime (small δpe) the trans-

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mission through a metamaterial sample becomes lower
at higher levels of excitation in spite of bleaching of the
exciton absorption (compare with Fig. 4b).
In summary we have demonstrated that single walled
semiconductor carbon nanotubes can be used as a very
efficient agent of nonlinearity in metallic metamaterial
structures. Exciton-plasmon coupling and strong reso-
nant local fields of the metamaterial create an ultrafast
nonlinear response that is at least an order of magnitude
stronger than that of a bare CNT film. Importantly, the
metamaterial environment allows to spectrally tailor the
nonlinear response and even reverse the sign of optical
nonlinearity. We argue that carbon nanotubes on meta-
materials promise to offer performance that is robust, sta-
ble and free from permanent bleaching. Indeed, the res-
onance nonlinear properties of the suggested composite
metamaterial can be easily tuned throughout the near-IR
(including technologically important wavelengths such as
1.06 µm and 1.55 µm) by employing carbon nanotubes
of different diameter and appropriately scaling the meta-
material. On the other hand, the anisotropic nature of
the metamaterial offers the possibility to realize polar-
ization sensitive nonlinearities, where nonlinear changes
in transmission and reflection can even present different
signs for different polarizations. This makes carbon nan-
otube metamaterials very promising media for various
nanophotonic applications, such as optical limiting and
control of laser emission.
The authors would like to acknowledge the financial
support of the Engineering and Physical Sciences Re-
search Council (U.K.).
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