# Excitonic Resonances in Coherent Anti-Stokes Raman Scattering from Single
Wall Carbon Nanotubes

Georgy Gordeev<EMAIL_ADDRESS>Freie Universität Berlin, Department of
Physics, Arnimallee 14, 14195 Berlin  Departamento de Física, Universidade
Federal de Minas Gerais, Belo Horizonte, Minas Gerais 30123-970, Brazil
Department of Physics and Materials Science, University of Luxembourg, L-4422
Belvaux, Luxembourg  Lucas Lafeta  Departamento de Física, Universidade
Federal de Minas Gerais, Belo Horizonte, Minas Gerais 30123-970, Brazil
Ludwig-Maximilians-Universität München, Department of Chemistry and Center for
NanoScience (CeNS), Butenandtstraße 5-13 (E), 81377 Munich, Germany  Benjamin
Scott Flavel  Institute of Nanotechnology, Karlsruhe Institute of Technology,
76201 Eggenstein-Leopoldshafen, Germany  Ado Jorio  Departamento de Física,
Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais 30123-970,
Brazil  Leandro M. Malard<EMAIL_ADDRESS>Departamento de Física,
Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais 30123-970,
Brazil

###### Abstract

In this work we investigate the role of exciton resonances in coherent anti-
Stokes Raman scattering (er-CARS) in single walled carbon nanotubes (SWCNTs).
We drive the nanotube system in simultaneous phonon and excitonic resonances,
where we observe a superior enhancement by orders of magnitude exceeding non-
resonant cases. We investigated the resonant effects in five $(n,m)$
chiralities and find that the er-CARS intensity varies drastically between
different nanotube species. The experimental results are compared with a
perturbation theory model. Finally, we show that such giant resonant non-
linear signals enable rapid mapping and local heating of individualized CNTs,
suggesting easy tracking of CNTs for future nanotoxology studies and
therapeutic application in biological tissues.

##  I Introduction

Raman spectroscopy has been extensively used to characterize materials and
biological specimens, however the Raman effect is intrinsically weak due to
the small its scattering cross-sections 1, 2, 3, 4, 5. Such low signals
prevents the application of the technique for rapid imaging of biological
cells, tissues and in-vivo applications 2, 5. On the other hand the use of
non-linear optical effects that are in resonance with vibrational states such
as Coherent Anti-Stokes Raman Spectroscopy and Stimulated Raman Scattering
have been recently used to overcome the weak signals in conventional Raman
Spectroscopy. The application of such techniques in combination with
nanomaterials may open new avenues in tracking and therapy applications 3, 4.
In this sense, single walled carbon nanotubes (SWCNTs) are known to easily
penetrate the living cells due to their unique aspect ratio 6. Here we show
that by simultaneously driving the SWCNTs into resonance with exciton and
phonon states, the CARS intensity in the SWCNTs is increased by orders of
magnitude exceeding non-resonant case. Moreover we studied different nanotube
chiralities and find that the CARS enhancement is sensitive to the energy of
excitonic resonance, which is modelled by a perturbation theory. In order to
explore applicability of CNTs for tracking or future nanotoxicology studies 7
and therapeutic applications 8, we show that by scanning individual tubes
deposited on transparent substrate we can achieve 16 $\mu s$ per pixel imaging
rates; and that the nanotubes can be heated locally by increasing the laser
powers up to 200 °C for therapeutic applications.

Coherent anti-Stokes Raman scattering (CARS) can be interpreted as a four-wave
mixing (FWM) process which is resonant with a phonon. It combines four
photons, two of equal energy (pump) and one lower energy (Stokes) incident in
the sample and the fourth photon emerging out of it. In CARS, the energy
difference between the Pump and Stokes beams are tuned to match a specific
vibrational mode, therefore enhancing the FWM signal by the anti-Stokes
process 1, 2. Furthermore if one of the beams matches real excitonic or
electronic transition, the CARS process becomes electronically (excitonically)
resonant, we refer to as excitonic resonant CARS (er-CARS)9. Such methodology
has been successfully applied to molecules improving significantly the
detection sensitivity of the induced Raman signal 10. Due to quantum
confinement, nanomaterials can have narrow bandwidth excitonic resonances and
thus are promising candidates for resonant er-CARS effects, however such
application has been so far been limited. For example CARS has been used to
probe nanomaterials inside biological specimens but without the use of
resonant effects. In the case of 2D materials, the broad electronic
contribution of graphene leads to the interference between the FWM and CARS
signals, making it hard to use such technique for imaging proposes 11, 12, 4.
On the other hand, the optical properties of semiconducting SWCNTs are
dictated by the excitonic properties only, with single particle contributions
being negligible.

Single walled carbon nanotubes are tubular structures, where one dimensional
confinement yields excitonic states with high energy13 phonons of $\sim 0.19$
eV with large exciton-phonon coupling.14, 15 For instance, this reflects in
high resonance Raman cross sections,16, 17 where single tubes can be
experimentally measured by Raman spectroscopy 18, 19. The linear absorption of
CNTs is dominated by sharp excitonic resonances at room temperature which are
determined by the nanotube chiral indices.20. CARS has been used to study
carbon nanotubes, either using raw soot ensembles of chiralities 21, 22 or
individual tube grew by chemical vapor deposition23, 24. In both cases the
excitonic resonant states were not well defined since the CNT were not single
chirality and therefore the electronic states were overlapped. Recently the
chirality separation techniques became available that can enrich a pure single
chirality 25, 26, 27. Here we show that such samples allow the use of er-CARS
in resonance with excitons in SWNT.

##  II Experimental Methods

The nanotube chirality enriched samples (8,3), (6,4), (7,5) SWCNTs were
prepared using gel permeation method 26 and the (10,3) SWCNTs using gel
chromatography25. The (6,5) SWCNTs were prepared from HiPco raw material
(NanoIntegris) as outlined previously using a gel permeation chromatography
system.26, 27 Due to the high affinity of (6,5) to the Sephacryl-S200 gel
(Amersham Biosciences) and their ability to displace other (n,m) species at
1.6 wt % SDS (Merck), 1 wt % sodium cholate (SC, $\gtrsim$ 99 %, Sigma
Aldrich) was used as an eluent in a one column approach without the use of a
pH gradient. The nanotube suspension was drop cased onto the thin quartz
substrate. The dried samples was put in a water beaker overnight to remove
surfactant residues. For resonant CARS measurements, a picosecond laser (APE
PicoEMERALD) was used. This laser system generated two laser beams that can be
spatially and temporally overlapped with wavelengths at 1064 nm $(E_{S})$ with
7 ps pulse duration and the second tunable between 730 and 960 nm ($E_{p}$)
with 5–6 ps pulse duration. The $E_{p}$ and is generated by pumping the
optical parametric oscillator cavity with the second harmonic of the 1064 nm
laser at 532 nm. The selected $E_{p}$, $E_{S}$, lasers were directed to the
sample by mirrors. The collection and detection parts were separated by a
beam-splitter, afterwards the anti-Stokes signal $E_{a}$ was filtered by a
short-pass filter and focused on a spectrometer slit of the spectrometer
(Andor Shamrock SR-303i-B) equipped with a charge-coupled device (iDus
DU420A-BEX2-DD). The laser powers on the sample were kept below $\sim$0.5 mW
for resonant experiments shown in Figures 2, 3. Only in the measurement shown
in Figure 5 higher laser power was used.

Same detection setup was used for Raman measurements, but for sample
excitation the diode laser at 561 nm was used combined with a long-pass filter
in order to separate Raman from Rayleigh scattering. For simultaneous
measurements with Raman and CARS the visible and IR beams were aligned
together using a beam splitter and focused onto the same spot on a sample.

In order to calibrate er-CARS intensity we need to account for difference in
laser power used and for different CNTs concentration under the laser spot.
The CARS signals are proportional to $P_{tot}=I_{p}^{2}I_{S}$, therefore the
integrated intensity of the CARS was first divided by $P_{tot}$. In order to
determine the concentration of the CNTs under the laser spot we utilize Raman
spectroscopy. When the laser energy matches the transition energy, the G mode
Raman intensity of one individual CNT is predicted to weakly depend on
chirality and diameter, due to similarity in matrix elements.15 We account for
different resonance energies between (n,m) by introducing an intensity factor
$f_{Ram}$. $f_{Ram}$ depends on energy difference between $E_{22}$ and
$E_{las}$. For the G mode this dependence is chirality specific, but is known
from previous experiments for all the species accept for the (10,3) SWCNTs,
where we approximate it to the (8,3) SWCNTs.28, 29 The CNTs concentration $C$
is then $I_{Ram}f_{Ram}$. Finally, the Raman intensity scales with $\sim C$,
but CARS intenisty is proportional to the $C^{2}$. In order to show resonant
effects we than calibrate $I_{CARS}$ as $I_{CARS}^{measured}/P_{tot}/C^{2}$,
accounting for laser powers and different concentrations. The error bars in
Figure 4 were computed using standard error propagation methods and is mainly
due to uncertainty in the estimation of the $E_{22}$ transition energy
influencing the resonant factor of Raman scattering.

For the CARS intensity image, we have redirected the $(E_{S})$ and $E_{p}$
pulses to a scanning laser microscope (LaVision Biotec). The scanning mirrors
allow the beams to map the sample when focused by the 60× apochromatic air
objective (numerical aperture of 0.95) in the scanning laser microscope. The
backscattered CARS signal is then directed to the photomultiplier. A short
pass filter eliminates laser contamination. The average scan contained
$10^{6}$ pixels and was completed within 16s.

##  III Results

Figure 1:  The concept of the er-CARS scattering in SWCNTs. (a) Exciton
dispersion for different (n,m) SWNT probed in this study, along with fixed
energies of pump ($E_{p}$), Stokes ($E_{S}$), and anti-Stokes beams ($E_{a}$).
(b) Scheme of of one er-CARS scattering pathway in an excitonic system. (c)
Feynman diagram representing sixth-order process, straight (curly) arrows
indicate an interaction with a photon (phonon), see discussion in text for
possible permutations.

Four-wave mixing comprises interaction of four photons energies, the incident
three photons can excite or deexcite the system yielding an emission of the
fourth one. We use the first and third photons of the same energy $E_{p}$,
Pump beam. The second photon has a smaller energy $E_{S}$, Stokes beam. The
energy of the fourth, anti-Stokes photon is pre-determined by the first three
and yields $E_{a}=2E_{p}-E_{S}$ 1. The energy of the Stokes beam is kept
constant $E_{S}=$1.165 eV whereas the energy of the pump beam is tunable. A
single vibration of the system can be resonantly excited by matching the
energy $E_{p}-E_{S}$ with phonon energy $E_{ph}$ 2. Intuitively one would
expect a more efficient CARS process whenever the $E_{i},(i=p,S,a)$ meets
excitonic resonance of the nanotube (er-CARS). The photon energies for
$E_{p}$, $E_{S}$ and $E_{a}$ are compared with the exciton energies used in
Figure 1a, where it is possible to observe different resonances. We therefore
need a model to describe the influence of resonant states explicitly 1.

Historically, four-wave mixing was mostly studied in zero dimensional systems,
such as molecules. In such systems the excitonic and vibrational states are
equal in treatment, and a density matrix approach is typically used to
describe non-linear interactions with light.30 However, in solid state systems
the excitonic and phonon states are independent quasi-particles and this
approach is not as applicable31. Instead, the interaction between phonons
states and electronic excitation occurs via electron-phonon Hamiltonian, where
the electron (exciton) can be scattered to a new state either by creating or
emitting a phonon. In a similar fashion, excitons can be scattered to new
states by photon absorption or emission through the exciton-photon
interaction. To understand the interplay between different matrix elements we
turn to the perturbation theory, widely used to describe resonant Raman
processes.31

Figure 1b depicts one possible CARS scattering process, where the energy
difference between Pump and Stokes equals an optical phonon energy. The same
process is shown in Figure 1c in form of a Feynman diagram. Each vertex of the
Feynman diagram represents an interaction with either photon or phonon and the
vertices are ordered in time. An arrow pointing to the system represent energy
increase, whereas an arrow pointing away from the system represents an energy
decrease. The phonon creation and eliminations occur at the vertices two and
five, respectively. By walking through the steps first (i) we see that the
system is excited by the $E_{p}$. Later on (ii) the interaction with a
negative component of $E_{S}$ electric filed deexcites the system towards the
ground state and (iii) the phonon is created $E_{ph}$. Next the third photon
$E_{p}$ excites the system into higher state (iv) and after it, the phonon
that was created before is destroyed (v). Finally, fourth wave photon emerges
out of the system (vi), bringing system back to the ground state, which
satisfies energy conservation principle, build in into the perturbation
theory.

Quantum interference between many scattering processes determines the total
er-CARS signal enhancement. Overall, there are 43 pathways that can be
obtained by changing order of the scattering events. To select them from full
permutation group consisting of 6!/2! members we use one physical constrain.
At any step of the process the total system energy is not allowed to drop
below the energy of the ground state. We impose the phonon emission and
scattering to be equally probable, since a large amount of photons are
incident on the sample during a pico-second laser pulse. Each of the 43
process contributes to the er-CARS intensity at the same time with equal
probability yielding an interference effect:

$\begin{split}I_{rCARS}=\left[\sum_{k}^{43}{I_{k}}\right]^{2},\end{split}$ (1)

where $I_{k}$ is the contribution of a $k$-th scattering pathway. The square
is taken after summation allowing the processes to interfere. The $I_{k}$ can
be expressed as:

$\begin{split}I_{k}(E_{11}[n,m])=\frac{M_{ex-q}^{2}(M_{ex-
ph})^{4}}{\prod_{l=1}^{5}(E_{11}[n,m]+\sum_{i}^{l}{\pm\hbar\omega_{i}}-I\gamma_{11})}.\end{split}$
(2)

The $M_{ex-ph}$ is exciton-photon and $M_{ex-q}$ is exciton-phonon matrix
elements, $\hbar\omega_{i}$ is the energy interacting at the i-th vertex,
either photon($E_{p},E_{S},E_{a}$) or phonon $E_{ph}$. $\gamma_{11}$ is the
broadening factors related to the excitonic lifetime. The sign of the
$\hbar\omega_{i}$ is determined by the direction of the arrow, either pointing
away or towards the system in a Feynman diagram, see example in Figure 1c. For
one possible process these energies are depicted in Figure 1b, c. From Eq. (1)
we expect that resonant enhancement of the CARS process, when either one of
three involved photons is close to the energy of the exciton. We can verify
this experimentally by using different nanotube chiralities (n,m), which would
enter Eq. (2) as $E_{11}[n,m]$. While (n,m) chiralities with $E_{11}$ exactly
matching $E_{p}$ will provide high enhancement, the most interesting
interference effects happen in between $E_{S}$ and $E_{a}$. We therefore focus
on (n,m) chiralities in this range.

Vibrational enhancement is superior for the longitudinal phonon, compared to
the transverse one. We investigate the effect of vibrational enhancement in
(6,5) nanotube. Figure 2a shows the FWM signal for the (6,5) SWNT for several
pump energies ($E_{p}$) spanning across vibrational resonance and for a fixed
Stokes energy ($E_{S}=1.164$ eV). When the pump energy approaches 1.362 eV
($E_{p}-E_{S}=$ 0.197 eV), which matches well the LO phonon energy of the
SWNT, the FWM intensity has a gigantic 2000 times enhancement. Such resonance
with the LO phonon is shown in Fig. 2b where the the integrated area of the
FWM signal is plotted with respect to $E_{p}-E_{S}$ (or $E_{a}-E_{p}$). The
enhancement reported here much larger than a previously reported 2x on-off
resonance contrast to Kim et al..24. We attribute this to the excitonic
resonance effect, discussed in the following paragraphs. We observe a smaller
enhancement for the TO phonon with $E_{TO}$ close to 0.189 eV (see Fig. 2b).
The resonant CARS with the LO phonon is $\sim$25 times higher than and with TO
phonon. On the other hand, in Raman scattering experiments the LO phonon is
only 5 times more intense than the TO phonon, see Fig. 2c. Such difference in
the LO/TO intensity ratio is well captured by our perturbation theory. Stokes
Raman scattering is proportional to $(M_{ex-q})$, since the phonon is emitted
only once. On the other hand CARS scales as $(M_{ex-q})^{2}$, because the
exciton-phonon interaction occurs twice when phonon is created and eliminated,
therefore the observed difference for the LO/TO enhancement factor fits well
with this theoretical interpretation.

Figure 2: Four-wave mixing (FWM) in the (6,5) CNT across high energy phonon
resonances (G modes). (a) Waterfall plot of the experimental FWM spectra, the
$x$ axis shows difference between anti-Stokes and Pump energies, $y$ axis
represents the pump energy $E_{p}$. (b) Integrated area of the $E_{a}$ signal
vs phonon energy. (c) Raman scattering intensity comparison between the LO and
TO resonances.

The phonon linewidth is slightly different between Raman and four wave mixing.
We measure the FWM signal close to the G mode resonances in different nanotube
chiralities, with the $E_{11}$ energy spanning between 1.1 eV in (10,3) SWCNTs
and 1.42 eV in $(6,4)$ CNTs, as shown in Figure 2a. In all the SWCNT
chiralities measured, the highest FWM signal was found for resonance with the
LO phonon, see red vertical line Figure 3a. The line-shape of the FWM profiles
is mainly determined by the lifetime of the phonon as $\sim\hbar/\tau_{ph}$. A
similar lifetime can be observed in the Raman spectra for the same SWNT as
shown in Figure 3b, where the widths of the Raman G band are compared.
Overall, the FWM profiles have higher full widths at half maximum (fwhm) than
measured by Raman spectroscopy, except for the (7,5) SWCNTs, where the full
width are almost identical with a values of 1.6 meV. The difference in
linewidths can be explained by higher electronic temperature generated in the
case of pulsed laser excitation as shown by previous works on graphene 32. In
such case the CARS linewidth are broader compared to Raman spectroscopy,11,
32, 12 where the excitation laser does not create a hot electron temperatures.

Figure 3:  Four-wave mixing in different (n,m) CNTs in resonance with the LO
phonon. (a) FWM profiles in different chiralities, solid lines are Lorentz
fits and their full width at half maxima is given by the numbers near the
plot. The Stokes and Pump intensities were 60, 150, 100, 590 $\mu W$, from top
to bottom, $E_{S}=1.165$ eV , $E_{p}=1.35-1.37$ eV. (b) Raman spectra taken at
the same spot, with laser energy of 2.2 eV.

The CARS intensity strongly varies between different chiralities due to
different resonance conditions. Figure 4 shows the dependence of the
enhancement at the LO phonon energy as function of nanotube exciton energy
$E_{11}$. The CARS intensity is normalized on laser powers $P_{p}^{2}P_{S}$
and calibrated by the nanotubes concentration, see Methods. The highest
signals was provided by the (7,5), (6,5) and (8,3) SWCNTs, with $E_{11}$
located between $E_{S}$ and $E_{p}$. We did not find any non-linear signal
from (6,4) SWCNTs, despite Raman showing clear signatures of the SWCNT in the
measured spot. The $E_{11}$ of (6,4) is on the high energy shoulder and lies
between $E_{p}$ and $E_{a}$. From Figure 4 we can see that experimental er-
CARS intensity is not symmetrically distributed between between Stokes, anti-
Stokes and Pump energies.

Figure 4: er-CARS intensities for different $(n,m)$. The energies of $E_{p}$,
$E_{S}$, and $E_{a}$ are fixed whereas the $E_{11}$ energy is varied. Symbols
represent experimental data, integrated area of the FWM peak normalized on
power and nanotube concentration obtained through Raman spectroscopy. The line
represents theoretical calculation by Eq. (1) with $\gamma_{11}=$ 40 meV,
$E_{S}=$1.165 eV, $E_{p}=$1.36 eV, and $E_{ph}=$0.196 eV.

Sixth-order perturbation theory yield asymmetric lineshape, similar to
experimental results. The calculated $I_{FWM}$ is plotted by lines as a
function of $E_{11}$ in Figure 4. The calculation is performed using Eqs. (1)
and (2) with constant matrix element approximation and damping factors set to
$\gamma_{11}=$ 40 meV, typical for the $E_{11}$ excitonic transition 33. The
values for the lasers energies are $E_{S}=$1.165 eV, $E_{p}=$1.36 eV, and for
the phonon is $E_{ph}=$0.196 eV are shown by vertical lines. Figure 4 shows
that the er-CARS intensity is enhanced when the $E_{11}$ transition energies
matches either the Stokes, pump or anti-Stokes beam energies. However the
distribution of intensities between these peaks is asymmetric due to the
interference effect. At lower energies between $E_{S}$ and $E_{p}$ the
interference is positive, whereas at higher energies between $E_{p}$ and
$E_{a}$ the interference is negative and almost no er-CARS enhancement is
expected. This reproduces well the experimental observations.

Figure 5: er-CARS microscopy and local heating of the (6,5) SWCNTs. (a)
Lateral spatial maps of the er-CARS signal with zero delay, collected within
16 s ($E_{S}=$1.165 eV, $E_{p}=$1.36 eV). (b) Same image as (a), but scanned
with 20 ps delay. (c) Monitoring local temperature by higher irradiation
powers in the (6,5) SWNCTs, the Raman excited with 2.2 eV laser. Inset shows
Position of the LO phonon as a function of total laser power $E_{p}+E_{S}$ ,
right scale extracted local temperature using -0.023 cm-1/K coefficient. 34

We use (6,5) nanotube to perform er-CARS microscopy, since most enriching
techniques target that species and shows positive er-CARS interference
effects. Figure 5a shows an er-CARS image at the phonon resonance with
200$\times$200 $\mu m$ in size of (6,5) SWCNTs dropcasted onto a quartz
substrate. The bright spots correspond to the individual (6,5) SWCNTs or small
bundles. The scan is performed within 16 s. In total 106 pixels were
collected, resulting in average speed of 16 $\mu s$ per pixel, where that
speed is mostly limited by the galvanometric mirrors. We confirm that the
bright spots originate from er-CARS process we scanned the same image with a
20 ps delay between the $E_{S}$ and $E_{p}$ pulses, $\sim$ 10 times
$\tau_{ph}$. As shown in Figure 5b, the bright spots disappear validating the
er-CARS nature of the observed signal. We further tested the 3D imaging option
by tuning the focus outside of the quartz surface, see Supplementary Video 1.
Out of focus the bright spots clearly loose the intensity and convert to
circular shapes, enabling z resolution. Our results show that er-CARS process
enables quick and precise localization of SWCNTs in 2D and 3D, enabling its
use for imaging CNT in vivo studies, where Raman or photoluminescence signals
from individual species are still fairly weak.

The CNTs can be used for the simultaneous er-CARS imaging and local heating
the CNT for targeted destruction of viruses and cancer cells.35 Most
biological tissues have transparency window in the IR region where the
$E_{11}$ transition energies of small-diameter CNTs are found, therefore the
heat wave can be localized near the CNT position. Now the temperature control
methods rely mostly on mathematical models.36, 35 In our setup we can directly
probe and control local temperature, using Raman signal of CNT as a
thermometer. We measured the Raman spectrum of a small CNT bundle with during
simultaneous irradiation with pulsed $E_{p}$ and $E_{S}$ beams of varying
powers. The Raman spectra are shown in Figure 5c from weak (black) to strong
(red) irradiation powers (the measured laser power is the sum of both pump and
Stokes beams). Notably, no defects were introduced to the sample, as the D
mode doesn’t grow in intensity37. Further, we observe that the LO phonon
broadens and shifts to smaller energies. We plot the LO phonon position as a
function of total power $P_{S}+P_{p}$ in the inset of Figure 5c. The Raman
shift is converted to temperature by a -0.023 cm-1/K coefficient 34. We can
easily achieve temperatures close to 200 °C, when even 80 °C will denaturate
the proteins in the living cells38. This means that CNT-based er-CARS
microscopy is suitable for tracking, local heating, and disruption of the
cancer cells.

##  IV Conclusions

We demonstrated that phonon and excitonic resonances can enhance four-wave
mixing signals by few orders of magnitude in SWCNTs giving rise to er-CARS
process. We investigated the resonant signals in five different CNT
chiralities. The intensity varied drastically and depends upon then relative
energy between pump and Stokes beams with respect to the first excitonic
transition. We developed a theory based on quantum interference between 43
scattering pathways, which delivered a qualitative agreement with experimental
results. Further we tested applicability of resonant wave mixing and imaged
individual (6,5) CNTs over 200x200 $\mu m^{2}$ quartz substrate in a time of
16 s. The time was only limited by the speed of our galvanometric mirrors and
even quicker scans can be achieved in the future. As a possible application
the simultaneous er-CARS imaging with local heating with lasers used in CARS
could be used for targeting and cell disruption in the future. Our work
demonstrates that the single walled carbon nanotubes are highly interesting
materials in terms of the resonant non-linear light-matter interaction with
potential applications in tracking and nanotoxicology.

##  V Acknowledgments

###### Acknowledgements.

G.G. gratefully acknowledges the German Research Foundation (DFG via SFB 658,
subproject A6). Dahlem research school (FU bright fellowship) and Focus Area
NanoScale of Freie Universitaet Berlin. L.L. gratefully acknowledges the
Alexander von Humboldt Foundation for the financial support. B.F. acknowledges
DFG grants FL 834/5-1, FL 834/7-1, FL 834/9-1 and FL 834/12-1. L.L, A.J. and
L.M.M acknowledges financial support from CNPq, CAPES, FAPEMIG, FINEP,
Brazilian Institute of Science and Technology (INCT) in Carbon Nanomaterials
and Rede Mineira de Materiais 2D (FAPEMIG). L.M.M. also acknowledges the CAPES
and Humboldt fellowship. All authors are thankful for fruitful discussions
with Prof. Riichiro Saito and Prof. Stephanie Reich.

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