APPLIED PHYSICS LETTERS 113, 081101 (2018)

Enhanced Raman scattering of graphene using double resonance in silicon
photonic crystal nanocavities
W. Gomulya,1,2 H. Machiya,2,3 K. Kashiwa,4 T. Inoue,4 S. Chiashi,4 S. Maruyama,4,5
and Y. K. Kato1,2,a)1

Quantum Optoelectronics Research Team, RIKEN Center for Advanced Photonics, Saitama 351-0198, Japan
Nanoscale Quantum Photonics Laboratory, RIKEN Cluster for Pioneering Research, Saitama 351-0198,
Japan
3
Department of Electrical Engineering, The University of Tokyo, Tokyo 113-8656, Japan
4
Department of Mechanical Engineering, The University of Tokyo, Tokyo 113-8656, Japan
5
Energy NanoEngineering Laboratory, National Institute of Advanced Industrial Science and Technology(AIST), Ibaraki 305-8564, Japan
2(Received 5 June 2018; accepted 8 August 2018; published online 21 August 2018)
We demonstrate enhancements of Raman scattering from graphene on two-dimensional photonic
crystals using double resonances, which originate from simultaneous enhancements by a localized
guided mode and a cavity mode. By adjusting the photonic crystal cavity parameters, the double
resonance can be tuned to the G0 Raman scattering. Excitation wavelength dependence measurements show a large Raman peak enhancement when the excitation and emission wavelengths meetthe double resonance condition. Furthermore, spatial imaging measurements are performed to confirm that the enhancement is localized at the cavity, and we find that the enhanced Raman intensity
is 60 times larger compared to the on-substrate Raman signal. The observed cavity enhancement ofRaman scattering opens up new possibilities for the development of graphene-based light sources
C 2018 Author(s). All article content, except where otherwise noted, isfor silicon photonics. V
licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/
licenses/by/4.0/). https://doi.org/10.1063/1.5042798

Graphene, a two-dimensional layer of carbon atoms,
exhibits remarkable mechanical, electrical, optical, and thermal properties.1 In particular, graphene shows strong lightmatter interactions and optical non-linearity, making it an
ideal material for optoelectronic devices,2 such as photodetectors,3,4 saturable absorbers,5 and optical switches.6 The use ofgraphene as a light source, however, still remains a challenge
due to its gapless nature. While interband radiative recombination is not expected to be strong, graphene exhibits anotheremission process known as Raman scattering. Remarkably,
Raman scattering associated with the G0 mode at 2700 cm1in monolayer graphene is stronger than graphite.7
Further emission enhancement by coupling graphene toa nanocavity is desirable for a more efficient light source.
Among various cavities, photonic crystal (PhC) cavities holdpromise as a tool for increasing the light-matter interactionsin nanomaterials by strong electric fields confined in a small
mode volume.8 By coupling the emission to the PhC cavities,
enhancement of Raman scattering in carbon nanotubes9 andquantum dots10 has been demonstrated. PhC cavities canalso be evanescently coupled to graphene for integrated photonics.11–15 Cavity-enhanced Raman scattering from graphene has been achieved by coupling to excitation laser.11
Here, we report on doubly resonant Raman scatteringenhancement from monolayer graphene in silicon PhC cavities. The Raman enhancement is obtained by exploiting
simultaneous resonance of excitation and emission,16 corresponding to the coupling to a localized guided mode (LGM)a)

Author to whom correspondence should be addressed: yuichiro.kato@
riken.jp0003-6951/2018/113(8)/081101/5

and a cavity mode, respectively. Using the double resonance,
we are able to enhance the Raman scattering by 60 times
compared to that on the un-etched substrate. Our work highlights the potential for using graphene and other twodimensional materials for monochromatic near-infrared lightsources.
The PhC nanocavities are fabricated from silicon-on-insulator (SOI) wafers.16,17 We define the L3 defect nanocavity byintroducing three linear missing air holes in a hexagonal lattice, and we vary the hole radius r and the lattice constant a totune the LGM and the cavity mode wavelengths.16,18 The
positions of the air holes at the ends of the cavity are displaced
outward by 0.17 a to improve the quality factor Q of the cavity.19 The PhC patterns are drawn by electron beam lithography, and the 200-nm-thick top silicon layer is etched throughby a dry-etching process. The 1-lm-thick buried SiO2 layer isthen removed by 20 wt. % hydrofluoric acid. Figure 1(a)shows a scanning electron microscopy (SEM) image of a typical device. The higher magnification image of the cavity
clearly shows the shifting of the end holes [Fig. 1(a) inset].
We characterize the PhC cavities with a home-built laserscanning confocal microscope. An output of a wavelengthtunable continuous-wave Ti:sapphire laser is focused onto thesample into a spot size of approximately 1 lm by an infraredobjective lens with a numerical aperture of 0.8. The same lenscollects the light emission from the samples, and a pinhole corresponding to a 2.7 lm aperture at the sample imaging plane isplaced at the entrance of a 300 mm spectrometer for confocal
detection. The emission is recorded by a liquid-nitrogen-cooled
InGaAs photodiode array attached to the spectrometer. The
sample is placed on a motorized three-dimensional stage to113, 081101-1

C Author(s) 2018.
V

081101-2

Gomulya et al.

FIG. 1. (a) An SEM image of a typical device. Red, green, and blue dots
indicate the positions at which the PL spectra with corresponding colors in(d) are taken. Inset shows the enlarged view of the cavity. The arrows define
the directions of x- and y-polarization for excitation. The scale bars are
1 lm. (b) A PL excitation map of a typical PhC cavity. The double resonance is at the intersection between the vertical line corresponding to thecavity mode and the horizontal line corresponding to the LGM. (c) A twodimensional PL image of the device in (b) measured with kex ¼ 911 nm. The
PL intensity IPL is integrated within a window of 25 nm centered at1146 nm. The scale bar is 1 lm. (d) Red, green, and blue thick lines indicate
the PL spectra taken at the cavity, patterned area, and un-etched SOI, respectively, excited at kex ¼ 911 nm. The thin red line is a PL spectrum at thecavity excited at kex ¼ 880 nm. Inset shows the excitation polarization
dependence of IPL excited with kex ¼ 911 nm. For (b)–(d), y-polarized laser
with a power of 1 mW is used for excitation.

accurately locate the devices, and all measurements are performed at room temperature in a nitrogen environment to prevent graphene oxidation.
We first determine the wavelengths of the LGM and thecavity mode of the PhCs before graphene deposition. The
cavities are designed to have double resonances close to the
1
G0 Raman condition k1
hxG0 , where kex is the exciex  kem ¼ 
tation wavelength, kem is the emission wavelength, h is the
Planck constant, and xG0 is the G0 mode frequency. Figure1(b) shows the photoluminescence (PL) excitation map of atypical device with r ¼ 85 nm and a ¼ 355 nm. The broad
emission with a peak at kem ¼ 1146 nm is the silicon photoluminescence. The map shows a sharp double resonance originating from the intersection of an LGM at kex ¼ 911 nm andthe 5th mode of the cavity at kem ¼ 1190 nm.
A two-dimensional PL image of the device is measured
at kex ¼ 911 nm with an integration window of 25 nm centered at kem ¼ 1146 nm [Fig. 1(c)], showing strong emission
localized at the ends of the cavity. Since the emission spectral integration window is chosen not to include any cavity
modes, the spatial image reflects the LGM profile. We notethat the spatial profile is strongly dependent on the excitation
wavelength and excitation polarization.16
In Fig. 1(d), the PL spectra from this device are shown.
The thin red line is the PL spectrum on the cavity taken at an
off-resonance excitation wavelength kex ¼ 880 nm. The fullwidth at half-maximum (FWHM) of the 5th mode of the cavity is 3.9 nm which corresponds to a Q-factor of 300. As theexcitation wavelength is increased to 911 nm (thick red line),

Appl. Phys. Lett. 113, 081101 (2018)

the 5th mode peak emission is enhanced by a factor of 7
compared to that excited at kex ¼ 880 nm. When we compare
the PL at the cavity to the un-etched SOI (blue thick curve),
we observe an approximately ninety-fold increase in the cavity peak intensity. This increased intensity results from a
combination of three mechanisms: collection efficiency
improvement by vertically directed emission, the Purcell
effect by the cavity mode, and excitation field enhancementby the LGM. Laser excitation polarization dependence measurements at the double resonance show a high degree of
excitation polarization [Fig. 1(d) inset], where the maximum
emission intensity is obtained near y-polarized excitation,corresponding to the polarization of the LGM.
After characterization of the silicon PhC cavity, we
deposit monolayer graphene flakes on top of the PhC cavities. The monolayer graphene layer is grown on a copper foil
by alcohol catalytic chemical vapor deposition (CVD).20
After the growth, the graphene layer is transferred onto the
PhCs via wet etching method using poly-methylmethacrylate(PMMA) layer as a mediator. The PMMA layer is spincoated on top of the graphene on Cu, followed by baking
at 100  C to solidify the PMMA. Iron trichloride is used toetch the copper foil, and then the graphene attached to the
PMMA is placed on the PhCs and left in air overnight to dry.
The PMMA layer is then dissolved by immersing the sample
in acetone. An additional annealing process at 200  C in airfor 6 h is performed to remove any residue.
The SEM image of the sample partially covered by graphene is displayed in Fig. 2(a), showing high homogeneity of
the graphene flake. The inset shows a magnified image, where
it can be observed that the graphene remains intact near thecavity. To verify the layer number, Raman spectroscopy under
off-resonance excitation at kex ¼ 532 nm is performed at different points on the sample. Typical on-cavity (red line) and

FIG. 2. (a) An SEM image of the devices integrated with CVD-grown graphene. The left side of the image shows devices covered by graphene. Inset
shows a higher magnification image of a PhC device. Scale bars in the main
image and in the inset are 20 lm and 1 lm, respectively. (b) Raman spectraof the monolayer graphene on the cavity (red line) and on the SOI (blueline), taken with 532 nm laser excitation. (c) An excitation spectroscopy
map of the G0 band Raman scattering of graphene for a device witha ¼ 355 nm and r ¼ 85 nm, taken with a laser power of 1 mW and polarization along the y-axis. (d) Raman peak intensity (black) and silicon PL peakintensity (red) obtained by fitting the excitation spectroscopy map in (c).

081101-3

Gomulya et al.

Appl. Phys. Lett. 113, 081101 (2018)

on-SOI (blue line) Raman spectra are shown in Fig. 2(b).
On the cavity, two sharp peaks centered at 1580 cm1 and2670 cm1 corresponding to the G and G0 bands, respectively,
are observed. The ratio of the G0 peak intensity IG0 to G peakintensity IG of 8 for the on-cavity graphene confirms that thegraphene is a single layer.7 The G0 band also shows symmetric
Lorentzian profile with a FWHM of 30.6 cm1, giving anotherevidence for monolayer graphene.21,22 The on-SOI G0 Raman
peak has IG0 =IG ¼ 0:96, and its center wavelength is blueshifted by 7 cm1 compared to the on-cavity Raman peak.
Similar blueshift and weaker G0 intensity have been reported
in the case of Raman scattering of graphene on SiO2/Si substrate to be due to unintentional doping from the interaction of
the graphene with the substrate.23
Figure 2(c) shows the excitation spectroscopy map of thedevice in Fig. 1(b) with graphene on top, where the cavity
mode intensity at 1190 nm has become lower after the graphene deposition. The bright diagonal line on the excitation
spectroscopy map arises from the G0 Raman scattering of thegraphene. The Raman intensity increases when the G0 modeis tuned to the double resonance, and then decreases as theexcitation wavelength is detuned from the double resonance.
To quantitatively calculate the Raman enhancement, we
perform curve fitting of emission spectra for each excitation
wavelength. Because the complex silicon PL spectra cannot
be fitted using a simple function, we use a linear combinationof an empirical spectrum of silicon PL and a Lorentzianpeak
Iem ðkem Þ ¼ ISi Sðkem Þ þ IRaman

ðw=2Þ2ðkem  k0 Þ2 þ ðw=2Þ2

þ I0 ;(1)

where Iem (kem) is the emission spectrum, ISi is the silicon
PL peak intensity, S(kem) is the normalized silicon spectrum,
IRaman is the Raman peak intensity, k0 is the center wavelength of the Raman peak, w is the Raman peak FWHM, andI0 is the offset intensity. In Fig. 2(d), IRaman and ISi are plotted as a function of the excitation wavelength. To quantify
the resonant enhancement, we use the ratio between the onresonance Raman peak and the off-resonance Raman peak at
kex ¼ 960 nm. The calculated ratio for the device shown in
Fig. 2(c) is 5.9. We have performed similar measurements
and analyses on 37 devices with the same design parameters,
and we obtain an average enhancement ratio of 6.1 with a standard deviation of 1.0 and a maximum enhancement ratio of 8.5.
To confirm that the enhancement originates from theRaman emission coupled to the double resonance of the PhC
cavity, we explore the spatial extent of the Raman signal. The
two-dimensional image of the Raman peak measured withkex ¼ 911 nm is displayed in Fig. 3(a), and we observe a spatial profile similar to the silicon PL image before graphene
deposition [Fig. 1(c)]. On this device, the highest Raman
scattering intensity is found at the ends of the cavity. We alsofind that the Raman intensity on the PhC pattern is higher
than the Raman scattering intensity on the un-etched SOI,
which can be explained by the higher collection efficiency ofthe emitted light in the direction normal to the slab planethrough the leaky modes.18,24,25

FIG. 3. (a) A two-dimensional emission image of the device in Fig. 2(c).
The emission intensity IR is integrated over a spectral window centered at
the Raman peak wavelength of 1190 nm with a width of 5.2 nm. The scalebar is 1 lm. (b) Emission spectra of the graphene on PhC taken at the cavity(red), on the pattern (green), and on the un-etched SOI (blue). Inset showsthe excitation polarization dependence of IRaman at the double resonance.
For (a) and (b), y-polarized laser with kex ¼ 911 nm and a power of 1 mW isused for excitation.

Figure 3(b) shows typical emission spectra of the graphene at different positions of the PhC structure with thesame color convention as in Figs. 1(a) and 1(d), where thered curve shows the strongest Raman intensity. Although thecavity emission due to the silicon PL is barely visible for offresonant excitation, we calculate the enhancement conservatively by assuming that the on-cavity emission peak contains
signals from Raman scattering and silicon PL. We estimate
the contribution of the silicon PL from the spectrum taken on
the device before graphene deposition [Fig. 1(d)], and findthat the double-resonance-enhanced cavity peak at 1190 nm
is 40% of the broad silicon peak intensity at 1146 nm. The
on-cavity Raman peak value taken from the red curve in Fig.
3(b) is then corrected by subtracting the estimated silicon
contribution using this fraction. After the correction, we
obtain a value of 4.2 for the enhancement of the Raman scattering by the PhC cavity compared to the Raman signal on
the PhC pattern (green curve). By comparing the on-cavity
Raman signal to that on the un-etched SOI (blue curve), thePhC cavity gives an enhancement by a factor of 60.
Furthermore, we perform polarization dependence measurements [Fig. 3(b) inset], and the Raman peak is found tohave a similar excitation polarization profile as the LGM.
The maximum intensity of the Raman scattering is 3.3 times
the minimum Raman intensity which would correspond to
the Raman intensity without LGM enhancement. This result
is similar to a previous report11 showing absorption enhancement factor of 3.41 for a PhC cavity with a Q-factor of 330.
By investigating a device with a different lattice constant, it is possible to separate the enhancement by the cavity
mode and the LGM. One typical excitation spectroscopy
map for a device with r ¼ 85 nm and a ¼ 370 nm is shown in
Fig. 4(a), where the double resonance shifts to the right sideof the diagonal Raman line. By performing a similar analysis
as before, we obtain fitting results of this device [Fig. 4(b)];the black curve for IRaman and the red curve for ISi. The excitation spectroscopy map and the Raman excitation spectra in
Figs. 4(a) and 4(b) clearly show two peaks at excitation
wavelengths of 930 nm and 937 nm, corresponding to Raman
scattering enhanced by the LGM and the cavity mode,
respectively. Again, using the ratio with respect to the offresonance Raman peak at kex ¼ 960 nm, the Raman enhancement by the LGM is calculated to be 2.7. The enhancement

081101-4

Gomulya et al.

Appl. Phys. Lett. 113, 081101 (2018)

coupling to the cavity double resonance, and we observe an
enhancement of the Raman intensity by a factor of 60 compared to that on the un-etched SOI. By varying the device
lattice constant, we are able to separate and estimate theenhancement contributions from the LGM and the cavity
mode. Furthermore, the enhanced Raman emission wavelength is tunable by varying the hole radius of the PhC. Our
results mark an important step towards the development of
monochromatic near-infrared light sources using grapheneand other two-dimensional materials for integrated silicon
nanophotonics, and may provide a way to study electronphonon interaction in nanomaterials.
See supplementary material for the calculation of cavity
enhancement, and excitation spectroscopy maps and Raman
fitting for devices with different r.
FIG. 4. Excitation spectroscopy maps taken with a laser power of 1 mW andpolarization along the y-axis for (a) a device with a double resonance not
located on the Raman line and (c) a device with a double resonance on the
Raman line with longer wavelength compared to the device in Fig. 2(c). (b)and (d) Excitation wavelength dependence of Raman peak intensity (black)and silicon PL peak intensity (red) of the devices in (a) and (c), respectively.

by the cavity mode is calculated differently due to the spectral overlap with the LGM (supplementary material Fig. S1).
After excluding the enhancement from the LGM, we find anenhancement of 1.3 by the cavity mode.
Finally, we demonstrate wavelength tuning of theRaman enhancement by the double resonance. In contrast tovarying the lattice constant, changing the PhC air hole radius
moves the double resonance nearly along the Raman line.
One typical excitation spectroscopy map for a device withr ¼ 75 nm and a ¼ 355 nm is shown in Fig. 4(c) and its fitting
results are displayed in Fig. 4(d). The double resonance islocated at kex ¼ 924 nm and kem ¼ 1214 nm, redshifted compared to that for the device shown in Figs. 2(c) and 2(d). The
enhancement by double resonance for this device is 2.8
when compared to the Raman peak at kex ¼ 960 nm. Similar
measurements are performed on devices with different r, andwe find that as the hole radius decreases, the double resonance wavelengths become longer and the enhancement
becomes lower (see supplementary material Fig. S2).
To further improve the Raman scattering emission, optimization of the coupling efficiency and the quality factor ofour devices is required. The evanescent field amplitude on
the surface can be controlled through the slab thickness toimprove the coupling efficiency between graphene and thecavity mode.11 The LGM has a lower quality factor which
could potentially be increased by engineering the PhC structure.25,26 Once we obtain a higher enhancement factor, lightemission can be made stronger by improving Raman scattering intensity, which could be achieved, for example, by
surface-enhanced Raman scattering.27
In summary, we have used double resonances in PhC
cavities to enhance the Raman scattering of graphene. We
have designed the PhC nanocavities to have double resonances on the G0 Raman line, and we obtain the maximum
Raman intensity when the laser is tuned to meet the resonant
excitation and emission conditions. Spatial imaging measurements confirm that the enhancement originates from theWork supported by JSPS (KAKENHI JP16K13613 andJP25107002) and MEXT (Photon Frontier Network Program,
Nanotechnology Platform). W.G. is an International Research
Fellow of JSPS [Postdoctoral Fellowship for Research in Japan(Standard)]. H.M. is supported by RIKEN Junior Research
Associate Program. We acknowledge technical support from
Advanced Manufacturing Support Team, RIKEN.
1

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6,
183 (2007).
2
Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband
optoelectronic devices,” ACS Nano 6, 3677 (2012).
3
F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia, and P. Avouris, “Ultrafast
graphene photodetector,” Nat. Nanotechnol. 4, 839 (2009).
4
T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for highspeed optical communications,” Nat. Photonics 4, 297 (2010).
5
Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F.
Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked
ultrafast laser,” ACS Nano 4, 803 (2010).
6
M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and
X. Zhang, “A graphene-based broadband optical modulator,” Nature 474,
64 (2011).
7
A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F.
Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim,“Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97,
187401 (2006).
8
S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1, 449 (2007).
9
H. Sumikura, E. Kuramochi, H. Taniyama, and M. Notomi, “Cavityenhanced Raman scattering of single-walled carbon nanotubes,” Appl.
Phys. Lett. 102, 231110 (2013).
10
T. M. Sweeney, S. G. Carter, A. S. Bracker, M. Kim, C. S. Kim, L. Yang,
P. M. Vora, P. G. Brereton, E. R. Cleveland, and D. Gammon, “Cavitystimulated Raman emission from a single quantum dot spin,” Nat.
Photonics 8, 442 (2014).
11
X. Gan, K. F. Mak, Y. Gao, Y. You, F. Hatami, J. Hone, T. F. Heinz, and
D. Englund, “Strong enhancement of light-matter interaction in graphene
coupled to a photonic crystal nanocavity,” Nano Lett. 12, 5626 (2012).
12
X. Gan, R.-J. Shiue, Y. Gao, K. F. Mak, X. Yao, L. Li, A. Szep, D.
Walker, J. Hone, T. F. Heinz, and D. Englund, “High-contrast electrooptic
modulation of a photonic crystal nanocavity by electrical gating of graphene,” Nano Lett. 13, 691 (2013).
13
A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13, 515 (2013).
14
Z. Shi, L. Gan, T.-H. Xiao, H.-L. Guo, and Z.-Y. Li, “All-optical modulation of a graphene-cladded silicon photonic crystal cavity,” ACS
Photonics 2, 1513 (2015).
15
M.-S. Hwang, H.-R. Kim, K.-H. Kim, K.-Y. Jeong, J.-S. Park, J.-H. Choi,
J.-H. Kang, J. M. Lee, W. I. Park, J.-H. Song, M.-K. Seo, and H.-G. Park,“Switching of photonic crystal lasers by graphene,” Nano Lett. 17, 1892
(2017).

081101-5
16

Gomulya et al.

X. Liu, T. Shimada, R. Miura, S. Iwamoto, Y. Arakawa, and Y. K. Kato,“Localized guided-mode and cavity-mode double resonance in photonic
crystal nanocavities,” Phys. Rev. Appl. 3, 014006 (2015).
17
R. Watahiki, T. Shimada, P. Zhao, S. Chiashi, S. Iwamoto, Y. Arakawa, S.
Maruyama, and Y. K. Kato, “Enhancement of carbon nanotube photoluminescence by photonic crystal nanocavities,” Appl. Phys. Lett. 101, 141124(2012).
18
M. Fujita, Y. Tanaka, and S. Noda, “Light emission from silicon in photonic crystal nanocavity,” IEEE J. Sel. Top. Quantum Electron. 14, 1090
(2008).
19
Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944 (2003).
20
X. Chen, P. Zhao, R. Xiang, S. Kim, J. Cha, S. Chiashi, and S. Maruyama,“Chemical vapor deposition growth of 5 mm hexagonal single-crystal graphene from ethanol,” Carbon 94, 810 (2015).
21
Y. Y. Wang, Z. H. Ni, T. Yu, Z. X. Shen, H. M. Wang, Y. H. Wu, W.
Chen, and A. T. Shen Wee, “Raman studies of monolayer graphene: The
substrate effect,” J. Phys. Chem. C 112, 10637 (2008).

Appl. Phys. Lett. 113, 081101 (2018)22

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L.
Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer
graphene,” Nano Lett. 7, 238 (2007).
23
S. Berciaud, S. Ryu, L. E. Brus, and T. F. Heinz, “Probing the intrinsic
properties of exfoliated graphene: Raman spectroscopy of free-standing
monolayers,” Nano Lett. 9, 346 (2009).
24
M. Fujita, S. Takahashi, Y. Tanaka, T. Asano, and S. Noda, “Simultaneous
inhibition and redistribution of spontaneous light emission in photonic
crystals,” Science 308, 1296 (2005).
25
S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic
crystal slabs,” Phys. Rev. B 65, 235112 (2002).
26
A. Tandaechanurat, S. Iwamoto, M. Nomura, N. Kumagai, and Y.
Arakawa, “Increase of Q-factor in photonic crystal H1-defect nanocavities
after closing of photonic bandgap with optimal slab thickness,” Opt.
Express 16, 448 (2008).
27
F. Schedin, E. Lidorikis, A. Lombardo, V. G. Kravets, A. K. Geim, A. N.
Grigorenko, K. S. Novoselov, and A. C. Ferrari, “Surface-enhanced
Raman spectroscopy of graphene,” ACS Nano 4, 5617 (2010).