ARTICLE
Received 9 May 2014 | Accepted 16 Oct 2014 | Published 25 Nov 2014

DOI: 10.1038/ncomms6580

OPEN

Ultralow mode-volume photonic crystal nanobeam
cavities for high-efﬁciency coupling to individualcarbon nanotube emitters
R. Miura1, S. Imamura1, R. Ohta2, A. Ishii1, X. Liu1, T. Shimada1, S. Iwamoto2, Y. Arakawa2 & Y.K. Kato1

The unique emission properties of single-walled carbon nanotubes are attractive for achieving
increased functionality in integrated photonics. In addition to being room-temperaturetelecom-band emitters that can be directly grown on silicon, they are ideal for coupling tonanoscale photonic structures. Here we report on high-efﬁciency coupling of individual
air-suspended carbon nanotubes to silicon photonic crystal nanobeam cavities. Photoluminescence images of dielectric- and air-mode cavities reﬂect their distinctly differentmode proﬁles and show that ﬁelds in the air are important for coupling. We ﬁnd that the
air-mode cavities couple more efﬁciently, and estimated spontaneous emission coupling
factors reach a value as high as 0.85. Our results demonstrate advantages of ultralow
mode-volumes in air-mode cavities for coupling to low-dimensional nanoscale emitters.

1 Institute of Engineering Innovation, The University of Tokyo, Tokyo 113-8656, Japan. 2 Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505,
Japan. Correspondence and requests for materials should be addressed to Y.K.K. (email: ykato@sogo.t.u-tokyo.ac.jp).

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Results
Coupling individual nanotubes to nanobeam cavities. In
Fig. 1a,b, electron microscope images of typical devices areshown. We have performed ﬁnite-difference time-domain(FDTD) calculations for these cavity structures to map out the
proﬁles of the fundamental modes. Since nanotubes will be laying
at the top surface of the nanobeam, we plot the mode proﬁles atthat height in Fig. 1c,d. As expected, the dielectric-mode cavity
has high ﬁeld amplitudes within the Si material, with evanescentﬁelds extending out the edges. For the air-mode cavity, the ﬁelds
are mostly distributed within the air holes, with some evanescentﬁelds as in the case of the dielectric-mode cavity. The intense

ﬁelds in the air holes should be an advantage compared withcavities that conﬁne most of the optical ﬁelds in the high-index
medium21–23, because nanotube photoluminescence (PL) is
quenched when they are in contact with the substrate14,24. We
note that both the cavity modes are transverse electric modes, andtherefore the polarisation matches with the emission of nanotubes
that are perpendicular to the nanobeams.
To couple individual CNTs to nanobeam cavities, we havefabricated devices shown as a schematic in Fig. 2a. Catalyst
particles are placed across a trench from the cavity, and we
perform chemical vapour deposition to grow CNTs onto thecavities22. An electron micrograph of a device after nanotube
growth is shown in Fig. 2b.
In Fig. 2c, we present a PL spectrum from one such devices
taken with an excitation power P ¼ 1 mW and an excitation
wavelength lex ¼ 797 nm. On top of the broad direct emission
from the nanotube, there is a very sharp peak, which is the cavity
mode, indicating that the nanotube emission is optically coupled
to the cavity. To further characterise the device, PL excitation
spectroscopy is performed (Fig. 2d). We observe a single peak in
the PL excitation map, demonstrating that this is an isolated
single nanotube. Using tabulated data25, the chirality isdetermined to be (9,8). The intensity of the sharp cavity mode
is maximised at the same wavelength as the E22 resonance of thistube, showing that the absorption originates from the nanotube
and that the cavity mode is excited by the nanotube emission.
Comparison of dielectric- and air-mode cavities. On thosedevices coupled with single CNTs, we have performed confocal
PL imaging to locate the nanotube positions. Figure 3a,b show
images from typical dielectric- and air-mode devices, respectively.
By determining the positions of the highest PL intensity fromimages of 430 devices, the spatial displacements of the nanotubes with respect to the centre of the cavities have been mappedout (Fig. 3c,d). It is possible to identify qualitative differencesin the spatial distribution of nanotubes between the two typesof cavities. For the dielectric-mode cavities, the emission spot ofnanotubes is mostly located at the edges of the nanobeam or

Si
SiO 2

CNT

Catalyst

150
PL (counts s−1)Single-walled carbon nanotubes (CNTs) are known to
exhibit unique optical phenomena such as multiple
electron-hole pair generation1 and dimensionality effects
on excitons2, while their emission properties allow access to spin3
and quantum4 degrees of freedom. To utilise such exceptional
characteristics in monolithic optical circuits, efﬁcient coupling tophotonic structures is essential. In this regard, planar cavities5–8
are not ideal as the coupling would be distributed over acontinuum of modes.
Nanocavities with small mode-volumes would provide better
coupling, and in particular, photonic crystal nanobeam cavities
offer ﬂexible control over the cavity ﬁelds. In a nanobeam cavity,
a periodic array of air holes is etched into a waveguide to form aphotonic bandgap, which acts as a Bragg reﬂector. The bands
below the gap are called dielectric bands because the ﬁeld
amplitudes are maximised within the dielectric material, while thebands above the gap are known as air bands since they have large
ﬁelds in the air holes. The dielectric band modes can be conﬁned
by locally reducing the lattice constant a, as the energy of themodes will become higher and the photons will be surrounded by
the photonic band gap9,10. Similarly, air-band modes can be
conﬁned by introducing a larger lattice constant region11,12.
Here we demonstrate spontaneous emission coupling efﬁciency
exceeding 85% for a single CNT coupled to a silicon photonic
crystal nanobeam cavity with an ultralow mode-volume. We takeadvantage of the excellent optical properties of as-grown airsuspended CNTs13–16, and integrate them with specially designed
cavities with large ﬁelds in the air, distinctly different from thestandard dielectric-mode cavities10,17–20. Our approach is also
applicable to other low-dimensional materials, opening up apathway for efﬁcient use of nanoscale emitters in integrated
photonics for both classical and quantum applications.

100

Data
CNT
CavityP = 1 μW
ex= 797 nm

50

0
1,355

1,370

1,385

Emission wavelength (nm)1

Ey (a.u.)yzxz = 130 nm

Figure 1 | Photonic crystal nanobeam cavities. (a,b) Scanning electron
micrographs of dielectric- and air-mode cavities, respectively. (c,d) Proﬁlesof normalised y-component of electric ﬁelds Ey at z ¼ 130 nm. The origin of
the coordinate system is the centre of the cavity. For c, a dielectric-mode
cavity with a ¼ 390 nm, cavity-centre period of 0.84a, and 200 nm by
530 nm holes is used for the calculation. For d, an air-mode cavity witha ¼ 430 nm, cavity-centre period of 1.16a, and 220 nm by 510 nm holes isused. All panels share the 2-mm scale bar as in a.
2

850
800
750

2
(9,8)

1

P = 10 μW

1,100

1,300
1,200
1,400
Emission wavelength (nm)1,500

PL (a.u.)0ex (nm)–1

0Figure 2 | An individual carbon nanotube coupled to a nanobeam cavity.
(a) A schematic of a device. (b) Scanning electron microscope image of adevice with a suspended nanotube. Scale bar is 2 mm. (c) Typical PL
spectrum of an air-mode device coupled to a nanotube. The dots are data
and the lines are Lorentzian ﬁts. (d) PL excitation map of the device shownin c taken with P ¼ 10 mW and the laser polarisation perpendicular to the
nanobeam.

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2

1
0
−1
−2

1

3

0

2

−1

1

−2
−2

−1 0
1
2
x position (μm)

−2

2

−1 0
1
2
x position (μm)

Number of devices
16
17

b*
0.18±0.16
0.37±0.30

Q3,500±1,400
2,000±700

Devices are measured with P ¼ 10 mW and lex tuned to the E22 resonance. The error values are
standard deviations.

Air

−2

−1

0

Δx (μm)

1

2

−2

−2

−1

0

1

2

Δx (μm)Figure 3 | Spatial distribution of nanotubes that show coupling. (a,b) PL
images of representative dielectric- and air-mode cavities, respectively,
taken with lex ¼ 800 nm. IPL is obtained by integrating PL over a 0.53 nm
wide spectral window centred at the cavity resonance. Excitation powers of
P ¼ 10 mW and 20 mW are used for (a,b), respectively. The centre of thecavities are taken as the origin of the coordinate system. (c,d) Spatial
distribution of PL peak intensity locations for dielectric- and air-mode
cavities, respectively. The peak locations are determined by ﬁtting to a
two-dimensional Gaussian function, and they are plotted as a function of
the displacement from the centre of the cavity.

within the trench, while for the air-mode devices, the emission is
on top of the nanobeam itself.
These differences highlight the distinctness of the two types ofcavities, and show that coupling occurs predominantly throughﬁelds in the air. For dielectric-mode cavities, ﬁelds within air
holes in the nanobeams are weak, and evanescent ﬁelds leaking
out from the edges are responsible for coupling (Fig. 1c). In
comparison, ﬁelds in the air holes dominate for air-mode cavities(Fig. 1d) and nanotubes are coupled when they are placed on topof the air holes.
Next, we further compare the dielectric- and air-mode cavities
by analysing the PL spectra. By performing a bi-Lorentzian ﬁt todata (Fig. 2c), we obtain the peak area and the line width for boththe nanotube and the cavity emission. We let Icav and ICNT be thePL peak area of the cavity and direct CNT emission, respectively,
and use b* ¼ Icav/(ICNT þ Icav) as a measure of the coupling
efﬁciency. We ﬁnd that the average value of b* for the air-mode
devices is more than twice the value for the dielectric-mode
cavities (Table 1), consistent with the expectation from themode proﬁles. We also obtain the quality factor (Q) of the mode
from the line width of the cavity peak, but it is likely that theobserved values are limited by fabrication errors as the FDTD
calculations predict Q4105.
High-efﬁciency coupling. On a few air-mode cavities, we haveobserved very high values of b*. In Fig. 4a, we plot the PL
spectrum of a device with the highest observed b* ¼ 0.92. It iscompletely dominated by the cavity mode, and the direct nanotube emission is barely observable (Fig. 4b and Supplementary
Fig. 1). Since such a spectrum is expected for devices that arelasing, we have performed excitation power dependence measurements in search for any signs of laser oscillation.
In Fig. 4c, excitation power dependence of the PL emission
intensities for the cavity and the direct CNT peaks are plotted.
The cavity emission increases linearly for powers up to B20 mW

1.0

0.5

0.0
Data
CNT
Cavity
Fit

30
20
10
0

1,360
1,380
1,400
Emission wavelength (nm)Icav, ICNT (a.u.)

−1

Data
Fit

FWHM (nm)−1

0

P = 120 μW
ex= 799 nm

Wavelength (nm)0PL (103 counts s−1)

1.5

1

PL (counts s−1)1Δy (μm)Δy (μm)0

Cavity type
DielectricAir

2
Dielectric−2

Table 1 | b* and Q of dielectric- and air-mode cavities.

4
Air
I PL(a.u.)Dielectric

y position (μm)

y position (μm)

2103Cavity

102
101

CNT

0.8
0.7

Cavity1,385

Cavity

1,380
1,375
CNT

1,370
1
10
100
Excitation power (μW)

Figure 4 | Efﬁcient coupling of a nanotube to an air-mode cavity.
(a) Photoluminescence (PL) spectrum of an efﬁciently coupled device takenwith P ¼ 120 mW and lex ¼ 799 nm. The dots are data and the line is a ﬁt.
(b) An enlarged view of the low-intensity region of the data shown in a.
The dots are data, thin solid line is the ﬁt to the cavity mode, thin broken
line is the ﬁt to the CNT emission, and the thick line is the bi-Lorentzian ﬁt.
(c) Excitation power dependence of Icav (ﬁlled circles) and ICNT (opencircles). The line is a linear function. (d) P dependence of the cavity mode
full-width at half-maximum (FWHM). (e) The centre wavelength of thecavity mode (ﬁlled circles) and the nanotube peak (open circles) as afunction of P. The solid lines are linear ﬁts. In c–e, lex ¼ 799 nm is used, andthe error bars are smaller than the symbols for the cavity mode.

and becomes slightly sublinear for higher powers, with noindication of a superlinear increase that should occur at athreshold. In addition, under lasing conditions, the direct CNT
emission should saturate, because excited state population
becomes constant as all the pump power is converted to cavity
photon population26. We do not observe such saturation but the
CNT peak increases linearly throughout all the powers.
Furthermore, the line width of the cavity mode plotted inFig. 4d does not show the narrowing expected during lasing.
From all of these observations, it is unlikely that laser oscillation
is taking place.
Under the assumption that stimulated emission is negligible,
we can attribute all of the PL to spontaneous emission. Letting
gcav and gCNT be the spontaneous emission rate into the cavity
mode and all the other modes, respectively, the spontaneousemission coupling factor b is given by
gcav
Icav
b¼
¼
;
ð1Þ
gCNT þ gcav ðZcav =ZCNT ÞICNT þ Icav
where Zcav and ZCNT are collection efﬁciencies for the cavity modeand direct nanotube emission, respectively (Supplementary
Note 1). A conservative estimate of b is made by taking thelargest possible value of the ratio Zcav/ZCNT. We let Zcav ¼ 1,

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supposing that all of the light emitted from the cavity mode into
the upper hemisphere is collected by the objective. For the direct
nanotube emission, we use the dipole radiation pattern as if thenanotube is emitting into free space, although we expect higher
collection efﬁciencies because of reduced emission rate for inplane directions caused by the photonic bandgap. This results in
ZCNT ¼ 0.49 with the numerical aperture of 0.8 for the objective
lens. Using these values and the ﬁtting parameters for the data
shown in Fig. 4a,b, we obtain b ¼ 0.85.
Discussion
It is remarkable that the value of b is already comparable withthose for the well-established quantum-dot microcavity systems17,18,27–29, particularly because the Purcell effect is limited by
the broad line width of nanotube emitters30. Nevertheless, such ahigh value of b is reasonable because of ultralow mode-volume of
the air-mode cavities. From the FDTD calculation shown in
Fig. 1d, mode volume V ¼ 2.37  10  2(l/n)3 is obtained, wherel ¼ 1.38 mm is the cavity resonance wavelength, and n ¼ 1 is theindex of refraction for air. The maximum spontaneous emission
enhancement factor is given by F ¼ (3l3Qe)/(4p2n3V) ¼ 316,
where we use Q of the emitter Qe ¼ 99 instead of the cavity Q,
as the nanotube emission line width is much wider than the cavity
line width30. Even at the top surface of the nanobeam where thenanotubes are placed, an enhancement factor over 100 is obtained
within the centre air-hole, easily explaining the observed high b.
Finally, we would like to comment on the behaviour at higher
powers. In Fig. 4e, power dependence of the centre wavelengths
for the cavity mode and the nanotube peak are plotted. The cavity
redshifts linearly with power due to heating17, while the nanotube
peak blueshifts as observed previously14. As a result, the cavity
mode and the nanotube emission become detuned, and therefore
the coupling becomes weaker. At the highest power, the detuningis 8.8 nm, and this is likely the cause of the sublinear increase ofcavity mode emission at high powers (Fig. 4c).
Although we did not ﬁnd any signs of laser oscillations so far,with such an efﬁcient coupling, it is expected that optimisation ofcavity design and fabrication would ultimately lead to lasing ofindividual carbon nanotubes. The air-mode cavities with ultralow
mode-volumes should also allow higher coupling efﬁciencies
for other low-dimensional materials with weak dielectric
screening31,32.
Methods
Photonic crystal nanobeam fabrication. We fabricate the photonic crystal
nanobeam cavities from silicon-on-insulator substrates with 260 nm of top Si layerand 2 mm of buried oxide. Electron beam lithography and dry etching processes areused to form the nanobeam structure with a width of 670 nm, and the buried oxide
layer is removed by wet etching. The cavities are designed to have reduced orincreased lattice constant in a parabolic manner9,10,18 over 12 periods fordielectric-mode and air-mode cavities, respectively. The lattice constants and thehole sizes have been chosen to match the nanotube emission wavelengths.
PL microscopy. The emission properties of devices are characterised using ahome-built confocal microspectroscopy system14,21. The objective lens has anumerical aperture of 0.8 and a working distance of 3.4 mm, and a pinhole
corresponding to B3 mm diameter at the image plane is used for confocal
collection. The samples are excited with a wavelength-tunable continuous-wave
Ti:sapphire laser, and PL is detected by an InGaAs photodiode array attached to aspectrometer. The laser polarisation angle is adjusted to maximise the PL signal
unless otherwise noted, and all measurements are done in air at room temperature.
The samples are mounted on an automated three-dimensional stage, allowing forthousands of devices to be interrogated overnight to identify devices coupled tosingle nanotube emitters.

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Acknowledgements
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1. Gabor, N. M., Zhong, Z., Bosnick, K., Park, J. & McEuen, P. L. Extremely
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4

This work was supported by SCOPE, KAKENHI (24340066, 24654084, 26610080,
26870167), Asahi Glass Foundation, Canon Foundation, KDDI Foundation, as well as
the Project for Developing Innovation Systems and the Photon Frontier Network
Program of MEXT, Japan. A.I. is supported by MERIT and JSPS Research Fellowship.

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The devices were fabricated at the Center for Nano Lithography & Analysis at The
University of Tokyo.

Competing ﬁnancial interests: The authors declare no competing ﬁnancial
interests.

Author contributions

Reprints and permission information is available online at http://npg.nature.com/
reprintsandpermissions/

Y.K.K. conceived the experiments and supervised the project. R.M. fabricated thedevices and performed the measurements. S.Im., R.O. and T.S. helped develop andoptimise the device fabrication processes. R.O., S.Iw. and Y.A. contributed to the
nanobeam cavity designs and the calculations. S.Im., A.I. and X.L. assisted the microscopy measurements. T.S. captured the electron micrographs. R.M. and Y.K.K. analysed
the data and prepared the manuscript. All authors discussed the results and commented
on the manuscript.

Additional information
Supplementary Information accompanies this paper at http://www.nature.com/
naturecommunications

How to cite this article: Miura, R. et al. Ultralow mode-volume photonic crystal
nanobeam cavities for high-efﬁciency coupling to individual carbon nanotube emitters.
Nat. Commun. 5:5580 doi: 10.1038/ncomms6580 (2014).
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