APPLIED PHYSICS LETTERS 112, 021101 (2018)

Spectral tuning of optical coupling between air-mode nanobeam cavities andindividual carbon nanotubes
H. Machiya,1,2 T. Uda,1,3 A. Ishii,1,4 and Y. K. Kato1,4,a)1

Nanoscale Quantum Photonics Laboratory, RIKEN, Saitama 351-0198, Japan
Department of Electrical Engineering, The University of Tokyo, Tokyo 113-8656, Japan3
Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan
4
Quantum Optoelectronics Research Team, RIKEN Center for Advanced Photonics, Saitama 351-0198, Japan
2(Received 5 October 2017; accepted 21 December 2017; published online 8 January 2018)
We demonstrate control over optical coupling between air-suspended carbon nanotubes and airmode nanobeam cavities by spectral tuning. Taking advantage of the large dielectric screening
effects caused by adsorbed molecules, laser heating is used to blueshift the nanotube photoluminescence. A significant increase in the cavity peak is observed when the nanotube emission is brought
into resonance, and the spontaneous emission enhancement is estimated from the photoluminescence spectra. We find that the enhancement shows good correlation with the spectral overlap of
the nanotube emission and the cavity peak. Our technique offers a convenient method for controlC 2018 Author(s). All
ling the optical coupling of air-suspended nanotubes to photonic structures. V
article content, except where otherwise noted, is licensed under a Creative Commons Attribution(CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5008299

Semiconducting carbon nanotubes (CNTs) are attractive
materials for integrated photonics owing to their exceptionally small size,1 and CNT-based discrete components such as
electrically driven emitters,2,3 photodetectors,4,5 and single
photon sources6,7 have been demonstrated. Optical coupling
to photonic structures1,8–12 is one of the next key requirements for on-chip integration. Cavities, in particular, offer
quantum electrodynamical effects for increased performanceand functionality by confining electric fields into a small
mode volume with a low optical loss. Exciton polaritons canform when nanotube emission is strongly coupled to a cavity,12 whereas the interaction of CNTs with cavities results
in an increased spontaneous emission rate in the weak coupling regime.1,8–11 The spectral overlap of the emission withthe cavity is an important factor in determining these effects,
and the overlap can be changed by preparing samples withdifferent cavity lengths for coupling to ensembles of
CNTs.12 Sophisticated fiber microcavities enable in-situ tunable coupling to individual CNTs,6 but it still remains a challenge to perform post-fabrication tuning for on-chip cavities.
In this work, we demonstrate spectral tuning of airsuspended carbon nanotubes coupled to integrated nanobeam
cavities. We utilize air-mode cavities1,10,13 with large electric fields in air for efficient coupling to suspended CNTs.
Laser heating is used to desorb molecules from the nanotubes, which offers a simple method for adjusting the nanotube emission through reduction of dielectric screening. We
are able to modify the detuning by as much as 25 meV,
inducing a drastic change in the cavity peak intensity. The
cavity quantum electrodynamics model is used to analyze
the data, and we find that the enhancement of the cavity
mode can mostly be explained by the spectral overlap of thenanotube emission with the cavity peak.
a)Author to whom correspondence should be addressed: yuichiro.kato@
riken.jp0003-6951/2018/112(2)/021101/5

The air-mode nanobeam cavities10 [Fig. 1(f) inset] are fabricated from silicon-on-insulator wafers diced into 20-mm
square chips. Electron beam lithography defines the cavity pattern, and the 260-nm-thick top silicon layer is etched through bya Bosch process in an inductively coupled plasma etcher. The
1-lm-thick buried oxide layer is then removed by 20% hydrofluoric acid, followed by another electron beam lithography
process which defines the catalyst area. We finally spin-coat
Fe/silica catalyst and grow CNTs onto the cavity by alcohol
chemical vapor deposition at 800  C.14 A scanning electron
microscopy image of a typical device is shown in Fig. 1(a).
The devices are measured using a room-temperature
confocal microscope system.15 An output of a wavelengthtunable Ti:sapphire laser is focused onto the sample using an
objective lens with a numerical aperture of 0.8 and a working
distance of 3.4 mm. We mount the sample on a motorized
three-dimensional feedback stage, which allows for efficient
automated measurements. Photoluminescence (PL) is collected using the same objective lens and detected using a liquid-nitrogen-cooled InGaAs diode array attached to aspectrometer. Laser reflection comes back through the objective lens and is detected with a Si photodiode, which is used
to align to the cavity position. Samples are placed in nitrogento avoid oxidation of nanotubes at high excitation powers.
The cavities are designed to have resonances near theemission energy of chiralities with large population to maximize the probability of coupling, and more than 10 000 cavities are prepared on a chip. Nanotubes optically coupled tothe cavity are located by one-dimensional PL scans over the
nanobeams. The automated scan results are filtered by performing peak detection and linewidth estimation. Since thecavity linewidth is considerably narrower than the nanotube
linewidth at room temperature, devices showing a sharp
peak component are chosen for detailed characterization.
A typical PL spectrum of a single CNT coupled to a cavity is shown in Fig. 1(b) where the excitation laser power

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FIG. 1. (a) Scanning electron microscopy image of a fabricated cavity withan air-suspended CNT. The scale bar is 2 lm. (b) Typical PL spectrum of acavity coupled to a CNT. Black dots are data and solid lines are theLorentzian multi-peak fits. P ¼ 1 lW and an excitation laser energy of
1.594 eV are used. (c) and (d) Spectrally resolved PL images of the cavity
emission and the nanotube PL, respectively. PL spectra are fitted to two
Lorentzian functions with fixed center energies and linewidths corresponding to the cavity and the CNT peaks. The peak areas are used to construct
the images. (e) Reflectivity image taken simultaneously with (c) and (d). For(c)–(e), P ¼ 200 lW and an excitation energy of 1.590 eV are used, and thescale bars are 2 lm. (f) PL excitation map of the device taken withP ¼ 50 lW. The inset is a schematic of a device. In (b) and (f), spectra aretaken where the cavity emission is maximized. For all PL measurements,
laser polarization is perpendicular to the nanobeam.

P ¼ 1 lW is used. We use two Lorentzian functions todecompose the spectrum into the sharp cavity mode (blue)
and the broad nanotube emission (red), and spectrally
resolved PL images [Figs. 1(c) and 1(d)] are obtained by spatially mapping each peak area. Combined with the reflectivity image [Fig. 1(e)], we find that the sharp component islocalized at the center of the device [Fig. 1(c)], consistent
with the spatial extent of the cavity mode. In comparison,
the spectrally broad component is distributed across thewidth of the trench [Fig. 1(d)], showing the location and thelength of the CNT. To confirm that the CNT is individual,
the PL excitation map is also taken [Fig. 1(f)]. A single peakin the map confirms that the cavity is coupled to an individual CNT, and its chirality is assigned to be (10,5) by comparing to tabulated data.15
Looking at Fig. 1(b), the nanotube emission needs blueshifting by 10 meV to achieve resonance. In order to tune
the optical transition energy, we take advantage of the sensitivity of air-suspended nanotubes to dielectric screening. By
controlling the amount of adsorbed molecules through temperature or pressure, large spectral shifts of up to 30 meV havebeen observed.16–19 We utilize laser heating to induce molecular desorption in our devices, which is a simple and convenient method. As the excitation power is increased, thenanotube peak blueshifts due to molecular desorption while
the cavity peak gradually brightens [Fig. 2(a)]. The nanotube
emission is brought into resonance at P  200 lW, enhancing
cavity emission intensity. By further increasing the excitation

Appl. Phys. Lett. 112, 021101 (2018)

power, the cavity peak becomes weaker again as the nanotube
peak continues to blueshift. Above P  250 lW, we do notfind additional blueshifting because the molecules are fully
desorbed.
In Fig. 2(b), we compare on- and off-resonance spectra,
which are indicated by orange and green curves, respectively. We find an enhancement of the cavity peak height bya factor of 10 at resonance, while the nanotube peak heightremains comparable due to the increased non-radiative
recombination rate at high powers.15 The significant difference in the cavity peak height indicates that the optical coupling to the nanotube emission is modified by the spectral
shift. The spectral lineshape of the nanotube peak is changed
at high powers (green curve), probably due to the inhomogeneous molecular desorption.
To quantitatively characterize the spectral tuning effect,the excitation power dependence is analyzed by decomposing
the spectra into the cavity and the nanotube peak components.
We first fit the sharp cavity peak to a single Lorentzian function using a fitting window of 10 meV, yielding the cavity
peak energy hxcav , linewidth c, and peak area Icav. Due to thecomplex nanotube lineshape, we let the nanotube peak spectrum LCNT (x) to be the fitting residual, where x is the frequency.ÐThe nanotube peak area ICNT is defined as the integral
ICNT ¼ LCNT ðxÞdx, while the peak energy hxCNT is definedÐ
xLCNT ðxÞdx
as the weighted average hxCNT ¼ h Ð.
LCNT ðxÞdxIn Fig. 2(c), we plot the peak energies as a function of theexcitation power, and blueshifting of the nanotube peak by asmuch as 18 meV (red open circles) is observed. A slight redshift of the cavity peak (blue dots) likely originates from theheating-induced increase of the refractive index.20 The energy
shifts of the nanotube and cavity together allow for energy

FIG. 2. (a) Excitation power dependence of PL. PL is normalized withrespect to the nanotube peak height. Vertical dashed lines indicate the powers where PL spectra in (b) are taken. (b) Comparison of PL spectra taken at
P ¼ 200 lW (orange) and 300 lW (green). (c) and (d) Excitation power
dependence of the peak center energy and peak area, respectively. Red open
circles are obtained from the CNT peak, and the blue dots are taken from thecavity emission. The peak center energies are plotted as the difference fromthe resonant energy 
hx0 ¼ 1:018 eV. For (a)–(d), excitation laser energy istuned to E22 resonance and laser polarization is perpendicular to the
nanobeam.

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detuning 
hxcav  
hxCNT to be changed from þ9 meV to14 meV. The tuning range is sufficiently large for modulating the optical coupling of the nanotubes to the cavity, as it
considerably exceeds the nanotube emission linewidth atroom temperature. We note that the shifts are reversible upon
reduction of the excitation power (supplementary figure in the
supplementary material).
We now turn our attention to the excitation power dependence of emission intensities [Fig. 2(d)]. ICNT increases linearly
at low excitation powers and then becomes sublinear as a resultof the exciton-exciton annihilation process,15 with a drastic
drop at P ¼ 250 lW [Fig. 2(d), red open circles]. Since the E22
resonance also blueshifts by molecular desorption,17–19 thesudden drop can be understood by the shifting of the E22 resonance away from the excitation energy. In comparison, we
observe a linear increase of Icav with excitation power, for theregion below P ¼ 190 lW [Fig. 2(d), blue dots]. The sublinearity of ICNT is likely cancelled out by the improvement of coupling, because the nanotube peak approaches resonance in thispower region. The cavity peak area then rapidly reduces above
P ¼ 200 lW as a result of the increased energy detuning.
Since we are changing the excitation power, we need tocharacterize the optical coupling by evaluating emission
enhancement. Assuming that stimulated emission is negligible, the spontaneous emission enhancement factor is given by
Icav =gcav
F ¼ ICNT=gCNT , where gCNT and gcav are the collection efficiencies of the nanotube and the cavity emission, respectively. To
obtain conservative estimates of F, gCNT =gcav ¼ 0:49 isused.10
We have calculated F using the data shown in Fig. 2,
and the results are plotted in Fig. 3(a). As the excitation
power is increased up to P ¼ 190 lW, the enhancement factor increases from 0.056 to 0.19, and F rapidly decreases by
a factor of 15 at P ¼ 250 lW. The large modification to theenhancement factor is consistent with the spectral shifts inthis range. Above P ¼ 250 lW, we do not observe much
excitation power dependence.
The enhancement factor is known to be determined by
the spectral overlap, spatial overlap, and polarization matching.21,22 If we assume that the nanotube does not move during our experiment, F should only depend on the spectral
overlap. As the nanotube lineshape is complex, we need to

FIG. 3. (a) and (b) Excitation power dependence of F and S, respectively. F
and S are calculated from the results in Fig. 2. (c) F as a function of S. Opencircles indicate red-detuned nanotube emission (P  190 lW) and crosses
correspond to blue-detuned conditions (P > 190 lW).

Appl. Phys. Lett. 112, 021101 (2018)

evaluate the spectral overlap without assuming a particularemitter lineshape. We first consider a simple case of a monochromatic emitter coupled to a cavity with a Lorentzianlineshape. The spontaneous emission enhancement at a frequency x is then given by  
3 k30
x
ðc=2Þ2;(1)
2
4p V
c ðx  xcav Þ2 þ ðc=2Þ2where k0 and V are the wavelength and the mode volume of
the cavity, respectively.23 We multiply the cavity enhancement and the normalized lineshape of the nanotube emission
and integrate over the full spectrum to obtain
 
3 k30
S;
(2)
F¼ 2
4p V
where the integral
S¼

ð 
x
ðc=2Þ2LCNT ðxÞ
dxc ðx  xcav Þ2 þ ðc=2Þ2 ICNT

(3)

is the generalized form of the spectral overlap. 1/S reduces to
1=Qcav þ 1=QCNT under an assumption that the nanotube
lineshape is a Lorentzian resonant with the cavity,23 where
Qcav and QCNT are the quality factors of the cavity and thenanotube peaks, respectively. If Qcav is considerably larger
than QCNT, the upper bound of S would be given by QCNT.
The spectral overlap can be calculated for arbitrary lineshapes using Eq. (3), and the results of numerical integration
are plotted in Fig. 3(b). When the excitation power isincreased, we observe a crossover from a gradual increase toa rapid decrease at P ¼ 190 lW as the nanotube peak shifts
through the cavity peak. The maximum spectral overlap
S ¼ 73 is reasonable, considering that QCNT 80.
Correlation between the enhancement factor and thespectral overlap is examined in Fig. 3(c). Indeed, F increases
monotonically with S as expected from Eq. (2). We note thatthe detuning changes sign above and below P ¼ 190 lW, butsimilar enhancements are obtained for red- (open circles)
and blue-detuned (crosses) nanotube emission. It is reasonable that detuning sign does not have an effect, because Fshould only depend on S.
In Fig. 4, we present two additional devices that have different initial detunings. In the second device, the nanotube peak isinitially resonant with the cavity at the lowest excitation power[Fig. 4(a)]. When the excitation power is increased, moleculardesorption shifts the nanotube peak away from the cavity, reducing the enhancement [Fig. 4(b)]. The blueshifting results in the
spectral overlap to decrease as well [Fig. 4(c)], explaining the
behavior of F. The third device has an initial detuning evenlarger than the first device [Fig. 4(d)]. Even for the fully desorbed state, there exists considerable emission enhancement[Fig. 4(e)]. The spectral overlap increases with the excitation
power but shows a less pronounced increase at the resonancecompared to F [Fig. 4(f)]. The peak values of F are comparable
to the average enhancement previously reported.10
Figures 4(g) and 4(h) are the F–S plots of the second
and third devices, respectively. We observe a monotonic
increase of F as observed in the first device, consistent with

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Appl. Phys. Lett. 112, 021101 (2018)

In summary, spectral tuning of air-suspended carbon
nanotubes coupled to air-mode nanobeam cavities is demonstrated by laser-heating-induced molecular desorption. We
have performed excitation power dependence measurements
and have shown that such molecular-scale effects provide aconvenient in-situ method for controlling the coupling of asgrown CNTs to photonic structures. The excitation power
dependence is characterized using the enhancement factor,
and we find that the numerically calculated spectral overlap
can explain the behavior. The tunability of optical coupling
would be a key not only for fundamental understanding of
the light-matter interaction in CNTs but also for reconfigurable optical devices in the telecom band on a silicon platform.
See supplementary material for the down-sweep excitation power dependence.

FIG. 4. (a) Normalized PL, (b) F, and (c) S as a function of excitation power
for the second device. (d) Normalized PL, (e) F, and (f) S as a function of
excitation power for the third device. (g) and (h) S dependence of F for thesecond and third devices, respectively. Excitation laser energy and polarization are tuned to maximize the signal.

We thank S. Chiashi and S. Maruyama for the use of theelectron microscope. This work was supported by JSPS
(KAKENHI JP16H05962 and JP16K13613) and MEXT
(Photon Frontier Network Program, Nanotechnology Platform).
The samples were fabricated at the Center for Nano
Lithography & Analysis at The University of Tokyo. H.M. was
supported by RIKEN Junior Research Associate Program, andT.U. was supported by ALPS and JSPS Research Fellowship.
1

the understanding that the enhancement factor is determinedby the spectral overlap. It is interesting to note that the slope
k3of the F–S plot should be 4p3 2 V0 ¼ 3:2 for perfect spatial andpolarization overlaps.10 The linear fits to our experimental
data, in comparison, yield slopes on the order of 103, whichsuggests that there remains a lot of room for improving thecoupling. Better spatial and polarization alignment could bepossible by site-controlled transfer of nanotubes or photonic
crystal structures by micromanipulation.24,25 We also notethat the experimental slope may be an underestimate becauseof our conservative calculation of F. The actual F is expected
to be higher since the collection efficiency of the nanotube
emission should be enhanced due to the photonic crystal
structure.10,21
It is intriguing that we observe a slight superlinearity in
the F–S plots for the first and third devices [Figs. 3(c) and4(h)]. One possible explanation is the cavity-resonant opticalforces. We assume in our analysis that the spatial overlap
does not change during our measurements, but the overlap
may improve at resonance if the CNTs are pulled towards
the electric field maximum.26,27 Another possibility is stimulated emission which contributes to additional emission into
the cavity mode. In the first and third devices, the spectral
overlap becomes larger at high excitation powers, which ispreferable for stimulated emission. The second device, incomparison, has a smaller spectral overlap at high powers,
which may explain why the superlinearity cannot be
observed. By controlling the pressure or temperature, it
should be possible to keep the resonant condition and perform excitation power dependence measurements as well as
photon correlation measurements28 to identify the contribution from stimulated emission.

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