ARTICLE

Received 30 May 2013 | Accepted 31 Jul 2013 | Published 23 Aug 2013 DOI: 10.1038/ncomms3376 OPEN

Single-mode tunable laser emission in the

single-exciton regime from colloidal nanocrystals
Christos Grivas1, Chunyong Li1, Peristera Andreakou1, Pengfei Wang2, Ming Ding2, Gilberto Brambilla2,
Liberato Manna3,4 & Pavlos Lagoudakis1

Whispering-gallery-mode resonators have been extensively used in conjunction with different

materials for the development of a variety of photonic devices. Among the latter, hybrid
structures, consisting of dielectric microspheres and colloidal core/shell semiconductor
nanocrystals as gain media, have attracted interest for the development of microlasers and
studies of cavity quantum electrodynamic effects. Here we demonstrate single-exciton,
single-mode, spectrally tuned lasing from ensembles of optical antenna-designed, colloidal
core/shell CdSe/CdS quantum rods deposited on silica microspheres. We obtain single-
exciton emission by capitalizing on the band structure of the specific core/shell architecture
that strongly localizes holes in the core, and the two-dimensional quantum confinement of
electrons across the elongated shell. This creates a type-II conduction band alignment
driven by coulombic repulsion that eliminates non-radiative multi-exciton Auger recombi-
nation processes, thereby inducing a large exciton–bi-exciton energy shift. Their ultra-low
thresholds and single-mode, single-exciton emission make these hybrid lasers appealing for
various applications, including quantum information processing.

1 School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK. 2 Optoelectronics Research Centre, University of Southampton,

Southampton SO17 1BJ, UK. 3 Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa, Italy. 4 Kavli Institute of Nanoscience, Delft University of Technology,
PO Box 5046, Delft 2600, The Netherlands. Correspondence and requests for materials should be addressed to C.G. (email: chr.grivas@gmail.com).

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3376

R
esearch in developing lasers based on semiconductor the length of the shell upon optical excitation result in the
nanocrystals for applications, such as telecommunications, development of electric field within their volume, which induces a
optical interconnects and quantum information processing, Stark shift of the absorption wavelength with respect to the
has experienced significant growth over the past decade. This emission one and allows for single-exciton lasing. One advantage
activity has resulted in the demonstration of a whole range of of the dot (core)/rod (shell) architecture adopted here, which
sources, including ultra-short (B100 fs) pulse lasers with a few represents the simplest extension to the basic spherical core/shell
kHz narrow linewidths1, operating with GHz-repetition rates2, geometry6, is that it provides additional options for shape
and ultra-low timing jitter as well as single-photon sources based engineering and, in turn, for manipulation of the carriers’
on photonic crystals3, micropillars4 and nanowires5. Although wavefunction distributions, and the optical and electronic
epitaxial growth techniques that are compatible with comple- properties of the nanocrystals35–38. Furthermore, nanocrystals
mentary metal-oxide-semiconductor technology represent an with elongated geometries exhibit higher absorption coefficients
established approach to produce self-assembled nanocrystals compared with their spherical counterparts, which allows them to
for photonic devices, the use of wet-chemistry methods has act in a way as antennas for optical excitation7.
emerged in recent years as a simpler and cost-effective fabrication
alternative. Attractive features of chemically synthesized nano-
crystals include the ease of control over their size, shape, com- Results
positional and surface chemical properties, and the wealth of Hybrid lasers with whispering-gallery-mode microresonators.
possibilities for their incorporation into micro- and nanocavities, The colloidal CdSe/CdS nanorods were synthesized by the seeded-
photonic crystals, feedback schemes and material matrices. growth approach29. They could produce PL quantum yields as
Among the different types of colloidal nanocrystals, core/shell high as 65%29, and had an effective refractive index of nnc ¼ 2.5 at
heterostructures, consisting of a quantum dot (core) embedded in l ¼ 610 nm, a wavelength that corresponds to their ensemble PL
a nanoshell, predominantly with spherical and, more recently, peak. Their structure was asymmetric, consisting of a spherical,
with linear6 branched7 and platelet8,9 geometries, have been optically active CdSe core with a diameter of 4.0±0.7 nm
under vigorous research investigation for the development of embedded in one end of the elongated (28±2 nm) CdS shell.
microlasers10–19, fundamental studies of light–matter interactions Because of its large absorption cross-section, the latter acts as a
and solid-state cavity quantum electrodynamic effects20,21, sensitizer by efficiently absorbing pump light and conferring the
where the end goal is to realize functions, such as entanglement photoexcitation to the CdSe core. As the valence band (VB) offset
of distinguishable quantum systems and controlled coherent between the two materials is 0.78 eV39, holes experience a three-
coupling. The potential of these nanostructures in lasing dimensional confinement within the core. On the other hand, the
applications with respect to bare quantum dots relies on their offset of their CBs depends on the aspect ratio of the nanorods and
ability to reduce surface/interface defects and suppress non- their growth conditions, ranging from  0.3 to 0.3 eV (refs 39–41).
radiative Auger recombination effects, as it has been demonstrated The microspheres were produced by CO2 laser thermal
using different approaches, involving the use of shells with large processing of fibre tapers (see Methods) to which they remained
thickness or gradual composition, or engineering of the carrier attached after the completion of the fabrication process. They had
wavefunctions in the volume of the nanostructure22–25. This diameters from 8 to 40 mm, measured Q-factors in excess of 108
provides prospects for realization of lasing in the single-exciton and were coated with a thin layer of nanorods by immersion in a
regime, involving the recombination of a single electron–hole pair toluene solution of the latter. The density of the nanorods
(exciton). Optical gain in bare quantum dots instead relies on attached on the microsphere surface was controlled by varying
multi-exciton states and experiences a fast decay resulting from their concentration in the solution, the immersion time and the
non-radiative Auger recombination triggered by quantum-con- withdrawal speed of the microspheres from the solution.
finement-enhanced Coulombic carrier–carrier interactions26,27. A schematic of the experimental setup and an image of a
Furthermore, in core/shell nanocrystals the encapsulating shell typical microsphere used in our work are shown in Figs 1 and 2a,
protects the core from photodegradation, thereby ensuring respectively. The spheres were pumped at wavelengths B400 nm
significantly higher photoluminescence (PL) quantum yields28,29. with a tuneable frequency-doubled Ti:sapphire amplifier, opera-
An effective approach to circumvent the detrimental Auger ting at 250 KHz and emitting 180-fs-short pulses with a linewidth
recombination effect and obtain single-exciton emission has been of 5 nm. The pump light was evanescently coupled to the
recently demonstrated in a vertical cavity surface emitting lasing microsphere resonators using tapered optical fibres with adiabatic
configuration using core/shell, dot/dot CdSe/Zn0.5Cd0.5S nano- transitions, drawn from single-mode fibres at 405 nm (see
crystals with type-I conduction band (CB) alignment18 as a gain Methods). This method ensures efficient incoupling and out-
medium. The alloyed shell in these structures ensured a smooth coupling of the pump and laser beam, respectively, as well as
profile for the confinement (interfacial core/shell) potential, selectivity in the excitation of the modes42,43.
which has been associated with lower Auger recombination rates, To measure their optical power and record their spectra, the
resulting from the attenuation of high-frequency components in laser signals were collected by the same taper used for pumping.
the ground-state hole wavefunction30,31. The supressed Auger In cases when the laser output characteristics of the hybrid source
rates allowed for low lasing thresholds for an ensemble averaged were studied, a probe fibre tip44 (Fig. 2b) with a diameter of
number of excitons of /NS o1 (ref. 18). B50 nm, a size that ensured sufficient resolution was employed
Here we demonstrate for the first time single-mode, single- for in-situ monitoring of the laser spectra (see Methods for
exciton, tunable laser emission from an ensemble of colloidal fabrication details). To enhance pump efficiency and prevent
type-II CdSe/CdS core/shell nanorods on a silica microsphere. excitation of whispering-gallery modes (WGMs) with high radial
Core/shell nanocrystals with type-II bandgap alignment at the index, n, phase-matching of the propagation coefficients between
core/shell interface have been extensively studied over recent the propagating fundamental mode in the taper and a funda-
years, as they represent another promising route for realizing mental WGM in the microsphere (that is, matching of the spatial
single-exciton lasers32–34. The CBs of the CdSe core and the CdS period of the optical waves in both the taper and microsphere
shell in our nanorods are engineered such that the lowest energy resonator, and hence constructive interference) was established
states for holes and electrons reside in the core and shell, by suitably choosing the size of taper diameter (typically from
respectively. The Coulombic repulsive forces that developed along 1 to 2 mm) with respect to that of the sphere42. Establishing phase

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3376 ARTICLE

Spectrum Supporting fibre Figure 3a shows the laser spectrum for the single WGM
analyser stem operation at 628.32 nm of a microsphere with a diameter of
CdSe/CdS nanorod coated
9.2 mm, along with the inhomogeneously broadened fluorescence
silica microsphere spectrum from an ensemble of nanocrystals and the PL emission
Laser/residual
pump light spectrum from the hybrid microsphere. The latter exhibits a
Fibre tip modulation by a number of peaks with the characteristic WGM
Coupling microscope
objective distribution. The laser spectrum was obtained by resonantly
pumping a fundamental WG pump mode with jmj ¼ l, with m
Tapered fibre and l being the azimuthal and polar numbers, respectively, above
Optical filter an absorbed pump power of 100 mW. Such modes, with low n
Power meter Pump beam numbers, have very small volumes and are confined to the
~400 nm (tunable), equatorial ring of the sphere (defined as the area parallel to the
180 fs, 250 KHz
taper fibre axis perpendicular to the stem) close to its surface45.
Figure 1 | Experimental setup for demonstration of lasing in CdSe/CdS They were identified by a dip observed in the transmission
colloidal nanorods. Self-assembled nanorods on silica microspheres were through the taper when the pumping wavelength was tuned. The
excited by bringing the evanescent field of the fibre taper in the proximity of laser line corresponds to the single-exciton transition and its full-
the microsphere, thereby establishing an overlap of the fundamental optical width at half-maximum (FWHM) value of Dl ¼ 0.06 nm suggests
mode of the taper with the WGMs. The position of the taper relative to the a Q-factor value of l/DlB104 for the hybrid cavity. This lower
microsphere was controlled by high-resolution, three-axis nano-positioning value, with respect to the uncoated sphere, is attributed to the
stages, allowing for tuning of the phase-matching conditions and surface roughness introduced by the gain medium and the
optimization of coupling. The tip could be brought into contact with the associated scattering loss at the boundaries with the silica
sphere and then moved on the surface along a meridian to the desired microsphere and the surrounding air. Losses from the presence
plane. Emission spectra were recorded with an optical spectrum analyser. of the fibre may also have contributed to the deterioration of the
The absorbed pump power was measured as the difference of the power Q-factor, as experiments were conducted near the overcoupled
launched into the taper and that transmitted after the taper. To obtain the regime. Parameters that are crucial for achieving single-mode
power of the laser signal that was evanescently coupled from the laser emission from the hybrid microsphere are the bandwidth of
microsphere into taper, unabsorbed pump light transmitted through the the pump pulse at B400 nm, the microsphere size, and the
latter was removed from the laser emission light with a suitable filter. establishment of phase-matching pumping conditions. Micro-
spheres with sufficiently small size have a free-spectral range
(FSR) that is comparable to or larger than the bandwidth of the
pulse, which allows for spatially selective excitation of a single
mode. Phase matching of this mode with the pump taper mode
ensures maximum optical pump power transfer. In this case, the
optical power transferred to other non-phase-matched modes is
significantly smaller and insufficient to produce lasing because of
large absorption of the pump wavelength by the microsphere and
the associated high losses in the resonator.
Figure 3b shows the laser output characteristics as a function of
absorbed pump power for the single WGM operation of the
microsphere, indicating a lasing threshold of 67.5 mW and a
maximum output power of 5.5 mW for 155 mW of absorbed
power, which corresponds to a slope efficiency of Z ¼ 6.4%. The
evolution of the emission line for different absorbed pump
powers around the lasing threshold of the hybrid source is
displayed in Fig. 3c, exhibiting a progressive spectral narrowing
of the linewidth with increasing pump power from B1.3 nm
(FWHM) just below threshold at 66 mW, to 0.06 nm at absorbed
pump powers near and in excess of 119 mW. Furthermore, a
significant increase in the emission peak intensity above threshold
can be observed, which follows a linear behaviour as shown in
Fig. 3b.
Figure 2 | Microsphere template and optical fibre tip images. Optical Microspheres with larger diameters produced a multi-mode
microscope images of (a) a silica microsphere with a diameter of B30 mm, laser emission due to the smaller FSR, DlFSR, in between the
used as a template for the CdSe/CdS quantum rods and (b) an optical fibre modes with adjacent l indices. Figure 3d shows a laser-emission
tip with a diameter of 50 nm and a 2-mm-long taper transition used to spectrum obtained from a microsphere with a diameter of
collect signals from the CdSe/CdS nanocrystal/silica microsphere hybrid 29.4 mm by pumping at the equatorial zone. The lasing modes in
resonators. Scale bars, (a) 30 mm; (b) 125 mm. the spectrum appear at wavelengths separated by a distance of
2.4 nm, which is very close to the value of DlFSR ¼ 2.375 of the
matching of the fundamental taper mode to a given WGM also hybrid microsphere derived from the equation46
improved the coupling ‘ideality’ defined as the ratio of power
coupled to a desired mode divided by the power coupled or lost to    1=2 !
l2L tan  1 ðns =nnc Þ2  1
all modes43. Because of the large absorption by the nanorods at DlFSR ¼  1=2 ð1Þ
the pump wavelength and, hence, the large round-trip loss in the 2  p  RH  n2 ðns =nnc Þ2  1
microsphere resonator, any mode other than the fundamental
that may have been excited by the fraction the pump power that where lL ¼ 628.32 nm is the emission wavelength of the first
was not transferred to fundamental WGMs would be eliminated. mode, ns ¼ 1.47 is the refractive index of the silica microsphere,

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3376

a Nanocrystal fluorescence
b 6
WGM laser emission Single-mode laser operation
1.0

Normalized intesity (a.u.)

WGM fluorescence 5 Pth = 67.5 µW /  = 6.4%

Output power (µW)

0.8 4

0.6 3

0.4 2

0.2 1

0.0 0
560 570 580 590 600 610 620 630 640 650 60 70 80 90 100 110 120 130 140 150 160
Wavelength (nm) Absorbed pump power (µW)

c 6
d Nanocrystal fluorescence
66 µW
WGM laser emission
70 µW

Normalized intensity (a.u.)

5 1.0

Intensity (a.u.)
77 µW 4
83.5 µW 0.8
3
119 µW
2 0.6
1
0.4
0
×1
×4 0.2
×4
×4
×8 0.0
570 580 590 600 610 620 630 640 650
580 590 600 610 620 630 640 650
Wavelength (nm)
Wavelength (nm)

Figure 3 | Fluorescence and laser emission characteristics. (a) Single-mode, single-exciton laser (black line) and WGM fluorescence (blue line) emission
spectra obtained from a 9.2-mm-diameter hybrid sphere by pumping an equatorial ring region. In the background, the fluorescence produced by the
ensemble of CdSe/CdS nanorods attached to the sphere is also presented (red line). (b) Output power as a function of absorbed pump power for
the single-mode, single-exciton laser operation of a 9.2-mm-large hybrid microsphere. (c) Evolution of the laser-emission spectral line for different
absorbed pump powers near the lasing threshold. (d) Laser emission spectrum obtained from a microsphere with a diameter of 29.4 mm by pumping at its
equatorial zone. The distance between the modes (B2.4 nm) corresponds to the FSR of the sphere.

whereas RH ¼ 14.7 mm is the radius of the hybrid sphere, which As an additional verification of the assignment of the laser lines
was assumed to be equal to that of the silica template. in Fig. 4a to the single-exciton and bi-exciton CdSe transitions,
we calculated their energies. To this end, we derived the
wavefunctions ce (electron) and ch (hole) from the Schrödinger
Laser emission by single-exciton and bi-exciton transitions. equations by using an iterative process involving the effective
The modality of the laser emission can also be tuned by varying mass approximation method, and taking into account the
the coupling conditions and the optical pump power. Hence, Coulomb interaction (see Methods). Effective mass approxi-
evanescent coupling of the pump beam into the resonator away mation has emerged over the years as a reliable approach for
from its equatorial zone results in a multi-mode laser emission as reproducing the energy spectra of confined excitons in semi-
shown in Fig. 4a, where, apart from the laser line at 628.32 nm, a conducting nanocrystals, by successfully addressing the problem
second laser line emerges at lower wavelengths near 592.6 nm. of choosing the actual electrical potential felt by each carrier in
Non-equatorial pumping effectively invalidates the afore- the corresponding Schrödinger equations47,48. In this process, we
mentioned conditions for single modality, as it leads to the first sequentially varied the CB offset and the nanorod diameter
excitation of a number of modes with different radial and azi- following the Hartree self-consistent potential approach49 so as to
muthal numbers, thereby inducing multi-mode lasing. This match the single-exciton emission wavelength with that of the
multi-mode behaviour becomes evident by moving the tapered experimental line at 628.32 nm. In this process, the nanorod
fibre by a distance of approximately half the width of the tapered length was maintained fixed at a value of 28 nm, as this parameter
fibre (that is of the order of 0.5 mm) away from the equator. has insignificant impact on the confinement effect within the
Figure 4b shows the output characteristics of the two laser lines, limits of the deviation (±2 nm) from this value associated with
revealing pump power thresholds of 68.5 and 123.3 mW for the the nanocrystal synthesis process. As a result, we obtained very
low-energy and high-energy transitions, respectively. The data good agreement by assuming an offset value of  0.09 eV and a
points were obtained by using suitable wavelength cut-off filters diameter of 4.34 nm; the energy eigenvalues derived for the
to isolate the laser emission of each transition. The dependency of electron and the hole with respect to the bottom of the
the optical power of the two lines on absorbed pump power in the conduction and VBs of CdSe were 0.14876 eV and 0.14349 eV,
pre-lasing (linear) regime is displayed in a log–log plot in Fig. 4c. respectively, thereby suggesting single-exciton lasing at 628.6 nm.
The slope efficiencies of ZE1 and 2 derived suggest a linear and a Figure 5a displays a schematic of the nanorod along with a band
quadratic dependence for the transitions in the low- and high- alignment diagram at the heterointerface between its core and
energy spectral area, which are typical of single- and bi-excitonic shell, indicating the values adopted for the core diameter and the
gain mechanisms, respectively. Furthermore, the threshold of the CB offset in our calculations. The calculated wavefunctions
laser emission at 592.6 nm is approximately twice as high as that are displayed in Fig. 5b, showing spatial separation between the
at 628.32 nm, thereby providing an additional proof of their hole and the electron charge densities with the holes remaining
bi-excitonic and single-excitonic nature of the corresponding confined to the CdSe core and the electrons being delocalized in
transition, respectively. one dimension over the entire nanostructure. Such carrier

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3376 ARTICLE

Nanocrystal fluorescence
emission at 593.3 nm, which is very close to the spectral line
WGM laser emission Single-exciton
observed at 592.6 nm.
Normalized intensity (a.u.) 1.0 emission To evaluate the potential of the gain medium to produce
optical gain by single-exciton states without any involvement of
0.8 multi-excitons, we have derived the gain threshold /NthS
Bi-exciton
emission expressed in terms of the average number of excitons per
0.6 nanocrystal33:
2
0.4 hNth i ¼   ð2Þ
3  exp  D2xx =G2
0.2
where Dxx ¼ 119 meV represents the spacing between the single-
and bi-exciton line at 626.32 nm and at 592.6 nm, respectively,
0.0
570 580 590 600 610 620 630 640 650 and G is the emission linewidth of a single nanocrystal at room
Wavelength (nm) temperature.
For the latter, we have adopted an upper value of G ¼ 65 meV,
Single-exciton lasing (Pth = 68.5 µW)
which was recorded for the emission of a single CdSe/CdS core/
4
Bi-exciton lasing (Pth = 123.3 µW) shell tetrapod-shaped nanocrystal with an arm-length of 30 nm50
at room temperature. From equation (2), we obtain a value of
/NthS ¼ 0.675, which is well below the theoretical value of
Output power (µW)

3
/NthS ¼ 1 for bi-exciton gain in homogeneously broadened
type-I nanocrystals and very near to that of ideal type-II
2 nanocrystals (/NS ¼ 2/3)33. The latter are associated with
considerably larger Dxx values with respect to the transition
linewidth, thereby allowing for the elimination of absorption
1 losses and, hence, for optical gain from single-exciton states.

0 Wavelength-tuneable laser emission. Tuning the emission from

60 80 100 120 140 160 180 200 220 spherical microcavities has been realized either by modulating the
Absorbed pump power (µW) pump power, thereby exploiting the thermo-optical effect of the
active material51, or by using external heating sources52, or with
8
7 Single-exciton emission ( = 1.04) the application of pressure or strain53. Although the tuning
6 Bi-exciton emission ( = 1.94) ranges achieved with the strain method can even approach the
5 frequency separation between adjacent resonance peaks of the
WGMs53, thereby exceeding those obtained by temperature
Intensity (a.u.)

4
variation, the latter has the attraction of enhanced accuracy of
3 control over the emission wavelength. In this work, the lasing
wavelength, lL, was tuned by heating the 9.2-mm large hybrid
2 microsphere with 3.5-mm pulses of 200 fs duration and 80 MHz
repetition rate from a tunable femtosecond laser, which were
directed onto the microsphere by a microscope objective. The
optical power of the infrared laser beam was raised in successive
1 steps, and for each step the wavelength of the pump laser was
12 30 60 90 120 modulated so as to excite resonant WGMs that were gradually
Absorbed pump power (µW) shifted in wavelength due to the temperature elevation.
Figure 4 | Laser operation in the single-exciton and bi-exciton regimes. Throughout these experiments, the evanescently coupled power
(a) Laser spectrum obtained for 130 mW of absorbed power by non- was maintained constant at 100 mW. The laser spectrum was
equatorial pumping, showing emission on the single- and bi-exciton recorded for each pump power setting, indicating a maximum
transitions; (b) Output characteristics of the single-exciton and bi-exciton wavelength red shift of 2.1 nm within the available power range of
laser emission; (c) input–output characteristics of the single-exciton 60 mW (Fig. 6a), which corresponds to B30% of the FSR at lL.
and bi-exciton emission in the preleasing regime, exhibiting slopes of B1 As at l ¼ 3.5 mm the nanorods are transparent, the observed
and B2, respectively. shift is expected to result from a temperature-induced increase in
the size of the absorbing silica microsphere; other contributions
originate from changes of the thermo-optic coefficient (dnnc/
distributions are typical of type-II core/shell nanocrystals, and dT ¼ 1  10  4 K  1), bandgap energy (DEg) and the nanorods
result in very small overlaps hce j ch i2 of their wavefunctions. size due to a temperature rise induced by heat conduction from
Next, we calculated the wavefunction distributions and emission the microsphere. The effect of these factors on the tuning range of
wavelength for the bi-exciton, by adopting the same values for the the lasing wavelength DlL can be described by:
  
offset and the nanorod size used for our calculations in the single- dnnc =dT
exciton regime. Figure 5c shows the calculated wavefunctions, DlL ¼ lL  DT  anc þ as þ þ Dlbg ð3Þ
nnc
wherein one exciton there is a zero charge density, whereas in the
other same-sign charges are spatially well separated. The where DT is the temperature rise in the hybrid microsphere,
calculated energy eigenvalues for the pairs of electrons and holes as ¼ 5.5  10  7 K  1 and anc ¼ 4.5  10  6 K  1 are the thermal
are (0.15162 and 0.15363 eV) and (0.19835 and 0.19835 eV), expansion coefficients of silica and the nanorods, respectively,
respectively. These values, which are unique within the size limits and Dlbg represents the wavelength shift resulting from DEg. For
of the nanocrystals used in our experiment yield bi-exciton laser anc and dnnc/dT, we adopted the values of the bulk CdS crystal.

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Single exciton
e
CdSe E = –0.09 eV

0.3 eV CdS
CB h

0.6 eV
Energy (eV)

1.68 eV
2.46 eV e

0.87 eV
h

Bi-exciton
VB
4.34 nm
e
CdSe CdS

7 nm h
28 nm

Figure 5 | Electronic structure and calculated wavefunctions in CdSe/CdS core/shell nanorods. (a) Schematics of a CdSe/CdS dot/rod nanocrystal
along with the interfacial band alignment of the CdSe and CdS constituent materials. The core diameter (4.34 nm) and the CB offset (  0.09 eV, inset)
correspond to the values adopted for the calculation of the electronic wavefunctions and lasing wavelengths. The values of the VB offset (0.87 eV)
along with those of the bandgaps for CdSe (1.68 eV) and CdS (2.46 eV) are also shown. The blue shadowed area indicates the range of potential values
for the CB offset. (b,c) Calculated wavefunctions for the electrons (ce) and holes (ch) for the laser emission in (b) the single-exciton regime at
628.6 nm, exhibiting mixed carrier dimentionality and small overlap, and (c) the bi-exciton regime at 593.3 nm, indicating that for the first exciton the
hole/electron wavefunctions are localized in/near the core, and for the second exciton they are separated and are located in the core and the shell,
respectively.

To investigate the consistency of the experimentally obtained

1.0 Infrared-laser power:
0 mW (no illumination)
tuning range, we estimated DT and Dlbg, and subsequently
Normalized intensity (a.u.)

20 mW calculated DlL from equation (3). To derive an analytical

0.8 40 mW expression for DT, we assumed that the impact of the thin
60 mW
nanorod layer on the temperature of the laser-heated silica
0.6 sphere is negligible, meaning that they both have effectively the
same temperature (see Methods). The microcavity can be
0.4 therefore considered as a solid consisting of a single material
(silica), which is heated by a focused laser beam in the
0.2 surrounding air. As the latter is transparent at the illumination
wavelength, it is expected to reduce the temperature of the hybrid
0.0 microsphere. Following an approach used to address a similar
623 624 625 626 627 628 629 630 631 problem54 based on solving the heat equation, we derived by
Wavelength (nm) adopting appropriate boundary conditions (see Methods) for DT
the expression:
Microsphere thermal expansion (cal)
2.5    
Nanorod thermal expansion (cal) Po  Pabs  ð1  Rfr Þ  Pg ka  1
Nanorod (dn/dt)-change (cal) DT ¼ pffiffiffi  1þ ð4Þ
2.0 Bandgap change (cal) 2  p  Rs  ks ks
Wavelength shift (nm)

Total contribution (cal)

Total contribution (exp) where ka ¼ 2.6  10  2 mW m  1 K  1 and ks ¼ 1.38 
1.5
10 mW m  1 K  1 are the thermal conductivities of the air
 3
and silica, respectively, Po is the illumination laser power and
1.0 ð1 þ ka =ks Þ  1 is the heat transferred from the sphere to the air.
The term Pabs ¼ 0.65 represents the optical power fraction
0.5 absorbed by the silica, with Rfr being the Fresnel reflection at
the air/nanorods and nanorods/silica interfaces given by:
0.0    
0 10 20 30 40 50 60 nnc  na 2 nnc  ns 2
Infrared-laser power (mW)
Rfr ¼ þ ð5Þ
nnc þ na nnc þ ns
Figure 6 | Tunable laser emission from CdSe/CdS nanorods. (a) Laser with na ¼ 1 being the refractive index of the air. In calculating DT
emission obtained from a 9.2-mm large hybrid microsphere for different in equation (4), one has to consider that due to the Gaussian
output powers of the infrared laser that served as a heating source. beam profile and the spherical shape of the microcavity, parts of
(b) Calculated (black line) and measured (symbols) red shift of the lasing the beam impinging on the sphere at angles that deviate
wavelength as a function of output power of the infrared laser. The considerably from the normal experience high reflections and,
dotted line is a guide for the eye for the experimental results. The coloured therefore, have a negligible contribution to DT. As a satisfactory
lines represent the calculated contributions of the thermal expansion approximation, we assumed that only the optical power included
of the silica microsphere (cyan) and the CdSe/CdS nanorods (purple), within the FWHM of the beam, that is 50% of the total power,
as well as of the nanorods’ thermo-optic coefficient (blue) and the change contributes effectively to the temperature elevation. To account
of their bandgap size (red). for this effect, we introduced the term Pg ¼ 0.5 in equation (4),
which then yields for the maximum available infrared-laser power

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3376 ARTICLE

of 60 mW a value of DT ¼ 32.7 K. Returning to equation (3), we translation stages of submicron precision. This method can produce taper
calculated Dlbg from the expression transitions of well-defined length and shape, and extremely uniform waists, with
submicron diameters by controlling the heating and stretching speed. The tapers
 l2bg used had adiabatic transitions to preserve the low propagation loss inherent to the
Dlbg ¼  DEg ð6Þ fundamental fibre mode.
1; 239:6 The microspheres were produced by thermal processing of a fibre taper (stem)
by a CO2 laser beam. Tapers enabled fabrication of microspheres with diameters
where the wavelength that corresponds to the bandgap energy lbg considerably smaller than the fibre outer diameter, and were drawn from standard
is set equal to lL. For the calculated temperature increase of telecom silica fibres (outer diameter ¼ 125 mm) following the process described in
DT ¼ 32.7 K, DEg can be derived from the previous paragraph. The uniform waist-tapered region formed was cut in its
centre and then one of the taper ends was heated by the CO2 laser beam to a
a  T2 temperature in excess of 1,000 °C, causing it to reflow and mould into a spherical-
Eg ðT Þ ¼ Eg ð0Þ  ð7Þ shaped structure due to surface tension. Thanks to the high viscosity of the silica
bþT
glass, the reflowed structure was highly spherical and extremely uniform, with
with b ¼ 216 K, a ¼ 1.8  10  4 eV/K and Eg(0) ¼ 2.13 eV being intrinsically very low surface roughness and, hence, very low scattering loss. After
correspondingly the Debye temperature, a temperature constant the fabrication process had been completed, they remained attached to their stems,
which did not affect the optical modes near the equatorial plane that were excited
and the bandgap at 0 K. to produce laser emission.
Figure 6b shows the calculated effect of each of the four The fibre tips were manufactured using a commercial micropipette puller, in
individual parameters and their combined impact on Dl together which the heating source was a CO2 laser, and the pulling process was controlled
with the experimentally obtained wavelength shifts. The latter are by a microprocessor. The device enabled fabrication of tips with tapered transition
lengths between 1 and 2 mm, and a diameter as small as 40 nm, from fibres with an
smaller than the calculated ones, arguably because of a weaker outer diameter of 125 mm. The taper angle of the tip was designed to be small
absorption of the heating beam from the microsphere than that enough to adiabatically convert the fundamental mode in the fibre core into a
assumed and/or an imperfect alignment of the infrared-laser fundamental mode guided by the cladding/air interface allowing for transmissions
beam with respect to the microsphere, meaning that in reality the larger than 98%.
DT induced was about 28 K, as it can be derived from
equation (4). It is worth noting that for DT ¼ 32.7 K, the increase Calculation of laser energies for the single-exciton and bi-exciton transitions.
in the nanorod size would not exceed 0.01 nm, which precludes In the single-exciton case, the carrier wavefunctions were calculated from the
Schrödinger equations:
any contribution to the laser wavelength shift from a change of 
the quantum confinement energy. h2 2

 r þ qe ðfh þ Vcb Þ ce ¼ Ee ce ð8Þ
2me
Discussion 
2 2
h
We have demonstrated single-mode laser emission on the single- 
2mh
r þ qh ðfe þ Vvb Þ ch ¼ Eh ch ð9Þ
exciton recombination transition in core/shell nanorods with a
type-II band offset. The simplicity of the wet-chemical synthesis where : is the reduced Plank constant, me and mh are the effective masses of the
electron and hole, respectively, which are material dependent (me ¼ 0:13me and
of the nanorods in combination with the high Q-factors of the mh ¼ 0:45me for the CdSe core, and me ¼ 0:2me and me ¼ 0:7me 57,58 for
spherical silica resonators and the efficiency of the fibre-coupling the CdS shell), qe, Ee, qh and Eh are the charges and energy eigenvalues of the
approach for optical pumping make such hybrid systems electrons and the holes, whereas Vcb and Vvb are the potentials of the CB and VB,
excellent candidates for studies of the lasing properties of novel respectively. Finally, in equations (8) and (9), fe, and fh represent the electric
potentials of the electron and hole, respectively, which account for the Coulombic
gain media and cavity quantum electrodynamic effects. In electron–hole interaction and were calculated from the Poisson equations:
addition to the single-excitonic nature of the laser emission, r
other laser-operating characteristics, such as its single-mode r 2 fe ¼  e ð10Þ
ee0
emission, which is associated with low levels of noise, and the
ultra-low lasing thresholds that were obtained (thanks to the rh
r2 fh ¼  ð11Þ
larger dipole oscillation strength of the antenna-designed ee0
here, re and rh stand for the electron and hole distributions in the nanorod,
nanocrystals), are appealing for quantum information processing. respectively, whereas e and eo represent the relative permittivity and the vacuum
Furthermore, the ability to tune the emission wavelength of these permittivity, respectively, given by:
WGM microlasers in the visible spectral range is interesting for
c2e
applications related to biosensing. Considering the inherent re ¼ qe ð12Þ
hce j ce i
potential of colloidal nanocrystals for hybrid integration onto a
wide range of platforms and optical resonators, one could c2h
envisage the use of optically or even electrically pumped single- rh ¼ qh ð13Þ
hch j ch i
exciton lasers based on specialist nanocrystal designs for we note that contributions of the CB and VB to the hole and electron wave-
integrated photonic, lab-on-a-chip and optical interconnect functions, ch and ce, respectively, were neglected, as CdSe and CdS are wide
applications. Advances in the development of colloidal nano- bandgap semiconductors. The wavefunctions were solved iteratively using a finite
crystalline gain media like the recent demonstration of nearly element method with sequential variation of the nanorod diameter and the energy
offset of the CBs, as well as optimization of fe, and fh following the Hartree self-
temperature-insensitive threshold for amplified spontaneous consistent potential approach, to match the single-exciton emission line. For the
emission from CdSe/CdS quantum core/shell (dot/rod) struc- single exciton, we started by setting in the Schrodinger equation (8) the initial
tures55 can pave the way for the realization of such miniature potential to zero on the basis of which ce was calculated and introduced into the
integrated sources. Poisson equation (10). From the latter, the potential generated by the electron was
computed and the value derived was introduced into the Schrodinger equation (9)
to calculate the ch. The resulting wavefunction was in turn introduced into the
Methods Poisson equation (11) to obtain the potential generated by the hole. The derived
Fabrication of silica fibre-optical devices. Coupling of pump light to the circum- potential was introduced into the Schrodinger equation (8), which was solved to
ference of microsphere resonators can be realized either with free-space optics or obtain a new expression for ce. This procedure was continued until further
by evanescent wave coupling with the use of channel waveguides in integrated iterations left unaltered the carriers’ wavefunctions and potentials. In this case, self-
optics configurations, prisms, side-polished fibre couplers and tapered fibres45. We consistency was achieved and the derived values were taken as the actual
adopted the latter method for our experiments and used tapers fabricated by the wavefunctions and potentials, respectively. We stress that although the zero
flame-brushing technique56, which involves heating of a section of the fibre with a potential chosen to initiate the calculation process may give the impression that the
‘O’-shaped resistive microheater operated at a temperature of B1,400 °C. The electron–hole interaction was not taken into account, the final carrier potentials
microheater was scanned along the fibre section, while at the same time the two were indeed introduced in the calculation through the iteration process followed,
fibre ends were pulled in opposite directions by a pair of computer-controlled providing optimal description of the specific quantum system.

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms3376

The Schrödinger equations used for the bi-exciton are essentially similar to (c) The temperature rise at infinity shall vanish:
those described above, with the only difference being that the electric potentials
Ta ðr ! 1; tÞ ¼ Ts ðr ! 1; tÞ ¼ Tð1Þ ð29Þ
generated by all the carriers (that is, the two electrons fe1 and fe2, and the two
holes fh1 and fh2) were considered: In the following, we demonstrate the validity of our assumption that the impact
 of the thin layer of nanocrystals on the temperature of the laser-heated silica sphere
h2 2 is negligible and that both media have effectively the same temperature. For this
 r þ qe ðfe2 þ fh1 þ fh2 þ Vcb Þ ce1 ¼ Ee1 ce1 ð14Þ
2me purpose, we consider the heat transported from the sphere given by:
 
 J  4  p  w2  h ks  rT ð30Þ
2 2
h
 r þ qh ðfe1 þ fe2 þ fh2 þ Vvb Þ ch1 ¼ Eh1 ch1 ð15Þ where, h ¼ 4 nm is the coating thickness and ks ¼ 1.38  10  3 mW m  1 K  1 is
2mh
the thermal conductivity of silica. The infrared laser beam radius can be
 approximated as being equal to the microsphere radius, w ¼ RH ¼ 4.6 mm. From
h2 2
 r þ qe ðfe1 þ fh1 þ fh2 þ Vcb Þ ce2 ¼ Ee2 ce2 ð16Þ equation (30), it can be then derived that the relative change in the surface
2me temperature caused by the nanorod coating is:
  
h2 2 2  h  kn  1
 r þ qh ðfe1 þ fe2 þ fh1 þ Vvb Þ ch2 ¼ Eh2 ch2 ð17Þ DT   1 þ ð31Þ
2mh w  ks
The electric potentials in the above equations were derived by the Poisson where kn ¼ 2  10  2 mW m  1 K  1 is the thermal conductivity of the nanorods,
equations: for which we assumed to be equal to the corresponding value of the bulk CdS
r crystal. As kn is an order of magnitude higher than ks, it becomes clear that the
r2 fe1 ¼  e1 ð18Þ reduction of the temperature of the microsphere due to the heat transport to the
ee0
nanocrystal layer is insignificant.
rh1 Finally, with regard to the term ð1 þ ka =ks Þ  1 in equation (4), which represents
r2 fh1 ¼  ð19Þ the heat transported from the sphere to the air, the ratio ka/ks was derived by
ee0
considering that the heat originating from the hybrid sphere is shared with the air,
re2 implying that the fluxes from the sphere (Js) and the air (Ja) should satisfy the
r2 fe2 ¼  ð20Þ
ee0 equation:
rh2 Ja ðka  I=ka þ ks Þ ka
r2 fh2 ¼  ð21Þ ¼ ¼ ð32Þ
ee0 Js ðks  I=ka þ ks Þ ks
with re1, re2 and rh1, rh2 being the electron and hole distributions in the nanorod, where I is the intensity of the infrared light.
respectively, that can be derived from:
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