Supplementary Information
Fabrication of single-crystalline microspheres
with high sphericity from anisotropic materials
Shinya Okamoto1, Kazuhiro Inaba1, Takuya Iida2, Hajime Ishihara3, Satoshi Ichikawa4
and Masaaki Ashida1,*
1
Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyamacho,
Toyonaka, Osaka 560-8531, Japan
2
Nanoscience and Nanotechnology Research Center, Osaka Prefecture University, 1-2,
Gakuencho, Nakaku, Sakai, Osaka 599-8570, Japan
3
Department of Physics and Electronics, Osaka Prefecture University, 1-1 Gakuencho,
Sakai, Osaka 599-8531, Japan
4
Institute for NanoScience Design, Osaka University, 1-3 Machikaneyamacho,
Toyonaka, Osaka 560-8531, Japan
*e-mail: ashida@mp.es.osaka-u.ac.jp
1
Supplementary Figure S1 | A schematic illustration in the cryostat for the laser
ablation. Experimental setup of laser ablation in superfluid helium. The inset shows
a picture of a sample cell in the cryostat seen through the front optical window.
2
Supplementary Figure S2 | A picture of the sample cell in Fig. S1. Sample cell for
the laser ablation in superfluid helium from the front.
3
Supplementary Note | WGM lasing in ZnO microspheres
WGM resonators are of significant interest in quantum optics and photonics1–3 because
of their large Q values and small mode volumes. Though WGM semiconductor lasers of
wide gap materials such as GaN16, 17and ZnO18–21, which emit in the UV and/or visible
region, have been studied previously, the fabrication of microspheres that show
extremely high Q values because of three-dimensional confinement has been difficult
using such hexagonal materials. In this study, however, we succeeded in achieving
efficient lasing.
The micro-PL measurements were performed at room temperature using the SH of a
continuous-wave, single-mode Ti:sapphire laser with a wavelength of 367 nm. The
beam of the excitation laser was focused on the sample using an objective lens with a
numerical aperture of 0.90. The spot size was 2 μm. The PL emitted from an individual
ZnO microsphere was focused onto an optical fibre and directed to a 30 cm
spectrometer equipped with a liquid-nitrogen-cooled charge-coupled device detector.
Figure S3a shows the lasing spectrum at room temperature of a microsphere with a
diameter of 1.8 μm for an excitation intensity of 254 W/cm2. The lasing threshold was
found to be approximately 100 W/cm2. This value is much smaller than that in the case
of UV lasing in a ZnO microwire21 (255 kW/cm2), even though lasing in the visible
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region, which is caused by defects, is more difficult to achieve. The efficient lasing
achieved is due to the relatively high Q value (of the order of one thousand) of the
microspheres, which, in turn, is owing to their high sphericity. This is also confirmed by
comparing the experimentally obtained lasing spectrum (Fig. S3a) with that calculated
(Fig. S3b) while assuming that the corresponding ZnO microsphere has a diameter of
1.79 µm and is completely spherical. The positions of the transverse electric (TE)
modes in the WGM are also shown, along with the theoretically determined mode and
order numbers.
In order to calculate the WGMs of the fabricated ZnO microspheres, we used the
Mie theory22, while taking into account the fact that the refractive index of ZnO in the
visible region is frequency dependent19. ZnO exhibits birefringence and has different
refractive indices for the transverse electric (TE) and transverse magnetic (TM) modes,
respectively. Moreover, we added a correction term, -0.005, to the equation for the TE
mode19 as follows:
2
4



 2  h 
3  h  
n  1.916  1.145  10 
  1.1651  10 
   0.005 .

 eV 
 eV  


(1)
In addition, it is assumed that a Gaussian distribution expresses the green band of ZnO
when acting as a lasing source with a centre photon energy of 2.2422 eV. Finally, its full
width at half maximum (FWHM) is 0.55eV.
5
The energy positions of the main sharp peaks in the lasing spectrum and those of the
peaks of the calculated TE modes with the highest Q values coincide with each other
over the entire visible region. It is also found that the mode number ranges from 13 to
21, with the order number of all the modes being 1. The loss caused by diffraction is
lower in such modes that it is in modes with higher order numbers. Thus, the
comparison in Fig. S3 shows that the observed lasing modes correspond to those with
the highest Q values, which are theoretically estimated to be on the order of 104–107 on
the basis of the peaks in the lasing spectrum. These Q values would also cause the
lasing threshold to be very low, which was the case as mentioned earlier. That all the
peak positions could be calculated on the basis of the assumption that the ZnO
microsphere was perfectly spherical is further proof of its good sphericity. In addition,
we assume that the other peaks correspond to the second-order modes of TE or to TM
modes whose amplitudes exist inside the sphere. This indicates that only the surface of
the sphere but also its inner shells possess good crystalline quality. It should be
mentioned that a high crystalline quality is crucial for efficient lasing since any
scattering or loss caused by the domain boundaries in polycrystals reduces the Q values.
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Supplementary Figure S3 | Comparison of the experimentally determined and calculated
emission spectra of a ZnO microsphere. a, Lasing emission spectrum of a ZnO microsphere
with a diameter of 1.8 μm at room temperature. An optical image showing it exhibiting green
lasing can be seen in the inset. b, Spectrum of the same microsphere calculated using the Mie
theory. The positions of the TE modes with high Q values as determined by the theoretical
calculations are shown by the dotted lines. The mode and order numbers for the various TE
modes are given as subscripts, respectively, on top.
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Supplementary References
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fabricated by photoelectrochemical etching. Appl. Phys. Lett. 85, 5179–5181 (2004).
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microdisks. Nature Photon. 1, 61–64 (2007).
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Gallery Modes in Nanosized Dielectric Resonators with Hexagonal Cross Section. Phys.
Rev. Lett. 93, 103903 (2004).
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hexagonal nanocavities. Phys. Rev. A 72, 063806 (2005).
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Phys. Lett. 92, 241102 (2008).
21. Dai, J., XU, C. X., Zheng, K., Lv, C. G. & Cui, Y. P. Whispering gallery-mode lasing
in ZnO microrods at room temperature. Appl. Phys. Lett. 95, 241110 (2009).
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Particles. (Wiley Interscience, New York, 1983).
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