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,*
1Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyamacho,
Toyonaka, Osaka 560-8531, Japan
2Nanoscience and Nanotechnology Research Center, Osaka Prefecture University, 1-2,
Gakuencho, Nakaku, Sakai, Osaka 599-8570, Japan
3Department of Physics and Electronics, Osaka Prefecture University, 1-1 Gakuencho,
Sakai, Osaka 599-8531, Japan
4Institute for NanoScience Design, Osaka University, 1-3 Machikaneyamacho,
Toyonaka, Osaka 560-8531, Japan
*e-mail: [email protected]
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
4 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 1.14510 1.165110 0.005 . (1) eV eV
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
5 width at half maximum (FWHM) is 0.55eV.
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.
6 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.
7 Supplementary References
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