Quasi-whispering gallery modes of exciton-polaritons in a ZnO microrod

doi:10.1364/OE.18.015371

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Quasi-whispering gallery modes of exciton-polaritons in a ZnO microrod

Liaoxin Sun, Hongxing Dong, Wei Xie, Zhenghua An, Xuechu Shen, and Zhanghai Chen »View Author Affiliations

Optics Express, Vol. 18, Issue 15, pp. 15371-15376 (2010)
http://dx.doi.org/10.1364/OE.18.015371

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– Abstract
1. Introduction
2. Experimental details
3. Results and discussion
4. Conclusions
– References and links

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Abstract

We report the photoluminescence (PL) investigations of quasi-whispering gallery mode (quasi-WGM) polaritons in a ZnO microrod at room temperature. By using the confocal micro-PL spectroscopic technique, we observe the clear optical quasi-WGMs. These quasi-WGMs appeared in the ultraviolet (UV) emission region where the cavity modes strongly couple with excitons and form polaritons. The quasi-WGMs polaritons can be well described by the plane wave interference and the coupling oscillator model.

1. Introduction

It has been proven that the strong interaction between light and the active medium can be greatly enhanced and manipulated by using optical microcavities [1

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992). [CrossRef] [PubMed]

–5

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007). [CrossRef] [PubMed]

]. In semiconductor microcavities, the new quasiparticles, named exciton-polartions, are formed due to the strong coupling between photons and excitons. It has been demonstrated that the efficiency of LED or laser should be greatly increased in this strong coupling regime [6

S. Christopoulos, G. B. von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J. F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007). [CrossRef] [PubMed]

L. S. Dang, D. Heger, R. André, F. Boeuf, and R. Romestain, “Stimulation of Polariton Photoluminescence in Semiconductor Microcavity,” Phys. Rev. Lett. 81(18), 3920–3923 (1998). [CrossRef]

]. Up to now, various types of microcavities have been fabricated and investigated widely. Among them, one of prospective microcavities is whispering gallery mode (WGM) microcavity, which is proposed to play an important role in optoelectronic devices [8

V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004). [CrossRef] [PubMed]

–10

C. Li, L. Zhou, S. Zheng, and A. W. Poon, “Silicon Polygonal Microdisk Resonators,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1438–1449 (2006). [CrossRef]

Recently, ZnO nanowires with hexagonal cross section functioned as WGM microcavities have been reported [11

T. Nobis, E. M. Kaidashev, A. Rahm, M. Lorenz, and M. Grundmann, “Whispering gallery modes in nanosized dielectric resonators with hexagonal cross section,” Phys. Rev. Lett. 93(10), 103903 (2004). [CrossRef] [PubMed]

,12

L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100(15), 156403 (2008). [CrossRef] [PubMed]

]. The incident light, from visible to UV with the photon energies below the band gap of ZnO can stimulate the standing wave eigen-modes in the hexagonal cross section plane of the ZnO nanowire, due to the internally total reflection at the interfaces inside a WG microcavity. The overlapping between the optical cavity modes and the elementary excitations, such as excitons in the cavity medium, can be nearly unity since the whole cavity volume is at the same time the active medium of the excitation. This is greatly different from the planar cavity where the active region can be as thin as a quantum well. Moreover, as a wide bandgap semiconductor, ZnO has a large exciton binding energy (~60 meV) and strong oscillator strength, making it an ideal material for the exploration of light-matter interaction physics and thus device applications at room temperature.

In a hexagonal cavity, besides the WGMs with a hexagonal light-path (Fig. 1(a) ), there exist the so-called quasi-WGMs whose light-path is triangular (Fig. 1(b)) (the critical angle for the internally total reflection at the medium-air interface is 23.5°, as simply calculated from the refraction indices [13

D. Wang, H. W. Seo, C.-C. Tin, M. J. Bozack, J. R. Williams, M. Park, and Y. Tzeng, “Lasing in whispering gallery mode in ZnO nanonails,” J. Appl. Phys. 99(9), 093112 (2006). [CrossRef]

]). Unlike the WGMs, the quasi-WGMs are difficult to be observed and are less understood due to the much smaller quality factor Q. In this work, we explore this kind of WGM, i.e. the quasi-WGMs, and their coupling with the excitons in a high quality ZnO tapered microrod. To our knowledge, the polariton effects of quasi-WGMs in ZnO microcavities have never been reported up to date.

Fig. 1 Schematic pictures of WGM polariton waveguide (a) and quasi-WGM polariton waveguide (b), (c) The WGMs (solid arrows) and quasi-WGMs (dashed arrows) appear in the TM polarized detection. The fitted red and green peaks with Lorentzian line shape correspond to WGMs and quasi-WGMs respectively. The inset, the PL spectra obtained at certain position of the microrod with unpolarized, TE and TM polarized detection, respectively. The dashed lines are guides for the eye.

2. Experimental details

The high quality ZnO microrods used in the experiment were synthesized on silicon substrate by vapor-phase transport method [14

K. Yu, Y. Zhang, R. Xu, S. Ouyang, D. Li, L. Luo, Z. Zhu, J. Ma, S. Xie, S. Han, and H. Geng, “Efficient field emission from tetrapod-like zinc oxide nanoneedles,” Mater. Lett. 59(14-15), 1866–1870 (2005). [CrossRef]

]. For the micro-PL measurement of a single microrod, we first disperse the microrods in ethanol by sonicating and then transfer them onto a transparent quartz slide. These microrods are single crystals with wurtzite structure and hexagonal cross section perpendicular to the longitudinal crystal axis (c-axis). The photoluminescence emission of single microrod is collected by using a confocal microscopic optics (JY-Horiba LabRam HR800 UV) with sub-μm spatial resolution; the excitation light source used in the measurements is a pulse laser with wavelength of 371 nm. The detection of photoluminescence signal is performed in different polarization configurations, i.e. in TE (with the electrical component of the emitted light perpendicular to the c-axis, E⊥c-axis), TM (E∥c-axis) and unpolarized configurations, respectively, while the excitation laser beam is polarized along c-axis in all measurements.

3. Results and discussion

We show in Fig. 1(c) the micro-PL spectrum measured in TM polarized detection and at a certain position of the ZnO microrod. The PL spectra measured at the same position but in different detection configurations, i.e. TE, TM and unpolarized detection configurations, respectively, are also shown in the inset of Fig. 1(c). It is seen that the spectra are composed of a series of peaks. The facts are related with the multi-mode behavior of the microcavity since the radius of the microrod used in the experiment is about 786 nm. In TM detection, the series of peaks can be attributed to the luminescence of the polaritons from the strong coupling between the cavity modes (of different orders) and the C-exciton of the ZnO medium, while in TE detection, those peaks are related with A- and B-excitonic polaritons [12

]. More importantly, it is also seen from Fig. 1(c) that there are fine structures in the luminescence bands. In general, the spectra measured in TM detection configuration are composed of sub-peak series, as shown by the fitted dotted and solid curves series in Fig. 1(c). To confirm the fine structures and explore their physical mechanism, we performed the scanning micro-PL measurement along the c-axis. The results are shown in Fig. 2 . It is demonstrated that the series of double peaks behavior persist in all the spectra measured at different positions, and blueshift in energy with the decrease of the radius of the tapered microrod. Here, we attribute the solid and dotted curve series to the quasi-WGMs and WGMs, respectively.

Fig. 2 Spatially resolved PL mapping along the tapered microrod with the detection of TM polarization. The quasi-WGMs with N of 22 and 23 are marked by dashed lines.

In theory, we can use the plane wave model to describe the optical cavity modes because the model is more accurate for small 1/Re(kR), where k is the wave-vector of light and R is the radius of the microrod. The physical idea of the model is that the light wave circulating inside a cavity can constructively interfere with itself when the total phase shift equal to an integer multiple of 2π [15

J. Wiersig, “Hexagonal dielectric resonators and microcrystal lasers,” Phys. Rev. A 67(2), 023807 (2003). [CrossRef]

]. This model has been successfully applied to the WG cavity modes and their polaritons in tapered ZnO nanorod with even smaller diameter [12

]. The radius of the circum-circle of the resonator, R is related with the mode parameters and can be written as:

R = \frac{h c}{3 \sqrt{3} n E} [N + \frac{6}{π} \arctan (\frac{1}{n} \sqrt{3 n^{2} - 4})]

(1)

for the WGMs established along the hexagonal path (Fig. 1(a)) inside the resonator in the TM detection configuration. The Eq. (1) can be revised and written as:

R = \frac{2 h c}{9 n E} [N + \frac{3}{π} \arctan (\frac{1}{n} \sqrt{\frac{1}{3} (n^{2} - 4)})]

(2)

for the quasi-WGM, i.e. the standing wave modes established along the triangle path shown in Fig. 1(b). Here, h is the Planck constant, n is the refractive index of ZnO and it is a function of light frequency, c is the light velocity. The integer N is the interference order of the resonance, and the term with arctangent function corresponds to the polarization dependent negative phase shift.

Since the energies of the optical modes in the UV region are close to those of the excitons, the strong interaction between these modes and the excitons is expected, and the excitonic polariton effect has to be included for proper understanding of the UV luminescence spectra of ZnO micro-structures. From the Lorentzian fitting of the TM polarized spectrum (Fig. 1(c)), one can see that the energy spacings between neighboring modes are becoming smaller with the energy blueshifting towards the exciton resonance for both TE and TM polarization. This phenomenon deviates from the classical WGM resonance. To get a better understanding of the spectral nature in UV emission region, one must take into account the polariton effects induced by the interaction between optical modes and excitons. The typical ZnO conduction band consists of s-like states and the valence band consists of p-like state which is split into three bands (namely A, B and C bands) due to the crystal-field effects and the spin-orbit interactions [16

D. C. Reynolds, D. C. Look, B. Jogai, C. W. Litton, G. Cantwell, and W. C. Harsch, “Valence-band ordering in ZnO,” Phys. Rev. B 60(4), 2340–2344 (1999). [CrossRef]

]. According to the selection rules, A and B excitonic transition are allowed in the σ polarization (E⊥c-axis and k⊥c-axis) but C-exciton transition is quite weak in this configuration, the C excitonic transition is permitted in the π polarization (E∥c-axis and k⊥c -axis), while A-exciton transition is forbidden, and B-exciton transition is weakly allowed. As a consequence, it is expected that the different polarized modes (TE, TM) will interact with different polarized free excitons (A, B and C exciton). In this case, the TE modes couple with A and B-exciton and the TM modes mainly couple with C-exciton.

Based on the above discussions, we give a theoretical computation to our experimental results. We find that the experimental behaviors can be well interpreted by using the plane wave mode equation for the WGM and the polariton dispersion of ZnO [12

,17

L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97(14), 147401 (2006). [CrossRef] [PubMed]

]. In the coupling oscillator model, the refractive index and the polariton dispersion can be described in the simple dielectric approximation form as follows:

n^{2} = ε_{\infty} (1 + \sum_{i = A, B, C} Ω_{i} \frac{ω_{i, L}^{2} - ω_{i, T}^{2}}{ω_{i, T}^{2} - ω^{2} - i ω Γ_{i}}) = \frac{c^{2} k^{2}}{ω^{2}}

(3)

where the ε_∞ is the background dielectric constant, ω_i,L and ω_i,T are the longitudinal and transverse resonance frequencies respectively, at k = 0, Γ _i is the damping constants, and Ω _i is a parameter determined by the ω_i,L and ω_i,T [18

J. Lagois, “Depth-dependent egienenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23(10), 5511–5520 (1981). [CrossRef]

]. A computational analysis is performed by combining the Eq. (1), (2) respectively with Eq. (3); and the calculated result for the dispersion of C-exciton polariton in k space is shown in Fig. 3 . It can be seen that the dispersion curves are coincident with each other for polaritons formed from WGMs and quasi-WGMs, observed in our experiments (Fig. 1(c)). From the excellent fitting between the calculation and experimental results, we conclude that the series of double peaks shown in Fig. 1(c) are from quasi-WGM polaritons with mode indices N of 21, 22, 23, and 24, and the WGM polaritons with N of 23, 24, 25, 26, and 27, as labeled by dashed and solid arrows in Fig. 1(c). In addition, it is surprising that both WGMs and quasi-WGMs follow the similar dispersion curve though the quality factor of quasi-WGMs is lower than that of the WGMs. As we know, the quality factor Q plays a key role in the light-matter interaction. However, our results indicate that the coupling strength of polaritons in ZnO very weakly depends on the Q factors of resonators. This behavior may be due to the extremely strong oscillator strength of excitons in ZnO.

Fig. 3 The comparison between the theoretically calculated dispersions and experimental results for TM configuration. The energies of B-, C-exciton are shown with black lines.

It should be mentioned that the series of double peaks behavior seems to be traceable in the luminescence spectra measured with unpolarized and TE detection configurations, respectively, though they are not as clear as in the case of TM configuration. This is probably due to the small quality factors Q of the TE polarized modes [11

,19

L. Sun, Z. Chen, Q. Ren, K. Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Phys. Status Solidi C 6(1), 133–136 (2009). [CrossRef]

]. In such a microrod resonator with waveguide modes along the vertical direction (c-axis), the vertical radiation will greatly influence the Q factors of the WGMs and the quasi-WGMs. For the TM polarized modes, the vertical radiation loss is negligible, while for the TE polarized modes, they can couple with the vertical waveguide modes, which results in a low Q factor [20

Y.-D. Yang, Y.-Z. Huang, W.-H. Guo, Q. Lu, and J. F. Donegan, “Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators,” Opt. Express 18(12), 13057–13062 (2010). [CrossRef] [PubMed]

4. Conclusions

In summary, we have demonstrated quasi-WGM polaritons in a ZnO microrod at room temperature. Due to the quality factor with polarization dependence, the quasi-WGMs can be observed in TM polarization detection. The spatially resolved PL mapping along the tapered ZnO microrod verified the observation of quasi-WGMs polaritons. Both WGMs and quasi-WGMs are well described by the corresponding mode equations and the ZnO dispersion relation. In addition, the similar dispersion behavior for the WGMs and the quasi-WGMs implied that the Q factors of resonators contribute very little to the coupling strength between cavity modes and excitons in ZnO. By optimizing the synthesis process or introducing nanofabrication techniques, one can further improve the surface quality of the cavity structures, and the quasi-WGMs would be easier to observe. This may provide alternative candidates for studying polariton physics and developing of polariton devices.

Acknowledgments

This work was supported by the National Fundamental Research Program Grant. 2006CB921106, the special funds for Major State Basic Research Project of China No. G2009CB929300, Natural Science Foundation of China.

References and links

1.	C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992). [CrossRef] [PubMed]
2.	A. Tredicucci, Y. Chen, V. Pellegrini V, M. Börger, L. Sorba, F. Beltram, and F. Bassani, “Controlled Exciton-Photon Interaction in Semiconductor Bulk Microcavities,” Phys. Rev. Lett. 75(21), 3906–3909 (1995). [CrossRef] [PubMed]
3.	D. Snoke, “Spontaneous Bose coherence of excitons and polaritons,” Science 298(5597), 1368–1372 (2002). [CrossRef] [PubMed]
4.	J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature 443(7110), 409–414 (2006). [CrossRef] [PubMed]
5.	R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007). [CrossRef] [PubMed]
6.	S. Christopoulos, G. B. von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J. F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007). [CrossRef] [PubMed]
7.	L. S. Dang, D. Heger, R. André, F. Boeuf, and R. Romestain, “Stimulation of Polariton Photoluminescence in Semiconductor Microcavity,” Phys. Rev. Lett. 81(18), 3920–3923 (1998). [CrossRef]
8.	V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004). [CrossRef] [PubMed]
9.	N. Ma, C. Li, and A. W. Poon, “Laterally Coupled Hexagonal Micropillar Resonator Add-Drop Filters in Silicon Nitride,” IEEE Photon. Technol. Lett. 16(11), 2487–2489 (2004). [CrossRef]
10.	C. Li, L. Zhou, S. Zheng, and A. W. Poon, “Silicon Polygonal Microdisk Resonators,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1438–1449 (2006). [CrossRef]
11.	T. Nobis, E. M. Kaidashev, A. Rahm, M. Lorenz, and M. Grundmann, “Whispering gallery modes in nanosized dielectric resonators with hexagonal cross section,” Phys. Rev. Lett. 93(10), 103903 (2004). [CrossRef] [PubMed]
12.	L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100(15), 156403 (2008). [CrossRef] [PubMed]
13.	D. Wang, H. W. Seo, C.-C. Tin, M. J. Bozack, J. R. Williams, M. Park, and Y. Tzeng, “Lasing in whispering gallery mode in ZnO nanonails,” J. Appl. Phys. 99(9), 093112 (2006). [CrossRef]
14.	K. Yu, Y. Zhang, R. Xu, S. Ouyang, D. Li, L. Luo, Z. Zhu, J. Ma, S. Xie, S. Han, and H. Geng, “Efficient field emission from tetrapod-like zinc oxide nanoneedles,” Mater. Lett. 59(14-15), 1866–1870 (2005). [CrossRef]
15.	J. Wiersig, “Hexagonal dielectric resonators and microcrystal lasers,” Phys. Rev. A 67(2), 023807 (2003). [CrossRef]
16.	D. C. Reynolds, D. C. Look, B. Jogai, C. W. Litton, G. Cantwell, and W. C. Harsch, “Valence-band ordering in ZnO,” Phys. Rev. B 60(4), 2340–2344 (1999). [CrossRef]
17.	L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97(14), 147401 (2006). [CrossRef] [PubMed]
18.	J. Lagois, “Depth-dependent egienenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23(10), 5511–5520 (1981). [CrossRef]
19.	L. Sun, Z. Chen, Q. Ren, K. Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Phys. Status Solidi C 6(1), 133–136 (2009). [CrossRef]
20.	Y.-D. Yang, Y.-Z. Huang, W.-H. Guo, Q. Lu, and J. F. Donegan, “Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators,” Opt. Express 18(12), 13057–13062 (2010). [CrossRef] [PubMed]

OCIS Codes
(250.5230) Optoelectronics : Photoluminescence
(140.3945) Lasers and laser optics : Microcavities
(160.4236) Materials : Nanomaterials

ToC Category:
Optoelectronics

History
Original Manuscript: May 28, 2010
Revised Manuscript: June 24, 2010
Manuscript Accepted: June 24, 2010
Published: July 2, 2010

Citation
Liaoxin Sun, Hongxing Dong, Wei Xie, Zhenghua An, Xuechu Shen, and Zhanghai Chen, "Quasi-whispering gallery modes of exciton-polaritons in a ZnO microrod," Opt. Express 18, 15371-15376 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-15371

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References

C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992). [CrossRef] [PubMed]
A. Tredicucci, Y. Chen, V. Pellegrini, M. Börger, L. Sorba, F. Beltram, and F. Bassani, “Controlled Exciton-Photon Interaction in Semiconductor Bulk Microcavities,” Phys. Rev. Lett. 75(21), 3906–3909 (1995). [CrossRef] [PubMed]
D. Snoke, “Spontaneous Bose coherence of excitons and polaritons,” Science 298(5597), 1368–1372 (2002). [CrossRef] [PubMed]
J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and S. Dang, “Bose-Einstein condensation of exciton polaritons,” Nature 443(7110), 409–414 (2006). [CrossRef] [PubMed]
R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose-Einstein condensation of microcavity polaritons in a trap,” Science 316(5827), 1007–1010 (2007). [CrossRef] [PubMed]
S. Christopoulos, G. B. von Högersthal, A. J. D. Grundy, P. G. Lagoudakis, A. V. Kavokin, J. J. Baumberg, G. Christmann, R. Butté, E. Feltin, J. F. Carlin, and N. Grandjean, “Room-temperature polariton lasing in semiconductor microcavities,” Phys. Rev. Lett. 98(12), 126405 (2007). [CrossRef] [PubMed]
L. S. Dang, D. Heger, R. André, F. Boeuf, and R. Romestain, “Stimulation of Polariton Photoluminescence in Semiconductor Microcavity,” Phys. Rev. Lett. 81(18), 3920–3923 (1998). [CrossRef]
V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Nonlinear optics and crystalline whispering gallery mode cavities,” Phys. Rev. Lett. 92(4), 043903 (2004). [CrossRef] [PubMed]
N. Ma, C. Li, and A. W. Poon, “Laterally Coupled Hexagonal Micropillar Resonator Add-Drop Filters in Silicon Nitride,” IEEE Photon. Technol. Lett. 16(11), 2487–2489 (2004). [CrossRef]
C. Li, L. Zhou, S. Zheng, and A. W. Poon, “Silicon Polygonal Microdisk Resonators,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1438–1449 (2006). [CrossRef]
T. Nobis, E. M. Kaidashev, A. Rahm, M. Lorenz, and M. Grundmann, “Whispering gallery modes in nanosized dielectric resonators with hexagonal cross section,” Phys. Rev. Lett. 93(10), 103903 (2004). [CrossRef] [PubMed]
L. Sun, Z. Chen, Q. Ren, K. Yu, L. Bai, W. Zhou, H. Xiong, Z. Q. Zhu, and X. Shen, “Direct observation of whispering gallery mode polaritons and their dispersion in a ZnO tapered microcavity,” Phys. Rev. Lett. 100(15), 156403 (2008). [CrossRef] [PubMed]
D. Wang, H. W. Seo, C.-C. Tin, M. J. Bozack, J. R. Williams, M. Park, and Y. Tzeng, “Lasing in whispering gallery mode in ZnO nanonails,” J. Appl. Phys. 99(9), 093112 (2006). [CrossRef]
K. Yu, Y. Zhang, R. Xu, S. Ouyang, D. Li, L. Luo, Z. Zhu, J. Ma, S. Xie, S. Han, and H. Geng, “Efficient field emission from tetrapod-like zinc oxide nanoneedles,” Mater. Lett. 59(14-15), 1866–1870 (2005). [CrossRef]
J. Wiersig, “Hexagonal dielectric resonators and microcrystal lasers,” Phys. Rev. A 67(2), 023807 (2003). [CrossRef]
D. C. Reynolds, D. C. Look, B. Jogai, C. W. Litton, G. Cantwell, and W. C. Harsch, “Valence-band ordering in ZnO,” Phys. Rev. B 60(4), 2340–2344 (1999). [CrossRef]
L. K. van Vugt, S. Rühle, P. Ravindran, H. C. Gerritsen, L. Kuipers, and D. Vanmaekelbergh, “Exciton polaritons confined in a ZnO nanowire cavity,” Phys. Rev. Lett. 97(14), 147401 (2006). [CrossRef] [PubMed]
J. Lagois, “Depth-dependent egienenergies and damping of excitonic polaritons near a semiconductor surface,” Phys. Rev. B 23(10), 5511–5520 (1981). [CrossRef]
L. Sun, Z. Chen, Q. Ren, K. Yu, W. Zhou, L. Bai, Z. Q. Zhu, and X. Shen, “Polarized photoluminescence study of whispering gallery mode polaritons in ZnO microcavity,” Phys. Status Solidi C 6(1), 133–136 (2009). [CrossRef]
Y.-D. Yang, Y.-Z. Huang, W.-H. Guo, Q. Lu, and J. F. Donegan, “Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators,” Opt. Express 18(12), 13057–13062 (2010). [CrossRef] [PubMed]

André, R.
Arakawa, Y.
Baas, A.
Bai, L.
Balili, R.
Bassani, F.
Baumberg, J. J.
Beltram, F.
Boeuf, F.
Börger, M.
Bozack, M. J.
Butté, R.
Cantwell, G.
Carlin, J. F.
Chen, Y.
Chen, Z.
Christmann, G.
Christopoulos, S.
Dang, L. S.
Dang, S.
Deveaud, B.
Donegan, J. F.
Feltin, E.
Geng, H.
Gerritsen, H. C.
Grandjean, N.
Grundmann, M.
Grundy, A. J. D.
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