1. Introduction

Exciton-polaritons are quasiparticles resulting from the strong coupling of photons and excitons in semiconductors. Cavity polaritons, i.e., the polaritons existing in semiconductor optical microcavities, have attracted much attention in recent years, due to the tunability of the coupling between excitons and the cavity confined photons [1–4]. Since the bosonic nature of cavity polaritons, Bose-Einstein condensation and thus coherent light emission from the condensate of polariton have been observed in various semiconductor microcavities with different morphologies, such as Fabry-Pérote (F-P) planar microcavity or hybird bulk microcavity (two-dimensional system with one-dimensional confinement), microdisk, nanonail or whispering gallery (WG) microcavity (one-dimensional system with two-dimensional confinement) [5–9]. However, despite the above achievements, there is a paucity of research on three-dimensionally confined polaritons. Indeed, the discrete confined momentum makes the light emitting angle precise and controllable. This also in turn generates good selectivity of frequency and polarization. These superiorities are crucial for understanding the dimensionality of cavity polaritons and are of importance for realizing optical modulation and polaritonic devices [10, 11].

Microcavities of ZnO themselves can be both the gain medium and the optical cavities, forming intriguing system for the study of confined polaritons. On one hand, the wide band gap (∼3.37 eV) of ZnO gives rise to the ultraviolet or visible (UV/V) light emission; the large exciton binding energy (∼60 meV) guarantees the stable existence of excitons in ZnO at room temperature; the large oscillator strength ensures the efficient exciton-photon interaction. On the other hand, ZnO has rich morphology and is easy to be synthesized. These regularly shaped ZnO microstructures provide efficient control of light field in multiple dimensions, forming low dimensional optical microcavities, such as WG cavities with high quality factor Q [9, 12]. Although confined polaritons in ZnO are extensively investigated in one-dimensional (1D) or two-dimensional (2D) microcavities, however, three-dimensional (3D) confinement of polariton, as well as its applications, has rarely been explored [2, 4, 13, 14]. So far, the realization of three-dimensionally confined polariton states in ZnO is still a challenging task. In this letter, we demonstrate an additional confinement on the initial 1D polariton systems, i.e., 3D polariton confinement. We used a simple method to synthesize micro-size ZnO cylinder with the hexagonal cross section. Because of the hexagonal cross section, we obtained WG microcavity of ZnO that gave 2D confinement, and the high quality F-P which was formed between the upper and lower smooth surface provided the other 1D confinement. By using the angle-resolved spectroscopic technique, the discrete exciton-polariton dispersions due to the 3D confinement were observed in a single ZnO microcylinder.

2. Experimental details

ZnO microcylinders (MCDs) were synthesized by a chemical vapor deposition method in a conventional horizontal tube furnace without any catalyst [15]. After being washed by de-ionized water, a n-type silicon wafer (111) (1 × 2 cm²) was set at the center of a quartz boat as the substrate of the product. About 0.5 g high-purity of Zn powder (99.9999%) was used as raw material. The boat with the Zn powder was inserted into the center of the horizontal quartz tube located in the middle of the furnace. After purging air in the quartz tube for 20 minutes with 2 L/h N₂, the furnace was heated up to 900°C within 50 minutes under a constant flow of N₂ gas at a rate of 1.5 L/h, then maintain it at 900°C for 40 minutes. In the reaction process, 0.5 L/h N₂ and 0.8 L/h O₂ was introduced into the quartz tube as carrier gas and oxygen source, respectively. After the system was naturally cooled down to room temperature under the constant flow of 1.0 L/h N₂, a layer of white product was obtained on the substrate.

The morphology and structure of the products were characterized using field emission scanning electron microscope (FE-SEM, Hitachi S-4800). Figure 1 shows the high-magnification top-view [Fig. 1(a)] and side-view [Fig. 1(b)] SEM images of the single MCD which was used in the following experiments. From the SEM image [Fig. 1(b)], the height (H) of the selected MCD can be measured as 6.8 µm, and radius R of the hexagonal cross section is about 4.0 µm. Most of the ZnO MCDs are vertically aligned on the substrate. From individual flat-on sample as shown in Fig. 1(c), we found both of the two end facets were flat and smooth, forming the surfaces of F-P microcavity. An energy-dispersive X-ray (EDX) spectroscopy facility attached to the FE-SEM was employed to analyze the chemical composition. Figure 1(d) shows a typical EDX spectrum of one single MCD which indicates the formation of pure ZnO microcrystal. X-ray diffraction analysis (not shown here) indicates that ZnO MCD has a wurtzite structure and preferred orientation along the [0001] direction [Fig. 1(c)].

 

Fig. 1 (a) (b) SEM images of one typical single microcylinder, top-view and side-view (30◦ tilt), respectively. (c) A cylinder 〉at-on the substrate with smooth top and bottom surface. (d) EDX spectrum of single microcylinder. The atom ratio is 48%: 52% for Zn and O.

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Since the size of the single ZnO MCD sample is in the scale of microns, optical confinement effects are expected. To investigate the multiple dimensional confinement of polaritons, we carried out angle-resolved PL spectroscopy measurements on the as-grown single MCD sample. For the optical excitation source we employed a cw He-Cd laser (325 nm). The luminescence of the MCD was collected by a UV objective lens with the numerical aperture of 0.5. As the cylinders grow vertically on the substrate, the laser beam (with a spot diameter of ∼2 µm) was focused on the top facet.

3. Results and discussion

For the polariton in the MCD, the momentum component in the x-y plane as shown in Fig. 2(a) , i.e., $k_{WG}$ is modulated due to the cross-sectional WG microcavity formed by the side facets. Similarly, the momentum component in c-axis $k_{F-P}$ is modulated by the F-P microcavity formed by the parallel end facets of MCD. Therefore, in a three-dimensionally confined microcavity, only some specific discrete values of $k_{polariton}$ ($k_{total}$) that simultaneously satisfy the resonant conditions of the cross-section WG microcavity and the F-P microcavity in c-axis, are allowed [16]. These confined polaritons can escape from every facet of the MCD. In our luminescence acquisition configuration, the signal that can be collected is from the top facet in the angle range of ± 30° (relative to the c-axis) and/or from the side facet in the range of 60°~90° (relative to the x-axis) [Fig. 2(a)]. The confined polaritons emitted from the top facet that can be collected by the objective lens cover the small in-x-y plane momentum (small $k_{WG}$) part of the F-P polariton dispersions. Along each F-P dispersion (E∼$k_{WG}$, fixed $k_{F-P}$) as shown in Fig. 2(c), enhanced polariton states with discrete value of $k_{WG}$ are expected and confirmed. Similarly, Figs. 2(b) and 2(d) show the polartions emitted from the side facets. The detected dispersions are the WG polariton dispersions (E∼$k_{F-P}$, fixed $k_{WG}$) at large momentum, i.e., 60°∼90° relative to the x-axis. The enhanced states with discrete values of $k_{F-P}$ are observed along the dispersions. Since the optical field of WG modes are mainly distributed at the margin area of the hexagonal MCD, the efficiency for WG modes formation is fairly high with the excitation at position A or C on the top facet as shown in Fig. 2(a) [17,18]. This makes the specific discrete spectra resulting from the 3D confinement effect even more clearly.

 

Fig. 2 (a) is the schematic diagram for excitation and collection. (b), (c) and (d) are the resolved PL spectral mapping of single MCD when excited at different positions as shown in the above schematic diagrams. The solid blue curves are theoretical results for F-P polariton modes and dashed red curves indicate the dispersion of WG polariton modes at large angle. The black dots are three-dimensionally confined polariton states by the theoretical simulation.

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As discussed above and shown in Fig. 2, since the micro-size ZnO cylinder confines the polariton in three dimensions, the WG or F-P polariton dispersions display interesting modulation which gives rise to discrete spectra. On one hand, along the c-axis, only particular values of the $k_{F-P}$ are allowed due to the Eq. (1).

Deeper insight into the three-dimensionally confined polariton can be obtained by analyzing the line width and intensity of the discrete spectra. Figure 3 is the luminescence intensity distribution along the two solid curves in Fig. 2(b). Along the red and black solid curves, the polaritons have fixed $k_{WG}$ and $k_{F-P}$, respectively. It can be seen that the obvious periodic oscillation of intensity with $k$manifests the 3D confinement of polaritons. We fit the oscillational data with Gaussian function. From the data fitting, one can obtained the fitness (F) of the cavity, defined as $\Delta k/k_{FWHM}$, where $k_{FWHM}$is the average full width at half maximum (FWHM) of the peaks, and $\Delta k$ is the average peak interval [20]. Larger value of F means higher quality of the cavity and stronger confinement. In Fig. 3(a), polaritons have fixed $k_{WG}$ but variable discrete $k_{F-P}$. This intensity modulation along the dispersion of WG polaritons can be seen clearly. The interval of the peaks is determined by H of the MCD, and the FWHM of the peak is due to the quality of F-P cavity. From the red fitting curve, we obtained $k_{FWHM}$and $\Delta k_{F-P}$ are∼1.76 × 10³ cm⁻¹ and∼5.94 × 10³ cm⁻¹, respectively. And thus the fitness of the F-P cavity, F_{F −P} is about 3.37. Similarly, the black curve in Fig. 3(b) is the fitting result for polaritons with fixed $k_{F-P}$but variable discrete $k_{WG}$. The fitness of the WG cavity F_WG is calculated to be about 3.49. The higher F_WG value compared with F_{F −P} indicates the stronger confinement from the WG modes.

 

Fig. 3 Fluorescence intensity distribute along the two solid curves in Fig. 2(b). The blue solid dots are experiment data fetched along the curves with fixed $k_{WG}$ and$k_{F-P}$, respectively. Solid lines here are theoretical fitting results.

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Figure 4 is magnification of one discrete three-dimensionally confined polariton state that has been circled in Fig. 2(b). It is marked by black cross in Fig. 4. The momentum components ($k_{F-P}$ and $k_{WG}$) of the three-dimensionally confined polariton are both fixed along a and b directions. The intensity distribution of the three-dimensionally confined polariton along the two directions (a (fixed $k_{WG}$) and b (fixed $k_{F-P}$) directions) can be obtained in Fig. 3, as indicated by the gray shadow areas. The polaritons at non-resonant states as the stars shown in Fig. 4 also have fixed momentum, but only along one direction. Taking the intensity of the resonant mode of three-dimensionally confined polariton as I_3D = 1, the relative intensities of these non-resonant modes are I_WG = 0.30, I_F−P = 0.18 respectively, i.e., the PL intensity of the confined polariton resonant mode I_3D = 1 is about twice as large as the sum intensity of I_WG and I_F−P. This is because only the confined polariton resonant modes are allowed due to the three-dimensionally confined conditions. Whilst the states, which do not satisfy the resonant conditions of the 3D confinement are forbidden and the intensity is suppressed [4, 14].

 

Fig. 4 The magnification of the discrete polariton state that has been circled in Fig. 2(b).

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4. Conclusions

In conclusion, we have reported the experimental observation of 3D confinement of polaritons in a single ZnO MCD. This optical microcavity is synthesized by using a simple vapor transportation deposition method and demonstrated to be an efficient three-dimensionally confined resonator with high quality and smooth surfaces. The emission of three-dimensionally confined polaritons is collected by using angle-resolved PL spectroscopic system at room temperature. The discrete energy momentum dispersions of polaritons demonstrated 3D confinement effect in our ZnO MCD. These three-dimensionally confined polariton states are described by the coupled oscillator model and the experiment data fits well with theoretical results. Our work provides a simple way to confine the polariton in a µ-size crystal and may have potential applications in the optical devices.