Optical modulation of ZnO microwire optical resonators with a parallelogram cross-section

Abstract

A novel ZnO microwire optical resonator with a parallelogram cross-section is fabricated, which can effectively control the light field in two dimensions. Wave-guided Fabry–Pérot modes with different polarizations are directly observed and further investigated systematically. Such a ZnO optical resonator offers another building block for the development of optoelectronic devices.

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Wide-band-gap semiconductor oxide microcavities have attracted much attention and become important for developing optoelectronic devices due to their microscopic size, high quality factor Q and low lasing threshold power.^1–3 In semiconductor micro/nanostructure optical resonators, the transmission of light can be at least restricted and modulated in two dimensions, and the electromagnetic field of light may be precisely controlled. These restrictions and modulations of light depend on the shape and structure of the semiconductor micro/nanostructure. To achieve precise manipulation of the light–matter interaction, the micro/nanostructure usually requires high crystal quality, regular geometrical structure, smooth surfaces and the structure to be approximately the same size as the wavelength. Because of these strict requirements, the investigations so far are limited to nanobelt/nanowire Fabry–Pérot (FP) microcavities⁴ and nanowires with hexagonal cross-section whispering gallery (WG) microcavities,^5–8 which can be easily obtained using a conventional chemical vapor deposition method. Other kinds of optical cavity are rarely reported due to the difficulty of the sample preparation. In a way, such cavity structure and resonant mode limitations will hinder fundamental physics research in the field of cavity quantum electrodynamics and the development of miniature optoelectronic devices. Thus, it is an imperative and challenging issue to develop new and efficient optical microcavities.

ZnO is one of the most promising materials for the development of high efficiency UV and visible optoelectronic devices due to its wide band gap (3.37 eV) and large exciton binding energy (∼60 meV). Intense efforts have been undertaken over the past decade to attain optical microcavities with different geometrical configurations using ZnO as an optical material.^9–13 Up to now, various synthesis methods have been developed to prepare 1D ZnO micro/nanostructures, such as vapor-phase deposition,^5,14 hydrothermal,^15,16 template-assisted¹⁷ and other wet chemical methods.^18,19 However, due to the intrinsic growth habit of wurtzite ZnO crystals with three fast growth directions of [0001], [101̄0] and [21̄1̄0], most of the 1D ZnO micro/nanostructures including nanowires, nanorods and nanotubes have hexagonal cross-sections along the c-axis direction, which has greatly restricted the development of ZnO microcavities and their applications. Here, we present the synthesis of a novel ZnO microcavity with a parallelogram cross-section, which can effectively control the light field. The optical modulations induced in such ZnO microcavities were directly observed at room temperature using a spatially resolved micro-confocal spectroscopic system. A wave-guided FP mode was identified using calculations based on the plane wave interference model and further confirmed by Finite Element Method (FEM) simulations. The Sellmeier dispersion function fitted well with the calculated wavelength-dependent refractive indices. Furthermore, the size-dependent cavity modulation behaviours of the optical resonators were also investigated in detail. Such a ZnO optical resonator with a parallelogram cross-section offers another new practical example for investigating cavity physics and developing novel optical devices, such as laser beam shaping devices and filter combined route switchers.

ZnO microwires were grown using a simple carbothermal reduction method in a horizontal tube furnace. In our experiment, a mixture of ZnO (99.99%), Sb₂O₃ (99.99%) and graphite (99.99%) powders (all reagents were purchased from Shanghai Chemical Reagent Co.) with a mole ratio 40 : 1 : 40 was put into a small quartz boat and covered with an alumina ceramic substrate. Sb₂O₃ was used as a dopant. The quartz boat was then placed in the center of the tube furnace and the air inside the tube was purged by high-purity N₂. The temperature of tube furnace was raised to 1000 °C with a N₂ flow rate of 60 sccm (standard-state cubic centimeter per minute). When the temperature reached 1000 °C, a mixed gas of N₂ (80 sccm) and O₂ (5 sccm) was introduced into the quartz tube for 30 min. After the reaction, a large quantity of crystal-like products was obtained on the substrate.

The morphology, composition and structure of the obtained products were characterized by field emission scanning electron microscopy (FE-SEM, Zeiss Auriga S40), high-resolution transmission electron microscopy (HRTEM, JEOL JEOL-2010), energy dispersive X-ray spectroscopy (EDS) and X-ray diffraction (XRD, PANalytical Empyrean) with Cu Kα radiation (λ = 1.54 Å). The optical properties of the ZnO microwires were measured using a confocal microphotoluminescence system (JY LabRAM HR800 UV) using a He–Cd laser of 325 nm as the excitation source. FEM simulations were performed using a commercial finite element software (COMSOL Multiphysics). In our calculations, a tiny loss was added to the dielectric constant of ZnO to make the spectra converge more easily.

Fig. 1(a) shows a typical SEM image of synthesized samples. It can be seen that a large quantity of wire-like microstructures with smooth surfaces was fabricated on the alumina ceramic substrate. Most of the microwires have diameters in the range of 4–6 μm and lengths exceeding 100 μm. Some microwires with smaller sizes of about a few hundred nanometers are also observed. Fig. 1(b) shows the detailed geometrical morphology of one single dispersed ZnO microwire with a diameter of about 5 μm and length of about several hundred micrometers. The inset of Fig. 1(b) shows the cross-section of the ZnO microwire observed by vertically rotating the sample. It is surprising to find that the obtained ZnO microwire has a non erratic parallelogram cross-section with an interior angle of 45°, which is rarely reported in previous literature. The corresponding XRD pattern (Fig. 1(c)) shows that these novel ZnO microwires are indexed as the typical hexagonal wurtzite-type ZnO (JCPDS no. 36-1451). The EDS data of the ZnO microwires indicate that the ZnO is indeed stoichiometric in composition. In addition, to get further information about the microstructure of the ZnO microwires, TEM analysis was performed. Fig. 1(d) shows the TEM image of one single ZnO microwire of a smaller size. The high-resolution TEM image taken from the rectangular region marked in Fig. 1(d) (Fig. 1(e)) and the corresponding selected area electron diffraction (SAED) pattern (inset in Fig. 1(e)) clearly illustrate the high crystalline quality nature of these novel ZnO microwires. In fact, ZnO microwires with a hexagonal cross-section were obtained if the Sb₂O₃ powders were removed from the source materials during the growth process (Fig. S1a†). Also, the X-ray photoelectron spectrum (XPS, Fig. S1b†) and Raman spectrum (Fig. S1c†) illustrated that a small amount of the element Sb has been introduced into the ZnO crystals.

Fig. 1 (a) Typical SEM image of the ZnO microwires. (b) SEM images of a single microwire dispersed on a Si wafer and its cross-section view (inset) from the rectangular region. (c) XRD pattern and EDS spectrum (inset) of the obtained ZnO microwires. (d) TEM image of a single ZnO nanowire. (e) HRTEM image and the corresponding SAED pattern (inset) from the rectangular region marked in (d).

Optical property measurements of individual ZnO microwires were carried out with a micro-confocal photoluminescence spectroscopic system. The experimental setup is shown in Fig. 2(a). The excitation laser was focused on a 2 μm spot on the ZnO microwire at the position that was marked by a red cross (inset SEM image of Fig. 2(a)). We performed photoluminescence (PL) measurements with detections of unpolarized, TE-polarized (the electrical component of light E⊥c-axis) and TM polarized (the electrical component of light E∥c-axis) signals respectively. Three different PL signals in the range of 360–700 nm with clear modulations were obtained, and the results are shown in Fig. 2(b). The origin of the visible emission is generally related to impurities and/or point defects.²⁰ The UV emission peak centered at about 385 nm is the band-edge emission resulting from exciton transitions and their photo replicas.²¹ These distinct modulations correspond to the resonance of optical modes, and both TE and TM polarized modes are clearly seen in the entire light emitting region.

Fig. 2 (a) Schematic setup for the microphotoluminescence experiments. (b) PL spectra with unpolarized, TE and TM polarized light and three different resonant mode types (insets) can be formed in the parallelogram cross-section of an individual ZnO microwire: simple FP modes (I and II), bow-tie like modes (III) and wave-guided FP modes (IV and V). (c) The related refractive indices of the ZnO microwire at every resonance peak. (d) Enlarged view of the resonance peaks between 380 and 410 nm of the ZnO microwires with TE and TM polarization configurations (dashed rectangular region marked in (b)). The two series of integers are the interference orders of the resonant modes.

From the point of view of geometrical optics, three kinds of resonant cavity modes can be formed (insets of Fig. 2(b)): (i) simple FP modes (I and II) formed between the two opposite facets, (ii) bow-tie like modes (III), formed by a crossing light beam as reported in the In₂O₃ octahedral microcavity²² and (iii) wave-guided FP modes (IV and V) formed in the two pairs of opposite facets with an incident angle of 45°. In order to determine the exact cavity mode related to the PL signal, two adjacent peaks (at λ₁ = 506.9 nm, λ₂ = 521.9 nm) were selected from the TM signal to calculate the effective optical path length L by the following function:

where n is the refractive index of the medium, and dn/dλ is the dispersion relation. The mode spacing Δλ between the two adjacent peaks is 15.0 nm. The refractive index n = 2.057 (λ₁ = 506.9 nm) and the related λdn/dλ = −0.639 were obtained according to the refractive dispersion of ZnO in ref. 9, and the calculated path length is about 6.35 μm. Geometrical optics and a typical plane wave model were used to give a further exploration of the characteristics of the ZnO microwire microcavities. The side lengths of the microwire used in the PL measurement are R₁ = 1.97 μm and R₂ = 1.94 μm, which were determined from the SEM image. If the resonant modes were simple FP modes, then the deduced path lengths were (mode I); (mode II). If the resonant modes were related to bow-tie like modes, the calculated (mode III). Obviously, the above calculated effective path lengths are all much smaller than the calculated effective path lengths (6.35 μm) according to eqn (1), which indicates that the resonant modes are from neither the simple FP modes nor bow-tie like modes. However, in the wave-guided FP modes, the relevant path lengths are (mode IV); (mode V), which are consistent with the L calculated in the above theoretical analysis. Thus, we can conclude that the measured resonant modes are attributed to the effect of the wave-guided FP mode-type microcavity. For such wave-guided FP modes, the incident angle is 45° and there are four total internal reflections (TIRs) along one full path. Two opposite parallel facets of microwires act as reflecting mirrors and the other two facets act as TIR interfaces. The light wave between two parallel faces must travel through two TIRs forward and another two TIRs back. Such a wave-guided FP mode microcavity can effectively control the transmission and enhancement of a light field, which may make it a good candidate for the development of relevant optical devices.

To further understand the modulation behaviour of the parallelogram microwire optical microcavity, the classical plane wave model was used to fit the experimental results. The effective cavity length can be obtained from the following equation:

here n is the refractive index of the ZnO sample, and N is the interference order of the resonant mode. The factor β depends on polarization; for TE polarization β = n, for TM polarization β = 1/n. The actual refractive index of the ZnO microwire can be obtained from the best fit of the above wave-guided FP equation (eqn (2)). The refractive dispersion of ZnO in the visible range⁹ and effective cavity length L = 6.67 μm were used to initially identify the interference order N for the TE and TM modes. We found that the calculated results are not in good agreement with the obtained peak positions. Considering the wavelength dependence of the refractive index, the best fit of the interference order (N_TE = 17–41, N_TM = 18–42) was obtained by varying N systematically and the cavity length L within the experimental error. Two series of integers (shown in Fig. 2(d)) are the interference orders for the relevant resonant modes between 380 nm and 410 nm. The accurate wavelength-dependent refractive dispersions (n_TE, n_TM) of the ZnO microwire were calculated using the obtained interference orders and the cavity length L, and the result is shown in Fig. 2(c). A similar fitting process has been applied to calculate the refractive indices of the ZnO nanowire.²³ From Fig. 2(c), it can be seen that there is a very slight difference between n_TE and n_TM at the same wavelength, which indicates that the birefringence phenomenon of the ZnO crystal is not obvious. The obtained scattered wavelength-dependent refractive indices can be fitted well with a Sellmeier dispersion function, and the dispersion formulas for the TE and TM polarization are described as follows:

FEM simulations were performed to identify the optical modes in the ZnO microcavity with a parallelogram cross-section. In our calculations, a 2D parallelogram model with the same dimensions as the sample in the PL measurement was created (the edge lengths set to R₁ = 1.97 μm, R₂ = 1.94 μm and the cross angle to 45°). Its refractive index was chosen from the values shown in Fig. 2(c). The microcavity was placed in a simulation box with an upper boundary of a plane wave source and the other boundaries set as perfectly matched layers to absorb the scattered electromagnetic fields. Illuminated by normally incident light on the top surface of the microcavity, the backward reflectance spectra were measured for both TE (shown in Fig. 3(b)) and TM (shown in Fig. 3(d)) polarization. The simulated resonance peaks for both the TE and TM cases perfectly match with the experimental results. To identify the nature of these resonance modes more clearly, we have also studied our system based on the eigenmode analysis simulation. The eigenfrequency analysis solver of COMSOL Multiphysics was employed to search the resonance modes supported by the parallelogram microcavity. Taking the dispersive property of ZnO fully into account, an iterative calculation method was employed to gradually approach the eigenmodes and finally get convergent results. The accuracy can be well controlled by the iteration number and the tolerance parameter. It can not only find the resonance wavelengths of the FP modes inside the microcavity, but also illustrate their mode field patterns. For example, several eigenmodes are illustrated in Fig. 4 with their wavelengths shown as insets. They perfectly match with the resonance positions of the reflectance spectra shown in Fig. 3. This means that the pictures of the optical modes observed in our experiments should look like the mode profiles shown in Fig. 4. Obviously, standing waves are formed between the upper and lower boundaries of the microcavity with the two inclined boundaries serving as totally reflective mirrors. They are just the wave-guided FP modes predicted by the above analysis based on a plane wave model.

Fig. 3 TE (a) and TM (c) polarized PL spectra of a single ZnO microwire. As a comparison, the FEM simulated backward reflectance spectra are shown in (b) and (d) with the corresponding polarizations to that of (a) and (c). In our calculations, a tiny loss is added in the dielectric constant of ZnO to make the spectra converge more easily.

Fig. 4 Simulated H_z (a) and E_z (b) field distributions of some resonance modes inside the parallelogram microcavity for TE (a) and TM (b) polarization. The resonance wavelength of each mode is inserted in the figures.

To investigate the relationship between the wave-guided FP resonance modes and the sizes of the microwire microcavities, the PL spectra of ZnO microwire microcavities with different side lengths (R = 1.38, 2.37, 4.28 μm) were measured. As shown in Fig. 5, the PL signals within the UV and visible spectral range are clearly modulated by different sizes of the microcavity. According to eqn (1), the mode spacing is inversely proportional to the effective length of the microcavity, which indicate that the number of resonance modes will increase within the same spectral range (360–700 nm) by an enlargement in the side length of the microwire. The measurement results show that the number of resonance modes increases while the mode spacing decreases distinctly with increasing side length of the microcavity. In addition, the mode peaks become more acute as the side length of microwire enlarges, indicating that a relatively larger cavity size can improve the mode quality.

Fig. 5 Modulated PL spectra of microwires with different side lengths detected at room temperature.

In summary, we have developed a novel but simple approach to obtain single crystalline ZnO microwires with a parallelogram cross-section. We demonstrated for the first time that such parallelogram microwires can be used as wave-guided FP optical resonators. Wave-guided FP modes with different polarizations were directly observed in the UV and visible spectral range at room temperature. Theoretical analyses based on the plane wave mode and FEM simulations agreed well with the experimental results. Furthermore, the size-dependent cavity modulation behaviours of microwire microcavities were also investigated in detail. The experimental and theoretical analyses demonstrated that such a new wave-guided FP microcavity may be an ideal candidate for developing novel optical devices.

Acknowledgements

This work was supported financially by the NSFC (61108059, 50802103, 51072207, 61178007), the program of the excellent academic leaders of Shanghai (10XD1404600) and the 100-Talent Program of Chinese Academy of Sciences and the starting grant of SIOM (1108221-JR0).

Notes and references

1. T. Nobis, E. M. Kaidashev, A. Rahm, M. Lorenz and M. Grundmann, Phys. Rev. Lett., 2004, 93, 103903.
2. F. Qian, Y. Li, S. Gradecak, H.-G. Park, Y. Dong, Y. Ding, Z. L. Wang and C. M. Lieber, Nat. Mater., 2008, 7, 701.
3. Y. Zhang, H. J. Zhou, S. W. Liu, Z. R. Tian and M. Xiao, Nano Lett., 2009, 9, 2109.
4. D. J. Gargas, M. E. Toimil-Molares and P. D. Yang, J. Am. Chem. Soc., 2009, 131, 2125.
5. J. Dai, C. X. Xu, X. W. Sun and X. H. Zhang, Appl. Phys. Lett., 2011, 98, 161110.
6. X. Y. Liu, C. X. Shan, S. P. Wang, Z. Z. Zhang and D. Z. Shen, Nanoscale, 2012, 4, 2843.
7. H. X. Dong, Z. H. Chen, L. X. Sun, J. Lu, W. Xie, H. H. Tan, C. Jagadish and X. C. Shen, Appl. Phys. Lett., 2009, 94, 173115.
8. G. P. Zhu, C. X. Xu, J. Zhu, C. G. Lv and Y. P. Cui, Appl. Phys. Lett., 2009, 94, 051106.
9. H. X. Dong, Z. H. Chen, L. X. Sun, W. Xie, H. H. Tan, J. Lu, C. Jagadish and X. C. Shen, J. Mater. Chem., 2010, 20, 5510.
10. X. L. Xu, F. S. F. Brossard, D. A. Williams, D. P. Collins, M. J. Holmes, R. A. Taylor and X. T. Zhang, Appl. Phys. Lett., 2009, 94, 231103.
11. J. Z. Liu, S. Lee, Y. H. Ahn, J.-Y. Park, K. H. Koh and K. H. Park, Appl. Phys. Lett., 2008, 92, 263102.
12. X. Duan, Y. Huang, R. Agarwal and C. M. Lieber, Nature, 2003, 421, 241.
13. S. Chu, G. P. Wang, W. H. Zhou, Y. Q. Lin, L. Chernyak, J. Z. Zhao, J. Y. Kong, L. Li, J. J. Ren and J. L. Liu, Nat. Nanotechnol., 2011, 97, 1.
14. M. M. Brewster, X. Zhou, S. K. Lim and S. Gradečak, J. Phys. Chem. Lett., 2011, 2, 586.
15. S. H. Ko, D. Lee, H. W. Kang, K. H. Nam, J. Y. Yeo, S. J. Hong, C. P. Grigoropoulos and H. J. Sung, Nano Lett., 2011, 11, 666.
16. X. J. Wang, Q. L. Zhang, Q. Wan, G. Z. Dai, C. J. Zhou and B. S. Zou, J. Phys. Chem. C, 2011, 115, 2769.
17. K. S. Kim, H. Jeong, M. S. Jeong and G. Y. Jung, Adv. Funct. Mater., 2010, 20, 3055.
18. Y. J. Kim, C. H. Lee, Y. J. Hong and G. C. Yi, Appl. Phys. Lett., 2006, 89, 163128.
19. M. A. Thomas and J. B. Cui, J. Phys. Chem. Lett., 2010, 1, 1090.
20. X. D. Gao, X. M. Li and W. D. Yu, J. Phys. Chem. B, 2005, 109, 1155.
21. F. H. Zhao, X. Y. Li, J. G. Zheng, X. F. Yang, F. L. Zhao, K. S. Wong, J. Wang, W. J. Lin, M. M. Wu and Q. Su, Chem. Mater., 2008, 20, 1197.
22. H. X. Dong, L. X. Sun, S. L. Sun, W. Xie, L. Zhou, X. C. Shen and Z. H. Chen, Appl. Phys. Lett., 2010, 97, 223114.
23. C. Czekalla, C. Sturm, R. Schmidt-Grund, B. Q. Cao, M. Lorenz and M. Grundmann, Appl. Phys. Lett., 2008, 92, 241102.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3nr00700f

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