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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 17 — Aug. 13, 2012
  • pp: 18555–18567
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Tubular oxide microcavity with high-index-contrast walls: Mie scattering theory and 3D confinement of resonant modes

Jiao Wang, Tianrong Zhan, Gaoshan Huang, Xugao Cui, Xinhua Hu, and Yongfeng Mei  »View Author Affiliations


Optics Express, Vol. 20, Issue 17, pp. 18555-18567 (2012)
http://dx.doi.org/10.1364/OE.20.018555


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Abstract

Tubular oxide optical microcavities with thin walls (< 100 nm) have been fabricated by releasing pre-stressed Y2O3/ZrO2 bi-layered nanomembranes. Optical characterization demonstrates strong whispering gallery modes with a high quality-factor and fine structures in the visible range, which are due to their high-index-contrast property (high refractive index in thin walls). Moreover, the strong axial light confinement observed in rolled-up circular nanomembranes well agrees with our theoretical calculation by using Mie scattering theory. Novel material design and superior optical resonant properties in such self-rolled micro-tubular cavities promise many potential applications e.g. in optofluidic sensing and lasing.

© 2012 OSA

1. Introduction

Such self-assembly tubular micro-cavities released from polymer sacrificial layers normally have sub-wavelength wall thickness and thus the corresponding resonances produced are very sensitive to the refractive index of ambient media [14

14. G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010). [CrossRef] [PubMed]

]. Experimental and theoretical works on those self-rolled micro-resonators have exhibited numerous potential applications including in optoelectronics, integrated optics and optical sensors for lab-on-a-chip applications [3

3. A. Bernardi, S. Kiravittaya, A. Rastelli, R. Songmuang, D. J. Thurmer, M. Benyoucef, and O. G. Schmidt, “On-chip Si/SiOx microtube refractometer,” Appl. Phys. Lett. 93(9), 094106 (2008). [CrossRef]

, 14

14. G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010). [CrossRef] [PubMed]

16

16. E. J. Smith, Z. W. Liu, Y. F. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10(1), 1–5 (2010). [CrossRef] [PubMed]

].The structures made from non-toxic materials may be especially of benefit in biological applications. However, the inadequately low Q-factors of the rolled-up micro-cavities consisting of oxides (typically, silicon oxides) have limited their future applications [8

8. K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical modes excited by evanescent-wave-coupled PbS nanocrystals in semiconductor microtube bottle resonators,” Nano Lett. 10(2), 627–631 (2010). [CrossRef] [PubMed]

, 13

13. V. A. Bolaños Quiñones, G. S. Huang, J. D. Plumhof, S. Kiravittaya, A. Rastelli, Y. F. Mei, and O. G. Schmidt, “Optical resonance tuning and polarization of thin-walled tubular microcavities,” Opt. Lett. 34(15), 2345–2347 (2009). [CrossRef] [PubMed]

, 14

14. G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010). [CrossRef] [PubMed]

]. For instance, the low Q-factor may hinder the tube-based optofluidic device from sensing tiny changes in refractive index because the mode peak itself is relatively broad and the spectral shift is therefore indistinguishable. To overcome this inconvenience, researchers have developed methods to enhance the Q-factor, e.g. covering the walls of micro-cavities with materials possessing a high refractive index via atom layer deposition [14

14. G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010). [CrossRef] [PubMed]

, 17

17. S. M. Harazim, V. A. Bolaños Quiñones, S. Kiravittaya, S. Sanchez, and O. G. Schmidt, “Lab-in-a-tube: on-chip integration of glass optofluidic ring resonators for label-free sensing applications,” Lab Chip 12(15), 2649–2655 (2012). [CrossRef] [PubMed]

]. Q-factors up to 2900 have recently been reported from the microcavities post-treated with additional coating layer [17

17. S. M. Harazim, V. A. Bolaños Quiñones, S. Kiravittaya, S. Sanchez, and O. G. Schmidt, “Lab-in-a-tube: on-chip integration of glass optofluidic ring resonators for label-free sensing applications,” Lab Chip 12(15), 2649–2655 (2012). [CrossRef] [PubMed]

]. Nevertheless, oxide micro-cavities without addition coating still suffer from low Q-factors, i.e. less than 1000. The reason is that the ultra-thin wall and low refractive indices of the oxides is an inherent limitation for light confinement in the cavity walls, which, unfortunately, deteriorates the Q-factors of the micro-cavities. In order to reduce the light loss in the wall of tubular cavity, high refractive index contrast between the wall and the surrounding medium is therefore demanded since high-index-contrast would support low-loss WGMs [18

18. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, P. Günter, R. Degl'Innocenti, and P. Guenter, “Electro-optically tunable microring resonators in lithium niobate,” Nat. Photonics 1(7), 407–410 (2007). [CrossRef]

, 19

19. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992). [CrossRef]

].

Aiming at production of high-quality optical micro-cavities via rolled-up nanotechnology on polymers, we consider introducing materials with high refractive indices into the nanomembranes while maintaining their ultra-thin thickness. Through this process, we have successfully fabricated Y2O3/ZrO2 bi-layer high-index-contrast micro-tubes by rolling circular nanomembranes with ultra-thin wall thicknesses on polymer sacrificial layers. The as-prepared micro-tubular resonators without further treatment are characterized by means of micro-photoluminescence (micro-PL) measurement, and WGMs with high Q-factor (> 1600) are observed due to the improved light confinement inside the Y2O3/ZrO2 nanomembrane. In addition, fine structures/sub-modes are also noticeable even without the incorporation of artificial micro-lobes, as previously used in tubular structures from epitaxial membranes [20

20. Ch. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, Ch. Heyn, D. Heitmann, and T. Kipp, “Optical microcavities formed by semiconductor microtubes using a bottlelike geometry,” Phys. Rev. Lett. 101(12), 127403 (2008). [CrossRef] [PubMed]

]. Theoretical calculations based on Mie scattering theory [21

21. T. R. Zhan, C. Xu, F. Y. Zhao, Z. Q. Xiong, X. H. Hu, G. S. Huang, Y. F. Mei, and J. Zi, “Optical resonances in tubular microcavities with subwavelength wall thicknesses,” Appl. Phys. Lett. 99(21), 211104 (2011). [CrossRef]

] and adiabatic separation [20

20. Ch. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, Ch. Heyn, D. Heitmann, and T. Kipp, “Optical microcavities formed by semiconductor microtubes using a bottlelike geometry,” Phys. Rev. Lett. 101(12), 127403 (2008). [CrossRef] [PubMed]

] carried out in present work disclose a novel confinement for light propagating along the tube axis, and good agreement is found between the experimental results and the theoretical simulation. This work introduces one cheap and simple way to fabricate oxide micro-tubular cavities with three-dimensional optical confinement which produces WGMs with high Q-factors.

2. Experiment

The fabrication process of tubular self-rolled micro-cavities is schematically displayed in Fig. 1(a)
Fig. 1 (a) Schematic diagram illustrating the fabrication process of a rolled-up Y2O3/ZrO2 micro-tubular cavity. The inset shows the optical microscope image of a micro-tubular cavity (d~9 μm) rolled from a circular nanomembrane. (b) The upper part shows the radial field intensity distributions of the TE modes for the tubes with a low refractive index (SiO/SiO2, nc ≅ 1.10 in Ref. 12) and the lower part with a high refractive index (Y2O3/ZrO2, nc ≅ 1.68 in this work). The wall thickness of these two tubes was set to 100 nm. (c) The PL spectrum from the middle of a micro-tubular cavity rolled from a circular SiO/SiO2 nanomembrane coated with 30 nm HfO2 (nc ≅ 1.53 in Ref. 14). The inset shows the fine structure of a mode with azimuthal number m = 46. (d) The PL spectrum from the middle of a micro-tubular cavity rolled from a circular Y2O3/ZrO2 nanomembrane (Y2O3/ZrO2, nc ≅ 1.68 in this work). The inset shows the fine structure of a mode with azimuthal number m = 48.
. A uniform ~2 μm thick ARP-3510 photo-resist (Allresist GmbH) layer on Si wafer was defined into circles with a diameter of 80 μm by photolithography and served as a sacrificial layer in the following rolling process. The strained Y2O3/ZrO2 bi-layer nanomembrane was deposited by e-beam evaporation employing angled deposition (the angle is 60°), consisting of an Y2O3 layer (11.5 nm grown at 2.5 Ǻ/s) and a ZrO2 layer (22 nm grown at 0.15 Ǻ/s). Acetone was used to selectively remove the photo-resist layer, releasing the active Y2O3/ZrO2 bi-layer, and the intrinsic stress gradient existing in the bi-layer nanomembrane caused it to self-assemble into a micro-tubular cavity [12

12. G. S. Huang, S. Kiravittaya, V. A. Bolaños Quiñones, F. Ding, M. Benyoucef, A. Rastelli, Y. F. Mei, and O. G. Schmidt, “Optical properties of rolled-up tubular microcavities from shaped nanomembranes,” Appl. Phys. Lett. 94(14), 141901 (2009). [CrossRef]

, 14

14. G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010). [CrossRef] [PubMed]

, 15

15. E. J. Smith, S. Schulze, S. Kiravittaya, Y. F. Mei, S. Sanchez, and O. G. Schmidt, “Lab-in-a-tube: detection of individual mouse cells for analysis in flexible split-wall microtube resonator sensors,” Nano Lett. 11(10), 4037–4042 (2011). [CrossRef] [PubMed]

].The rolled-up nanomembranes were then dried in the critical point dryer (Leica CPD 030) by using liquid CO2 as an inter-media to avoid the collapse of the micro-cavities. The morphologies of the samples were investigated using optical microscopy. The optical properties were characterized by micro-PL spectroscopy at room temperature with an excitation line at 514 nm, and the emission spectra were collected via a 50 × objective. The Q-factors are calculated using the formula Q=λ/Δλ, where λ and ∆λ are the mode position and the full width at half maximum (FWHM) of the mode respectively. Other experimental details and the fabrication procedure of the reference samples (Y2O3/ZrO2, Y2O3/TiO2, TiO2/TiO2, and HfO2 coated SiO/SiO2 tubular microcavities) are listed in Appendix.

3. Results and discussions

To go deep into the unique optical resonance in the present sample, theoretical simulation is demanded. Previously, WGM resonances in micro-tubular cavities have been explored mainly by waveguide approximation [6

6. R. Songmuang, A. Rastelli, S. Mendach, and O. G. Schmidt, “SiOx/Si radial superlattices and microtube optical ring resonators,” Appl. Phys. Lett. 90(9), 091905 (2007). [CrossRef]

], finite-difference time-domain (FDTD) simulation [3

3. A. Bernardi, S. Kiravittaya, A. Rastelli, R. Songmuang, D. J. Thurmer, M. Benyoucef, and O. G. Schmidt, “On-chip Si/SiOx microtube refractometer,” Appl. Phys. Lett. 93(9), 094106 (2008). [CrossRef]

], and Mie scattering methods [21

21. T. R. Zhan, C. Xu, F. Y. Zhao, Z. Q. Xiong, X. H. Hu, G. S. Huang, Y. F. Mei, and J. Zi, “Optical resonances in tubular microcavities with subwavelength wall thicknesses,” Appl. Phys. Lett. 99(21), 211104 (2011). [CrossRef]

]. Compared with waveguide approximation and FDTD simulation, rigorous formulas of Mie scattering theory can be used to simulate both the resonant wavelengths and Q-factors of cavities [21

21. T. R. Zhan, C. Xu, F. Y. Zhao, Z. Q. Xiong, X. H. Hu, G. S. Huang, Y. F. Mei, and J. Zi, “Optical resonances in tubular microcavities with subwavelength wall thicknesses,” Appl. Phys. Lett. 99(21), 211104 (2011). [CrossRef]

], which perfectly matches our requirement for evaluating energy storage in micro-cavities. Therefore, to shed light on the 3D optical confinement in the self-rolled micro-cavity from a circular nanomembrane, we applied a simulation engaging both adiabatic separation [20

20. Ch. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, Ch. Heyn, D. Heitmann, and T. Kipp, “Optical microcavities formed by semiconductor microtubes using a bottlelike geometry,” Phys. Rev. Lett. 101(12), 127403 (2008). [CrossRef] [PubMed]

] and Mie scattering method [21

21. T. R. Zhan, C. Xu, F. Y. Zhao, Z. Q. Xiong, X. H. Hu, G. S. Huang, Y. F. Mei, and J. Zi, “Optical resonances in tubular microcavities with subwavelength wall thicknesses,” Appl. Phys. Lett. 99(21), 211104 (2011). [CrossRef]

] as follows to explore the nature of the optical resonances in our sample.

By using the parameters plotted in Fig. 5, the Maxwell’s equation for m = 48 was solved with adiabatic separation [20

20. Ch. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, Ch. Heyn, D. Heitmann, and T. Kipp, “Optical microcavities formed by semiconductor microtubes using a bottlelike geometry,” Phys. Rev. Lett. 101(12), 127403 (2008). [CrossRef] [PubMed]

]. The WGMs with other azimuthal numbers can also be quantitatively analyzed using the same approach and the electric field intensity distribution acquired from the numerical solution is encoded in color and shown in Fig. 2(b). A good agreement between experimental and theoretical results can be noted, which means that the resonance of the light in the micro-cavity can be precisely tuned along the axis of the micro-cavity rolled-up from a circular nanomembrane: the WGMs shift to higher energy with decreasing wall thickness [12

12. G. S. Huang, S. Kiravittaya, V. A. Bolaños Quiñones, F. Ding, M. Benyoucef, A. Rastelli, Y. F. Mei, and O. G. Schmidt, “Optical properties of rolled-up tubular microcavities from shaped nanomembranes,” Appl. Phys. Lett. 94(14), 141901 (2009). [CrossRef]

].The theoretical results also proved that the emergence of sub-peaks (axial modes) is connected with the thickness modulation along the micro-cavity axis, which effectively introduces a quasi-potential as previously done by an artificial micro-lobe [20

20. Ch. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, Ch. Heyn, D. Heitmann, and T. Kipp, “Optical microcavities formed by semiconductor microtubes using a bottlelike geometry,” Phys. Rev. Lett. 101(12), 127403 (2008). [CrossRef] [PubMed]

].Furthermore, it is worth noting that, compared with the intensity distribution in experimental data (Fig. 2(a)), the FWHMs of WGMs in simulation results are smaller (Fig. 2(b)). The reason responsible for the discrepancy is believed to be the imperfection of fabricated micro-tubes [12

12. G. S. Huang, S. Kiravittaya, V. A. Bolaños Quiñones, F. Ding, M. Benyoucef, A. Rastelli, Y. F. Mei, and O. G. Schmidt, “Optical properties of rolled-up tubular microcavities from shaped nanomembranes,” Appl. Phys. Lett. 94(14), 141901 (2009). [CrossRef]

], which can cause the confinement potential to deviate from the one obtained from the perfect theoretical model.

To quantitatively evaluate the light confinement and energy storage inside the micro-tubular resonator in detail, the Q-factors of the modes need to be evaluated and here Mie scattering theory is adopted to obtain theoretical Q-factors for the micro-tubular cavities [21

21. T. R. Zhan, C. Xu, F. Y. Zhao, Z. Q. Xiong, X. H. Hu, G. S. Huang, Y. F. Mei, and J. Zi, “Optical resonances in tubular microcavities with subwavelength wall thicknesses,” Appl. Phys. Lett. 99(21), 211104 (2011). [CrossRef]

]. Figure 6
Fig. 6 (a) The experimental (red circle) and simulated (blue star) results of Q-factor changes along the z axis for a resonant mode (m = 48). (b) The experimental (red circle) and simulated (blue star) results of Q-factor as a function of the wavelength (z = 0 μm).
shows the comparison of experimental and simulation results of the micro-tubular cavities’ Q-factors. Figure 6 (a) shows that the Q-factors of azimuthal mode (m = 48) decrease with increasing z, indicating a continuous increase in light loss along the z direction due to the corresponding decrease in nc (Fig. 5(c)). This phenomenon is also consistent with the results in Fig. 5(b) since the kc~βc curve farther away from that of the light in air would suggest a high Q-factor [21

21. T. R. Zhan, C. Xu, F. Y. Zhao, Z. Q. Xiong, X. H. Hu, G. S. Huang, Y. F. Mei, and J. Zi, “Optical resonances in tubular microcavities with subwavelength wall thicknesses,” Appl. Phys. Lett. 99(21), 211104 (2011). [CrossRef]

]. In addition, a consistent discrepancy between the Q-factors from theoretical calculations and the experiments is noticed. The experimentally measured Q factors are generally much lower than the calculated ones due to scattering from surface roughness and impurities, absorption by the material, and simultaneous excitation of multiple closely spaced modes [28

28. A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4(3), 457–482 (2010). [CrossRef]

30

30. A. Boleininger, T. Lake, S. Hami, and C. Vallance, “Whispering gallery modes in standard optical fibres for fibre profiling measurements and sensing of unlabelled chemical species,” Sensors (Basel) 10(3), 1765–1781 (2010). [CrossRef] [PubMed]

]. This can be further proved by the abnormally small Q-factor at z = 15 μm (Fig. 6(a)), where a significant light loss is caused by the step produced by the external rotation.

Figure 6(b) indicates that the Q-factor increases with a decrease in wavelength (or increase of azimuthal number m). The tendency in the evolution of the theoretical results is similar to that of the experimental results (Fig. 6(b)) at longer wavelength (> 700 nm). However, the deviation at the short wavelength range (< 700 nm) becomes noticeable. Since the decrease of the Q-factor indicates an increased light loss [21

21. T. R. Zhan, C. Xu, F. Y. Zhao, Z. Q. Xiong, X. H. Hu, G. S. Huang, Y. F. Mei, and J. Zi, “Optical resonances in tubular microcavities with subwavelength wall thicknesses,” Appl. Phys. Lett. 99(21), 211104 (2011). [CrossRef]

, 31

31. J. Niehusmann, A. Vörckel, PP. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, “Ultrahigh-quality-factor silicon-on-insulator microring resonator,” Opt. Lett. 29(24), 2861 (2004). [CrossRef] [PubMed]

], the difference below 700 nm may result from energy dissipation, which is not considered in the present method, e.g. the absorption of light in the nanomembrane. To prove this, we measured the absorbance of the nanomembrane constituting the micro-cavity, and the results are displayed in Fig. 7
Fig. 7 Absorption spectrum of an Y2O3/ZrO2 bi-layer nanomembrane grown on a quartz substrate.
. A remarkable increase in light absorption within the short wavelength range indeed supports the above deduction. Therefore, in order to achieve a more comprehensive understanding of the optical resonance in our tubular microcavity, the model needs to be improved by taking absorption into consideration. The work is currently in progress.

Theoretical simulation also discloses the change in optical resonance at different positions of the micro-tubular cavity due to its structural evolution. Figures 8(a)
Fig. 8 Comparison of the PL spectra from different positions of the micro-tubular cavity: (a) experimental data; (b) simulation results.
and 8(b) show the experimental and simulative PL spectra from the different positions along the tube axis of the micro-tubular cavity. One can see that the experimental results fit well with the theory simulation data. However, as we have discussed before, the simulated Q-factor is slightly higher than that in experimental results (Fig. 6(a)), thus the FWHM of the peaks in experimental results (Fig. 8(a)) are broader compared to their counterparts in simulation (Fig. 8(b)). Since the Q-factor decreases along the z direction, the broadening of resonant peaks and the corresponding sub-peaks of each mode group combine together gradually, as displayed in Fig. 8. For instance, we note when the Q-factor is lower than 100 (Fig. 8(a), z = 22 μm), all the sub-peaks in each mode group are broadened and even merge together. This also indicates that such sub-peaks cannot be observed in the spectrum of cavities with low Q-factor even though the 3D light confinement exists. This clearly explains the experimental results in Fig. 1(c) where each mode has an asymmetrical line-shape with a tail at the high-energy side, because the low Q-factor of the HfO2-coated SiO/SiO2 micro-tubular cavity leads to the overlap of sub-peaks. Contrarily, the present Y2O3/ZrO2 self-rolled cavity possesses much better optical resonant properties because of the introduction of high refractive index materials even though the wall thickness is much smaller than the light wavelength (< 100 nm), and thus the fine structures’ emergence is accompanied by a high Q-factor. These interesting phenomena were also observed in other high-index-contrast tubular microcavities which fabricated by different oxide bilayer nanomembrane (see details in Fig. 9
Fig. 9 The PL spectra from the middle of a micro-tubular cavity rolled from circular (a)Y2O3/ZrO2 (nc ≅ 1.68), (b)Y2O3/TiO2 (nc ≅ 1.50), and (c)TiO2/TiO2 (nc ≅ 1.64) nanomembranes. (d) The PL spectrum from the middle of a micro-tubular cavity rolled from a circular SiO/SiO2 nanomembrane coated with 30 nm HfO2 (nc ≅ 1.10).
).

4. Summary

In conclusion, we have successfully fabricated high-index-contrast ultra-thin wall micro-cavities with a high Q-factor from rolled-up Y2O3/ZrO2 bi-layer circular nanomembranes via traditional lift-off processes without the need for further treatment. The geometry of the nanomembranes and the intrinsic refractive indices of materials play critical roles in the resonant properties of the micro-cavity. The fine structures of each mode observed in the PL spectra from the micro-tubular cavity and high Q-factor are considered to be due to the introduction of materials with a high refractive index. The experimental results are further analyzed with the assistance of theoretical calculation engaging Mie scattering. Light confinement along the tube axis is disclosed to be due to the thickness modulation in the cavity wall and the simulated results agree well with the experimental results. New materials and superior optical resonant properties indicate that this type of high-index-contrast micro-tubular cavities with ultra-thin wall thickness and high Q-factor are promising for the application in optical sensor devices.

Appendix

Fabrication procedure of the reference samples

The typical formation process of tubular micro-cavities is performed as follows. First, a uniform ~2 μm ARP-3510 photoresist (Allresist GmbH) layer on a Si substrate is defined into squares via photolithography. The different bi-layer nanomembranes are deposited with suitable thickness ratio onto the patterned photoresist (used as a sacrificial layer) onto the Si substrate via electron beam evaporation. Acetone was used to selectively remove the photo-resist layer, releasing the active bi-layer, and the intrinsic stress gradient existing in the bi-layer nanomembrane caused it to self-assemble into a micro-tubular cavity. The rolled-up nanomembranes were then dried in the critical point dryer (Leica CPD 030) by using liquid CO2 as an inter-media to avoid the collapse of the micro-cavities. After the formation of the rolled-up nanomembranes, the SiO/SiO2 micro-tubes are uniformly coated with HfO2 using ALD (Savannah 100, Cambridge NanoTech Inc.) to strengthen the optical micro-cavities mechanically and also improve intensity and Q-factor of optical modes. The oxide layers are deposited at 130 °C (1 Ǻ per cycle). For comparison purposes, different materials were chosen for fabrication of self-rolled tubular microcavities. The different materials for each tubular microcavities are summarized in Table 1

Table 1. Summary of the Materials for Fabrication of Tubular Optical Microcavities

table-icon
View This Table
. Fig. 10
Fig. 10 Optical microscope images of rolled-up circle (a) Y2O3/ZrO2 (nc ≅ 1.68), (b) Y2O3/TiO2 (nc ≅ 1.50), (c) TiO2/TiO2 (nc ≅ 1.64), and (d) SiO/SiO2 bilayer nanomembranes, of which the SiO/SiO2 self-rolled microtube coated with additional HfO2 coating layers on both inner and outer surfaces (nc ≅ 1.10).
displays the optical microscope images of these samples.

Mathematical derivation of WGMs

The micro-tube, formed spontaneously by rolling up a planar circular strained nanomembrane with a diameter of L and thickness of T (Fig. 3(a)), has a spiral cross section (Fig. 3(b)). The outer radius of the rolled-up nanomembrane depends on the angle position θ from the ending edge and can be defined by
Rr(θ)=R0T×θ/2π
(7)
where R0 is the outer radius of the ending edge. Assuming the measured outer diameter of the tube is D0, R0 can be determined by 2R0T/2=D0.

The winding number N of the tube can be calculated from the condition that integration of the spiral revolutions is equal to the rolling length Lz, i.e.,
Lz=θ=02πN[Rr(θ)T/2]dθ=2πNR0πN2T
(8)
where Lz=2[(L/2)2z2]1/2.

The micro-tube wall can be regarded as two coupled rolled-up planar waveguides with different thicknesses T1 and T2, and length L1 and L2 (Fig. 3(c)). The effective radius of the cross section can be defined

Rc=(L1+L2)/2π
(9)

(The subscript ‘c’ denotes cross section. We use this convention throughout this Appendix.)

In Fig. 4, we can observe that while N decreases along the length of the tube axis, Rc is almost constant and equal to 4.521 μm for the micro-tube under study.

βcRc=m
(11)

Hence, once geometry parameters of micro-tubes, such as the effective radius Rc, thickness and refractive index nw of the tube wall, are known, we can calculate WGMs position from Eq. (11).

We plot the peak position as a function of mode number in Fig. 11(b), exhibiting a linear dependence, which can be explored to derive the refractive index of the nanomembrane.

Spacing of adjacent modes can be obtained from Eq. (10) as

δ(β1/2π)L1+δ(β2/2π)L2=1
(12)

Since modes are equally spaced as observed in Fig. 4(b), we define nge=dβ/dk0, where k0=2π/λ0 and nge can be assumed a constant. Then, Eq. (12) becomes
nge,1L1+nge,2L2=1n(1/λ0)
(13)
where δ(1/λ0) is modes spacing from measured data. By defining nge,c=(nge,1L1+nge,2L2)/(L1+L2), and using Rc=(L1+L2)/2π(Eq. (9)), we can obtain

nge,c×2πRc=1δ(1/λ0)
(14)

Hence, once mode spacing is obtained from measured data, we can calculate nge,c from Eq. (14).

On the other hand, we can obtain nge,c as a function of nw by numerically solving the dispersion relationship of guiding modes in the micro-tube wall and using the definition of nge,c for an assigned nw.

Finally, the refractive index of the micro-tube wall can be obtained through linear interpolation at nge,c derived from measured data.

For the micro-tube in Fig. 4, we can obtain nge,c = 1.49 using Eq. (14). From Fig. 12
Fig. 12 Plot of nge,c as a function of the refractive index of the micro-tube wall nw for the micro-tube with the geometry parameters as in Fig. 4.
, we can obtain its refractive index of the wall nw = 1.68.

Absorption spectrum of an Y2O3/ZrO2 bi-layer nanomembrane

The strained Y2O3/ZrO2 bi-layer nanomembrane was deposited on transparent SiO2 glass substrate by e-beam evaporation employing angled deposition (the angle is 60°), consisting of an Y2O3 layer (11.5 nm grown at 2.5 Ǻ/s) and a ZrO2 layer (22 nm grown at 0.15 Ǻ/s). The absorption spectrum of this bi-layer nanomembrane in Fig. 7 indicates that the absorbance decreases with increasing wavelength.

Acknowledgments

This work is supported by the Natural Science Foundation of China (Nos. 61008029, 11104040 and 51102049), Program for New Century Excellent Talents in University (No. NCET-10-0345), Shanghai Pujiang Program (No. 11PJ1400900), Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20110071120009) and China Postdoctoral Science Foundation Funded Project (No. 2011M500731).

References and Links

1.

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003). [CrossRef] [PubMed]

2.

Y. Yamamoto and R. E. Slusher, “Optical processes in microcavities,” Phys. Today 46(6), 66–73 (1993). [CrossRef]

3.

A. Bernardi, S. Kiravittaya, A. Rastelli, R. Songmuang, D. J. Thurmer, M. Benyoucef, and O. G. Schmidt, “On-chip Si/SiOx microtube refractometer,” Appl. Phys. Lett. 93(9), 094106 (2008). [CrossRef]

4.

O. G. Schmidt and K. Eberl, “Nanotechnology. Thin solid films roll up into nanotubes,” Nature 410(6825), 168 (2001). [CrossRef] [PubMed]

5.

A. Cho, “Nanotechnology. Pretty as you please, curling films turn themselves into nanodevices,” Science 313(5784), 164–165 (2006). [CrossRef] [PubMed]

6.

R. Songmuang, A. Rastelli, S. Mendach, and O. G. Schmidt, “SiOx/Si radial superlattices and microtube optical ring resonators,” Appl. Phys. Lett. 90(9), 091905 (2007). [CrossRef]

7.

S. Vicknesh, F. Li, and Z. Mi, “Optical microcavities on Si formed by self-assembled InGaAs/GaAs quantum dot microtubes,” Appl. Phys. Lett. 94(8), 081101 (2009). [CrossRef]

8.

K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical modes excited by evanescent-wave-coupled PbS nanocrystals in semiconductor microtube bottle resonators,” Nano Lett. 10(2), 627–631 (2010). [CrossRef] [PubMed]

9.

I. M. White, H. Oveys, and X. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31(9), 1319–1321 (2006). [CrossRef] [PubMed]

10.

H. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. Fan, “Integrated refractive index optical ring resonator detector for capillary electrophoresis,” Anal. Chem. 79(3), 930–937 (2007). [CrossRef] [PubMed]

11.

Y. Mei, G. Huang, A. A. Solovev, E. B. Ureña, I. Mönch, F. Ding, T. Reindl, R. K. Y. Fu, P. K. Chu, and O. G. Schmidt, “Versatile approach for integrative and functionalized tubes by strain engineering of nanomembranes on polymers,” Adv. Mater. (Deerfield Beach Fla.) 20(21), 4085–4090 (2008). [CrossRef]

12.

G. S. Huang, S. Kiravittaya, V. A. Bolaños Quiñones, F. Ding, M. Benyoucef, A. Rastelli, Y. F. Mei, and O. G. Schmidt, “Optical properties of rolled-up tubular microcavities from shaped nanomembranes,” Appl. Phys. Lett. 94(14), 141901 (2009). [CrossRef]

13.

V. A. Bolaños Quiñones, G. S. Huang, J. D. Plumhof, S. Kiravittaya, A. Rastelli, Y. F. Mei, and O. G. Schmidt, “Optical resonance tuning and polarization of thin-walled tubular microcavities,” Opt. Lett. 34(15), 2345–2347 (2009). [CrossRef] [PubMed]

14.

G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano 4(6), 3123–3130 (2010). [CrossRef] [PubMed]

15.

E. J. Smith, S. Schulze, S. Kiravittaya, Y. F. Mei, S. Sanchez, and O. G. Schmidt, “Lab-in-a-tube: detection of individual mouse cells for analysis in flexible split-wall microtube resonator sensors,” Nano Lett. 11(10), 4037–4042 (2011). [CrossRef] [PubMed]

16.

E. J. Smith, Z. W. Liu, Y. F. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett. 10(1), 1–5 (2010). [CrossRef] [PubMed]

17.

S. M. Harazim, V. A. Bolaños Quiñones, S. Kiravittaya, S. Sanchez, and O. G. Schmidt, “Lab-in-a-tube: on-chip integration of glass optofluidic ring resonators for label-free sensing applications,” Lab Chip 12(15), 2649–2655 (2012). [CrossRef] [PubMed]

18.

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, P. Günter, R. Degl'Innocenti, and P. Guenter, “Electro-optically tunable microring resonators in lithium niobate,” Nat. Photonics 1(7), 407–410 (2007). [CrossRef]

19.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett. 60(3), 289–291 (1992). [CrossRef]

20.

Ch. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, Ch. Heyn, D. Heitmann, and T. Kipp, “Optical microcavities formed by semiconductor microtubes using a bottlelike geometry,” Phys. Rev. Lett. 101(12), 127403 (2008). [CrossRef] [PubMed]

21.

T. R. Zhan, C. Xu, F. Y. Zhao, Z. Q. Xiong, X. H. Hu, G. S. Huang, Y. F. Mei, and J. Zi, “Optical resonances in tubular microcavities with subwavelength wall thicknesses,” Appl. Phys. Lett. 99(21), 211104 (2011). [CrossRef]

22.

F. S. De Vicente, A. C. De Castro, M. F. De Souza, and M. Siu Li, “Luminescence and structure of Er3+ doped zirconia films deposited by electron beam evaporation,” Thin Solid Films 418(2), 222–227 (2002). [CrossRef]

23.

T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett. 96(7), 077403 (2006). [CrossRef] [PubMed]

24.

L. X. Yi, J. Heitmann, R. Scholz, and M. Zacharias, “Si rings, Si clusters, and Si nanocrystals—different states of ultrathin SiOx layers,” Appl. Phys. Lett. 81(22), 4248–4850 (2002). [CrossRef]

25.

F. Li, Z. T. Mi, and S. Vicknesh, “Coherent emission from ultrathin-walled spiral InGaAs/GaAs quantum dot microtubes,” Opt. Lett. 34(19), 2915–2917 (2009). [CrossRef] [PubMed]

26.

F. Li and Z. T. Mi, “Optically pumped rolled-up InGaAs/GaAs quantum dot microtube lasers,” Opt. Express 17(22), 19933–19939 (2009). [CrossRef] [PubMed]

27.

C. Strelow, C. M. Schultz, H. Rehberg, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Three dimensionally confined optical modes in quantum-well microtube ring resonators,” Phys. Rev. B 76(4), 045303 (2007). [CrossRef]

28.

A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev. 4(3), 457–482 (2010). [CrossRef]

29.

A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electron. 32(5), 377–400 (2002). [CrossRef]

30.

A. Boleininger, T. Lake, S. Hami, and C. Vallance, “Whispering gallery modes in standard optical fibres for fibre profiling measurements and sensing of unlabelled chemical species,” Sensors (Basel) 10(3), 1765–1781 (2010). [CrossRef] [PubMed]

31.

J. Niehusmann, A. Vörckel, PP. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, “Ultrahigh-quality-factor silicon-on-insulator microring resonator,” Opt. Lett. 29(24), 2861 (2004). [CrossRef] [PubMed]

OCIS Codes
(230.3990) Optical devices : Micro-optical devices
(230.4000) Optical devices : Microstructure fabrication
(230.5750) Optical devices : Resonators
(290.4020) Scattering : Mie theory
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Optical Devices

History
Original Manuscript: May 23, 2012
Revised Manuscript: July 20, 2012
Manuscript Accepted: July 20, 2012
Published: July 30, 2012

Citation
Jiao Wang, Tianrong Zhan, Gaoshan Huang, Xugao Cui, Xinhua Hu, and Yongfeng Mei, "Tubular oxide microcavity with high-index-contrast walls: Mie scattering theory and 3D confinement of resonant modes," Opt. Express 20, 18555-18567 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-17-18555


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References

  1. K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003). [CrossRef] [PubMed]
  2. Y. Yamamoto and R. E. Slusher, “Optical processes in microcavities,” Phys. Today46(6), 66–73 (1993). [CrossRef]
  3. A. Bernardi, S. Kiravittaya, A. Rastelli, R. Songmuang, D. J. Thurmer, M. Benyoucef, and O. G. Schmidt, “On-chip Si/SiOx microtube refractometer,” Appl. Phys. Lett.93(9), 094106 (2008). [CrossRef]
  4. O. G. Schmidt and K. Eberl, “Nanotechnology. Thin solid films roll up into nanotubes,” Nature410(6825), 168 (2001). [CrossRef] [PubMed]
  5. A. Cho, “Nanotechnology. Pretty as you please, curling films turn themselves into nanodevices,” Science313(5784), 164–165 (2006). [CrossRef] [PubMed]
  6. R. Songmuang, A. Rastelli, S. Mendach, and O. G. Schmidt, “SiOx/Si radial superlattices and microtube optical ring resonators,” Appl. Phys. Lett.90(9), 091905 (2007). [CrossRef]
  7. S. Vicknesh, F. Li, and Z. Mi, “Optical microcavities on Si formed by self-assembled InGaAs/GaAs quantum dot microtubes,” Appl. Phys. Lett.94(8), 081101 (2009). [CrossRef]
  8. K. Dietrich, C. Strelow, C. Schliehe, C. Heyn, A. Stemmann, S. Schwaiger, S. Mendach, A. Mews, H. Weller, D. Heitmann, and T. Kipp, “Optical modes excited by evanescent-wave-coupled PbS nanocrystals in semiconductor microtube bottle resonators,” Nano Lett.10(2), 627–631 (2010). [CrossRef] [PubMed]
  9. I. M. White, H. Oveys, and X. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett.31(9), 1319–1321 (2006). [CrossRef] [PubMed]
  10. H. Zhu, I. M. White, J. D. Suter, M. Zourob, and X. Fan, “Integrated refractive index optical ring resonator detector for capillary electrophoresis,” Anal. Chem.79(3), 930–937 (2007). [CrossRef] [PubMed]
  11. Y. Mei, G. Huang, A. A. Solovev, E. B. Ureña, I. Mönch, F. Ding, T. Reindl, R. K. Y. Fu, P. K. Chu, and O. G. Schmidt, “Versatile approach for integrative and functionalized tubes by strain engineering of nanomembranes on polymers,” Adv. Mater. (Deerfield Beach Fla.)20(21), 4085–4090 (2008). [CrossRef]
  12. G. S. Huang, S. Kiravittaya, V. A. Bolaños Quiñones, F. Ding, M. Benyoucef, A. Rastelli, Y. F. Mei, and O. G. Schmidt, “Optical properties of rolled-up tubular microcavities from shaped nanomembranes,” Appl. Phys. Lett.94(14), 141901 (2009). [CrossRef]
  13. V. A. Bolaños Quiñones, G. S. Huang, J. D. Plumhof, S. Kiravittaya, A. Rastelli, Y. F. Mei, and O. G. Schmidt, “Optical resonance tuning and polarization of thin-walled tubular microcavities,” Opt. Lett.34(15), 2345–2347 (2009). [CrossRef] [PubMed]
  14. G. S. Huang, V. A. Bolaños Quiñones, F. Ding, S. Kiravittaya, Y. F. Mei, and O. G. Schmidt, “Rolled-up optical microcavities with subwavelength wall thicknesses for enhanced liquid sensing applications,” ACS Nano4(6), 3123–3130 (2010). [CrossRef] [PubMed]
  15. E. J. Smith, S. Schulze, S. Kiravittaya, Y. F. Mei, S. Sanchez, and O. G. Schmidt, “Lab-in-a-tube: detection of individual mouse cells for analysis in flexible split-wall microtube resonator sensors,” Nano Lett.11(10), 4037–4042 (2011). [CrossRef] [PubMed]
  16. E. J. Smith, Z. W. Liu, Y. F. Mei, and O. G. Schmidt, “Combined surface plasmon and classical waveguiding through metamaterial fiber design,” Nano Lett.10(1), 1–5 (2010). [CrossRef] [PubMed]
  17. S. M. Harazim, V. A. Bolaños Quiñones, S. Kiravittaya, S. Sanchez, and O. G. Schmidt, “Lab-in-a-tube: on-chip integration of glass optofluidic ring resonators for label-free sensing applications,” Lab Chip12(15), 2649–2655 (2012). [CrossRef] [PubMed]
  18. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, P. Günter, R. Degl'Innocenti, and P. Guenter, “Electro-optically tunable microring resonators in lithium niobate,” Nat. Photonics1(7), 407–410 (2007). [CrossRef]
  19. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode microdisk lasers,” Appl. Phys. Lett.60(3), 289–291 (1992). [CrossRef]
  20. Ch. Strelow, H. Rehberg, C. M. Schultz, H. Welsch, Ch. Heyn, D. Heitmann, and T. Kipp, “Optical microcavities formed by semiconductor microtubes using a bottlelike geometry,” Phys. Rev. Lett.101(12), 127403 (2008). [CrossRef] [PubMed]
  21. T. R. Zhan, C. Xu, F. Y. Zhao, Z. Q. Xiong, X. H. Hu, G. S. Huang, Y. F. Mei, and J. Zi, “Optical resonances in tubular microcavities with subwavelength wall thicknesses,” Appl. Phys. Lett.99(21), 211104 (2011). [CrossRef]
  22. F. S. De Vicente, A. C. De Castro, M. F. De Souza, and M. Siu Li, “Luminescence and structure of Er3+ doped zirconia films deposited by electron beam evaporation,” Thin Solid Films418(2), 222–227 (2002). [CrossRef]
  23. T. Kipp, H. Welsch, Ch. Strelow, Ch. Heyn, and D. Heitmann, “Optical modes in semiconductor microtube ring resonators,” Phys. Rev. Lett.96(7), 077403 (2006). [CrossRef] [PubMed]
  24. L. X. Yi, J. Heitmann, R. Scholz, and M. Zacharias, “Si rings, Si clusters, and Si nanocrystals—different states of ultrathin SiOx layers,” Appl. Phys. Lett.81(22), 4248–4850 (2002). [CrossRef]
  25. F. Li, Z. T. Mi, and S. Vicknesh, “Coherent emission from ultrathin-walled spiral InGaAs/GaAs quantum dot microtubes,” Opt. Lett.34(19), 2915–2917 (2009). [CrossRef] [PubMed]
  26. F. Li and Z. T. Mi, “Optically pumped rolled-up InGaAs/GaAs quantum dot microtube lasers,” Opt. Express17(22), 19933–19939 (2009). [CrossRef] [PubMed]
  27. C. Strelow, C. M. Schultz, H. Rehberg, H. Welsch, C. Heyn, D. Heitmann, and T. Kipp, “Three dimensionally confined optical modes in quantum-well microtube ring resonators,” Phys. Rev. B76(4), 045303 (2007). [CrossRef]
  28. A. Chiasera, Y. Dumeige, P. Féron, M. Ferrari, Y. Jestin, G. Nunzi Conti, S. Pelli, S. Soria, and G. C. Righini, “Spherical whispering-gallery-mode microresonators,” Laser Photon. Rev.4(3), 457–482 (2010). [CrossRef]
  29. A. N. Oraevsky, “Whispering-gallery waves,” Quantum Electron.32(5), 377–400 (2002). [CrossRef]
  30. A. Boleininger, T. Lake, S. Hami, and C. Vallance, “Whispering gallery modes in standard optical fibres for fibre profiling measurements and sensing of unlabelled chemical species,” Sensors (Basel)10(3), 1765–1781 (2010). [CrossRef] [PubMed]
  31. J. Niehusmann, A. Vörckel, PP. H. Bolivar, T. Wahlbrink, W. Henschel, and H. Kurz, “Ultrahigh-quality-factor silicon-on-insulator microring resonator,” Opt. Lett.29(24), 2861 (2004). [CrossRef] [PubMed]

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