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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 14 — Jul. 6, 2009
  • pp: 11916–11925
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Selective excitation of whispering gallery modes in a novel bottle microresonator

Ganapathy Senthil Murugan, James S. Wilkinson, and Michalis N. Zervas  »View Author Affiliations


Optics Express, Vol. 17, Issue 14, pp. 11916-11925 (2009)
http://dx.doi.org/10.1364/OE.17.011916


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Abstract

Selective excitation of spheroidal whispering gallery modes and bottle modes in a robust bottle microresonator fabricated straightforwardly from a short section of optical fiber is demonstrated. Characteristic resonance spectra of long-cavity bottle modes were obtained by using a tapered fiber to excite evanescently bottle microresonator at different points along its axis. Compared to bare-fiber cylindrical resonators, the bottle microresonator results in a 35x increase of the observed Q factor.

© 2009 Optical Society of America

1. Introduction

So far, bottle microresonators have been fabricated primarily by “heat-and-pull” techniques, using modified fibre taper rigs [14

14. G. Kakaranzas, T. E. Dimmick, T. A. Birks, R. Le Roux, and P. St. J. Russell, “Miniature all-fiber devices based on CO2 laser micro structuring of tapered fibers,” Opt. Lett. 26, 1137–1139 (2001). [CrossRef]

-16

16. F. Warken, A. Rauschenbeutel, and T. Bartholomaus, “Fiber pulling profits from precise positioning,” Photonics Spectra 42, 73 (2008).

]. A CO2 laser has been used to heat the fibre locally while it is pulled in a controlled fashion. Early attempts [14

14. G. Kakaranzas, T. E. Dimmick, T. A. Birks, R. Le Roux, and P. St. J. Russell, “Miniature all-fiber devices based on CO2 laser micro structuring of tapered fibers,” Opt. Lett. 26, 1137–1139 (2001). [CrossRef]

,15

15. J. M. Ward, D. G. O’Shea, B. J. Shortt, M. J. Morrissey, K. Deasy, and S. G. Nic Chormaic, “Heat-and-pull rig for fiber taper fabrication,” Rev. Sci. Instrum. 77, 083105 (2006). [CrossRef]

] resulted, however, in rather poor resonator qualities and measured Q factors of about 3000-4000 [14

14. G. Kakaranzas, T. E. Dimmick, T. A. Birks, R. Le Roux, and P. St. J. Russell, “Miniature all-fiber devices based on CO2 laser micro structuring of tapered fibers,” Opt. Lett. 26, 1137–1139 (2001). [CrossRef]

]. In order to improve the bottle resonator quality, much more advanced fibre taper rigs have been recently developed utilizing two computer-controlled high precision linear motor stages [16

16. F. Warken, A. Rauschenbeutel, and T. Bartholomaus, “Fiber pulling profits from precise positioning,” Photonics Spectra 42, 73 (2008).

]. This technique produces microbottle resonators in two steps by sequentially micro-tapering the fiber in two adjacent places to form the “bottle”. Q factors of about 108 have been observed [17

17. M. P 6;öllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultra-high-Q tunable whispering-gallery-mode microresonator,” arXiv:0901.4921v1, (2009).

].

We have fabricated fiber WGM bottle microresonators from short sections of optical fiber by an alternative simple and versatile “soften-and-compress” technique using a standard fusion splicer to soften the fiber locally [18

18. M. N. Zervas, G. Senthil Murugan, and J. S. Wilkinson, “Demonstration of novel high-Q fiber WGM “bottle” microresonators,” in IEEE Proc. 10th anniversary International Conference on Transparent Optical Networks 4, 58–60 (2008). [CrossRef]

]. This technique produces robust bottle microresonators in a simple, rapid, single-step process. Fusion splicers are relatively inexpensive pieces of lab equipment with a number of sophisticated heating and motion controls already incorporated. The proposed technique can be modified to include alternative means of local heating, such as CO2 lasers or fibre micro-heaters. In this paper, we detail the new fabrication technique and present clear experimental evidence of the turning points and the associated intensity maxima of the bottle resonator modes [19

19. G. Senthil Murugan, J. S. Wilkinson, and M. N. Zervas, “Experimental demonstration of a bottle microresonator,” in Conference on Lasers and Electro-Optics 2009, OSA Technical Digest Series (Optical Society of America, 2009), paper JTuD87.

]. In addition, we show transmission spectral characteristics when the bottle is evanescently excited at different points along its length. Finally, by fitting the microbottle shape and assigning mode numbers to the transmission resonances, we provide clear physical insight into the observed variation of Q factors as a function of the excitation position.

2. “Soften-and-Compress” microbottle fabrication technique

Fiber splicing is a thermo-mechanical process in which the cleaved ends of two optical fibers are pushed towards each other while they are heated to a temperature at which they soften and fuse together. The heating is usually performed in one of two ways, either by resistive coil (filament) heating or by arc discharge. We have exploited these splicer actions on a piece of continuous fiber in order to soften a small region while simultaneously compressing it. These combined splicer actions produce a pronounced bulge along the fiber as shown in Fig. 1(a). The heating method used in the present study was arc discharge with arc duration of about one second. We used multiple short arcs in order to controllably soften the glass. This procedure results in a robust, double-neck bottle fiber microresonator with neck-to-neck distance L b, bottle diameter D b and stem diameter D s. The detailed “bottle” shape is also an important parameter in defining the spectral characteristics and optical properties of the resonator. The shape is defined by the softening temperature profile and the applied compression.

3. Experimental characterization

Fig. 1. (a) Optical micrograph of the bottle microresonator coupled to a tapered optical fiber (focus on the bottle), (b) Image of the bottle resonator when the light was coupled through the tapered fiber at the centre (focus on the tapered fiber), (c-g) Image of the bottle resonator when the light was coupled through the tapered fiber at about 52, 100, 150, 200 and 250 µm away from the centre on one side respectively, (h) Image of the bottle resonator when the tapered fiber was at 150 µm on the other side and (i) Image of the tapered fiber coupling to a normal stripped fiber with a cladding diameter of about 125 µm.

Fig. 2. (a-f) The resonance spectra for the bottle resonator excited using the tapered fiber at the positions shown in Fig 1. (g) The resonance spectrum for a normal stripped fiber with a diameter of 125 µm excited by a tapered fiber normal to it.

Figures 3(a)-3(f) show representative resonant features with the bottle microresonator excited at various places along its length using the tapered fibre. Fig. 3(g) corresponds to the stripped normal fibre stem and it is included for comparison. The wavelength span is varied to best demonstrate the observed Q. In Figs. 3(e)-3(g), adjacent resonances overlap strongly due to decreased Q factor. Figs. 3(a)-3(f) also include Lorentzian fits to the measured data in order to calculate the Q of the dominant resonances. The Q-factors as a function of excitation position are plotted in Fig. 4(a) and shown to decrease from 7×105 to 2×104 when the tapered fibre excitation moved from the centre of the bottle to 250µm away from the centre, well beyond the edge of the microbottle. The Q factor of the resonances obtained with the bare normal fiber stem is about 1.9×104. It is shown that the formation of the bottle microresonator results in a more than one order of magnitude, more precisely a factor of 35, increase of the Q-factor compared with the corresponding cylindrical resonator (i.e. bare fiber).

Fig. 3. (a-f) Individual transmission resonances and fitted Lorentzians used for the determination of Q factors of the bottle microresonator, for excitation at the positions shown in Fig. 1. (g) transmission resonance and fitted Lorentzian for bare normal fiber. Transmission is normalized to the local off-resonance transmission.

During the wavelength characterization, it was observed that the maximum transmitted power level was varied with the fiber taper position (not discernible in Fig. 2). In Fig. 4(b), we plot the variation of the average maximum transmission, corresponding to wavelengths between resonances (see Fig. 2) as a function of the position of the fiber taper. Comparing Figs. 4(a) and 4(b), it is observed that the Q factor variation shows the same functional relation with the transmission loss. As will be discussed below, the increased losses as the fibre taper is moved along the bottle length, are believed to be due to enhanced leakage into air and into the fibre stems in close proximity to the bottle necks. It should also be noted that there is a marked difference in the variation of both the measured Q factors and the maximum transmission power as the tapered fiber crosses the 200µm point and moves from the outside to well inside the bottle resonator. The Q and transmission loss variation when the tapered fiber is within the bottle resonator shows a strong exponential dependence. In earlier work on bottle resonators with a near-spherical shape, realized using the same technique [18

18. M. N. Zervas, G. Senthil Murugan, and J. S. Wilkinson, “Demonstration of novel high-Q fiber WGM “bottle” microresonators,” in IEEE Proc. 10th anniversary International Conference on Transparent Optical Networks 4, 58–60 (2008). [CrossRef]

], Q-factors above 107 were achieved, showing that the Q-factor here is not limited by scattering or by material absorption but predominantly by leakage into the fibre stems. The design of the optimum bottle resonator profiles which control the extent of this leakage is the subject of further investigation.

Fig. 4. (a) Q-factors and (b) average maximum transmission as a function of the fiber taper position.

4. Theoretical results

To gain further physical insight into the experimental results, the shape of the bottle microresonator under study was fitted with various shape functions, such as harmonic oscillator, parabolic and cosine profiles. The comparison between harmonic oscillator and parabolic profiles is shown in Fig. 5(a). The cosine profile is not shown as it was almost identical to parabolic. The best fitting function for the outer fiber diameter was found to be the truncated harmonic oscillator profile, namely:

D(z)=Db[1+(Δkz)2]12zLb2Dsz>Lb2
(1)

λmq=2πn0[(mRb)2+(q+12)ΔEm]12
(2)

and

zc=[4ΔEm(q+12)]12
(3)

respectively, as a function of the mode numbers m and q, where ΔEm=2mΔk/Rb and p=1 (Rb=Db/2). In analogy with quantum-mechanical WKB quantization, the microbottle resonator, in addition to a radial potential (similar to microsphere resonators) [22

22. B.R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993). [CrossRef]

,23

23. J.U Nöckel, “Resonances in nonintegrable open systems,” PhD Thesis, pp.92–105, Yale University (1997).

], is characterized by an axial potential given by [11

11. M. Sumetsky, “Whispering-gallery-bottle microcavities: the three-dimensional etalon,” Opt. Lett. 29, 8–10 (2004). [CrossRef] [PubMed]

,12

12. Y. Louyer, D. Meshede, and A. Rauschenbeutel “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72, 031801(R) (2005). [CrossRef]

] V(z)=(m/R(z))2 - (m/Rb)2. In the case of harmonic oscillator it takes the form V(z)=(ΔEmz/2)2 where R(z)=(D(z)/2), while the total energy is given by Empq=k 2 mpq - (m/Rb)2=(q+1/2)ΔEm.

For p=1 and effective turning point of about 50µm, from Eqs. (2) and (3) it can be deduced that the corresponding b-WGMs are characterized by q and m mode-numbers around 40 and 535, respectively, with resonant wavelengths in the 1550nm spectral range. On the other hand, when the fiber taper is moved towards the bottle neck (Figs. 1(d)-1(f) and 1(h)), a different sub-set of b-WGMs, with high q-number, relatively low m-number, and widely separated turning points are preferentially excited. The results are summarized in Table 1. It is shown that as the turning point moves towards the bottle neck, the m mode number decreases, while the corresponding q number increases monotonically. Group of b-WGMs with mode numbers in the vicinity of the ones shown in Table 1 show pronounced field maxima around the turning point and are, therefore, expected to overlap strongly with the excitation tapered-fiber beam. Of course, the degree of excitation will also depend critically on the phase-matching conditions.

Fig. 5. (a) Harmonic oscillator and parabolic profiles for parameters similar to the experiment. The inset shows a magnified version to visualize the profile differences. (b) The microbottle resonator shown in Fig. 1(a) fitted with truncated harmonic oscillator profile, with Db=185 µm, D s=125 µm and Δk=0.00545 µm-1.

Table 1. Azimuthal and axial mode numbers corresponding to different turning points along the bottle axis. The resonant wavelength is around 1550nm and the radial mode number p=1.

table-icon
View This Table

Figure 6 shows the potential (solid) and the total energy (dashed) of the b-WGMs corresponding to turning points 50µm (red), 150µm (green) and 200µm (blue). It is shown that as the turning point moves closer to the bottle neck, the potential becomes shallower, due to the m-number decrease, while the total energy increases, primarily due to the q-number increase. As a result, the total mode energy reaches fast the top of the bottle axial potential and, therefore, it becomes easier for the mode to leak into the stems, in the presence of small surface roughness and other irregularities. It is believed that this leakage effect results in the fast, quasi-exponential decrease of the observed Q factors as the excitation point moved closer to the bottle neck. The quasi-exponential dependence of the Q factor on the mode azimuthal number m has also been predicted for cylindrical dielectric resonators [23

23. J.U Nöckel, “Resonances in nonintegrable open systems,” PhD Thesis, pp.92–105, Yale University (1997).

] and microspheres [24

24. S. M. Lacey, “Ray and wave dynamics in three dimensional asymmetric optical resonators,” PhD Thesis, pp.141–147, University of Oregon (2003).

].

Fig. 6. The potential (solid) and the total energy (dashed) of the b-WGMs corresponding to turning points 50µm (red), 150µm (green) and 200µm (blue).

5. Conclusion

Free-spectral ranges corresponding to long effective-cavity path lengths have been observed, as expected for bottle modes. The small free-spectral range (FSR) observed is expected to be beneficial in CQED experiments since it requires much lower tuning effort (e.g. mechanical strain) to fully cover the FSR. The pronounced lift of degeneracy and strong spectral overlap of the various mode orders can be quite beneficial in “white-light resonator” applications, such as coherent cavity ringdown [25

25. A. A. Savchenkov, A. A. Matsko, and L. Maleki, “White-light whispering gallery mode resonators,” Opt. Lett. 31, 92–94 (2006). [CrossRef] [PubMed]

]. The “soften-and-compress” bottle microresonator fabrication technique has been demonstrated using standard 125µm fibres. However, fibres with smaller diameter, or pre-tapered fibres can be used when larger FSR is required.

Another important microresonator parameter is the mode volume V. Bottle microresonators can show a large range of mode volumes, which can be accurately controlled by the relative position of the excitation fiber micro-taper. The smallest V is achieved when the resonator is excited at the centre (see Fig. 2(b)). At this point V is proportional to the “bottle” waist. On the other hand, large Vs are achieved when the excitation is moved towards the micro-bottle “necks” (see Figs. 2(e)-2(f)). While small V/Q ratios are beneficial for CQED experiments [26

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

], not all photonic applications benefit from small V. For example, when group delay is important, such as in microresonator-based optical delay lines, large-V configurations may be preferable. In addition, compared to microspheres, the b-WGMs occupy a much larger fraction of the resonator volume, and this is expected to improve the output power and efficiency of optically pumped WGM bottle microresonator lasers significantly. Therefore, large-V resonators are potentially advantageous for these applications, and work is underway to demonstrate these features.

Acknowledgements

The authors thank Dr. Yongmin Jung for providing the tapered fiber coupler and Dr. Yuh Tat Cho for providing the fusion splicer. This work was funded by the UK EPSRC under grant GR/S96500/01.

References and links

1.

B. E. Foresi, J. S. Little, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO2 microring resonator optical channel dropping filters,” IEEE Photon. Technol. Lett. 10, 549–551 (1998). [CrossRef]

2.

M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, “Fiber-coupled microsphere laser,” Opt. Lett. 25, 1430–1432 (2000). [CrossRef]

3.

C.- Yen Chao and L. Jay Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527–1529 (2003). [CrossRef]

4.

F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, and Th. J. A. Popma, “Experimental study of integrated-optics microcavity resonators: Toward an all-optical switching device,” Appl. Phys. Lett. 71, 747–749 (1997). [CrossRef]

5.

W. Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin “Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy,” Opt. Lett. 26, 166–168 (2001). [CrossRef]

6.

M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, “Ultimate Q of optical microsphere resonators,” Opt. Lett. 21, 453–455 (1996). [CrossRef] [PubMed]

7.

J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, “Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler,” IEEE Photon. Technol. Lett. 12, 1004–1006 (2000). [CrossRef]

8.

G. Senthil Murugan, Y. Panitchob, E. Tull, P. N. Bartlett, and J.S. Wilkinson, “Micropositioning of Microsphere Resonators on Planar Optical Waveguides,” in Proceedings of Conference on Optics-Photonics Design and Fabrication, Nara, Japan, 7PD2-01 (2006).

9.

E. J. Tull, P. N. Bartlett, G. Senthil Murugan, and J. S. Wilkinson “Manipulating Spheres That Sink: Assembly of Micrometer Sized Glass Spheres for Optical Coupling,” Langmuir 25, 1872–1880 (2009). [CrossRef] [PubMed]

10.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003). [CrossRef] [PubMed]

11.

M. Sumetsky, “Whispering-gallery-bottle microcavities: the three-dimensional etalon,” Opt. Lett. 29, 8–10 (2004). [CrossRef] [PubMed]

12.

Y. Louyer, D. Meshede, and A. Rauschenbeutel “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72, 031801(R) (2005). [CrossRef]

13.

M. L. Gorodetsky and A. E. Fomin, “Geometrical theory of whispering-gallery modes,” IEEE J. Sel. Top. Quantum Electron. 12, 33–39 (2006). [CrossRef]

14.

G. Kakaranzas, T. E. Dimmick, T. A. Birks, R. Le Roux, and P. St. J. Russell, “Miniature all-fiber devices based on CO2 laser micro structuring of tapered fibers,” Opt. Lett. 26, 1137–1139 (2001). [CrossRef]

15.

J. M. Ward, D. G. O’Shea, B. J. Shortt, M. J. Morrissey, K. Deasy, and S. G. Nic Chormaic, “Heat-and-pull rig for fiber taper fabrication,” Rev. Sci. Instrum. 77, 083105 (2006). [CrossRef]

16.

F. Warken, A. Rauschenbeutel, and T. Bartholomaus, “Fiber pulling profits from precise positioning,” Photonics Spectra 42, 73 (2008).

17.

M. P 6;öllinger, D. O’Shea, F. Warken, and A. Rauschenbeutel, “Ultra-high-Q tunable whispering-gallery-mode microresonator,” arXiv:0901.4921v1, (2009).

18.

M. N. Zervas, G. Senthil Murugan, and J. S. Wilkinson, “Demonstration of novel high-Q fiber WGM “bottle” microresonators,” in IEEE Proc. 10th anniversary International Conference on Transparent Optical Networks 4, 58–60 (2008). [CrossRef]

19.

G. Senthil Murugan, J. S. Wilkinson, and M. N. Zervas, “Experimental demonstration of a bottle microresonator,” in Conference on Lasers and Electro-Optics 2009, OSA Technical Digest Series (Optical Society of America, 2009), paper JTuD87.

20.

G. Chen, Md. M. Mazumder, R. K. Chang, J. C. Swindalt, and W. P. Ackert, “Laser diagnostics for droplet characterization: application of morphology-dependent resonances,” Prog. Energy Combust. Sci. 22, 163–188 (1996). [CrossRef]

21.

L. Maleki, V.S. Ilchenko, A.A. Savchenkov, and A.B. Matsko, “Crystalline Whispering Gallery Mode Resonators in Optics and Photonics,” in Practical Applications of Microresonators in Optics and Photonics, A.B. Matsko (ed.) pp. 145–147, CRC Press (2009).

22.

B.R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993). [CrossRef]

23.

J.U Nöckel, “Resonances in nonintegrable open systems,” PhD Thesis, pp.92–105, Yale University (1997).

24.

S. M. Lacey, “Ray and wave dynamics in three dimensional asymmetric optical resonators,” PhD Thesis, pp.141–147, University of Oregon (2003).

25.

A. A. Savchenkov, A. A. Matsko, and L. Maleki, “White-light whispering gallery mode resonators,” Opt. Lett. 31, 92–94 (2006). [CrossRef] [PubMed]

26.

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

OCIS Codes
(060.2340) Fiber optics and optical communications : Fiber optics components
(140.4780) Lasers and laser optics : Optical resonators
(230.5750) Optical devices : Resonators
(140.3948) Lasers and laser optics : Microcavity devices

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: April 14, 2009
Revised Manuscript: June 22, 2009
Manuscript Accepted: June 25, 2009
Published: June 30, 2009

Citation
Ganapathy Senthil Murugan, James S. Wilkinson, and Michalis N. Zervas, "Selective excitation of whispering gallery modes in a novel bottle microresonator," Opt. Express 17, 11916-11925 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11916


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References

  1. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998). [CrossRef]
  2. M. Cai, O. Painter, K. J. Vahala, and P. C. Sercel, "Fiber-coupled microsphere laser," Opt. Lett. 25, 1430-1432 (2000). [CrossRef]
  3. C.-Yen Chao and L. Jay Guo, "Biochemical sensors based on polymer microrings with sharp asymmetrical resonance," Appl. Phys. Lett. 83, 1527-1529 (2003). [CrossRef]
  4. F. C. Blom, D. R. van Dijk, H. J. W. M. Hoekstra, A. Driessen, and Th. J. A. Popma, "Experimental study of integrated-optics microcavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997). [CrossRef]
  5. W. Klitzing, R. Long, V. S. Ilchenko, J. Hare, and V. Lefèvre-Seguin, "Frequency tuning of the whispering-gallery modes of silica microspheres for cavity quantum electrodynamics and spectroscopy," Opt. Lett. 26, 166-168 (2001). [CrossRef]
  6. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Opt. Lett. 21, 453-455 (1996). [CrossRef] [PubMed]
  7. J.-P. Laine, B. E. Little, D. R. Lim, H. C. Tapalian, L. C. Kimerling, and H. A. Haus, "Microsphere resonator mode characterization by pedestal anti-resonant reflecting waveguide coupler," IEEE Photon. Technol. Lett. 12, 1004-1006 (2000). [CrossRef]
  8. G. Senthil Murugan, Y. Panitchob, E. Tull, P. N. Bartlett, J.S. Wilkinson, "Micropositioning of Microsphere Resonators on Planar Optical Waveguides," in Proceedings of Conference on Optics-Photonics Design and Fabrication, Nara, Japan, 7PD2-01 (2006).
  9. E. J. Tull, P. N. Bartlett, G. Senthil Murugan, and J. S. Wilkinson, "Manipulating Spheres That Sink: Assembly of Micrometer Sized Glass Spheres for Optical Coupling," Langmuir 25, 1872-1880 (2009). [CrossRef] [PubMed]
  10. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-928 (2003). [CrossRef] [PubMed]
  11. M. Sumetsky, "Whispering-gallery-bottle microcavities: the three-dimensional etalon," Opt. Lett. 29, 8-10 (2004). [CrossRef] [PubMed]
  12. Y. Louyer, D. Meshede, and A. Rauschenbeutel, "Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics," Phys. Rev. A 72, 031801(R) (2005). [CrossRef]
  13. M. L. Gorodetsky and A. E. Fomin, "Geometrical theory of whispering-gallery modes," IEEE J. Sel. Top. Quantum Electron. 12, 33-39 (2006). [CrossRef]
  14. G. Kakaranzas, T. E. Dimmick, T. A. Birks, R. Le Roux, and P. St. J. Russell, "Miniature all-fiber devices based on CO2 laser micro structuring of tapered fibers," Opt. Lett. 26, 1137-1139 (2001). [CrossRef]
  15. J. M. Ward, D. G. O’Shea, B. J. Shortt, M. J. Morrissey, K. Deasy, and S. G. Nic Chormaic, "Heat-and-pull rig for fiber taper fabrication," Rev. Sci. Instrum. 77, 083105 (2006). [CrossRef]
  16. F. Warken, A. Rauschenbeutel, and T. Bartholomaus, "Fiber pulling profits from precise positioning," Photonics Spectra 42, 73 (2008).
  17. M. Pöllinger, D. O'Shea, F. Warken and A. Rauschenbeutel, "Ultra-high-Q tunable whispering-gallery-mode microresonator," arXiv:0901.4921v1, (2009).
  18. M. N. Zervas, G. Senthil Murugan, and J. S. Wilkinson, "Demonstration of novel high-Q fiber WGM "bottle" microresonators," in IEEE Proc. 10th anniversary International Conference on Transparent Optical Networks 4, 58-60 (2008). [CrossRef]
  19. G. Senthil Murugan, J. S. Wilkinson, and M. N. Zervas, "Experimental demonstration of a bottle microresonator," in Conference on Lasers and Electro-Optics 2009, OSA Technical Digest Series (Optical Society of America, 2009), paper JTuD87.
  20. G. Chen, Md. M. Mazumder, R. K. Chang, J. C. Swindalt, and W. P. Ackert, "Laser diagnostics for droplet characterization: application of morphology-dependent resonances," Prog. Energy Combust. Sci. 22, 163-188 (1996). [CrossRef]
  21. L. Maleki, V. S. Ilchenko, A. A. Savchenkov, and A. B. Matsko, "Crystalline Whispering Gallery Mode Resonators in Optics and Photonics," in Practical Applications of Microresonators in Optics and Photonics, A. B. Matsko (ed.) pp. 145-147, CRC Press (2009).
  22. B. R. Johnson, "Theory of morphology-dependent resonances: shape resonances and width formulas," J. Opt. Soc. Am. A 10, 343-352 (1993). [CrossRef]
  23. J. U. Nöckel, "Resonances in nonintegrable open systems," PhD Thesis, pp.92-105, Yale University (1997).
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