Abstract

We theoretically analyze the ability of 3-dimensionally confined optofluidic ring resonators (OFRRs) for detection of a single nanoparticle in water and in air. The OFRR is based on a glass capillary, on which bottle-shaped and bubble-shaped ring resonators can form. The spectral position of the whispering gallery mode in the OFRR shifts when a nanoparticle is attached to the OFRR inner surface. For both ring resonator structures, the electric field at the inner surface can be optimized by choosing the right wall thickness. Meanwhile, different electric field confinement along the capillary longitudinal axis can be achieved with different curvatures. Both effects significantly increase the sensitivity of the ring resonator for single nanoparticle detection. It is found that the sensitivity is enhanced about 10 times, as compared to that of a solid microsphere biosensor recently reported, and that the smallest detectable nanoparticle is estimated to be less than 20 nm in radius for a Δλ/λ resolution of 10−8. The high sensitivity and the naturally integrated capillary based microfluidics make the OFRR a very promising sensing platform for detection of various nano-sized bio/chemical species in liquid as well as in air.

© 2010 OSA

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References

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    [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  7. M. Sumetsky, Y. Dulashko, and R. S. Windeler, “Optical microbubble resonator,” Opt. Lett. 35(7), 898–900 (2010).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  13. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
    [CrossRef] [PubMed]
  14. S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2007).
    [CrossRef]
  15. I. M. White, N. M. Hanumegowda, H. Oveys, and X. Fan, “Tuning whispering gallery modes in optical microspheres with chemical etching,” Opt. Express 13(26), 10754–10759 (2005).
    [CrossRef] [PubMed]
  16. C. M. Rice, “Flaviviridae: the viruses and their replication,” in Fields virology, D. M. Knipe, and P. M. Howley, eds. (Philadelphia: Lippincott-Raven, 1996), pp. 931–959.
  17. W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
    [CrossRef] [PubMed]
  18. S. I. Shopova, R. Rajmangal, Y. Nishida, and S. Arnold, “Ultra-sensitive nanoparticle detection using a portable whispering gallery mode biosensor driven by a PPLN doubled DFB laser,” Rev. Sci. Instrum. 81(10), 103110 (2010).
    [CrossRef] [PubMed]

2010

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010).
[CrossRef]

H. Li and X. Fan, “Characterization of sensing capability of optofluidic ring resonator biosensors,” Appl. Phys. Lett. 97(1), 011105 (2010).
[CrossRef]

S. I. Shopova, R. Rajmangal, Y. Nishida, and S. Arnold, “Ultra-sensitive nanoparticle detection using a portable whispering gallery mode biosensor driven by a PPLN doubled DFB laser,” Rev. Sci. Instrum. 81(10), 103110 (2010).
[CrossRef] [PubMed]

M. Sumetsky, Y. Dulashko, and R. S. Windeler, “Optical microbubble resonator,” Opt. Lett. 35(7), 898–900 (2010).
[CrossRef] [PubMed]

M. Sumetsky, Y. Dulashko, and R. S. Windeler, “Super free spectral range tunable optical microbubble resonator,” Opt. Lett. 35(11), 1866–1868 (2010).
[CrossRef] [PubMed]

2008

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008).
[CrossRef] [PubMed]

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[CrossRef] [PubMed]

2007

X. Fan, I. M. White, H. Zhu, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2007).
[CrossRef]

2005

Y. Louyer, D. Meschede, and A. Rauschenbeutel, “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72(3), 031801 (2005).
[CrossRef]

I. M. White, N. M. Hanumegowda, H. Oveys, and X. Fan, “Tuning whispering gallery modes in optical microspheres with chemical etching,” Opt. Express 13(26), 10754–10759 (2005).
[CrossRef] [PubMed]

2004

2003

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
[CrossRef] [PubMed]

Arnold, S.

S. I. Shopova, R. Rajmangal, Y. Nishida, and S. Arnold, “Ultra-sensitive nanoparticle detection using a portable whispering gallery mode biosensor driven by a PPLN doubled DFB laser,” Rev. Sci. Instrum. 81(10), 103110 (2010).
[CrossRef] [PubMed]

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008).
[CrossRef] [PubMed]

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2007).
[CrossRef]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
[CrossRef] [PubMed]

Chan, H. L. Y.

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

Chan, P. K. S.

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

Chen, D. R.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010).
[CrossRef]

Dulashko, Y.

Fan, X.

H. Li and X. Fan, “Characterization of sensing capability of optofluidic ring resonator biosensors,” Appl. Phys. Lett. 97(1), 011105 (2010).
[CrossRef]

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[CrossRef] [PubMed]

X. Fan, I. M. White, H. Zhu, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

I. M. White, N. M. Hanumegowda, H. Oveys, and X. Fan, “Tuning whispering gallery modes in optical microspheres with chemical etching,” Opt. Express 13(26), 10754–10759 (2005).
[CrossRef] [PubMed]

Hanumegowda, N. M.

He, L. N.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010).
[CrossRef]

Holler, S.

Keng, D.

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008).
[CrossRef] [PubMed]

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2007).
[CrossRef]

Khoshsima, M.

Kolchenko, V.

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2007).
[CrossRef]

Lee, N.

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

Leung, W. K.

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

Li, H.

H. Li and X. Fan, “Characterization of sensing capability of optofluidic ring resonator biosensors,” Appl. Phys. Lett. 97(1), 011105 (2010).
[CrossRef]

Li, L.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010).
[CrossRef]

Louyer, Y.

Y. Louyer, D. Meschede, and A. Rauschenbeutel, “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72(3), 031801 (2005).
[CrossRef]

Meschede, D.

Y. Louyer, D. Meschede, and A. Rauschenbeutel, “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72(3), 031801 (2005).
[CrossRef]

Nishida, Y.

S. I. Shopova, R. Rajmangal, Y. Nishida, and S. Arnold, “Ultra-sensitive nanoparticle detection using a portable whispering gallery mode biosensor driven by a PPLN doubled DFB laser,” Rev. Sci. Instrum. 81(10), 103110 (2010).
[CrossRef] [PubMed]

Oveys, H.

X. Fan, I. M. White, H. Zhu, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

I. M. White, N. M. Hanumegowda, H. Oveys, and X. Fan, “Tuning whispering gallery modes in optical microspheres with chemical etching,” Opt. Express 13(26), 10754–10759 (2005).
[CrossRef] [PubMed]

Ozdemir, S. K.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010).
[CrossRef]

Rajmangal, R.

S. I. Shopova, R. Rajmangal, Y. Nishida, and S. Arnold, “Ultra-sensitive nanoparticle detection using a portable whispering gallery mode biosensor driven by a PPLN doubled DFB laser,” Rev. Sci. Instrum. 81(10), 103110 (2010).
[CrossRef] [PubMed]

Ramjit, R.

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2007).
[CrossRef]

Rauschenbeutel, A.

Y. Louyer, D. Meschede, and A. Rauschenbeutel, “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72(3), 031801 (2005).
[CrossRef]

Shopova, S. I.

S. I. Shopova, R. Rajmangal, Y. Nishida, and S. Arnold, “Ultra-sensitive nanoparticle detection using a portable whispering gallery mode biosensor driven by a PPLN doubled DFB laser,” Rev. Sci. Instrum. 81(10), 103110 (2010).
[CrossRef] [PubMed]

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[CrossRef] [PubMed]

Sumetsky, M.

Sun, Y.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[CrossRef] [PubMed]

Sung, J. J. Y.

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

Suter, J. D.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[CrossRef] [PubMed]

X. Fan, I. M. White, H. Zhu, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

Teraoka, I.

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2007).
[CrossRef]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
[CrossRef] [PubMed]

To, K. F.

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

Vollmer, F.

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008).
[CrossRef] [PubMed]

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003).
[CrossRef] [PubMed]

White, I. M.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[CrossRef] [PubMed]

X. Fan, I. M. White, H. Zhu, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

I. M. White, N. M. Hanumegowda, H. Oveys, and X. Fan, “Tuning whispering gallery modes in optical microspheres with chemical etching,” Opt. Express 13(26), 10754–10759 (2005).
[CrossRef] [PubMed]

Windeler, R. S.

Wu, A. K. L.

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

Xiao, Y. F.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010).
[CrossRef]

Yang, L.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010).
[CrossRef]

Yuen, K. Y.

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

Zhu, H.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[CrossRef] [PubMed]

X. Fan, I. M. White, H. Zhu, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

Zhu, J. G.

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010).
[CrossRef]

Anal. Chim. Acta

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008).
[CrossRef] [PubMed]

Appl. Phys. Lett.

H. Li and X. Fan, “Characterization of sensing capability of optofluidic ring resonator biosensors,” Appl. Phys. Lett. 97(1), 011105 (2010).
[CrossRef]

Faraday Discuss.

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle photophysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83 (2007).
[CrossRef]

Gastroenterology

W. K. Leung, K. F. To, P. K. S. Chan, H. L. Y. Chan, A. K. L. Wu, N. Lee, K. Y. Yuen, and J. J. Y. Sung, “Enteric involvement of severe acute respiratory syndrome-associated coronavirus infection,” Gastroenterology 125(4), 1011–1017 (2003).
[CrossRef] [PubMed]

Nat. Photonics

J. G. Zhu, S. K. Ozdemir, Y. F. Xiao, L. Li, L. N. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4(1), 46–49 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

Y. Louyer, D. Meschede, and A. Rauschenbeutel, “Tunable whispering-gallery-mode resonators for cavity quantum electrodynamics,” Phys. Rev. A 72(3), 031801 (2005).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008).
[CrossRef] [PubMed]

Proc. SPIE

X. Fan, I. M. White, H. Zhu, J. D. Suter, and H. Oveys, “Overview of novel integrated optical ring resonator bio/chemical sensors,” Proc. SPIE 6452, 64520M (2007).
[CrossRef]

Rev. Sci. Instrum.

S. I. Shopova, R. Rajmangal, Y. Nishida, and S. Arnold, “Ultra-sensitive nanoparticle detection using a portable whispering gallery mode biosensor driven by a PPLN doubled DFB laser,” Rev. Sci. Instrum. 81(10), 103110 (2010).
[CrossRef] [PubMed]

Other

C. M. Rice, “Flaviviridae: the viruses and their replication,” in Fields virology, D. M. Knipe, and P. M. Howley, eds. (Philadelphia: Lippincott-Raven, 1996), pp. 931–959.

T. C. Mettenleiter, and F. Sobrino, Animal viruses: molecular biology (Caister Academic Press, Norfolk, UK, 2008).
[PubMed]

P. W. Ewald, The next fifty years, J. Brockman, ed.c (Vintage Books, New York, 2002), pp. 289–301.

C. F. Bohren, and D. R. Huffman, Absorption and scattering of light by small particles (Wiley, 1998).

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Figures (5)

Fig. 1
Fig. 1

Schematic of different ring resonators under study. (a) Cylindrical OFRR in cylindrical coordinates (r, θ and z with the origin at the arbitrary location on z axis). (b) Microbottle OFRR in cylindrical coordinates (r, θ and z with the origin at the bottle center). (c) Microbubble OFRR in spherical coordinates (r, θ and φ with the origin at the bubble center). (d) Solid microsphere in spherical coordinates (r, θ and φ with the origin at the sphere center).

Fig. 2
Fig. 2

The electric field distribution of the 3rd order mode in the radial direction with different wall thicknesses for the microbottle (a-c) and the microbubble (d-f). In all case, R 2=36 mm, n 1=1.33, n 2=1.45, n 3=1, m=288 for the microbottle, l=288 for the microbubble. (a) R 1=33.5 μm, λ=1022.543860 nm. (b) R 1=34.4 μm, λ=979.4255256 nm. (c) R 1=34.7 μm, λ=969.5206896 nm. (d) R 1=33.5 μm, λ=1020.959929 nm. (e) R 1=34.4 μm, λ=977.9460628 nm. (f) R 1=34.7 μm, λ=967.9444502 nm. (g) Field distribution of the 1st order mode of a microsphere in the radial direction. R 1=36 μm, n 1=1.45, n 2=1.33, l=288, λ=1040.227437 nm. (h) |Er 0|2 vs. R 1. Dashed line represents |Er 0 |2 of the microsphere in (g).

Fig. 3
Fig. 3

(a) The normalized 0th order mode field distribution of the microbottle and microsphere along the capillary with different Δk. For the microbottle, m=288, R 0=36 μm. For the microsphere, l=288, R 1=36 μm. Inset is their actual geometries. (b) The relation between |Ez 0|2 and Δk. z=0.

Fig. 4
Fig. 4

Results of single nanoparticle detection in water. The modes with the 3rd order in the r direction and the 0th order in the z direction are used. For the microbottle and microbubble, R 2=36 μm, m=288, l=288, n 1=1.33, n 2=1.45, n 3=1. For the microsphere, R 1=36 μm, m=288, l=288, n 1=1.45, n 2=1.33. The nanoparticle is located at the equator and at the inner surface of the OFRR based structures or at the outer surface of the microsphere. np =1.59. (a) Normalized wavelength shift caused by a single nanoparticle as a function of R 1. Wavelength shift from the microsphere is also shown for comparison. Nanoparticle radius is 50 nm. (b) The maximum wavelength shift vs. the nanoparticle radius for the microbottle with different Δk, microbubble, and microsphere. (c) The wavelength shift from the microbottle as a function of Δk. (d) The best wall thickness that gives the largest spectral shift as a function of the nanoparticle radius.

Fig. 5
Fig. 5

Results of single nanoparticle detection in air. R2 =36 μm, n1 =1, n2 =1.45, n3 =1, m=288, l=288. (a) Field distribution of the 3rd order mode of the microbubble. R1 =35 μm, λ=784.0225833 nm. (b) Q factor of the 3rd order mode of the microbubble as a function of the inner radius. (c) Fractional wavelength shift as a function of the inner radius. Shift from a solid microsphere is also plotted for comparison. Rp =50 nm, np =1.59 and the single nanoparticle is located at the equator and at the inner surface of the microbubble (or at the outer surface of the microsphere). (d) Fractional wavelength shift for the microbubble and for the microsphere with different nanoparticle radii. Τhe wall thickness of the microbubble is 1 μm.

Equations (6)

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R ( z ) = R 0 / 1 + ( Δ k z ) 2 ,
E r = { A J m ( k φ ( m , l ) n 1 r ) , r R 1 ( z ) B J m ( k φ ( m , l ) n 2 r ) + C H m ( 1 ) ( k φ ( m , l ) n 2 r ) , R 1 ( z ) < r R 2 ( z ) D H m ( 1 ) ( k φ ( m , l ) n 3 r ) , r > R 2 ( z )
E z = E 0 H q ( m Δ k R 0 z ) exp ( m Δ k 2 R 0 z 2 ) ,
E r = { A j m ( k ( m , l ) n 1 r ) , r R 1 B j m ( k ( m , l ) n 2 r ) + C h m ( 1 ) ( k φ ( m , l ) n 2 r ) , R 1 < r R 2 D h m ( 1 ) ( k ( m , l ) n 3 r ) , r > R 2 ,
E r = { A j m ( k ( m , l ) n 1 r ) , r R 1 B h m ( 1 ) ( k ( m , l ) n 2 r ) , r > R 1 ,
Δ λ λ = p a r t i c l e ( n p 2 n 2 ) | E | 2 d V 2 n 2 | E | 2 d V

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