Abstract

We propose the attachment of a periodic array of gold nanoparticles (epitopes) to the equator of a Whispering Gallery Mode Biosensor for the purpose of plasmonically enhancing nanoparticle sensing in a self-referencing manner while increasing the capture rate of analyte to antibodies attached to these plasmonic epitopes. Our approach can be applied to a variety of whispering gallery mode resonators from silicon/silica rings and disks to capillaries. The interpretation of the signals is particularly simple since the optical phase difference between the epitopes is designed to be an integer multiple of π, allowing the wavelength shift from each binding event to add independently.

© 2012 OSA

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  3. 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).
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  23. I. Teraoka and S. Arnold, “Resonance shifts of counterpropagating whispering-gallery modes: degenerate perturbation theory and application to resonator sensors with axial symmetry,” J. Opt. Soc. Am. B 26(7), 1321–1329 (2009).
  24. A. Mazzei, S. Götzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99(17), 173603 (2007).
  25. J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18(23), 23535–23543 (2010).
  26. L. Chantada, N. I. Nikolaev, A. L. Ivanov, P. Borri, and W. Langbein, “Optical resonances in microcylinders: response to perturbations for biosensing,” J. Opt. Soc. Am. B 25(8), 1312–1321 (2008).
  27. W. Kim, Ş. K. Özdemir, J. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98(14), 141106 (2011).
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2012

V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101(4), 043704 (2012).

M. S. Luchansky and R. C. Bailey, “High-Q Optical Sensors for Chemical and Biological Analysis,” Anal. Chem. 84(2), 793–821 (2012).

P. Zijlstra, P. M. R. Paulo, and M. Orrit, “Optical detection of single non-absorbing molecules using the surface plasmon resonance of a gold nanorod,” Nat. Nanotechnol. 7(6), 379–382 (2012).

W. Ahn, S. V. Boriskina, Y. Hong, and B. M. Reinhard, “Photonic-plasmonic mode coupling in on-chip integrated optoplasmonic molecules,” ACS Nano 6(1), 951–960 (2012).

2011

J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett. 99(24), 243109 (2011).

W. Kim, Ş. K. Özdemir, J. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98(14), 141106 (2011).

Y. Sun and X. Fan, “Optical ring resonators for biochemical and chemical sensing,” Anal. Bioanal. Chem. 399(1), 205–211 (2011).

S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. 98(24), 243104 (2011).

M. A. Santiago-Cordoba, S. V. Boriskina, F. Vollmer, and M. C. Demirel, “Nanoparticle-based protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 99(7), 073701 (2011).

M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express 19(14), 13551–13556 (2011).

M. Chamanzar and A. Adibi, “Hybrid nanoplasmonic-photonic resonators for efficient coupling of light to single plasmonic nanoresonators,” Opt. Express 19(22), 22292–22304 (2011).

2010

J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18(23), 23535–23543 (2010).

J. Zhu, Ş. K. Ozdemir, Y. F. Xiao, L. Li, L. 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).

W. Kim, Ş. K. Ozdemir, J. Zhu, L. He, and L. Yang, “Demonstration of mode splitting in an optical microcavity in aqueous environment,” Appl. Phys. Lett. 97(7), 071111 (2010).

2009

2008

L. Chantada, N. I. Nikolaev, A. L. Ivanov, P. Borri, and W. Langbein, “Optical resonances in microcylinders: response to perturbations for biosensing,” J. Opt. Soc. Am. B 25(8), 1312–1321 (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).

2007

A. Mazzei, S. Götzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99(17), 173603 (2007).

I. M. White, J. Gohring, and X. Fan, “SERS-based detection in an optofluidic ring resonator platform,” Opt. Express 15(25), 17433–17442 (2007).

2003

2001

S. Arnold, “Microspheres, photonic atoms, and the physics of nothing,” Am. Sci. 89, 414–421 (2001).

1999

1997

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).

Adibi, A.

Ahn, W.

W. Ahn, S. V. Boriskina, Y. Hong, and B. M. Reinhard, “Photonic-plasmonic mode coupling in on-chip integrated optoplasmonic molecules,” ACS Nano 6(1), 951–960 (2012).

Arnold, S.

V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101(4), 043704 (2012).

S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. 98(24), 243104 (2011).

S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, “Whispering Gallery Mode Carousel- a photonic mechanism for enhanced nanoparticle detection in biosensing,” Opt. Express 17(8), 6230–6238 (2009).

I. Teraoka and S. Arnold, “Resonance shifts of counterpropagating whispering-gallery modes: degenerate perturbation theory and application to resonator sensors with axial symmetry,” J. Opt. Soc. Am. B 26(7), 1321–1329 (2009).

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).

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).

S. Arnold, “Microspheres, photonic atoms, and the physics of nothing,” Am. Sci. 89, 414–421 (2001).

Averitt, R. D.

Bailey, R. C.

M. S. Luchansky and R. C. Bailey, “High-Q Optical Sensors for Chemical and Biological Analysis,” Anal. Chem. 84(2), 793–821 (2012).

Bauters, J. F.

Benson, O.

A. Mazzei, S. Götzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99(17), 173603 (2007).

Bian, R. X.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).

Blumenthal, D. J.

Boriskina, S. V.

W. Ahn, S. V. Boriskina, Y. Hong, and B. M. Reinhard, “Photonic-plasmonic mode coupling in on-chip integrated optoplasmonic molecules,” ACS Nano 6(1), 951–960 (2012).

M. A. Santiago-Cordoba, S. V. Boriskina, F. Vollmer, and M. C. Demirel, “Nanoparticle-based protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 99(7), 073701 (2011).

Borri, P.

Bowen, W. P.

J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett. 99(24), 243109 (2011).

Bowers, J. E.

Chamanzar, M.

Chantada, L.

Chen, D. R.

J. Zhu, Ş. K. Ozdemir, Y. F. Xiao, L. Li, L. 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).

Dantham, V. R.

V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101(4), 043704 (2012).

Demirel, M. C.

M. A. Santiago-Cordoba, S. V. Boriskina, F. Vollmer, and M. C. Demirel, “Nanoparticle-based protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 99(7), 073701 (2011).

Fan, X.

Y. Sun and X. Fan, “Optical ring resonators for biochemical and chemical sensing,” Anal. Bioanal. Chem. 399(1), 205–211 (2011).

I. M. White, J. Gohring, and X. Fan, “SERS-based detection in an optofluidic ring resonator platform,” Opt. Express 15(25), 17433–17442 (2007).

Gohring, J.

Gondarenko, A.

Götzinger, S.

A. Mazzei, S. Götzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99(17), 173603 (2007).

Halas, N. J.

He, L.

W. Kim, Ş. K. Ozdemir, J. Zhu, L. He, and L. Yang, “Demonstration of mode splitting in an optical microcavity in aqueous environment,” Appl. Phys. Lett. 97(7), 071111 (2010).

J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18(23), 23535–23543 (2010).

J. Zhu, Ş. K. Ozdemir, Y. F. Xiao, L. Li, L. 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).

Heck, M. J. R.

Holler, S.

V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101(4), 043704 (2012).

S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. 98(24), 243104 (2011).

S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, “Whispering Gallery Mode Carousel- a photonic mechanism for enhanced nanoparticle detection in biosensing,” Opt. Express 17(8), 6230–6238 (2009).

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).

Hong, Y.

W. Ahn, S. V. Boriskina, Y. Hong, and B. M. Reinhard, “Photonic-plasmonic mode coupling in on-chip integrated optoplasmonic molecules,” ACS Nano 6(1), 951–960 (2012).

Ivanov, A. L.

Keng, D.

S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, “Whispering Gallery Mode Carousel- a photonic mechanism for enhanced nanoparticle detection in biosensing,” Opt. Express 17(8), 6230–6238 (2009).

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).

Khoshsima, M.

Kim, W.

W. Kim, Ş. K. Özdemir, J. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98(14), 141106 (2011).

W. Kim, Ş. K. Ozdemir, J. Zhu, L. He, and L. Yang, “Demonstration of mode splitting in an optical microcavity in aqueous environment,” Appl. Phys. Lett. 97(7), 071111 (2010).

Knittel, J.

J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett. 99(24), 243109 (2011).

Kolchenko, V.

V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101(4), 043704 (2012).

Langbein, W.

Levy, J. S.

Li, L.

J. Zhu, Ş. K. Ozdemir, Y. F. Xiao, L. Li, L. 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).

Lipson, M.

Luchansky, M. S.

M. S. Luchansky and R. C. Bailey, “High-Q Optical Sensors for Chemical and Biological Analysis,” Anal. Chem. 84(2), 793–821 (2012).

Mazzei, A.

A. Mazzei, S. Götzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99(17), 173603 (2007).

Menezes, L. S.

A. Mazzei, S. Götzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99(17), 173603 (2007).

Nikolaev, N. I.

Novotny, L.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).

Orrit, M.

P. Zijlstra, P. M. R. Paulo, and M. Orrit, “Optical detection of single non-absorbing molecules using the surface plasmon resonance of a gold nanorod,” Nat. Nanotechnol. 7(6), 379–382 (2012).

Ozdemir, S. K.

W. Kim, Ş. K. Ozdemir, J. Zhu, L. He, and L. Yang, “Demonstration of mode splitting in an optical microcavity in aqueous environment,” Appl. Phys. Lett. 97(7), 071111 (2010).

J. Zhu, Ş. K. Ozdemir, Y. F. Xiao, L. Li, L. 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).

Özdemir, S. K.

W. Kim, Ş. K. Özdemir, J. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98(14), 141106 (2011).

J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18(23), 23535–23543 (2010).

Paulo, P. M. R.

P. Zijlstra, P. M. R. Paulo, and M. Orrit, “Optical detection of single non-absorbing molecules using the surface plasmon resonance of a gold nanorod,” Nat. Nanotechnol. 7(6), 379–382 (2012).

Rajmangal, R.

S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. 98(24), 243104 (2011).

Reinhard, B. M.

W. Ahn, S. V. Boriskina, Y. Hong, and B. M. Reinhard, “Photonic-plasmonic mode coupling in on-chip integrated optoplasmonic molecules,” ACS Nano 6(1), 951–960 (2012).

Sandoghdar, V.

A. Mazzei, S. Götzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. 99(17), 173603 (2007).

Santiago-Cordoba, M. A.

M. A. Santiago-Cordoba, S. V. Boriskina, F. Vollmer, and M. C. Demirel, “Nanoparticle-based protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 99(7), 073701 (2011).

Shopova, S. I.

S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. 98(24), 243104 (2011).

S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, “Whispering Gallery Mode Carousel- a photonic mechanism for enhanced nanoparticle detection in biosensing,” Opt. Express 17(8), 6230–6238 (2009).

Spencer, D. T.

Sun, Y.

Y. Sun and X. Fan, “Optical ring resonators for biochemical and chemical sensing,” Anal. Bioanal. Chem. 399(1), 205–211 (2011).

Swaim, J. D.

J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett. 99(24), 243109 (2011).

Teraoka, I.

Tien, M.-C.

Vollmer, F.

M. A. Santiago-Cordoba, S. V. Boriskina, F. Vollmer, and M. C. Demirel, “Nanoparticle-based protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 99(7), 073701 (2011).

S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, “Whispering Gallery Mode Carousel- a photonic mechanism for enhanced nanoparticle detection in biosensing,” Opt. Express 17(8), 6230–6238 (2009).

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).

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).

Wan, Z.

V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. 101(4), 043704 (2012).

Westcott, S. L.

White, I. M.

Xiao, Y. F.

J. Zhu, Ş. K. Ozdemir, Y. F. Xiao, L. Li, L. 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).

Xie, X. S.

L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. 79(4), 645–648 (1997).

Yang, L.

W. Kim, Ş. K. Özdemir, J. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98(14), 141106 (2011).

J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express 18(23), 23535–23543 (2010).

J. Zhu, Ş. K. Ozdemir, Y. F. Xiao, L. Li, L. 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).

W. Kim, Ş. K. Ozdemir, J. Zhu, L. He, and L. Yang, “Demonstration of mode splitting in an optical microcavity in aqueous environment,” Appl. Phys. Lett. 97(7), 071111 (2010).

Zhu, J.

W. Kim, Ş. K. Özdemir, J. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. 98(14), 141106 (2011).

W. Kim, Ş. K. Ozdemir, J. Zhu, L. He, and L. Yang, “Demonstration of mode splitting in an optical microcavity in aqueous environment,” Appl. Phys. Lett. 97(7), 071111 (2010).

J. Zhu, Ş. K. Ozdemir, Y. F. Xiao, L. Li, L. 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).

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Figures (7)

Fig. 1
Fig. 1

Illustration of an oblate spheroidal whispering gallery mode (WGM) resonator with functionalized periodic nano-plasmonic epitopes, that is driven at a frequency that produces a symmetric standing wave.

Fig. 2
Fig. 2

(a) Maximum electric field intensity enhancement at T or B, and the corresponding peak wavelength location of the dipole mode of a gold nanoshell 50 nm in diameter having a thickness ranging from 3.5 to 15 nm (inset). Note that the wavelength shift for an infinitesimally small bio-particle binding at T or B on a nanoshell grows by a factor of ~340. (b) Maximum field intensity enhancement at the tip (T or B) and the corresponding peak wavelength location of the plasmon mode of a gold ellipsoidal nanoparticle having an aspect ratio ranging from 1.0 to 4.2, calculated using quasi-static approximation [20]. Here 2b is 25 nanometers.

Fig. 3
Fig. 3

Illustration of a WGM ring resonator with one epitope.

Fig. 4
Fig. 4

Variation of the frequency shift of the WGM in the presence of 10 epitopes adsorbed on a microcavity as a function of phase difference between the consecutive epitopes.

Fig. 5
Fig. 5

Two states of a WGM ring with 10 plasmonic epitopes. Here optical phase difference between the consecutive epitopes is π.

Fig. 6
Fig. 6

Comparison between the mode splitting magnitude upon adsorbing 8 randomly located viruses to a bare microsphere equator (black) with the additional splitting for binding the same viruses to periodic plasmonic nanoshell epitopes (N = 4) on a similar microsphere (red).

Fig. 7
Fig. 7

A multiplexed ring resonator sensor on a chip.

Equations (28)

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1 r 2 2 E θ φ 2 + k 2 E θ =0,
E θ ~ e ±ikrφ .
E θ (φ+2πm)= E θ (φ),
|ccw>= E 1 θ (r,θ) 2 e imφ , and |cw>= E 1 θ (r,θ)* 2 e imφ , }
δω <ccw| α ex δ(r- r 1 )|ccw> .
δω=g= α ex | E 1 θ ( r 1 ,π/ 2) | 2 2 ε(r) | E 1 θ (r) | 2 dV ω.
( <ccw| α ex δ(r r 1 )|ccw> <ccw| α ex δ(r r 1 )|cw> <cw| α ex δ(r r 1 )|ccw> <cw| α ex δ(r r 1 )|cw> )( a ccw a cw )=δω( a ccw a cw ),
|ν>= a ccw |ccw>+ a cw |cw>.
| <ccw| α ex δ(r r 1 )|ccw> δω <ccw| α ex δ(r r 1 )|cw> <cw| α ex δ(r r 1 )|ccw> <cw| α ex δ(r r 1 )|cw> δω |=0.
| gδω g e i2 Φ 1 g e +i2 Φ 1 gδω |=0,
δ ω ± =gg(i.e.δ ω + =0,δ ω =2g),
( g (δω) ± g e i2 Φ 1 g e +i2 Φ 1 g (δω) ± ) ( a ccw a cw ) ± =0.
( g (δω) ± g g g (δω) ± ) ( a ccw a cw ) ± =0.
| ν + =i E θ 1 ( r,θ ) 2 sinΦ,
| ν = E θ 1 ( r,θ ) 2 cosΦ.
| ( g 1 + g 2 )δω ( g 1 e i2 Φ 1 + g 2 e i2 Φ 2 ) ( g 1 e i2 Φ 1 + g 2 e i2 Φ 2 ) ( g 1 + g 2 )δω |=0,
δ ω ± =( g 1 + g 2 ) g 1 2 + g 2 2 +2 g 1 g 2 cos2( Φ 1 Φ 2 ) .
( 2g (δω) ± 2g 2g 2g (δω) ± ) ( a ccw a cw ) ± =0.
| ( Ngδω ) g j=1 N e i Φ j g k=1 N e +i Φ k ( Ngδω ) |=0.
( Ngδω ) 2 g 2 ( N+ j,k jk e i( Φ k Φ j ) )=0.
| (Ngδω) M 12 M 12 * (Ngδω) |=0,
δ ω ± =Ng| M 12 |=Ngg| sin(NΔΦ) sin(ΔΦ) |,
δ ω ± =NgNg(i.e.δ ω + =0,δ ω =2Ng)
( Ng (δω) ± Ng Ng Ng (δω) ± ) ( a ccw a cw ) ± =0,
| j=1 N g j δω e i2 Φ 1 j=1 N g j e i2(j1)ΔΦ e i2 Φ 1 k=1 N g k e i2(k1)ΔΦ j=1 N g j δω |=0,
δ ω ± = g j g j g k =N g N g ( i.e.δ ω + =0,δ ω =2N g ).
N| 2g |>N Γ e + Γ 0 | 2g |> Γ e + Γ 0 N ,
Re[ α eff ] α Re p + | 1+ 2 α p 4π ε 0 ε m a p 3 | 2 α d ,

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