Abstract

We theoretically investigate a novel scheme to detect target molecule induced, or suppressed, aggregation of nanoparticles. High-Q optical resonators are used to both optically trap gold nanoparticle clusters and to detect their presence via a shift in the resonance wavelength. The well depth of the optical trap is chosen to be relatively low compared to the thermal energy of the nanoparticles, so that trapping of single nanoparticles is marginal and results in a comparatively small wavelength shift. Aggregation of functionalized gold nanoparticles is mediated or suppressed via binding to a target molecule. The well depth for the resulting nanoparticle clusters scales much more favorably relative to Brownian motion, resulting in large nanoparticle concentration enhancements in the evanescent field region of the resonator. We predict a target molecule sensitivity in the tens of fM range. In order to predict the resonator response, a complete theory of time resolved nanoparticle cluster trapping dynamics is derived. In particular, the formalism of Kramers’ escape time is adapted to 2D (silicon wire) and 3D (ring resonator) optical traps.

© 2011 OSA

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  1. J. G. Gordon and S. Ernst, “Surface plasmons as a probe of the electrochemical interface,” Surf. Sci. 101(1-3), 499–506 (1980).
    [CrossRef]
  2. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators 54(1-2), 3–15 (1999).
    [CrossRef]
  3. F. Mitschke, “Fiber-optic sensor for humidity,” Opt. Lett. 14(17), 967–969 (1989).
    [CrossRef] [PubMed]
  4. G. Mitchell, “A review of Fabry-Perot interferometer sensors,” Proc. Phys. 44, 450–457 (1989).
  5. R. W. Boyd and J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40(31), 5742–5747 (2001).
    [CrossRef]
  6. 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]
  7. E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, “Ultra-compact biochemical sensor built with two-dimensional photonic crystal microcavity,” Opt. Lett. 29(10), 1093–1095 (2004).
    [CrossRef] [PubMed]
  8. A. Ksendzov and Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30(24), 3344–3346 (2005).
    [CrossRef]
  9. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
    [CrossRef] [PubMed]
  10. K. D. Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
    [CrossRef] [PubMed]
  11. M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
    [CrossRef]
  12. R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, and C. A. Mirkin, “Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles,” Science 277(5329), 1078–1081 (1997).
    [CrossRef] [PubMed]
  13. J. J. Storhoff, A. D. Lucas, G. Viswanadham, Y. P. Bao, and U. R. Müller, “Homogeneous detection of unamplified genomic DNA sequences based on colorimetric scatter of gold nanoparticle probes,” Nat. Biotechnol. 22(7), 883–887 (2004).
    [CrossRef] [PubMed]
  14. J. I. L. Chen, Y. Chen, and D. S. Ginger, “Plasmonic nanoparticle dimers for optical sensing of DNA in complex media,” J. Am. Chem. Soc. 132(28), 9600–9601 (2010).
    [CrossRef] [PubMed]
  15. F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
    [CrossRef] [PubMed]
  16. D. Aili, R. Selegárd, L. Baltzer, K. Enander, and B. Liedberg, “Colorimetric protein sensing by controlled assembly of gold nanoparticles functionalized with synthetic receptors,” Small 5(21), 2445–2452 (2009).
    [CrossRef] [PubMed]
  17. Y. N. Tan, X. Su, E. T. Liu, and J. S. Thomsen, “Gold-nanoparticle-based assay for instantaneous detection of nuclear hormone receptor-response elements interactions,” Anal. Chem. 82(7), 2759–2765 (2010).
    [CrossRef] [PubMed]
  18. J.-S. Lee, M. S. Han, and C. A. Mirkin, “Colorimetric Detection of Mercuric Ion (Hg2+) in Aqueous Media using DNA-Functionalized Gold Nanoparticles,” Angew. Chem. 119(22), 4171–4174 (2007).
    [CrossRef]
  19. F. Chai, C. Wang, T. Wang, L. Li, and Z. Su, “Colorimetric detection of Pb2+ using glutathione functionalized gold nanoparticles,” ACS Appl Mater Interfaces 2(5), 1466–1470 (2010).
    [CrossRef] [PubMed]
  20. S. O. Obare, R. E. Hollowell, and C. J. Murphy, “Sensing Strategy for Lithium Ion Based on Gold Nanoparticles,” Langmuir 18(26), 10407–10410 (2002).
    [CrossRef]
  21. K. Svoboda and S. M. Block, “Optical trapping of metallic Rayleigh particles,” Opt. Lett. 19(13), 930–932 (1994).
    [CrossRef] [PubMed]
  22. P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
    [CrossRef] [PubMed]
  23. M. Pelton, M. Liu, H. Y. Kim, S. Glenna, P. Guyot-Sionnest, and N. F. Scherer, “Optical trapping and alignment of single gold nanorods using plasmon resonances,” Proc. SPIE 6323, 63230E 1–9 (2006).
  24. L. N. Ng, B. J. Luff, M. N. Zervas, and J. S. Wilkinson, “Propulsion of gold nanoparticles on optical waveguides,” Opt. Commun. 208(1-3), 117–124 (2002).
    [CrossRef]
  25. Y. Seol, A. E. Carpenter, and T. T. Perkins, “Gold nanoparticles: enhanced optical trapping and sensitivity coupled with significant heating,” Opt. Lett. 31(16), 2429–2431 (2006).
    [CrossRef] [PubMed]
  26. T. J. Davis, “Brownian diffusion of nano-particles in optical traps,” Opt. Express 15(5), 2702–2712 (2007).
    [CrossRef] [PubMed]
  27. A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
    [CrossRef] [PubMed]
  28. T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 1-3 (2005).
    [CrossRef]
  29. J. M. Choi, R. K. Lee, and A. Yariv, “Control of critical coupling in a ring resonator-fiber configuration: application to wavelength-selective switching, modulation, amplification, and oscillation,” Opt. Lett. 26(16), 1236–1238 (2001).
    [CrossRef]
  30. H. A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica 7(4), 284–304 (1940).
    [CrossRef]
  31. S. Ke, J. C. Wright, and G. S. Kwon, “Intermolecular interaction of avidin and PEGylated biotin,” Bioconjug. Chem. 18(6), 2109–2114 (2007).
    [CrossRef] [PubMed]
  32. C. Tropini and A. Marziali, “Multi-nanopore force spectroscopy for DNA analysis,” Biophys. J. 92(5), 1632–1637 (2007).
    [CrossRef]
  33. D. W. Lynch and W. R. Hunter, Handbook of Optical Constants of Solids, ed. Palik, E., Academic Press, Orlando, FL, 286–295 (1985).
  34. N. J. Lynch, P. K. Kilpatrick, and R. G. Carbonell, “Aggregation of ligand-modified liposomes by specific interactions with proteins. I: Biotinylated liposomes and avidin,” Biotechnol. Bioeng. 50(2), 151–168 (1996).
    [CrossRef] [PubMed]
  35. S. Y. Park, J.-S. Lee, D. Georganopoulou, C. A. Mirkin, and G. C. Schatz, “Structures of DNA-linked nanoparticle aggregates,” J. Phys. Chem. B 110(25), 12673–12681 (2006).
    [CrossRef] [PubMed]
  36. C. R. Snyder and J. F. J. Douglas, “Determination of the Dielectric Constant of Nanoparticles. 1. Dielectric Measurements of Buckminsterfullerene Solutions,” Phys. Chem. B 104(47), 11058–11065 (2000).
    [CrossRef]
  37. J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010).
    [CrossRef] [PubMed]
  38. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
    [CrossRef]

2010 (6)

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

J. I. L. Chen, Y. Chen, and D. S. Ginger, “Plasmonic nanoparticle dimers for optical sensing of DNA in complex media,” J. Am. Chem. Soc. 132(28), 9600–9601 (2010).
[CrossRef] [PubMed]

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Y. N. Tan, X. Su, E. T. Liu, and J. S. Thomsen, “Gold-nanoparticle-based assay for instantaneous detection of nuclear hormone receptor-response elements interactions,” Anal. Chem. 82(7), 2759–2765 (2010).
[CrossRef] [PubMed]

F. Chai, C. Wang, T. Wang, L. Li, and Z. Su, “Colorimetric detection of Pb2+ using glutathione functionalized gold nanoparticles,” ACS Appl Mater Interfaces 2(5), 1466–1470 (2010).
[CrossRef] [PubMed]

J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010).
[CrossRef] [PubMed]

2009 (2)

D. Aili, R. Selegárd, L. Baltzer, K. Enander, and B. Liedberg, “Colorimetric protein sensing by controlled assembly of gold nanoparticles functionalized with synthetic receptors,” Small 5(21), 2445–2452 (2009).
[CrossRef] [PubMed]

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

2007 (6)

T. J. Davis, “Brownian diffusion of nano-particles in optical traps,” Opt. Express 15(5), 2702–2712 (2007).
[CrossRef] [PubMed]

K. D. Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
[CrossRef] [PubMed]

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

J.-S. Lee, M. S. Han, and C. A. Mirkin, “Colorimetric Detection of Mercuric Ion (Hg2+) in Aqueous Media using DNA-Functionalized Gold Nanoparticles,” Angew. Chem. 119(22), 4171–4174 (2007).
[CrossRef]

S. Ke, J. C. Wright, and G. S. Kwon, “Intermolecular interaction of avidin and PEGylated biotin,” Bioconjug. Chem. 18(6), 2109–2114 (2007).
[CrossRef] [PubMed]

C. Tropini and A. Marziali, “Multi-nanopore force spectroscopy for DNA analysis,” Biophys. J. 92(5), 1632–1637 (2007).
[CrossRef]

2006 (2)

Y. Seol, A. E. Carpenter, and T. T. Perkins, “Gold nanoparticles: enhanced optical trapping and sensitivity coupled with significant heating,” Opt. Lett. 31(16), 2429–2431 (2006).
[CrossRef] [PubMed]

S. Y. Park, J.-S. Lee, D. Georganopoulou, C. A. Mirkin, and G. C. Schatz, “Structures of DNA-linked nanoparticle aggregates,” J. Phys. Chem. B 110(25), 12673–12681 (2006).
[CrossRef] [PubMed]

2005 (3)

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 1-3 (2005).
[CrossRef]

A. Ksendzov and Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30(24), 3344–3346 (2005).
[CrossRef]

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[CrossRef] [PubMed]

2004 (3)

E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, “Ultra-compact biochemical sensor built with two-dimensional photonic crystal microcavity,” Opt. Lett. 29(10), 1093–1095 (2004).
[CrossRef] [PubMed]

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

J. J. Storhoff, A. D. Lucas, G. Viswanadham, Y. P. Bao, and U. R. Müller, “Homogeneous detection of unamplified genomic DNA sequences based on colorimetric scatter of gold nanoparticle probes,” Nat. Biotechnol. 22(7), 883–887 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (2)

L. N. Ng, B. J. Luff, M. N. Zervas, and J. S. Wilkinson, “Propulsion of gold nanoparticles on optical waveguides,” Opt. Commun. 208(1-3), 117–124 (2002).
[CrossRef]

S. O. Obare, R. E. Hollowell, and C. J. Murphy, “Sensing Strategy for Lithium Ion Based on Gold Nanoparticles,” Langmuir 18(26), 10407–10410 (2002).
[CrossRef]

2001 (2)

2000 (1)

C. R. Snyder and J. F. J. Douglas, “Determination of the Dielectric Constant of Nanoparticles. 1. Dielectric Measurements of Buckminsterfullerene Solutions,” Phys. Chem. B 104(47), 11058–11065 (2000).
[CrossRef]

1999 (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators 54(1-2), 3–15 (1999).
[CrossRef]

1997 (1)

R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, and C. A. Mirkin, “Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles,” Science 277(5329), 1078–1081 (1997).
[CrossRef] [PubMed]

1996 (1)

N. J. Lynch, P. K. Kilpatrick, and R. G. Carbonell, “Aggregation of ligand-modified liposomes by specific interactions with proteins. I: Biotinylated liposomes and avidin,” Biotechnol. Bioeng. 50(2), 151–168 (1996).
[CrossRef] [PubMed]

1994 (1)

1989 (2)

F. Mitschke, “Fiber-optic sensor for humidity,” Opt. Lett. 14(17), 967–969 (1989).
[CrossRef] [PubMed]

G. Mitchell, “A review of Fabry-Perot interferometer sensors,” Proc. Phys. 44, 450–457 (1989).

1980 (1)

J. G. Gordon and S. Ernst, “Surface plasmons as a probe of the electrochemical interface,” Surf. Sci. 101(1-3), 499–506 (1980).
[CrossRef]

1940 (1)

H. A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica 7(4), 284–304 (1940).
[CrossRef]

Aili, D.

D. Aili, R. Selegárd, L. Baltzer, K. Enander, and B. Liedberg, “Colorimetric protein sensing by controlled assembly of gold nanoparticles functionalized with synthetic receptors,” Small 5(21), 2445–2452 (2009).
[CrossRef] [PubMed]

Armani, A. M.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Arnold, S.

Baehr-Jones, T.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010).
[CrossRef] [PubMed]

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 1-3 (2005).
[CrossRef]

Baets, R.

K. D. Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
[CrossRef] [PubMed]

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Bailey, R. C.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

Baltzer, L.

D. Aili, R. Selegárd, L. Baltzer, K. Enander, and B. Liedberg, “Colorimetric protein sensing by controlled assembly of gold nanoparticles functionalized with synthetic receptors,” Small 5(21), 2445–2452 (2009).
[CrossRef] [PubMed]

Bao, Y. P.

J. J. Storhoff, A. D. Lucas, G. Viswanadham, Y. P. Bao, and U. R. Müller, “Homogeneous detection of unamplified genomic DNA sequences based on colorimetric scatter of gold nanoparticle probes,” Nat. Biotechnol. 22(7), 883–887 (2004).
[CrossRef] [PubMed]

Bartolozzi, I.

Beckx, S.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Ben, B. Y.H.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Bhatia, V. K.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[CrossRef] [PubMed]

Bienstman, P.

K. D. Vos, I. Bartolozzi, E. Schacht, P. Bienstman, and R. Baets, “Silicon-on-Insulator microring resonator for sensitive and label-free biosensing,” Opt. Express 15(12), 7610–7615 (2007).
[CrossRef] [PubMed]

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Block, S. M.

Bogaerts, W.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Boyd, R. W.

Carbonell, R. G.

N. J. Lynch, P. K. Kilpatrick, and R. G. Carbonell, “Aggregation of ligand-modified liposomes by specific interactions with proteins. I: Biotinylated liposomes and avidin,” Biotechnol. Bioeng. 50(2), 151–168 (1996).
[CrossRef] [PubMed]

Carpenter, A. E.

Chai, F.

F. Chai, C. Wang, T. Wang, L. Li, and Z. Su, “Colorimetric detection of Pb2+ using glutathione functionalized gold nanoparticles,” ACS Appl Mater Interfaces 2(5), 1466–1470 (2010).
[CrossRef] [PubMed]

Chen, J. I. L.

J. I. L. Chen, Y. Chen, and D. S. Ginger, “Plasmonic nanoparticle dimers for optical sensing of DNA in complex media,” J. Am. Chem. Soc. 132(28), 9600–9601 (2010).
[CrossRef] [PubMed]

Chen, Y.

J. I. L. Chen, Y. Chen, and D. S. Ginger, “Plasmonic nanoparticle dimers for optical sensing of DNA in complex media,” J. Am. Chem. Soc. 132(28), 9600–9601 (2010).
[CrossRef] [PubMed]

Choi, J. M.

Chow, E.

Davis, T. J.

Douglas, J. F. J.

C. R. Snyder and J. F. J. Douglas, “Determination of the Dielectric Constant of Nanoparticles. 1. Dielectric Measurements of Buckminsterfullerene Solutions,” Phys. Chem. B 104(47), 11058–11065 (2000).
[CrossRef]

Dumon, P.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Elghanian, R.

R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, and C. A. Mirkin, “Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles,” Science 277(5329), 1078–1081 (1997).
[CrossRef] [PubMed]

Enander, K.

D. Aili, R. Selegárd, L. Baltzer, K. Enander, and B. Liedberg, “Colorimetric protein sensing by controlled assembly of gold nanoparticles functionalized with synthetic receptors,” Small 5(21), 2445–2452 (2009).
[CrossRef] [PubMed]

Erickson, D.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Ernst, S.

J. G. Gordon and S. Ernst, “Surface plasmons as a probe of the electrochemical interface,” Surf. Sci. 101(1-3), 499–506 (1980).
[CrossRef]

Flagan, R. C.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Fraser, S. E.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators 54(1-2), 3–15 (1999).
[CrossRef]

Georganopoulou, D.

S. Y. Park, J.-S. Lee, D. Georganopoulou, C. A. Mirkin, and G. C. Schatz, “Structures of DNA-linked nanoparticle aggregates,” J. Phys. Chem. B 110(25), 12673–12681 (2006).
[CrossRef] [PubMed]

Ginger, D. S.

J. I. L. Chen, Y. Chen, and D. S. Ginger, “Plasmonic nanoparticle dimers for optical sensing of DNA in complex media,” J. Am. Chem. Soc. 132(28), 9600–9601 (2010).
[CrossRef] [PubMed]

Girolami, G.

Gleeson, M. A.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

Gong, X.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Gordon, J. G.

J. G. Gordon and S. Ernst, “Surface plasmons as a probe of the electrochemical interface,” Surf. Sci. 101(1-3), 499–506 (1980).
[CrossRef]

Grot, A.

Gunn, L. C.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

Gunn, W. G.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

Han, M. S.

J.-S. Lee, M. S. Han, and C. A. Mirkin, “Colorimetric Detection of Mercuric Ion (Hg2+) in Aqueous Media using DNA-Functionalized Gold Nanoparticles,” Angew. Chem. 119(22), 4171–4174 (2007).
[CrossRef]

Hansen, P. M.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[CrossRef] [PubMed]

Harrit, N.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[CrossRef] [PubMed]

Heebner, J. E.

Heeger, A. J.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Hochberg, M.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

J. Witzens, T. Baehr-Jones, and M. Hochberg, “Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links,” Opt. Express 18(16), 16902–16928 (2010).
[CrossRef] [PubMed]

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 1-3 (2005).
[CrossRef]

Holler, S.

Hollowell, R. E.

S. O. Obare, R. E. Hollowell, and C. J. Murphy, “Sensing Strategy for Lithium Ion Based on Gold Nanoparticles,” Langmuir 18(26), 10407–10410 (2002).
[CrossRef]

Homola, J.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators 54(1-2), 3–15 (1999).
[CrossRef]

Iqbal, M.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

Kang, D.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Ke, S.

S. Ke, J. C. Wright, and G. S. Kwon, “Intermolecular interaction of avidin and PEGylated biotin,” Bioconjug. Chem. 18(6), 2109–2114 (2007).
[CrossRef] [PubMed]

Khoshsima, M.

Kilpatrick, P. K.

N. J. Lynch, P. K. Kilpatrick, and R. G. Carbonell, “Aggregation of ligand-modified liposomes by specific interactions with proteins. I: Biotinylated liposomes and avidin,” Biotechnol. Bioeng. 50(2), 151–168 (1996).
[CrossRef] [PubMed]

Klug, M.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Kramers, H. A.

H. A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica 7(4), 284–304 (1940).
[CrossRef]

Ksendzov, A.

Kulkarni, R. P.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Kwon, G. S.

S. Ke, J. C. Wright, and G. S. Kwon, “Intermolecular interaction of avidin and PEGylated biotin,” Bioconjug. Chem. 18(6), 2109–2114 (2007).
[CrossRef] [PubMed]

Lee, J.-S.

J.-S. Lee, M. S. Han, and C. A. Mirkin, “Colorimetric Detection of Mercuric Ion (Hg2+) in Aqueous Media using DNA-Functionalized Gold Nanoparticles,” Angew. Chem. 119(22), 4171–4174 (2007).
[CrossRef]

S. Y. Park, J.-S. Lee, D. Georganopoulou, C. A. Mirkin, and G. C. Schatz, “Structures of DNA-linked nanoparticle aggregates,” J. Phys. Chem. B 110(25), 12673–12681 (2006).
[CrossRef] [PubMed]

Lee, R. K.

Letsinger, R. L.

R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, and C. A. Mirkin, “Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles,” Science 277(5329), 1078–1081 (1997).
[CrossRef] [PubMed]

Li, L.

F. Chai, C. Wang, T. Wang, L. Li, and Z. Su, “Colorimetric detection of Pb2+ using glutathione functionalized gold nanoparticles,” ACS Appl Mater Interfaces 2(5), 1466–1470 (2010).
[CrossRef] [PubMed]

Liedberg, B.

D. Aili, R. Selegárd, L. Baltzer, K. Enander, and B. Liedberg, “Colorimetric protein sensing by controlled assembly of gold nanoparticles functionalized with synthetic receptors,” Small 5(21), 2445–2452 (2009).
[CrossRef] [PubMed]

Lin, Y.

Lipson, M.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Liu, E. T.

Y. N. Tan, X. Su, E. T. Liu, and J. S. Thomsen, “Gold-nanoparticle-based assay for instantaneous detection of nuclear hormone receptor-response elements interactions,” Anal. Chem. 82(7), 2759–2765 (2010).
[CrossRef] [PubMed]

Lucas, A. D.

J. J. Storhoff, A. D. Lucas, G. Viswanadham, Y. P. Bao, and U. R. Müller, “Homogeneous detection of unamplified genomic DNA sequences based on colorimetric scatter of gold nanoparticle probes,” Nat. Biotechnol. 22(7), 883–887 (2004).
[CrossRef] [PubMed]

Luff, B. J.

L. N. Ng, B. J. Luff, M. N. Zervas, and J. S. Wilkinson, “Propulsion of gold nanoparticles on optical waveguides,” Opt. Commun. 208(1-3), 117–124 (2002).
[CrossRef]

Luyssaert, B.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Lynch, N. J.

N. J. Lynch, P. K. Kilpatrick, and R. G. Carbonell, “Aggregation of ligand-modified liposomes by specific interactions with proteins. I: Biotinylated liposomes and avidin,” Biotechnol. Bioeng. 50(2), 151–168 (1996).
[CrossRef] [PubMed]

Marziali, A.

C. Tropini and A. Marziali, “Multi-nanopore force spectroscopy for DNA analysis,” Biophys. J. 92(5), 1632–1637 (2007).
[CrossRef]

Mirkarimi, L. W.

Mirkin, C. A.

J.-S. Lee, M. S. Han, and C. A. Mirkin, “Colorimetric Detection of Mercuric Ion (Hg2+) in Aqueous Media using DNA-Functionalized Gold Nanoparticles,” Angew. Chem. 119(22), 4171–4174 (2007).
[CrossRef]

S. Y. Park, J.-S. Lee, D. Georganopoulou, C. A. Mirkin, and G. C. Schatz, “Structures of DNA-linked nanoparticle aggregates,” J. Phys. Chem. B 110(25), 12673–12681 (2006).
[CrossRef] [PubMed]

R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, and C. A. Mirkin, “Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles,” Science 277(5329), 1078–1081 (1997).
[CrossRef] [PubMed]

Mitchell, G.

G. Mitchell, “A review of Fabry-Perot interferometer sensors,” Proc. Phys. 44, 450–457 (1989).

Mitschke, F.

Moore, S. D.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Mucic, R. C.

R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, and C. A. Mirkin, “Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles,” Science 277(5329), 1078–1081 (1997).
[CrossRef] [PubMed]

Müller, U. R.

J. J. Storhoff, A. D. Lucas, G. Viswanadham, Y. P. Bao, and U. R. Müller, “Homogeneous detection of unamplified genomic DNA sequences based on colorimetric scatter of gold nanoparticle probes,” Nat. Biotechnol. 22(7), 883–887 (2004).
[CrossRef] [PubMed]

Murphy, C. J.

S. O. Obare, R. E. Hollowell, and C. J. Murphy, “Sensing Strategy for Lithium Ion Based on Gold Nanoparticles,” Langmuir 18(26), 10407–10410 (2002).
[CrossRef]

Ng, L. N.

L. N. Ng, B. J. Luff, M. N. Zervas, and J. S. Wilkinson, “Propulsion of gold nanoparticles on optical waveguides,” Opt. Commun. 208(1-3), 117–124 (2002).
[CrossRef]

Obare, S. O.

S. O. Obare, R. E. Hollowell, and C. J. Murphy, “Sensing Strategy for Lithium Ion Based on Gold Nanoparticles,” Langmuir 18(26), 10407–10410 (2002).
[CrossRef]

Oddershede, L.

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[CrossRef] [PubMed]

Park, S. Y.

S. Y. Park, J.-S. Lee, D. Georganopoulou, C. A. Mirkin, and G. C. Schatz, “Structures of DNA-linked nanoparticle aggregates,” J. Phys. Chem. B 110(25), 12673–12681 (2006).
[CrossRef] [PubMed]

Perkins, T. T.

Plaxco, K. W.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Schacht, E.

Schatz, G. C.

S. Y. Park, J.-S. Lee, D. Georganopoulou, C. A. Mirkin, and G. C. Schatz, “Structures of DNA-linked nanoparticle aggregates,” J. Phys. Chem. B 110(25), 12673–12681 (2006).
[CrossRef] [PubMed]

Scherer, A.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 1-3 (2005).
[CrossRef]

Schmidt, B. S.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Selegárd, R.

D. Aili, R. Selegárd, L. Baltzer, K. Enander, and B. Liedberg, “Colorimetric protein sensing by controlled assembly of gold nanoparticles functionalized with synthetic receptors,” Small 5(21), 2445–2452 (2009).
[CrossRef] [PubMed]

Seol, Y.

Sigalas, M.

Snyder, C. R.

C. R. Snyder and J. F. J. Douglas, “Determination of the Dielectric Constant of Nanoparticles. 1. Dielectric Measurements of Buckminsterfullerene Solutions,” Phys. Chem. B 104(47), 11058–11065 (2000).
[CrossRef]

Spaugh, B.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

Storhoff, J. J.

J. J. Storhoff, A. D. Lucas, G. Viswanadham, Y. P. Bao, and U. R. Müller, “Homogeneous detection of unamplified genomic DNA sequences based on colorimetric scatter of gold nanoparticle probes,” Nat. Biotechnol. 22(7), 883–887 (2004).
[CrossRef] [PubMed]

R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, and C. A. Mirkin, “Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles,” Science 277(5329), 1078–1081 (1997).
[CrossRef] [PubMed]

Su, X.

Y. N. Tan, X. Su, E. T. Liu, and J. S. Thomsen, “Gold-nanoparticle-based assay for instantaneous detection of nuclear hormone receptor-response elements interactions,” Anal. Chem. 82(7), 2759–2765 (2010).
[CrossRef] [PubMed]

Su, Z.

F. Chai, C. Wang, T. Wang, L. Li, and Z. Su, “Colorimetric detection of Pb2+ using glutathione functionalized gold nanoparticles,” ACS Appl Mater Interfaces 2(5), 1466–1470 (2010).
[CrossRef] [PubMed]

Svoboda, K.

Taillaert, D.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Tan, Y. N.

Y. N. Tan, X. Su, E. T. Liu, and J. S. Thomsen, “Gold-nanoparticle-based assay for instantaneous detection of nuclear hormone receptor-response elements interactions,” Anal. Chem. 82(7), 2759–2765 (2010).
[CrossRef] [PubMed]

Teraoka, I.

Thomsen, J. S.

Y. N. Tan, X. Su, E. T. Liu, and J. S. Thomsen, “Gold-nanoparticle-based assay for instantaneous detection of nuclear hormone receptor-response elements interactions,” Anal. Chem. 82(7), 2759–2765 (2010).
[CrossRef] [PubMed]

Tropini, C.

C. Tropini and A. Marziali, “Multi-nanopore force spectroscopy for DNA analysis,” Biophys. J. 92(5), 1632–1637 (2007).
[CrossRef]

Tybor, F.

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

Vahala, K. J.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

Vallée-Bélisle, A.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Van Campenhout, J.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Van Thourhout, D.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Viswanadham, G.

J. J. Storhoff, A. D. Lucas, G. Viswanadham, Y. P. Bao, and U. R. Müller, “Homogeneous detection of unamplified genomic DNA sequences based on colorimetric scatter of gold nanoparticle probes,” Nat. Biotechnol. 22(7), 883–887 (2004).
[CrossRef] [PubMed]

Vollmer, F.

Vos, K. D.

Walker, C.

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 1-3 (2005).
[CrossRef]

Wang, C.

F. Chai, C. Wang, T. Wang, L. Li, and Z. Su, “Colorimetric detection of Pb2+ using glutathione functionalized gold nanoparticles,” ACS Appl Mater Interfaces 2(5), 1466–1470 (2010).
[CrossRef] [PubMed]

Wang, T.

F. Chai, C. Wang, T. Wang, L. Li, and Z. Su, “Colorimetric detection of Pb2+ using glutathione functionalized gold nanoparticles,” ACS Appl Mater Interfaces 2(5), 1466–1470 (2010).
[CrossRef] [PubMed]

Wiaux, V.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Wilkinson, J. S.

L. N. Ng, B. J. Luff, M. N. Zervas, and J. S. Wilkinson, “Propulsion of gold nanoparticles on optical waveguides,” Opt. Commun. 208(1-3), 117–124 (2002).
[CrossRef]

Witzens, J.

Wouters, J.

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

Wright, J. C.

S. Ke, J. C. Wright, and G. S. Kwon, “Intermolecular interaction of avidin and PEGylated biotin,” Bioconjug. Chem. 18(6), 2109–2114 (2007).
[CrossRef] [PubMed]

Xia, F.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Xiao, Y.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Yang, A. H. J.

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Yang, R.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Yariv, A.

Yee, S. S.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators 54(1-2), 3–15 (1999).
[CrossRef]

Yuen, J. D.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Zervas, M. N.

L. N. Ng, B. J. Luff, M. N. Zervas, and J. S. Wilkinson, “Propulsion of gold nanoparticles on optical waveguides,” Opt. Commun. 208(1-3), 117–124 (2002).
[CrossRef]

Zuo, X.

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

ACS Appl Mater Interfaces (1)

F. Chai, C. Wang, T. Wang, L. Li, and Z. Su, “Colorimetric detection of Pb2+ using glutathione functionalized gold nanoparticles,” ACS Appl Mater Interfaces 2(5), 1466–1470 (2010).
[CrossRef] [PubMed]

Anal. Chem. (1)

Y. N. Tan, X. Su, E. T. Liu, and J. S. Thomsen, “Gold-nanoparticle-based assay for instantaneous detection of nuclear hormone receptor-response elements interactions,” Anal. Chem. 82(7), 2759–2765 (2010).
[CrossRef] [PubMed]

Angew. Chem. (1)

J.-S. Lee, M. S. Han, and C. A. Mirkin, “Colorimetric Detection of Mercuric Ion (Hg2+) in Aqueous Media using DNA-Functionalized Gold Nanoparticles,” Angew. Chem. 119(22), 4171–4174 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. Baehr-Jones, M. Hochberg, C. Walker, and A. Scherer, “High-Q optical resonators in silicon-on-insulator-based slot waveguides,” Appl. Phys. Lett. 86(8), 081101 1-3 (2005).
[CrossRef]

Bioconjug. Chem. (1)

S. Ke, J. C. Wright, and G. S. Kwon, “Intermolecular interaction of avidin and PEGylated biotin,” Bioconjug. Chem. 18(6), 2109–2114 (2007).
[CrossRef] [PubMed]

Biophys. J. (1)

C. Tropini and A. Marziali, “Multi-nanopore force spectroscopy for DNA analysis,” Biophys. J. 92(5), 1632–1637 (2007).
[CrossRef]

Biotechnol. Bioeng. (1)

N. J. Lynch, P. K. Kilpatrick, and R. G. Carbonell, “Aggregation of ligand-modified liposomes by specific interactions with proteins. I: Biotinylated liposomes and avidin,” Biotechnol. Bioeng. 50(2), 151–168 (1996).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

M. Iqbal, M. A. Gleeson, B. Spaugh, F. Tybor, W. G. Gunn, M. Hochberg, T. Baehr-Jones, R. C. Bailey, and L. C. Gunn, “Label-Free Biosensor Arrays Based on Silicon Ring Resonators and High-Speed Optical Scanning Instrumentation,” IEEE J. Sel. Top. Quantum Electron. 16(3), 654–661 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. Van Thourhout, and R. Baets, “Low-loss SOI Photonic Wires and Ring Resonators Fabricated with Deep UV Lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004).
[CrossRef]

J. Am. Chem. Soc. (1)

J. I. L. Chen, Y. Chen, and D. S. Ginger, “Plasmonic nanoparticle dimers for optical sensing of DNA in complex media,” J. Am. Chem. Soc. 132(28), 9600–9601 (2010).
[CrossRef] [PubMed]

J. Phys. Chem. B (1)

S. Y. Park, J.-S. Lee, D. Georganopoulou, C. A. Mirkin, and G. C. Schatz, “Structures of DNA-linked nanoparticle aggregates,” J. Phys. Chem. B 110(25), 12673–12681 (2006).
[CrossRef] [PubMed]

Langmuir (1)

S. O. Obare, R. E. Hollowell, and C. J. Murphy, “Sensing Strategy for Lithium Ion Based on Gold Nanoparticles,” Langmuir 18(26), 10407–10410 (2002).
[CrossRef]

Nano Lett. (1)

P. M. Hansen, V. K. Bhatia, N. Harrit, and L. Oddershede, “Expanding the optical trapping range of gold nanoparticles,” Nano Lett. 5(10), 1937–1942 (2005).
[CrossRef] [PubMed]

Nat. Biotechnol. (1)

J. J. Storhoff, A. D. Lucas, G. Viswanadham, Y. P. Bao, and U. R. Müller, “Homogeneous detection of unamplified genomic DNA sequences based on colorimetric scatter of gold nanoparticle probes,” Nat. Biotechnol. 22(7), 883–887 (2004).
[CrossRef] [PubMed]

Nature (1)

A. H. J. Yang, S. D. Moore, B. S. Schmidt, M. Klug, M. Lipson, and D. Erickson, “Optical manipulation of nanoparticles and biomolecules in sub-wavelength slot waveguides,” Nature 457(7225), 71–75 (2009).
[CrossRef] [PubMed]

Opt. Commun. (1)

L. N. Ng, B. J. Luff, M. N. Zervas, and J. S. Wilkinson, “Propulsion of gold nanoparticles on optical waveguides,” Opt. Commun. 208(1-3), 117–124 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (7)

Phys. Chem. B (1)

C. R. Snyder and J. F. J. Douglas, “Determination of the Dielectric Constant of Nanoparticles. 1. Dielectric Measurements of Buckminsterfullerene Solutions,” Phys. Chem. B 104(47), 11058–11065 (2000).
[CrossRef]

Physica (1)

H. A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica 7(4), 284–304 (1940).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

F. Xia, X. Zuo, R. Yang, Y. Xiao, D. Kang, A. Vallée-Bélisle, X. Gong, J. D. Yuen, B. Y.H. Ben, A. J. Heeger, and K. W. Plaxco, “Colorimetric detection of DNA, small molecules, proteins, and ions using unmodified gold nanoparticles and conjugated polyelectrolytes,” Proc. Natl. Acad. Sci. U.S.A. 107(24), 10837–10841 (2010).
[CrossRef] [PubMed]

Proc. Phys. (1)

G. Mitchell, “A review of Fabry-Perot interferometer sensors,” Proc. Phys. 44, 450–457 (1989).

Science (2)

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007).
[CrossRef] [PubMed]

R. Elghanian, J. J. Storhoff, R. C. Mucic, R. L. Letsinger, and C. A. Mirkin, “Selective colorimetric detection of polynucleotides based on the distance-dependent optical properties of gold nanoparticles,” Science 277(5329), 1078–1081 (1997).
[CrossRef] [PubMed]

Sens. Actuators (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators 54(1-2), 3–15 (1999).
[CrossRef]

Small (1)

D. Aili, R. Selegárd, L. Baltzer, K. Enander, and B. Liedberg, “Colorimetric protein sensing by controlled assembly of gold nanoparticles functionalized with synthetic receptors,” Small 5(21), 2445–2452 (2009).
[CrossRef] [PubMed]

Surf. Sci. (1)

J. G. Gordon and S. Ernst, “Surface plasmons as a probe of the electrochemical interface,” Surf. Sci. 101(1-3), 499–506 (1980).
[CrossRef]

Other (2)

D. W. Lynch and W. R. Hunter, Handbook of Optical Constants of Solids, ed. Palik, E., Academic Press, Orlando, FL, 286–295 (1985).

M. Pelton, M. Liu, H. Y. Kim, S. Glenna, P. Guyot-Sionnest, and N. F. Scherer, “Optical trapping and alignment of single gold nanorods using plasmon resonances,” Proc. SPIE 6323, 63230E 1–9 (2006).

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Figures (14)

Fig. 1
Fig. 1

Waveguide coupled slot waveguide ring resonator capturing gold NP clusters after target molecule induced aggregation. Single NPs are only marginally trapped, NP accumulation in the evanescent field of the ring only occurs in the presence of clusters.

Fig. 2
Fig. 2

Waveguide cross-section and trapping energy (in units of kBT) for (a) a slot waveguide and (c) a ridge waveguide. (b) and (d) show the corresponding trapping energy through the center plane of the waveguides (x = 0). The mode in (a) is x-polarized, while the mode in (c) is y-polarized in order to maximize the E-field strengths in the solution.

Fig. 3
Fig. 3

Well shape used in the classic Kramers escape problem.

Fig. 4
Fig. 4

Concentration distribution induced by a ring shaped particle sink with a 400 nm width and a 20 μm radius, as simulated in cylindrical coordinates. (b) Extracted value of the coefficient I as a function of the domain size d. (c) Coefficient I as a function of the estimated number of accumulated particles. The blue curve corresponds to the final number of accumulated particles for a 400 nm wide ridge waveguide (R = 20 μm) at NU 0 = 12.5 kBT. The red line corresponds to 10% of that number.

Fig. 5
Fig. 5

Example of a transmission spectrum for a slot waveguide resonator immersed in pure water (black), after addition of 10 pM of gold NPs (blue) and after addition of a sufficient amount of target to obtain 10% extent of aggregation (red). The trapping energy for single NPs is U 0/kBT = 6.2 and the assay stabilization time is 60s.

Fig. 6
Fig. 6

Effective NP concentration at the assay readout time as a function of cluster size N and single NP trap energy U 0/kBT for (a) 1 minute assay stabilization time and (b) 10 minutes assay stabilization time. The NP concentration is 10 pM and the extent of aggregation is assumed to be 10%.

Fig. 7
Fig. 7

Resonant wavelength shift as a function of target concentration and trapping strength for a 60s assay stabilization time. Curves correspond to U 0/kBT ranging from 2 to 14 in increments of 2. The initial NP concentration is 10 pM and the assay stabilization time 60s. (a) assumes diffusion limited cluster formation and (b) assumes reaction limited cluster formation.

Fig. 8
Fig. 8

Assay sensitivity as a function of stabilization time. The trapping energy is implicitly varied as described in the text, cNP is assumed to be set at 10× the sensitivity floor, and ϕ is assumed to be equal to c T /c NP .

Fig. 9
Fig. 9

Particle escape time as a function of boundary position for NU 0/kBT = 12, as determined with the 1D model. The fit given by Eq. (35) is shown by the dashed line.

Fig. 10
Fig. 10

Constant concentration contours generated by a 400 nm wide particle trap (trap boundary corresponding to c = 0) with R = 20 μm, simulated in cylindrical coordinates. The dashed line shows the ri = 1 μm boundary of the 2D analytical calculation.

Fig. 12
Fig. 12

(a) Constant particle flux contours and (b) l(y) as defined in Eq. (38) as simulated from a flat 400 nm wide particle sink in cylindrical coordinates.

Fig. 11
Fig. 11

Constant trapping energy contours for NU 0/kBT = 12. The contours correspond to kBT/4, kBT/2, kBT, 2kBT, 4kBT and 8kBT.

Fig. 13
Fig. 13

Coefficient I lim as calculated with Eq. (40) in the absence of an optical trapping field (U 0 = 0, w=400 nm, dashed line) and with U 0 = 12 kBT (continuous line, δ=100 nm).

Fig. 14
Fig. 14

(a) 2D transient trap loading time simulated in the time domain for δ = 100 nm and (blue crosses) w = 125 nm, r 0 = 150 nm (black dots) w = 630 nm, r 0 = 300 nm (red stars) w = 3150 nm, r 0 = 1100 nm. The continuous lines show the prediction given by Eq. (43). It can be seen that it is accurate for large trapping energies in all three cases. For the case of the black dots, 2δw/πr 0 2 = 0.45 is close to 1 and it can be seen that Eq. (43) is also accurate at low trapping energies. (b) shows the simulated 3D correction term (1.56 in Eq. (40) as a function of R when ri is held constant at 1 μm (black dots). The dashed line shows the prediction given by Eq. (45) (with r 0 set to 1 μm). The continuous curve shows the corresponding prediction for the loading time of the 400 nm wide ridge waveguide (with r 0 set to 270 nm).

Equations (51)

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U = 1 2 ε 0 ε w N V Re ( 3 ε g ε w ε g + 2 ε w ) E 2 = 1 2 ε 0 ε w N V Re ( α ) E 2 = N U 0
D ( N ) c ( N ) ( U ) γ ( N ) c ( N ) = 0
c ( N ) = c 0 ( N ) e N U 0 k B T
c 0 ( N ) = c N P υ ( N ) ϕ N 1 + O ( ϕ N )
n = ε w + ε w N c 0 ( N ) e N U 0 k B T n A N V α n w ( 1 + 1 2 n A V α N N c 0 ( N ) e N U 0 k B T ) n w ( 1 + 1 2 n A V α e U 0 k B T c N P N υ ( N ) N ( ϕ e U 0 k B T ) N 1 )
Δ n e f f ( N ) = Δ n max ( N ) Γ ( N U 0 k B T )
Γ ( N U 0 k B T ) = n w E 2 e N U 0 k B T ( E 2 max ( E 2 ) 1 ) d x d y Z 0 Re ( E × H * ) d x d y
Δ n e f f = n w 1 2 n A V α N N c 0 ( N ) e N U 0 k B T Γ ( N U 0 k B T )
Δ n e f f = n w 1 2 n A V α N N c 0 ( N ) e N U 0 k B T Γ ( N U 0 k B T ) ( 1 e t τ l o a d ( N ) )
M t = ( 2 π R w ) η c 0 M τ l o a d .
M e q = 2 π R c 0 e N U 0 k B T ( E 2 max ( E 2 ) ) d x d y = c 0 e N U 0 k B T 2 π R w ( e N U 0 k B T ( E 2 max ( E 2 ) 1 ) e N U 0 k B T ) d y + c 0 2 π R w h = c 0 e N U 0 k B T 2 π R w h t r a p ( N U 0 k B T ) + c 0 2 π R w h
τ l o a d = e N U 0 k B T h t r a p η .
η = D I w
τ l o a d = I w h t r a p ( N ) D ( N ) e N U 0 k B T
U ( y ) = N U 0 e - y δ
δ = 2 π U d 2 U d y 2
h t r a p ( N U 0 k B T ) = δ e N U 0 k B T 0 N U 0 k B T ( e z z 1 z ) d z δ N U 0 k B T
h t r a p ( N U 0 k B T ) e 1 2 N U 0 k B T 2 π y 2 δ 2 d y = δ N U 0 k B T
τ l o a d = I w h t r a p ( N ) D ( N ) e N U 0 k B T I w δ D ( N ) e N U 0 k B T ( N U 0 k B T ) χ = τ 0 e N U 0 k B T ( N U 0 k B T ) χ
E 2 e N U 0 k B T ( E 2 max ( E 2 ) 1 ) d x d y max ( E 2 ) w h t r a p ( N U 0 k B T )
Γ ( N U 0 k B T ) n w max ( E 2 ) w δ Z 0 Re ( E × H * ) d x d y h t r a p ( N U 0 k B T ) δ = Γ 0 h t r a p ( N U 0 k B T ) δ
Γ ( N U 0 k B T ) n w max ( E 2 ) w δ Z 0 Re ( E × H * ) d x d y ( 1 e N U 0 k B T ) 1 N U 0 k B T
Γ ( N U 0 k B T ) n w max ( E 2 ) w δ Z 0 Re ( E × H * ) d x d y ( 1 0.5 N U 0 k B T ) 1 N U 0 k B T
Δ n e f f ( N ) ( 1 2 n w n A V α ) N c 0 ( N ) e N U 0 k B T Γ ( N U 0 k B T ) t τ l o a d ( N ) ( 1 2 n w n A V α ) N υ ( N ) c N P ϕ N 1 Γ 0 t τ 0 ( N )
c 0 ( N ) = ( 1 ϕ ) 2 ϕ N 1
c 0 ( N ) = ( 1 ϕ ) e N ϕ ( N ϕ ) N 1 N !
ζ = γ 2 m ω 0
J = 1 γ U y c D c y = D e U ( y ) k B T y ( e U ( y ) k B T c ( y ) )
J = η c 0 = D ( e U ( y a ) k B T c ( y a ) e U ( y b ) k B T c ( y b ) ) y a y b e U ( y ) k B T d y
τ = η 1 c 0 1 c ( y ) d y = 1 D y a y b e U ( y ) k B T d y 0 y b e U ( y ) k B T d y
η 1 = 1 D 0 δ log ( 4 N U 0 k B T ) e N U 0 k B T e y δ d y = δ D 1 / 4 N U 0 k B T e z z d z δ D
τ t h e r m = δ ( h t r a p ( N ) e N U 0 k B T + h ) D ( N ) δ δ D ( N ) e N U 0 k B T ( N U 0 k B T ) χ
τ = δ 2 D N U 0 k B T e y b δ N U 0 k B T e z z d z N U 0 k B T e y b δ N U 0 k B T e z z d z
τ δ 2 D ( N U 0 k B T e y b δ 0.01 1 z d z + 0.01 e z z d z ) ( δ log ( 4 N U 0 k B T ) y b y b y y b y a d y + 1 / 4 N U 0 k B T e z z d z )
τ y b 2 2 D + ( y b δ ( 0.567 + log ( N U 0 k B T ) ) ) δ D e N U 0 k B T N U 0 k B T = y b 2 2 D + ( y b y 0 ) δ D e N U 0 k B T N U 0 k B T
τ = r a r b c ( r ) d r 2 π D r 0 c 0 2 π R S t r a p ( N U 0 k B T ) e N U 0 k B T + r 0 r b ( r 0 r r 0 r b ) 2 π r 2 d r 2 π D r 0
τ 2 π R w h t r a p ( N U 0 k B T ) e N U 0 k B T 2 π D r 0 + r b 2 6 D
c i = c 0 1 + 1.56 η 2D w D
J = w η 2D c i = D ( e U ( y a ) k B T c ( y a ) e U ( y i ) k B T c ( y i ) ) y a y i 1 l ( y ) e U ( y ) k B T d y
J = J ( 0 , y ) l ( y )
l ( y ) = π r 2 r + w 2 + π 2 w
I lim = D c 0 J = D c 0 w η 2 D c i = ( 1 + 1.56 ( 0 1 μ m 1 l ( y ) e N U 0 k B T e y δ d y ) 1 ) 0 1 μ m 1 l ( y ) e N U 0 k B T e y δ d y = 0 1 μ m 1 l ( y ) e N U 0 k B T e y δ d y + 1.56
0 r b 1 l ( y ) e N U 0 k B T e y δ d y = r 0 r b 1 π r d r
e 2 log ( r b r 0 ) 2 log ( r b r 0 ) = 2 δ w π r 0 2 e N U 0 k B T ( N U 0 k B T ) χ
τ l o a d ( N U 0 k B T ) 2 π δ w D e ( N U 0 k B T ) ( N U 0 k B T ) = δ w e ( N U 0 k B T ) 2 π D
I ( N U 0 k B T ) 2 π
I lim = 0 r i 1 l ( y ) e N U 0 k B T e y δ d y + 1 π log ( 6.7 R r i ) = 1 π log ( 6.7 R r 0 )
Δ T = P a b s 4 π ( a N 1 / 3 / 0.74 1 / 3 ) C w = 0.9 N 2 / 3 U 0 k B T k B T c γ λ a C w Im ( α ) Re ( α )
P a b s = 2 π λ n w N V Im ( α ) I o p t
I o p t = n w ε 0 c γ E 2
q = β I o p t = 2 c γ k B T V Re ( α ) n w β U 0 k B T

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