Abstract

We present a treatment of metallic nanoparticles on waveguide (WG) structures, treating the scenario where the spacing between the metallic nanoparticles is much less than the wavelength of light. We derive an effective medium treatment of the layer containing the nanoparticles, introducing transfer matrices for the layer. The coefficients of the transfer matrices take into account the interaction of the nanoparticles with each other, as well as local field corrections to the interaction of the nanoparticles with the material beneath them. Used with the WG mode pole expansions for the Fresnel coefficients of the WG structure, this allows for simple expressions for the shift and width of the WG mode resonance wave vector induced by the nanoparticles. As an example, we work out the simple case where the nanoparticles are treated as point dipoles, and use it to investigate the potential of this kind of structure for sensing applications.

© 2013 Optical Society of America

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Corrections

T. Cheng, C. Rangan, and J. E. Sipe, "Metallic nanoparticles on waveguide structures: effects on waveguide mode properties and the promise of sensing applications: erratum," J. Opt. Soc. Am. B 31, 2845-2845 (2014)
https://www.osapublishing.org/josab/abstract.cfm?uri=josab-31-11-2845

References

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  1. W. Lukosz and K. Tiefenthaler, “Directional switching in planar waveguides effected by absorbtion-desorbtion processes,” in Proceedings of the Second European Conference of Integrated Optics, IEE Conference Publication No. 227 (IEE, 1983), pp. 152–155.
  2. H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
    [CrossRef]
  3. C. Yu and J. Irudayaraj, “A multiplex biosensor using gold nanorods,” Anal. Chem. 79, 572–579 (2007).
    [CrossRef]
  4. A. Ulman, An Introduction to Ultrathin Films (Academic, 1991).
  5. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
  6. C. J. Kiely, J. Fink, M. Burst, D. Bethell, and D. J. Schiffrin, “Spontaneous ordering of bimodal ensembles of nanoscopic gold clusters,” Nature 396, 444–446 (1998).
    [CrossRef]
  7. A. J. Haes, D. A. Stuart, S. Nie, and R. P. Van Duyne, “Using solution phase nanoparticles, surface-confined nanoparticle arrays, and single nanoparticles as biological sensing platforms,” J. Flouresc. 14, 355–367 (2004).
    [CrossRef]
  8. S. Busse, J. Käshammer, S. Krämer, and S. Mittler, “Gold and thiol surface functionalized integrated optical Mach–Zehnder interferometer for sensing purposes,” Sens. Actuators B 60, 148–154 (1999).
  9. K. A. Willets and R. P. van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Ann. Rev. Phys. Chem. 58, 267–297 (2007).
    [CrossRef]
  10. Z. M. Qi, N. Matsuda, J. Santos, T. Yoshida, A. Takatsu, and K. Kato, “In situ monitoring of metal nanoparticle self-assembly on protein-functionalized glass by broadband optical waveguide spectroscopy,” J. Colloid. Interface Sci. 271, 249–253 (2004).
    [CrossRef]
  11. A. K. A. Aliganga, I. Lieberwirth, G. Glasser, A.-S. Duwez, Y. Sun, and S. Mittler, “Fabrication of equally oriented pancake shaped gold nanoparticles by SAM templated OMCVD and their optical response,” Org. Electron. 8, 161–174 (2007).
    [CrossRef]
  12. P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
    [CrossRef]
  13. S. M. Hashemi Rafsanjani, T. Cheng, C. Rangan, and S. Mittler, “A novel biosensing approach based on linear arrays of immobilized gold nanoparticles,” J. Appl. Phys. 107, 094303 (2010).
    [CrossRef]
  14. H. Jiang, T. Manifar, J. Sabarinathan, and S. Mittler, “3-D FDTD analysis of gold nanoparticle based photonic crystal on slab waveguide,” J. Lightwave Technol. 27, 2264–2270 (2009).
    [CrossRef]
  15. S. Mittler, “Gold nanoparticles on waveguides for and toward sensing application,” in Optical Guided-wave Chemical and Biosensors I, M. Zourob and A. Lakhtakia, eds., Springer Series on Chemical Sensors and Biosensors (Springer, 2010), Vol. 7, Part 2, pp. 209–229.
  16. J. E. Sipe and J. Becher, “Surface energy transfer enhanced by optical cavity excitation: a pole analysis,” J. Opt. Soc. Am. 72, 288–295 (1982).
    [CrossRef]
  17. J. E. Sipe, “Bulk-selvedge coupling theory for the optical properties of surfaces,” Phys. Rev. B 22, 1589–1599 (1980).
    [CrossRef]
  18. G. A. Wurtz, J. S. Im, S. K. Gray, and G. P. Wiederrecht, “Optical scattering from isolated metal nanoparticles and arrays,” J. Phys. Chem. B 107, 14191–14198 (2003).
    [CrossRef]
  19. L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and widths,” J. Phys. Chem. B 107, 7343–7350 (2003).
    [CrossRef]
  20. V. A. Markel, “Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure,” J. Mod. Opt. 40, 2281–2291 (1993).
    [CrossRef]
  21. T. D. Backes and D. S. Citrin, “Plasmon polaritons in 2-D nanoparticle arrays,” IEEE J. Sel. Top. Quantum Electron. 14, 1530–1535 (2008).
    [CrossRef]
  22. Y.-R. Zhen, K. H. Fung, and C. T. Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
    [CrossRef]
  23. S. M. R. Z. Bajestani, M. Shahabadi, and N. Talebi, “Analysis of plasmon propagation along a chain of metal nanospheres using the generalized multipole technique,” J. Opt. Soc. Am. B 28, 937–943 (2011).
    [CrossRef]
  24. E. Simsek, “On the surface plasmon resonance modes of metal nanoparticle chains and arrays,” Plasmonics 4, 223–230 (2009).
    [CrossRef]
  25. A. Semichaevsky and A. Akyurtlu, “Homogenization of metamaterial-loaded substrates and superstrates for antennas,” Prog. Electromagn. Res. PIER 71, 129–147 (2007).
    [CrossRef]
  26. A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit homogenization for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
    [CrossRef]
  27. Y. Wu and Z.-Q. Zhang, “Dispersion relations and their symmetry properties of electromagnetic and elastic metamaterials in two dimensions,” Phys. Rev. B 79, 195111 (2009).
    [CrossRef]
  28. P. A. Belov and C. R. Simovski, “Homogenization of electromagnetic crystals formed by uniaxial resonant scatterers,” Phys. Rev. E 72, 026615 (2005).
    [CrossRef]
  29. J. V. Kranendonk and J. E. Sipe, “Foundations of the macroscopic electromagnetic theory of dielectric solids,” in Progress in Optics XV, E. Wolf, ed. (North-Holland, 1977), pp. 247–350.
  30. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  31. J. E. Sipe, “New Green function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
    [CrossRef]
  32. A. Bagchi, R. G. Barrera, and R. Fuchs, “Local-field effect in optical reflectance from adsorbed overlayers,” Phys. Rev. B 25, 7086–7096 (1982).
    [CrossRef]
  33. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  34. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  35. P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
    [CrossRef]
  36. J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105, 489–504 (1981).
    [CrossRef]
  37. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989).

2011 (1)

2010 (1)

S. M. Hashemi Rafsanjani, T. Cheng, C. Rangan, and S. Mittler, “A novel biosensing approach based on linear arrays of immobilized gold nanoparticles,” J. Appl. Phys. 107, 094303 (2010).
[CrossRef]

2009 (4)

H. Jiang, T. Manifar, J. Sabarinathan, and S. Mittler, “3-D FDTD analysis of gold nanoparticle based photonic crystal on slab waveguide,” J. Lightwave Technol. 27, 2264–2270 (2009).
[CrossRef]

H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
[CrossRef]

E. Simsek, “On the surface plasmon resonance modes of metal nanoparticle chains and arrays,” Plasmonics 4, 223–230 (2009).
[CrossRef]

Y. Wu and Z.-Q. Zhang, “Dispersion relations and their symmetry properties of electromagnetic and elastic metamaterials in two dimensions,” Phys. Rev. B 79, 195111 (2009).
[CrossRef]

2008 (4)

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
[CrossRef]

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

T. D. Backes and D. S. Citrin, “Plasmon polaritons in 2-D nanoparticle arrays,” IEEE J. Sel. Top. Quantum Electron. 14, 1530–1535 (2008).
[CrossRef]

Y.-R. Zhen, K. H. Fung, and C. T. Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
[CrossRef]

2007 (4)

A. K. A. Aliganga, I. Lieberwirth, G. Glasser, A.-S. Duwez, Y. Sun, and S. Mittler, “Fabrication of equally oriented pancake shaped gold nanoparticles by SAM templated OMCVD and their optical response,” Org. Electron. 8, 161–174 (2007).
[CrossRef]

K. A. Willets and R. P. van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Ann. Rev. Phys. Chem. 58, 267–297 (2007).
[CrossRef]

C. Yu and J. Irudayaraj, “A multiplex biosensor using gold nanorods,” Anal. Chem. 79, 572–579 (2007).
[CrossRef]

A. Semichaevsky and A. Akyurtlu, “Homogenization of metamaterial-loaded substrates and superstrates for antennas,” Prog. Electromagn. Res. PIER 71, 129–147 (2007).
[CrossRef]

2005 (1)

P. A. Belov and C. R. Simovski, “Homogenization of electromagnetic crystals formed by uniaxial resonant scatterers,” Phys. Rev. E 72, 026615 (2005).
[CrossRef]

2004 (2)

A. J. Haes, D. A. Stuart, S. Nie, and R. P. Van Duyne, “Using solution phase nanoparticles, surface-confined nanoparticle arrays, and single nanoparticles as biological sensing platforms,” J. Flouresc. 14, 355–367 (2004).
[CrossRef]

Z. M. Qi, N. Matsuda, J. Santos, T. Yoshida, A. Takatsu, and K. Kato, “In situ monitoring of metal nanoparticle self-assembly on protein-functionalized glass by broadband optical waveguide spectroscopy,” J. Colloid. Interface Sci. 271, 249–253 (2004).
[CrossRef]

2003 (2)

G. A. Wurtz, J. S. Im, S. K. Gray, and G. P. Wiederrecht, “Optical scattering from isolated metal nanoparticles and arrays,” J. Phys. Chem. B 107, 14191–14198 (2003).
[CrossRef]

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and widths,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

2002 (1)

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit homogenization for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

1999 (1)

S. Busse, J. Käshammer, S. Krämer, and S. Mittler, “Gold and thiol surface functionalized integrated optical Mach–Zehnder interferometer for sensing purposes,” Sens. Actuators B 60, 148–154 (1999).

1998 (1)

C. J. Kiely, J. Fink, M. Burst, D. Bethell, and D. J. Schiffrin, “Spontaneous ordering of bimodal ensembles of nanoscopic gold clusters,” Nature 396, 444–446 (1998).
[CrossRef]

1993 (1)

V. A. Markel, “Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure,” J. Mod. Opt. 40, 2281–2291 (1993).
[CrossRef]

1987 (1)

1982 (2)

A. Bagchi, R. G. Barrera, and R. Fuchs, “Local-field effect in optical reflectance from adsorbed overlayers,” Phys. Rev. B 25, 7086–7096 (1982).
[CrossRef]

J. E. Sipe and J. Becher, “Surface energy transfer enhanced by optical cavity excitation: a pole analysis,” J. Opt. Soc. Am. 72, 288–295 (1982).
[CrossRef]

1981 (1)

J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105, 489–504 (1981).
[CrossRef]

1980 (1)

J. E. Sipe, “Bulk-selvedge coupling theory for the optical properties of surfaces,” Phys. Rev. B 22, 1589–1599 (1980).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Akyurtlu, A.

A. Semichaevsky and A. Akyurtlu, “Homogenization of metamaterial-loaded substrates and superstrates for antennas,” Prog. Electromagn. Res. PIER 71, 129–147 (2007).
[CrossRef]

Aliganga, A. K. A.

A. K. A. Aliganga, I. Lieberwirth, G. Glasser, A.-S. Duwez, Y. Sun, and S. Mittler, “Fabrication of equally oriented pancake shaped gold nanoparticles by SAM templated OMCVD and their optical response,” Org. Electron. 8, 161–174 (2007).
[CrossRef]

Anderson, A. S.

H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
[CrossRef]

Arriaga, J.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit homogenization for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Backes, T. D.

T. D. Backes and D. S. Citrin, “Plasmon polaritons in 2-D nanoparticle arrays,” IEEE J. Sel. Top. Quantum Electron. 14, 1530–1535 (2008).
[CrossRef]

Bagchi, A.

A. Bagchi, R. G. Barrera, and R. Fuchs, “Local-field effect in optical reflectance from adsorbed overlayers,” Phys. Rev. B 25, 7086–7096 (1982).
[CrossRef]

Bajestani, S. M. R. Z.

Barrera, R. G.

A. Bagchi, R. G. Barrera, and R. Fuchs, “Local-field effect in optical reflectance from adsorbed overlayers,” Phys. Rev. B 25, 7086–7096 (1982).
[CrossRef]

Becher, J.

Belov, P. A.

P. A. Belov and C. R. Simovski, “Homogenization of electromagnetic crystals formed by uniaxial resonant scatterers,” Phys. Rev. E 72, 026615 (2005).
[CrossRef]

Berini, P.

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
[CrossRef]

Bethell, D.

C. J. Kiely, J. Fink, M. Burst, D. Bethell, and D. J. Schiffrin, “Spontaneous ordering of bimodal ensembles of nanoscopic gold clusters,” Nature 396, 444–446 (1998).
[CrossRef]

Böhmer, V.

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

Burst, M.

C. J. Kiely, J. Fink, M. Burst, D. Bethell, and D. J. Schiffrin, “Spontaneous ordering of bimodal ensembles of nanoscopic gold clusters,” Nature 396, 444–446 (1998).
[CrossRef]

Busse, S.

S. Busse, J. Käshammer, S. Krämer, and S. Mittler, “Gold and thiol surface functionalized integrated optical Mach–Zehnder interferometer for sensing purposes,” Sens. Actuators B 60, 148–154 (1999).

Chan, C. T.

Y.-R. Zhen, K. H. Fung, and C. T. Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
[CrossRef]

Cheng, T.

S. M. Hashemi Rafsanjani, T. Cheng, C. Rangan, and S. Mittler, “A novel biosensing approach based on linear arrays of immobilized gold nanoparticles,” J. Appl. Phys. 107, 094303 (2010).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Citrin, D. S.

T. D. Backes and D. S. Citrin, “Plasmon polaritons in 2-D nanoparticle arrays,” IEEE J. Sel. Top. Quantum Electron. 14, 1530–1535 (2008).
[CrossRef]

Duwez, A.-S.

A. K. A. Aliganga, I. Lieberwirth, G. Glasser, A.-S. Duwez, Y. Sun, and S. Mittler, “Fabrication of equally oriented pancake shaped gold nanoparticles by SAM templated OMCVD and their optical response,” Org. Electron. 8, 161–174 (2007).
[CrossRef]

Fink, J.

C. J. Kiely, J. Fink, M. Burst, D. Bethell, and D. J. Schiffrin, “Spontaneous ordering of bimodal ensembles of nanoscopic gold clusters,” Nature 396, 444–446 (1998).
[CrossRef]

Fuchs, R.

A. Bagchi, R. G. Barrera, and R. Fuchs, “Local-field effect in optical reflectance from adsorbed overlayers,” Phys. Rev. B 25, 7086–7096 (1982).
[CrossRef]

Fung, K. H.

Y.-R. Zhen, K. H. Fung, and C. T. Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
[CrossRef]

Glasser, G.

A. K. A. Aliganga, I. Lieberwirth, G. Glasser, A.-S. Duwez, Y. Sun, and S. Mittler, “Fabrication of equally oriented pancake shaped gold nanoparticles by SAM templated OMCVD and their optical response,” Org. Electron. 8, 161–174 (2007).
[CrossRef]

Grace, K. M.

H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
[CrossRef]

Grace, W. K.

H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
[CrossRef]

Gray, S. K.

G. A. Wurtz, J. S. Im, S. K. Gray, and G. P. Wiederrecht, “Optical scattering from isolated metal nanoparticles and arrays,” J. Phys. Chem. B 107, 14191–14198 (2003).
[CrossRef]

Haes, A. J.

A. J. Haes, D. A. Stuart, S. Nie, and R. P. Van Duyne, “Using solution phase nanoparticles, surface-confined nanoparticle arrays, and single nanoparticles as biological sensing platforms,” J. Flouresc. 14, 355–367 (2004).
[CrossRef]

Halevi, P.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit homogenization for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Hartman, N.

H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
[CrossRef]

Hashemi Rafsanjani, S. M.

S. M. Hashemi Rafsanjani, T. Cheng, C. Rangan, and S. Mittler, “A novel biosensing approach based on linear arrays of immobilized gold nanoparticles,” J. Appl. Phys. 107, 094303 (2010).
[CrossRef]

Hassanzadeh, A.

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

Im, J. S.

G. A. Wurtz, J. S. Im, S. K. Gray, and G. P. Wiederrecht, “Optical scattering from isolated metal nanoparticles and arrays,” J. Phys. Chem. B 107, 14191–14198 (2003).
[CrossRef]

Irudayaraj, J.

C. Yu and J. Irudayaraj, “A multiplex biosensor using gold nanorods,” Anal. Chem. 79, 572–579 (2007).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Jiang, H.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Käshammer, J.

S. Busse, J. Käshammer, S. Krämer, and S. Mittler, “Gold and thiol surface functionalized integrated optical Mach–Zehnder interferometer for sensing purposes,” Sens. Actuators B 60, 148–154 (1999).

Kato, K.

Z. M. Qi, N. Matsuda, J. Santos, T. Yoshida, A. Takatsu, and K. Kato, “In situ monitoring of metal nanoparticle self-assembly on protein-functionalized glass by broadband optical waveguide spectroscopy,” J. Colloid. Interface Sci. 271, 249–253 (2004).
[CrossRef]

Kelly, K. L.

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and widths,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

Kiely, C. J.

C. J. Kiely, J. Fink, M. Burst, D. Bethell, and D. J. Schiffrin, “Spontaneous ordering of bimodal ensembles of nanoscopic gold clusters,” Nature 396, 444–446 (1998).
[CrossRef]

Krämer, S.

S. Busse, J. Käshammer, S. Krämer, and S. Mittler, “Gold and thiol surface functionalized integrated optical Mach–Zehnder interferometer for sensing purposes,” Sens. Actuators B 60, 148–154 (1999).

Kranendonk, J. V.

J. V. Kranendonk and J. E. Sipe, “Foundations of the macroscopic electromagnetic theory of dielectric solids,” in Progress in Optics XV, E. Wolf, ed. (North-Holland, 1977), pp. 247–350.

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Krokhin, A. A.

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit homogenization for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Lieberwirth, I.

A. K. A. Aliganga, I. Lieberwirth, G. Glasser, A.-S. Duwez, Y. Sun, and S. Mittler, “Fabrication of equally oriented pancake shaped gold nanoparticles by SAM templated OMCVD and their optical response,” Org. Electron. 8, 161–174 (2007).
[CrossRef]

Lukosz, W.

W. Lukosz and K. Tiefenthaler, “Directional switching in planar waveguides effected by absorbtion-desorbtion processes,” in Proceedings of the Second European Conference of Integrated Optics, IEE Conference Publication No. 227 (IEE, 1983), pp. 152–155.

Manifar, T.

H. Jiang, T. Manifar, J. Sabarinathan, and S. Mittler, “3-D FDTD analysis of gold nanoparticle based photonic crystal on slab waveguide,” J. Lightwave Technol. 27, 2264–2270 (2009).
[CrossRef]

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

Markel, V. A.

V. A. Markel, “Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure,” J. Mod. Opt. 40, 2281–2291 (1993).
[CrossRef]

Martinez, J. S.

H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
[CrossRef]

Matsuda, N.

Z. M. Qi, N. Matsuda, J. Santos, T. Yoshida, A. Takatsu, and K. Kato, “In situ monitoring of metal nanoparticle self-assembly on protein-functionalized glass by broadband optical waveguide spectroscopy,” J. Colloid. Interface Sci. 271, 249–253 (2004).
[CrossRef]

Mittler, S.

S. M. Hashemi Rafsanjani, T. Cheng, C. Rangan, and S. Mittler, “A novel biosensing approach based on linear arrays of immobilized gold nanoparticles,” J. Appl. Phys. 107, 094303 (2010).
[CrossRef]

H. Jiang, T. Manifar, J. Sabarinathan, and S. Mittler, “3-D FDTD analysis of gold nanoparticle based photonic crystal on slab waveguide,” J. Lightwave Technol. 27, 2264–2270 (2009).
[CrossRef]

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

A. K. A. Aliganga, I. Lieberwirth, G. Glasser, A.-S. Duwez, Y. Sun, and S. Mittler, “Fabrication of equally oriented pancake shaped gold nanoparticles by SAM templated OMCVD and their optical response,” Org. Electron. 8, 161–174 (2007).
[CrossRef]

S. Busse, J. Käshammer, S. Krämer, and S. Mittler, “Gold and thiol surface functionalized integrated optical Mach–Zehnder interferometer for sensing purposes,” Sens. Actuators B 60, 148–154 (1999).

S. Mittler, “Gold nanoparticles on waveguides for and toward sensing application,” in Optical Guided-wave Chemical and Biosensors I, M. Zourob and A. Lakhtakia, eds., Springer Series on Chemical Sensors and Biosensors (Springer, 2010), Vol. 7, Part 2, pp. 209–229.

Mukundan, H.

H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
[CrossRef]

Nie, S.

A. J. Haes, D. A. Stuart, S. Nie, and R. P. Van Duyne, “Using solution phase nanoparticles, surface-confined nanoparticle arrays, and single nanoparticles as biological sensing platforms,” J. Flouresc. 14, 355–367 (2004).
[CrossRef]

Podoprygorina, G.

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

Qi, Z. M.

Z. M. Qi, N. Matsuda, J. Santos, T. Yoshida, A. Takatsu, and K. Kato, “In situ monitoring of metal nanoparticle self-assembly on protein-functionalized glass by broadband optical waveguide spectroscopy,” J. Colloid. Interface Sci. 271, 249–253 (2004).
[CrossRef]

Rangan, C.

S. M. Hashemi Rafsanjani, T. Cheng, C. Rangan, and S. Mittler, “A novel biosensing approach based on linear arrays of immobilized gold nanoparticles,” J. Appl. Phys. 107, 094303 (2010).
[CrossRef]

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

Rezaee, A.

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

Rooney, P.

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

Sabarinathan, J.

Santos, J.

Z. M. Qi, N. Matsuda, J. Santos, T. Yoshida, A. Takatsu, and K. Kato, “In situ monitoring of metal nanoparticle self-assembly on protein-functionalized glass by broadband optical waveguide spectroscopy,” J. Colloid. Interface Sci. 271, 249–253 (2004).
[CrossRef]

Schatz, G. C.

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and widths,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

Schiffrin, D. J.

C. J. Kiely, J. Fink, M. Burst, D. Bethell, and D. J. Schiffrin, “Spontaneous ordering of bimodal ensembles of nanoscopic gold clusters,” Nature 396, 444–446 (1998).
[CrossRef]

Semichaevsky, A.

A. Semichaevsky and A. Akyurtlu, “Homogenization of metamaterial-loaded substrates and superstrates for antennas,” Prog. Electromagn. Res. PIER 71, 129–147 (2007).
[CrossRef]

Shahabadi, M.

Simovski, C. R.

P. A. Belov and C. R. Simovski, “Homogenization of electromagnetic crystals formed by uniaxial resonant scatterers,” Phys. Rev. E 72, 026615 (2005).
[CrossRef]

Simsek, E.

E. Simsek, “On the surface plasmon resonance modes of metal nanoparticle chains and arrays,” Plasmonics 4, 223–230 (2009).
[CrossRef]

Sipe, J. E.

J. E. Sipe, “New Green function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
[CrossRef]

J. E. Sipe and J. Becher, “Surface energy transfer enhanced by optical cavity excitation: a pole analysis,” J. Opt. Soc. Am. 72, 288–295 (1982).
[CrossRef]

J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105, 489–504 (1981).
[CrossRef]

J. E. Sipe, “Bulk-selvedge coupling theory for the optical properties of surfaces,” Phys. Rev. B 22, 1589–1599 (1980).
[CrossRef]

J. V. Kranendonk and J. E. Sipe, “Foundations of the macroscopic electromagnetic theory of dielectric solids,” in Progress in Optics XV, E. Wolf, ed. (North-Holland, 1977), pp. 247–350.

Stuart, D. A.

A. J. Haes, D. A. Stuart, S. Nie, and R. P. Van Duyne, “Using solution phase nanoparticles, surface-confined nanoparticle arrays, and single nanoparticles as biological sensing platforms,” J. Flouresc. 14, 355–367 (2004).
[CrossRef]

Sun, Y.

A. K. A. Aliganga, I. Lieberwirth, G. Glasser, A.-S. Duwez, Y. Sun, and S. Mittler, “Fabrication of equally oriented pancake shaped gold nanoparticles by SAM templated OMCVD and their optical response,” Org. Electron. 8, 161–174 (2007).
[CrossRef]

Swanson, B. I.

H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
[CrossRef]

Takatsu, A.

Z. M. Qi, N. Matsuda, J. Santos, T. Yoshida, A. Takatsu, and K. Kato, “In situ monitoring of metal nanoparticle self-assembly on protein-functionalized glass by broadband optical waveguide spectroscopy,” J. Colloid. Interface Sci. 271, 249–253 (2004).
[CrossRef]

Talebi, N.

Tiefenthaler, K.

W. Lukosz and K. Tiefenthaler, “Directional switching in planar waveguides effected by absorbtion-desorbtion processes,” in Proceedings of the Second European Conference of Integrated Optics, IEE Conference Publication No. 227 (IEE, 1983), pp. 152–155.

Ulman, A.

A. Ulman, An Introduction to Ultrathin Films (Academic, 1991).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

van Duyne, R. P.

K. A. Willets and R. P. van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Ann. Rev. Phys. Chem. 58, 267–297 (2007).
[CrossRef]

A. J. Haes, D. A. Stuart, S. Nie, and R. P. Van Duyne, “Using solution phase nanoparticles, surface-confined nanoparticle arrays, and single nanoparticles as biological sensing platforms,” J. Flouresc. 14, 355–367 (2004).
[CrossRef]

Vollmer, M.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Wiederrecht, G. P.

G. A. Wurtz, J. S. Im, S. K. Gray, and G. P. Wiederrecht, “Optical scattering from isolated metal nanoparticles and arrays,” J. Phys. Chem. B 107, 14191–14198 (2003).
[CrossRef]

Willets, K. A.

K. A. Willets and R. P. van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Ann. Rev. Phys. Chem. 58, 267–297 (2007).
[CrossRef]

Wolf, E.

J. V. Kranendonk and J. E. Sipe, “Foundations of the macroscopic electromagnetic theory of dielectric solids,” in Progress in Optics XV, E. Wolf, ed. (North-Holland, 1977), pp. 247–350.

Wu, Y.

Y. Wu and Z.-Q. Zhang, “Dispersion relations and their symmetry properties of electromagnetic and elastic metamaterials in two dimensions,” Phys. Rev. B 79, 195111 (2009).
[CrossRef]

Wurtz, G. A.

G. A. Wurtz, J. S. Im, S. K. Gray, and G. P. Wiederrecht, “Optical scattering from isolated metal nanoparticles and arrays,” J. Phys. Chem. B 107, 14191–14198 (2003).
[CrossRef]

Xu, S.

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989).

Yoshida, T.

Z. M. Qi, N. Matsuda, J. Santos, T. Yoshida, A. Takatsu, and K. Kato, “In situ monitoring of metal nanoparticle self-assembly on protein-functionalized glass by broadband optical waveguide spectroscopy,” J. Colloid. Interface Sci. 271, 249–253 (2004).
[CrossRef]

Yu, C.

C. Yu and J. Irudayaraj, “A multiplex biosensor using gold nanorods,” Anal. Chem. 79, 572–579 (2007).
[CrossRef]

Zhang, Z.-Q.

Y. Wu and Z.-Q. Zhang, “Dispersion relations and their symmetry properties of electromagnetic and elastic metamaterials in two dimensions,” Phys. Rev. B 79, 195111 (2009).
[CrossRef]

Zhao, L.

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and widths,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

Zhen, Y.-R.

Y.-R. Zhen, K. H. Fung, and C. T. Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
[CrossRef]

Anal. Chem. (1)

C. Yu and J. Irudayaraj, “A multiplex biosensor using gold nanorods,” Anal. Chem. 79, 572–579 (2007).
[CrossRef]

Ann. Rev. Phys. Chem. (1)

K. A. Willets and R. P. van Duyne, “Localized surface plasmon resonance spectroscopy and sensing,” Ann. Rev. Phys. Chem. 58, 267–297 (2007).
[CrossRef]

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

T. D. Backes and D. S. Citrin, “Plasmon polaritons in 2-D nanoparticle arrays,” IEEE J. Sel. Top. Quantum Electron. 14, 1530–1535 (2008).
[CrossRef]

J. Appl. Phys. (1)

S. M. Hashemi Rafsanjani, T. Cheng, C. Rangan, and S. Mittler, “A novel biosensing approach based on linear arrays of immobilized gold nanoparticles,” J. Appl. Phys. 107, 094303 (2010).
[CrossRef]

J. Colloid. Interface Sci. (1)

Z. M. Qi, N. Matsuda, J. Santos, T. Yoshida, A. Takatsu, and K. Kato, “In situ monitoring of metal nanoparticle self-assembly on protein-functionalized glass by broadband optical waveguide spectroscopy,” J. Colloid. Interface Sci. 271, 249–253 (2004).
[CrossRef]

J. Flouresc. (1)

A. J. Haes, D. A. Stuart, S. Nie, and R. P. Van Duyne, “Using solution phase nanoparticles, surface-confined nanoparticle arrays, and single nanoparticles as biological sensing platforms,” J. Flouresc. 14, 355–367 (2004).
[CrossRef]

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

V. A. Markel, “Coupled-dipole approach to scattering of light from a one-dimensional periodic dipole structure,” J. Mod. Opt. 40, 2281–2291 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

J. Phys. Chem. B (2)

G. A. Wurtz, J. S. Im, S. K. Gray, and G. P. Wiederrecht, “Optical scattering from isolated metal nanoparticles and arrays,” J. Phys. Chem. B 107, 14191–14198 (2003).
[CrossRef]

L. Zhao, K. L. Kelly, and G. C. Schatz, “The extinction spectra of silver nanoparticle arrays: influence of array structure on plasmon resonance wavelength and widths,” J. Phys. Chem. B 107, 7343–7350 (2003).
[CrossRef]

Nature (1)

C. J. Kiely, J. Fink, M. Burst, D. Bethell, and D. J. Schiffrin, “Spontaneous ordering of bimodal ensembles of nanoscopic gold clusters,” Nature 396, 444–446 (1998).
[CrossRef]

New J. Phys. (1)

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” New J. Phys. 10, 105010 (2008).
[CrossRef]

Org. Electron. (1)

A. K. A. Aliganga, I. Lieberwirth, G. Glasser, A.-S. Duwez, Y. Sun, and S. Mittler, “Fabrication of equally oriented pancake shaped gold nanoparticles by SAM templated OMCVD and their optical response,” Org. Electron. 8, 161–174 (2007).
[CrossRef]

Phys. Rev. B (7)

P. Rooney, A. Rezaee, S. Xu, T. Manifar, A. Hassanzadeh, G. Podoprygorina, V. Böhmer, C. Rangan, and S. Mittler, “Control of surface plasmon resonances in dielectrically-coated proximate gold nanoparticles immobilized on a substrate,” Phys. Rev. B 77, 235446 (2008).
[CrossRef]

J. E. Sipe, “Bulk-selvedge coupling theory for the optical properties of surfaces,” Phys. Rev. B 22, 1589–1599 (1980).
[CrossRef]

A. Bagchi, R. G. Barrera, and R. Fuchs, “Local-field effect in optical reflectance from adsorbed overlayers,” Phys. Rev. B 25, 7086–7096 (1982).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Y.-R. Zhen, K. H. Fung, and C. T. Chan, “Collective plasmonic modes in two-dimensional periodic arrays of metal nanoparticles,” Phys. Rev. B 78, 035419 (2008).
[CrossRef]

A. A. Krokhin, P. Halevi, and J. Arriaga, “Long-wavelength limit homogenization for two-dimensional photonic crystals,” Phys. Rev. B 65, 115208 (2002).
[CrossRef]

Y. Wu and Z.-Q. Zhang, “Dispersion relations and their symmetry properties of electromagnetic and elastic metamaterials in two dimensions,” Phys. Rev. B 79, 195111 (2009).
[CrossRef]

Phys. Rev. E (1)

P. A. Belov and C. R. Simovski, “Homogenization of electromagnetic crystals formed by uniaxial resonant scatterers,” Phys. Rev. E 72, 026615 (2005).
[CrossRef]

Plasmonics (1)

E. Simsek, “On the surface plasmon resonance modes of metal nanoparticle chains and arrays,” Plasmonics 4, 223–230 (2009).
[CrossRef]

Prog. Electromagn. Res. PIER (1)

A. Semichaevsky and A. Akyurtlu, “Homogenization of metamaterial-loaded substrates and superstrates for antennas,” Prog. Electromagn. Res. PIER 71, 129–147 (2007).
[CrossRef]

Sens. Actuators B (1)

S. Busse, J. Käshammer, S. Krämer, and S. Mittler, “Gold and thiol surface functionalized integrated optical Mach–Zehnder interferometer for sensing purposes,” Sens. Actuators B 60, 148–154 (1999).

Sensors (1)

H. Mukundan, A. S. Anderson, W. K. Grace, K. M. Grace, N. Hartman, J. S. Martinez, and B. I. Swanson, “Review: waveguide-based biosensors for pathogen detection,” Sensors 9, 5783–5809 (2009).
[CrossRef]

Surf. Sci. (1)

J. E. Sipe, “The dipole antenna problem in surface physics: a new approach,” Surf. Sci. 105, 489–504 (1981).
[CrossRef]

Other (8)

A. Yariv, Quantum Electronics, 3rd ed. (Wiley, 1989).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

J. V. Kranendonk and J. E. Sipe, “Foundations of the macroscopic electromagnetic theory of dielectric solids,” in Progress in Optics XV, E. Wolf, ed. (North-Holland, 1977), pp. 247–350.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

W. Lukosz and K. Tiefenthaler, “Directional switching in planar waveguides effected by absorbtion-desorbtion processes,” in Proceedings of the Second European Conference of Integrated Optics, IEE Conference Publication No. 227 (IEE, 1983), pp. 152–155.

A. Ulman, An Introduction to Ultrathin Films (Academic, 1991).

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

S. Mittler, “Gold nanoparticles on waveguides for and toward sensing application,” in Optical Guided-wave Chemical and Biosensors I, M. Zourob and A. Lakhtakia, eds., Springer Series on Chemical Sensors and Biosensors (Springer, 2010), Vol. 7, Part 2, pp. 209–229.

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Figures (14)

Fig. 1.
Fig. 1.

Schematic of a multilayer structure with a medium (cladding) of refractive index n1 above it. A selvedge layer of closely spaced GNPs lies along the interface between the multilayer and cladding.

Fig. 2.
Fig. 2.

Typical length scales in the problem. The thickness of the selvedge layer d and the interparticle spacing a are much smaller than the wavelength of light λ. Δ is a characteristic length scale such that aΔλ.

Fig. 3.
Fig. 3.

Inserting an infinitesimal layer of cladding beneath the selvedge and above the multilayer. This allows us to work with only coarse-grained fields in the transfer-matrix treatment.

Fig. 4.
Fig. 4.

(a) Square lattice of spherical NPs of radius bwith lattice spacing a at a height h above the substrate; (b) a disordered arrangement of spherical NPs of radius b, with average interparticle spacing a at a height h above the substrate.

Fig. 5.
Fig. 5.

λ2ρ13C versus its argument D/λ, as discussed in the text. The refractive indices chosen are n1=1.0, n2=1.535, and n3=1.51967. The graph indicates that there is a minimum value of WG thickness D below which a WG mode cannot be supported.

Fig. 6.
Fig. 6.

(a) Absorption coefficient αabs as a function of wavelength for arrays of GNPs on the surface of the WG. The thickness of the guiding layer D=3μm, and the indices are those given or the maximum response in Fig. 5. (b) The mode shift Re(κoκo) for the same structures.

Fig. 7.
Fig. 7.

Peak wavelengths of the absorption curve as a function of cladding relative permittivity. The dotted curve represents a single particle, and the solid curve shows the NP-coated WG. The WG properties are as specified in Fig. 6, and the NP array parameters are given in the legend.

Fig. 8.
Fig. 8.

Mie theory calculations of the absorption cross section of a single GNP compared with the absorption spectrum of a WG, with parameters given in Fig. 6, when coated with an array of GNPs. The spherical particles are just resting on top of the WG. All curves have been normalized to have a maximum of unity.

Fig. 9.
Fig. 9.

Sensitivity factor H for (a) a BSPS and (b) a BNWS, as described in the text. In the latter example we take a=30nm, b=h=10nm. The cladding’s relative permittivity ε1 ranges from 1.0 (top curve) to 1.5 (bottom curve) in increments of 0.1.

Fig. 10.
Fig. 10.

Coated NP parameters. The radius of the GNP core is bcore, and that of the coated NP is bcoat. The height of the GNP center from the WG h is chosen to be the same as bcoat.

Fig. 11.
Fig. 11.

Modification of mode properties of an NP-coated WG, as the relative permittivity εcoat of the coating is varied from εcoat=1.0 (bottom curve) to εcoat=1.5 (top curve) in increments of 0.05. (a) The mode shift Re(κoκo), (b) the absorption coefficient αabs. The mode shift is high at the same wavelength as the absorption.

Fig. 12.
Fig. 12.

Sensitivity factor G for WG sensing. The relativity permittivity of the analyte εcoat varies from εcoat=1.0 (top curve) to εcoat=1.5 (bottom curve) in increments of 0.05.

Fig. 13.
Fig. 13.

Same plots as in Fig. 11, but for the surface plasmon sensor.

Fig. 14.
Fig. 14.

Same plot as in Fig. 12, but for the surface plasmon sensor.

Equations (199)

Equations on this page are rendered with MathJax. Learn more.

f(R;z;t)=f(R;z)eiωt+c.c.
P(R;z)=ϵ0χ(R;z)E(R;z).
Ep(R;z)=G(RR;z,z)·P(R;z)dRdz,
G(RR;z,z)=Go(RR;z,z)+GR(RR;z,z),
E(R;z)=Eh(R;z)+Ep(R;z).
P(R;z)=ϵ0χ(R;z)(Eh(R;z)+G(RR;z,z)·P(R;z)dRdz).
Eh(R;z)=eiκi·RFh(z),
P(R;z)=eiκi·Rp(R;z),
p(R;z)=ϵ0χ(R;z)F(R;z),
F(R;z)=Fh(z)+eiκi·(RR)G(RR;z,z)·p(R;z)dRdz,
dλ.
aΔλ.
κiΔ1.
W(R)dR=1.
W(RR)p(R;z)dR.
χ(R;z)=KχK(z)eiK·R,
p(R;z)=KpK(z)eiK·R.
P(z)W(RR)p(R;z)dR
p˜(R;z)p(R;z)P(z),
QP(z)dz.
E¯(R;z)W(RR)E(R;z)dR.
E(R;z)=dκ(2π)2E(κ;z)eiκ·R,
E¯(R;z)=E¯h(R;z)+E¯p(R;z).
E¯h(R;z)Eh(R;z)=eiκi·RFh(z).
E¯p(R;z)=W(RR)G(RR;z,z)·P(R;z)dRdRdz=G(RR;z,z)·P¯(R;z)dRdz,
P¯(R;z)eiκi·RP(z),
E¯p(R;z)=G(RR;z,z)·eiκi·RP(z)dRdz=eiκi·RG(κi;z,z)·P(z)dz,
G(R;z,z)=dκ(2π)2G(κ;z,z)eiκ·R,Go,R(R;z,z)=dκ(2π)2Go,R(κ;z,z)eiκ·R,
E¯(R;z)=eiκi·R(Fh(z)+G(κi;z,z)·P(z)dz).
F(R;z)=Fh(z)+Fo(R,z)+FR(R,z),
Fo,R(R,z)eiκi·(RR)Go,R(RR;z,z)·p(R;z)dRdz.
Fo(R,z)=F>(R,z)+F<(R,z),
F(R,z)|RR|Δeiκi·(RR)Go(RR;z,z)·p(R;z)dRdz.
F>(R,z)=|RR|>Δ(eiκi·(RR)1)Go(RR;z,z)·P(z)dRdz+|RR|>ΔGo(RR;z,z)·P(z)dRdz.
F>(R,z)=(Go(κi;z,z)Go(0;z,z))·P(z)dz+|RR|>ΔGo(RR;z,z)·P(z)dRdz,
Fo(R,z)=|RR|<ΔGo(RR;z,z)·p(R;z)dRdz+|RR|>ΔGo(RR;z,z)·P(z)dRdz+(Go(κi;z,z)Go(0;z,z))·P(z)dz.
Go(RR;z,z)=GLo(RR;z,z)+GTo(RR;z,z)
Go(κi;z,z)=GTo(κi;z,z)+GLo(κi;z,z).
4πϵ0GTo(RR;z,z)=ω˜22r(U+r^r^)+23iω˜3n1U+,
Fo(R,z)=GLo(RR;z,z)·p(R;z)dRdz+(Go(κi;z,z)GLo(0;z,z))·P(z)dz,
FR(R,z)=F¯R(R,z)+F˜R(R,z),
F¯R(R,z)=eiκi·(RR)GR(RR;z,z)·P(z)dRdz=GR(κi;z,z)·P(z)dz,
F˜R(R,z)=eiκi·(RR)GR(RR;z,z)·p˜(R;z)dRdz.
F¯R(R,z)=iω˜22ε0w1ieiw1iz(s^iR1Ns(κi)s^i+p^1+iR1Np(κi)p^1i)·eiw1izP(z)dz,
wl=ω˜2εlκ2,
s^κ^×z^,
p^l±κz^wlκ^ω˜nl
F˜R(R,z)=F˜IR(R,z)+F˜CR(R,z),
F˜I,CR(R,z)eiκi·(RR)GI,CR(RR;z,z)·p˜(R;z)dRdz,
GR(κ;z,z)=GIR(κ;z,z)+GCR(κ;z,z).
p˜I(R;z)ε2ε1ε2+ε1(z^z^x^x^y^y^)·p˜(R;z)
F˜IR(R,z)=eiκi·(RR)GLo(RR;z,z)·p˜I(R,z)dzdR
F˜IR(R,z)=|RR|<ΔGLo(RR;z,z)·p˜I(R;z)dRdzGLo(RR;z,z)·p˜I(R;z)dRdzGLo(RR;z,z)·pI(R;z)dRdz,
pI(R;z)ε2ε1ε2+ε1(z^z^x^x^y^y^)·p(R;z)
FR(R,z)=GLo(RR;z,z)·pI(R;z)dRdz+iω˜22ε0w1ieiw1iz(s^iR1Ns(κi)s^i+p^1+iR1Np(κi)p^1i)·eiw1izP(z)dz+eiκi·(RR)GCR(RR;z,z)·p˜(R;z)dRdz.
p˜(R;z)=K0pK(z)eiK·R,
eiκi·(RR)GCR(RR;z,z)·p˜(R;z)dRdz=K0eiK·Rei(κi+K)·(RR)GCR(RR;z,z)·pK(z)dRdz=K0eiK·RGCR(κi+K;z,z)·pK(z)dz.
F(R;z)=Fh+eiw1iz+Fheiw1iz+GLo(RR;z,z)·(p(R;z)+pI(R;z))dRdz+(Go(κi;z,z)GLo(0;z,z))·P(z)dz+iω˜22ε0w1ieiw1iz(s^iR1Ns(κi)s^i+p^1+iR1Np(κi)p^1i)·eiw1izP(z)dz,
F(R;z)=Fh+(κi)+Fh(κi)+GS(κi)·Q+GLo(RR;z,z)·(p(R;z)+pI(R;z))dRdz+L(κi;zz)·P(z)dz,
Fh+(κ)=Fh++iω˜22ε0w1(s^R1Ns(κ)s^+p^1+R1Np(κ)p^1)·Q,Fh(κ)=Fh,
GS(κ)=GTo(κ)+κ2ε0ε1(z^z^κ^κ^)=12ε0[iω˜2w1s^s^+iκ2ε1w1z^z^+iw1ε1κ^κ^],
L(κ;zz)κ2ε0ε1(z^z^κ^κ^iz^κ^i^κ^z^)[θ(zz)12]+κ2ε0ε1(z^z^κ^κ^+iz^κ^+i^κ^z^)[θ(zz)12].
p(R;z)=ϵ0χ(R;z)F(R;z)
F(R;z)=F+GLo(RR;z,z)·(p(R;z)+pI(R;z))dRdz+L(κ;zz)·P(z)dz,
FFh+(κ)+Fh(κ)+GS(κ)·Q
Q=W(RR)p(R;z)dzdR.
Q=4πε0Λ·F
0ddz0ddzL(κ;zz)=0.
p(R;z)=ε0χ(R;z)F(R;z),
F(R;z)=F+GLo(RR;z,z)·(p(R;z)+pI(R;z))dRdz
E¯(R;d+)=E¯+(d+)eiκ·R+E¯(d+)eiκ·R,E¯(R;0l)=E¯+(0l)eiκ·R+E¯(0l)eiκ·R,
E¯+(d+)=Fh+(κ)+iω˜22ε0w1(s^s^+p^1+p^1+)·Q,E¯(d+)=Fh(κ),E¯+(0l)=Fh+(κ),E¯(0l)=Fh(κ)+iω˜22ε0w1(s^s^+p^1p^1)·Q.
E¯+(d+)=E¯+(0l)+iω˜22ε0w1(s^s^+p^1+p^1+)·Q,E¯(d+)=E¯(0l)iω˜22ε0w1(s^s^+p^1p^1)·Q,
Q=4πε0Λ·(E¯+(0l)+E¯(0l)iκ2ε0ε1(z^κ^+κ^z^)·Q),
Λ=Λss^s^+Λκκ^κ^+Λzz^z^.
Qs=4πϵ0Λs(E¯+(0l)+E¯(0l)),
E¯+(d+)=(1+nos)E¯+(0l)+nosE¯(0l),E¯(d+)=nosE¯+(0l)+(1nos)E¯(0l),
nos2πiω˜2w1Λs.
[E¯+(d+)E¯(d+)]=ms[E¯+(0l)E¯(0l)],
ms=[1+nosnosnos1nos].
E¯+(0l)=E¯+(0l)p^1+,E¯(0l)=E¯(0l)p^1,
E¯+(d+)=E¯+(d+)p^1+,E¯(d+)=E¯(d+)p^1.
E¯+(d+)=E¯+(0l)+(noznoκ)E¯(0l)+(noz+noκ+2noznoκ)E¯+(0l)1noznoκ,E¯(d+)=E¯(0l)(noz+noκ2noznoκ)E¯(0l)+(noznoκ)E¯+(0l)1noznoκ,
noz2πiκ2ε1w1Λz,noκ2πiw1ε1Λκ.
noznoκ=4π2κ2ΛzΛκε12.
E¯+(d+)=E¯+(0l)+nE¯(0l)+n+E¯+(0l),E¯(d+)=E¯(0l)n+E¯(0l)nE¯+(0l),
n±noz±noκ,
[E¯+(d+)E¯(d+)]=mp[E¯+(0l)E¯(0l)],
mp=[1+n+nn1n+],
m=[T+T+R+R+T+R+T+R+T+1T+],
T+=T+=11nosts,
R+=R+=nos1nosrs,
ms=[ts2rs2tsrstsrsts1ts].
R+=R+=n1n+,T+=11n+,T+=14noznoκ1n+.
T+11n+
T+=T+=11n+tp,
R+=R+=n1n+rp,
mp[tp2rp2tprptprptp1tp],
mp=[1n21n+nn1n+].
[T1NT1NR1NR1NT1NR1NT1NR1NT1N1T1N]=[t2r2trtrt1t][T1NTN1R1NRN1T1NR1NT1NRN1T1N1T1N],
T1N=tT1N1rR1N,R1N=r+tR1Nt1rR1N,R1N=RN1+TN1rT1N1rR1N,T1N=TN1t1rR1N.
T1Nτ1Nκκo,TN1τN1κκo,R1Nρ1Nκκo,RN1ρN1κκo,
τ1NτN1ρ1NρN1=0,
T1NTN1R1NRN1T1NΓ1N
RN1=RN1+rΓ1NT1N1rR1N.
TN1=tτ1Nκκorρ1N,RN1=r+tρ1Ntκκorρ1N,RN1=ρN1+rΓ1Nτ1Nκκorρ1N,TN1=τN1tκκorρ1N,
κ0=κo+rρ1N.
χ(R,z)=αχ(α)(R,z),
χ(α)(R,z)=(εε1)θ(b|rr(α)|),
p(R,z)=αp(α)(R,z),
p(α)(R,z)3μ4πb3θ(b|rr(α)|),
p(α)(R,z)μδ(Rr(α))
Q=μA.
GLo(RR;z,z)·p(α)(R,z)dRdz=μ4πε0ε1b3for|rr(α)|<b.
GLo(RR;z,z)·p(α)(R,z)dRdz=GLo(RR(α);z,h)·μ,for|rr(α)|<bandαα.
GLo(RR;z,z)·p(R,z)dRdz=μ4πϵ0ε1b3+ααGLo(RR(α);z,h)·μ,for|rr(α)|<b.
Mε2ε1ε2+ε1(z^z^x^x^y^y^),
pI(R,z)=M·p(R,z).
pI(R,z)=M·αμδ(RR(α))δ(z+h).
F(R;z)=Fμ4πϵ0ε1b3+ααGLo(RR(α);z,h)·μ+αGLo(RR(α);z,h)·M·μ,for|rr(α)|<b.
p(α)(R,z)=ε0χ(α)(R,z)F(R;z)
μ4π3b3ϵ0(εε1)=Fμ4πϵ0ε1b3+ααGLo(R(α)R(α);h,h)·μ+αGLo(R(α)R(α);h,h)·M·μ.
μ4π3b3ϵ0(3ε1(εε1)ε+2ε1)=F+ααGLo(R(α)R(α);h,h)·μ+αGLo(R(α)R(α);h,h)·M·μ,
S4πϵ0A3/2ααGLo(R(α)R(α);h,h)+4πϵ0A3/2αGLo(R(α)R(α);h,h)·M=4πϵ0A3/2α0GLo(R(α);h,h)+4πϵ0A3/2αGLo(R(α);h,h)·M,
Q=[ε1(εε1)ε+2ε1b3A][4πϵ0F+1A1/2S·Q],
Λ[ε1(εε1)ε+2ε1b3A](Uε1(εε1)ε+2ε1b3A3/2S)1,
Λ=Λz^z^+Λ(x^x^+y^y^)=Λz^z^+Λ(s^s^+κ^κ^)
S=4πϵ0A3/2GLo(R=0;h,h)·M+4πϵ0A3/2R=(A/π)1/2ϕ=02πdRAGLo(R;h,h)+4πϵ0A3/2R=(A/π)1/2ϕ=02πdRAGLo(R;h,h)·M,
χ(R,z)=(εε1)for0<z<d,χ(R,z)=0otherwise.
p(R,z)=p(z)=P(z),
GLo(RR;z,z)·p(R,z)dRdz=GLo(RR;z,z)·p(z)dRdz=GLo(κ=0;z,z)·p(z)dz=1ϵ0ε1z^z^·p(z),for0<z<d,
GLo(RR;z,z)·pI(R,z)dRdz=0for0<z<d
P(z)=ϵ0(εε1)[F1ε0ε1z^z^·P(z)]for0<z<d.
Λs=εε14πd,Λκ=εε14πd,Λz=ε1εεε14πd.
nos=iω˜22w1(εε1)dnoκ=iw12ε1(εε1)dnoz=iκ22w1εε1εd.
S=1ε1A(12x^x^+12y^y^z^z^)+1ε1B(h¯)(12x^x^+12y^y^+z^z^),
A=m,n1(m2+n2)3/29.03,(square lattice)
B(h¯)=ε2ε1ε2+ε1m,n3h¯2[m2+n2+d¯2][m2+n2+(h¯)2]5/2=ε2ε1ε2+ε1m,n(2π)2m2+n2e2π(h¯m2+n2),(square lattice)
A=2ππ11.14,B(h¯)=ε2ε1ε2+ε1[1h¯32(2h¯2+π1)3/2],(random arrangement)
nos=(εε1)(ε+2ε1)C1(εε1)(ε+2ε1)b3a3(A+B(h¯)2),
C2πiε1ω˜w1(ω˜a)b3a3.
r=Cγ,
γ(εε1)(ε+2ε1)1(εε1)(ε+2ε1)C,
CC+b3a3A+B(h¯)2
κoκo=κo+rρ13=κo+ρ13Cγ,
ρ13C=f(D/λ)/λ2,
(Dλ)cut-off=12π(ε2ε3)1/2tan1(ε3ε1ε2ε3)1/2,
Imγ=3εmi(ω)ε1(εmi(ω))2(1C)2+(εmr(ω)(1C)+ε1(C+2))2,
εmr(ω)=(C+2)/(C1)ε1.
σabs/(πb2)=4ω˜ε1bIm[εε1ε+2ε1]
H(Re[κo])/(ε1)Im[κo],
κSP=ω˜εm(ω)ε1εm(ω)+ε1,
εav=εcoat1+2bcore3bcoat3εεcoatε+2εcoat1bcore3bcoat3εεcoatε+2εcoat,
G=(Reκo)/(εcoat)Imκo=(Reγ)/(εcoat)Imγ
κSPκSP=κSP+rpρ1m,
ε=z^z^ε+(x^x^+y^y^)ε.
Λs=εε14πd,Λκ=εε14πd,Λz=ε1εεε14πd.
εeffε1=1+4πΛdε1,εeffε1=(14πΛzdε1)1,
4πϵ0Go(r)=3r^r^Uε1(eiω˜n1rr3iω˜n1eiω˜n1rr2)+ω˜2(Ur^r^)eiω˜n1rr4π3ε1δ(r)U,
4πϵ0GLo(r)=3r^r^Uε1r34π3ε1δ(r)U,
Go(κ;z,z)=iω˜22ϵ0w1(s^s^+p^1+p^1+)θ(zz)eiw1(zz)+iω˜22ϵ0w1(s^s^+p^1p^1)θ(zz)eiw1(zz)z^z^ϵ0ε1δ(zz)
GR(κ;z,z)=iω˜22ϵ0w1(s^R1Nss^+p^1+R1Npp^1)eiw1(z+z),
rijs=wiwjwi+wj,tijs=2wiwi+wj
rijp=wiεjwjεiwiεj+wjεi,tijp=2ninjwiwiεj+wjεi
R1N=r12+t12R2Nt21e2iw2D21R2Nr21e2iw2D2
wliκ
rijs0,rijpεjεiεj+εi.
R1Ns0,R1Npε2ε1ε2+ε1.
GIR(κ;z,z)=κ2ϵ0ε1ε2ε1ε2+ε1(z^z^+κ^κ^+iz^κ^iκ^z^)eκ(z+z),
GCR(κ;z,z)=iω˜22ϵ0w1(s^R1Nss^+p^1+R1Npp^1)eiw1(z+z)κ2ϵ0ε1ε2ε1ε2+ε1(z^z^+κ^κ^+iz^κ^iκ^z^)eκ(z+z),
GLo(κ;z,z)=κ2ϵ0ε1(z^z^κ^κ^iz^κ^i^κ^z^)θ(zz)eκ(zz)+κ2ϵ0ε1(z^z^κ^κ^+iz^κ^+i^κ^z^)θ(zz)eκ(zz)z^z^ϵ0ε1δ(zz).
VI(R;z)ε2ε1ε2+ε1(z^z^x^x^y^y^)·V(R;z),
VI(κ;z)ε2ε1ε2+ε1(z^z^x^x^y^y^)·V(κ;z),
GIR(κ;z,z)·V(κ,z)dz=GLo(κ;z,z)·VI(κ,z)dz
GIR(RR;z,z)·V(R,z)dzdR=GLo(RR;z,z)·VI(R,z)dzdR.
V(R;z)=eiκi·Rv(R;z),VI(R;z)=eiκi·RvI(R;z),
eiκi·(RR)GIR(RR;z,z)·v(R,z)dzdR=eiκi·(RR)GLo(RR;z,z)·vI(R,z)dzdR.
GTo(κ;z,z)12ϵ0[iω˜2w1s^s^+1ε1(iκ2w1κ)z^z^+1ε1(iw1+κ)κ^κ^]GTo(κ)forw1z,w1z,κz,κz1,
eiκi·RE¯(R;d+)=Fh+eiw1id++Fheiw1id++iω˜22ϵ0w1i(s^is^i+p^1+ip^1+i)eiw1id+·eiw1izP(z)dz+iω˜22ϵ0w1i(s^iR1Ns(κi)s^i+p^1+iR1Np(κi)p^1i)eiw1id+·eiw1izP(z)dz,
eiκi·RE¯(R;0l)=Fh+eiw1i0l+Fheiw1i0l+iω˜22ϵ0w1i(s^is^i+p^1ip^1i)eiw1i0l·eiw1izP(z)dz+iω˜22ϵ0w1i(s^iR1Ns(κi)s^i+p^1+iR1Np(κi)p^1i)eiw1i0l·eiw1izP(z)dz.
E¯+(d+)=Fh+(κi)eiw1id++iω˜22ϵ0w1i(s^is^i+p^1+ip^1+i)eiw1id+·eiw1izP(z)dz.
E¯(d+)=Fh(κi)eiw1id+.
E¯+(0l)=Fh+(κi)eiw1i0l.
E¯(0l)=Fh(κi)eiw1i0l+iω˜22ϵ0w1i(s^is^i+p^1ip^1i)eiw1i0l·eiw1izP(z)dz.
Fh+(κi)=Fh++iω˜22ϵ0w1i(s^iR1Ns(κi)s^i+p^1+iR1Np(κi)p^1i)·eiw1izP(z)dzFh(κi)=Fh.
r1mp=w1εmwmε1w1εm+wmε1,t1mp=2n1nmw1w1εm+wmε1,
κSP=ω˜εmε1εm+ε1,
r1mρ1mκκSP,t1mτ1mκκSP,
ρ1m=2w1SP(wmSP)2ε1κSP(wmSPεm+w1SPε1),τ1m=2n1nm(w1SP)2wmSPκSP(wmSPεm+w1SPε1),
w1SPω˜2ε1κSP2=ω˜ε12εm+ε1,wmSPω˜2εmκSP2=ω˜εm2εm+ε1.
T13=t12t23eiw2D1r21r23e2iw2D,R13=r12+r23e2iw2D1r21r23e2iw2D,
1r21r23e2iw2D=0.
cot(hD)=hPQhQ+P,
h=ω˜2n22κ2,Q=aQκ2ω˜2n12,P=aPκ2ω˜2n32,
aQ=aP=1(spolarized),aQ=n22n12,aP=n22n33(ppolarized).
R13ρ13κκo,T13τ13κκo,
ρ13=2ho2QoκoDeff(ho2+Qo2),τ13=2ho2Qoa13κoDeff(ho2+Qo2)(ho2+Po2),
a13=1(spolarized),a13=n1n3(ppolarized),
Deff=D+Qo1(aQ2ho2+Qo2ho2+Qo2)+Po1(aP2ho2+Po2ho2+Po2).

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