Abstract

In this paper, an efficient analytical method for characterizing large array of plasmonic nanoparticles located over planarly layered substrate is introduced. The model is called dipole mode complex image (DMCI) method since the main idea lies in modeling a subwavelength spherical nanoparticle at its electric scattering resonance with an induced electric dipole and representing the electromagnetic (EM) fields of this electric dipole over the layered substrate in terms of finite complex images. The major advantages of the proposed method are its accuracy and rapid calculation in characterizing various kinds of large periodic and aperiodic arrays of nanoparticles on layered substrates. The computational time can be reduced significantly in compared to the traditional methods. The accuracy of the theoretical model is validated through comparison with numerical integration of Sommerfeld integrals. Moreover, the analytical results are compared well with those determined by full-wave finite difference time domain (FDTD) method. To demonstrate the capability of our technique, the performances of large arrays of nanoparticles on layered silicon substrates for efficient sunlight energy incoupling are studied.

© 2011 OSA

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    [CrossRef]

2010

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater. 9(1), 3–4 (2010).
[CrossRef]

A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A nonlinear inverse scattering design approach,” Phys. Rev. B 82(3), 035117 (2010).
[CrossRef]

Y. Lia, H. J. Schluesenerb, and S. Xua, “Gold nanoparticle-based biosensors,” Gold Bull. 43(1), 29–41 (2010).
[CrossRef]

A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express 18(1), 123–133 (2010).
[CrossRef] [PubMed]

M. M. Tajdini and A. A. Shishegar, “A novel analysis of microstrip structures using the Gaussian Green’s function method,” IEEE Trans. Antenn. Propag. 58(1), 88–94 (2010).
[CrossRef]

A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microw. Theory Tech. 58(3), 602–613 (2010).
[CrossRef]

2009

S. Ghadarghadr and H. Mosallaei, “Coupled dielectric nanoparticles manipulating metamaterials optical characteristics,” IEEE Trans. NanoTechnol. 8(5), 582–594 (2009).
[CrossRef]

H. Alaeian and R. Faraji-Dana, “A fast and accurate analysis of 2-D periodic devices using complex images Green’s functions,” J. Lightwave Technol. 27(13), 2216–2223 (2009).
[CrossRef]

S. M. Sadeghi, “Plasmonic metaresonances: Molecular resonances in quantum dot–metallic nanoparticle conjugates,” Phys. Rev. B 79(23), 233309 (2009).
[CrossRef]

Y. Jin and X. Gao, “Plasmonic fluorescent quantum dots,” Nat. Nanotechnol. 4(9), 571–576 (2009).
[CrossRef] [PubMed]

S. Ghadarghadr, Z. Hao, and H. Mosallaei, “Plasmonic array nanoantennas on layered substrates: modeling and radiation characteristics,” Opt. Express 17(21), 18556–18570 (2009).
[CrossRef]

2008

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78(15), 153111 (2008).
[CrossRef]

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544–5555 (2008).
[CrossRef] [PubMed]

D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express 16(12), 9222–9238 (2008).
[CrossRef] [PubMed]

2007

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, “Optical antenna arrays in the visible range,” Opt. Express 15(6), 3478–3487 (2007).
[CrossRef] [PubMed]

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76(24), 245403 (2007).
[CrossRef]

2006

J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. 88(13), 131109 (2006).
[CrossRef]

S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part I,” Photon. Spectra 40, 58–66 (2006).

S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part II,” Photon. Spectra 40, 66–72 (2006).

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74(3), 033402 (2006).
[CrossRef]

2005

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

A. Alù and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metallic/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005).
[CrossRef]

M. I. Aksun and G. Dural, “Clarification of issues on the closed-form Green’s functions in stratified media,” IEEE Trans. Antenn. Propag. 53(11), 3644–3653 (2005).
[CrossRef]

2003

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Y. Xiao, F. Patolsky, E. Katz, J. F. Hainfeld, and I. Willner, ““Plugging into Enzymes”: nanowiring of redox enzymes by a gold nanoparticle,” Science 299(5614), 1877–1881 (2003).
[CrossRef] [PubMed]

J. Liu and Y. Lu, “A colorimetric lead biosensor using DNAzyme-directed assembly of gold nanoparticles,” J. Am. Chem. Soc. 125(22), 6642–6643 (2003).
[CrossRef] [PubMed]

2001

B. Hu and W. C. Chew, “Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium,” IEEE Trans. Geosci. Rem. Sens. 39(5), 1028–1038 (2001).
[CrossRef]

2000

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(44 Pt B), 5797–5807 (2000).
[CrossRef] [PubMed]

1997

K. A. Michalski and J. R. Mosig, “Multilayered media Green’s function in integral equation formulations,” IEEE Trans. Antenn. Propag. 45(3), 508–519 (1997).
[CrossRef]

1992

J. J. Yang, Y. L. Chow, G. E. Howard, and D. G. Fang, “Complex images of an electric dipole in homogenous and layered dielectrics between two ground planes,” IEEE Trans. Microw. Theory Tech. 40(3), 595–598 (1992).
[CrossRef]

1991

Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. 39(3), 588–592 (1991).
[CrossRef]

1987

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[CrossRef] [PubMed]

1986

P. C. Waterman and N. E. Pedersen, “Electromagnetic scattering by periodic arrays of particles,” J. Appl. Phys. 59(8), 2609–2618 (1986).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

1971

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D Part. Fields 3(4), 825–839 (1971).
[CrossRef]

Ahmadi, A.

Aksun, M. I.

A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microw. Theory Tech. 58(3), 602–613 (2010).
[CrossRef]

M. I. Aksun and G. Dural, “Clarification of issues on the closed-form Green’s functions in stratified media,” IEEE Trans. Antenn. Propag. 53(11), 3644–3653 (2005).
[CrossRef]

Alaeian, H.

Alparslan, A.

A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microw. Theory Tech. 58(3), 602–613 (2010).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).
[CrossRef]

Atwater, H. A.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express 16(12), 9222–9238 (2008).
[CrossRef] [PubMed]

J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. 88(13), 131109 (2006).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metallic/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005).
[CrossRef]

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Biteen, J. S.

J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. 88(13), 131109 (2006).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part I,” Photon. Spectra 40, 58–66 (2006).

S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part II,” Photon. Spectra 40, 66–72 (2006).

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater. 9(1), 3–4 (2010).
[CrossRef]

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78(15), 153111 (2008).
[CrossRef]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Catchpole, K. R.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Chappell, S.

Chew, W. C.

B. Hu and W. C. Chew, “Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium,” IEEE Trans. Geosci. Rem. Sens. 39(5), 1028–1038 (2001).
[CrossRef]

Chow, Y. L.

J. J. Yang, Y. L. Chow, G. E. Howard, and D. G. Fang, “Complex images of an electric dipole in homogenous and layered dielectrics between two ground planes,” IEEE Trans. Microw. Theory Tech. 40(3), 595–598 (1992).
[CrossRef]

Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. 39(3), 588–592 (1991).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Colocci, M.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Dal Negro, L.

R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544–5555 (2008).
[CrossRef] [PubMed]

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Dallapiccola, R.

Dural, G.

M. I. Aksun and G. Dural, “Clarification of issues on the closed-form Green’s functions in stratified media,” IEEE Trans. Antenn. Propag. 53(11), 3644–3653 (2005).
[CrossRef]

Engheta, N.

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76(24), 245403 (2007).
[CrossRef]

A. Alù and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).
[CrossRef]

Errington, R.

Fang, D. G.

J. J. Yang, Y. L. Chow, G. E. Howard, and D. G. Fang, “Complex images of an electric dipole in homogenous and layered dielectrics between two ground planes,” IEEE Trans. Microw. Theory Tech. 40(3), 595–598 (1992).
[CrossRef]

Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. 39(3), 588–592 (1991).
[CrossRef]

Faraji-Dana, R.

Ferry, V. E.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

Gaburro, Z.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Gao, X.

Y. Jin and X. Gao, “Plasmonic fluorescent quantum dots,” Nat. Nanotechnol. 4(9), 571–576 (2009).
[CrossRef] [PubMed]

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(44 Pt B), 5797–5807 (2000).
[CrossRef] [PubMed]

Ghadarghadr, S.

Gopinath, A.

Green, M. A.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Hainfeld, J. F.

Y. Xiao, F. Patolsky, E. Katz, J. F. Hainfeld, and I. Willner, ““Plugging into Enzymes”: nanowiring of redox enzymes by a gold nanoparticle,” Science 299(5614), 1877–1881 (2003).
[CrossRef] [PubMed]

Håkanson, U.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

Hao, Z.

Howard, G. E.

J. J. Yang, Y. L. Chow, G. E. Howard, and D. G. Fang, “Complex images of an electric dipole in homogenous and layered dielectrics between two ground planes,” IEEE Trans. Microw. Theory Tech. 40(3), 595–598 (1992).
[CrossRef]

Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. 39(3), 588–592 (1991).
[CrossRef]

Hryciw, A.

A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater. 9(1), 3–4 (2010).
[CrossRef]

Hu, B.

B. Hu and W. C. Chew, “Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium,” IEEE Trans. Geosci. Rem. Sens. 39(5), 1028–1038 (2001).
[CrossRef]

Iguchi, K.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[CrossRef] [PubMed]

Jin, Y.

Y. Jin and X. Gao, “Plasmonic fluorescent quantum dots,” Nat. Nanotechnol. 4(9), 571–576 (2009).
[CrossRef] [PubMed]

Johnson, P.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Jun, Y. C.

A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater. 9(1), 3–4 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78(15), 153111 (2008).
[CrossRef]

Katz, E.

Y. Xiao, F. Patolsky, E. Katz, J. F. Hainfeld, and I. Willner, ““Plugging into Enzymes”: nanowiring of redox enzymes by a gold nanoparticle,” Science 299(5614), 1877–1881 (2003).
[CrossRef] [PubMed]

Kekatpure, R. D.

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78(15), 153111 (2008).
[CrossRef]

Koenderink, A. F.

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74(3), 033402 (2006).
[CrossRef]

Kohmoto, M.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[CrossRef] [PubMed]

Kühn, S.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

Lagendijk, A.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Lewis, N. S.

J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. 88(13), 131109 (2006).
[CrossRef]

Lezec, H. J.

Li, J.

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76(24), 245403 (2007).
[CrossRef]

Lia, Y.

Y. Lia, H. J. Schluesenerb, and S. Xua, “Gold nanoparticle-based biosensors,” Gold Bull. 43(1), 29–41 (2010).
[CrossRef]

Liu, J.

J. Liu and Y. Lu, “A colorimetric lead biosensor using DNAzyme-directed assembly of gold nanoparticles,” J. Am. Chem. Soc. 125(22), 6642–6643 (2003).
[CrossRef] [PubMed]

Lu, Y.

J. Liu and Y. Lu, “A colorimetric lead biosensor using DNAzyme-directed assembly of gold nanoparticles,” J. Am. Chem. Soc. 125(22), 6642–6643 (2003).
[CrossRef] [PubMed]

Maier, S. A.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metallic/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005).
[CrossRef]

Martin, O. J. F.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(44 Pt B), 5797–5807 (2000).
[CrossRef] [PubMed]

Matthews, D. R.

Mertens, H.

J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. 88(13), 131109 (2006).
[CrossRef]

Michalski, K. A.

A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microw. Theory Tech. 58(3), 602–613 (2010).
[CrossRef]

K. A. Michalski and J. R. Mosig, “Multilayered media Green’s function in integral equation formulations,” IEEE Trans. Antenn. Propag. 45(3), 508–519 (1997).
[CrossRef]

Mosallaei, H.

A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express 18(1), 123–133 (2010).
[CrossRef] [PubMed]

A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A nonlinear inverse scattering design approach,” Phys. Rev. B 82(3), 035117 (2010).
[CrossRef]

S. Ghadarghadr, Z. Hao, and H. Mosallaei, “Plasmonic array nanoantennas on layered substrates: modeling and radiation characteristics,” Opt. Express 17(21), 18556–18570 (2009).
[CrossRef]

S. Ghadarghadr and H. Mosallaei, “Coupled dielectric nanoparticles manipulating metamaterials optical characteristics,” IEEE Trans. NanoTechnol. 8(5), 582–594 (2009).
[CrossRef]

Mosig, J. R.

K. A. Michalski and J. R. Mosig, “Multilayered media Green’s function in integral equation formulations,” IEEE Trans. Antenn. Propag. 45(3), 508–519 (1997).
[CrossRef]

Nakayama, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

Njoh, K.

Oton, C. J.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Pacifici, D.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express 16(12), 9222–9238 (2008).
[CrossRef] [PubMed]

Patolsky, F.

Y. Xiao, F. Patolsky, E. Katz, J. F. Hainfeld, and I. Willner, ““Plugging into Enzymes”: nanowiring of redox enzymes by a gold nanoparticle,” Science 299(5614), 1877–1881 (2003).
[CrossRef] [PubMed]

Paulus, M.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(44 Pt B), 5797–5807 (2000).
[CrossRef] [PubMed]

Pavesi, L.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Pedersen, N. E.

P. C. Waterman and N. E. Pedersen, “Electromagnetic scattering by periodic arrays of particles,” J. Appl. Phys. 59(8), 2609–2618 (1986).
[CrossRef]

Penninkhof, J. J.

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

Pillai, S.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Polman, A.

J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. 88(13), 131109 (2006).
[CrossRef]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74(3), 033402 (2006).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

Rashidi, A.

A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A nonlinear inverse scattering design approach,” Phys. Rev. B 82(3), 035117 (2010).
[CrossRef]

Righini, R.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Rogobete, L.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

Sadeghi, S. M.

S. M. Sadeghi, “Plasmonic metaresonances: Molecular resonances in quantum dot–metallic nanoparticle conjugates,” Phys. Rev. B 79(23), 233309 (2009).
[CrossRef]

Salandrino, A.

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76(24), 245403 (2007).
[CrossRef]

Sandoghdar, V.

S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

Schluesenerb, H. J.

Y. Lia, H. J. Schluesenerb, and S. Xua, “Gold nanoparticle-based biosensors,” Gold Bull. 43(1), 29–41 (2010).
[CrossRef]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Shalaev, V. M.

S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part II,” Photon. Spectra 40, 66–72 (2006).

S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part I,” Photon. Spectra 40, 58–66 (2006).

Shishegar, A. A.

M. M. Tajdini and A. A. Shishegar, “A novel analysis of microstrip structures using the Gaussian Green’s function method,” IEEE Trans. Antenn. Propag. 58(1), 88–94 (2010).
[CrossRef]

Smith, P.

Stellacci, F.

Summers, H. D.

Sutherland, B.

M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987).
[CrossRef] [PubMed]

Sweatlock, L. A.

D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express 16(12), 9222–9238 (2008).
[CrossRef] [PubMed]

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

Tajdini, M. M.

M. M. Tajdini and A. A. Shishegar, “A novel analysis of microstrip structures using the Gaussian Green’s function method,” IEEE Trans. Antenn. Propag. 58(1), 88–94 (2010).
[CrossRef]

Tanabe, K.

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

Trupke, T.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

Walters, R. J.

Waterman, P. C.

P. C. Waterman and N. E. Pedersen, “Electromagnetic scattering by periodic arrays of particles,” J. Appl. Phys. 59(8), 2609–2618 (1986).
[CrossRef]

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D Part. Fields 3(4), 825–839 (1971).
[CrossRef]

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78(15), 153111 (2008).
[CrossRef]

Wiersma, D. S.

L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[CrossRef] [PubMed]

Willner, I.

Y. Xiao, F. Patolsky, E. Katz, J. F. Hainfeld, and I. Willner, ““Plugging into Enzymes”: nanowiring of redox enzymes by a gold nanoparticle,” Science 299(5614), 1877–1881 (2003).
[CrossRef] [PubMed]

Xiao, Y.

Y. Xiao, F. Patolsky, E. Katz, J. F. Hainfeld, and I. Willner, ““Plugging into Enzymes”: nanowiring of redox enzymes by a gold nanoparticle,” Science 299(5614), 1877–1881 (2003).
[CrossRef] [PubMed]

Xua, S.

Y. Lia, H. J. Schluesenerb, and S. Xua, “Gold nanoparticle-based biosensors,” Gold Bull. 43(1), 29–41 (2010).
[CrossRef]

Yang, J. J.

J. J. Yang, Y. L. Chow, G. E. Howard, and D. G. Fang, “Complex images of an electric dipole in homogenous and layered dielectrics between two ground planes,” IEEE Trans. Microw. Theory Tech. 40(3), 595–598 (1992).
[CrossRef]

Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. 39(3), 588–592 (1991).
[CrossRef]

Appl. Phys. Lett.

K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008).
[CrossRef]

J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. 88(13), 131109 (2006).
[CrossRef]

Gold Bull.

Y. Lia, H. J. Schluesenerb, and S. Xua, “Gold nanoparticle-based biosensors,” Gold Bull. 43(1), 29–41 (2010).
[CrossRef]

IEEE Trans. Antenn. Propag.

K. A. Michalski and J. R. Mosig, “Multilayered media Green’s function in integral equation formulations,” IEEE Trans. Antenn. Propag. 45(3), 508–519 (1997).
[CrossRef]

M. M. Tajdini and A. A. Shishegar, “A novel analysis of microstrip structures using the Gaussian Green’s function method,” IEEE Trans. Antenn. Propag. 58(1), 88–94 (2010).
[CrossRef]

M. I. Aksun and G. Dural, “Clarification of issues on the closed-form Green’s functions in stratified media,” IEEE Trans. Antenn. Propag. 53(11), 3644–3653 (2005).
[CrossRef]

IEEE Trans. Geosci. Rem. Sens.

B. Hu and W. C. Chew, “Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium,” IEEE Trans. Geosci. Rem. Sens. 39(5), 1028–1038 (2001).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. 39(3), 588–592 (1991).
[CrossRef]

J. J. Yang, Y. L. Chow, G. E. Howard, and D. G. Fang, “Complex images of an electric dipole in homogenous and layered dielectrics between two ground planes,” IEEE Trans. Microw. Theory Tech. 40(3), 595–598 (1992).
[CrossRef]

A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microw. Theory Tech. 58(3), 602–613 (2010).
[CrossRef]

IEEE Trans. NanoTechnol.

S. Ghadarghadr and H. Mosallaei, “Coupled dielectric nanoparticles manipulating metamaterials optical characteristics,” IEEE Trans. NanoTechnol. 8(5), 582–594 (2009).
[CrossRef]

J. Am. Chem. Soc.

J. Liu and Y. Lu, “A colorimetric lead biosensor using DNAzyme-directed assembly of gold nanoparticles,” J. Am. Chem. Soc. 125(22), 6642–6643 (2003).
[CrossRef] [PubMed]

J. Appl. Phys.

S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metallic/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005).
[CrossRef]

A. Alù and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005).
[CrossRef]

P. C. Waterman and N. E. Pedersen, “Electromagnetic scattering by periodic arrays of particles,” J. Appl. Phys. 59(8), 2609–2618 (1986).
[CrossRef]

J. Lightwave Technol.

Nano Lett.

V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008).
[CrossRef]

Nat. Mater.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010).
[CrossRef] [PubMed]

A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater. 9(1), 3–4 (2010).
[CrossRef]

Nat. Nanotechnol.

Y. Jin and X. Gao, “Plasmonic fluorescent quantum dots,” Nat. Nanotechnol. 4(9), 571–576 (2009).
[CrossRef] [PubMed]

Opt. Express

Photon. Spectra

S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part I,” Photon. Spectra 40, 58–66 (2006).

S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part II,” Photon. Spectra 40, 66–72 (2006).

Phys. Rev. B

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78(15), 153111 (2008).
[CrossRef]

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76(24), 245403 (2007).
[CrossRef]

A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A nonlinear inverse scattering design approach,” Phys. Rev. B 82(3), 035117 (2010).
[CrossRef]

L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005).
[CrossRef]

S. M. Sadeghi, “Plasmonic metaresonances: Molecular resonances in quantum dot–metallic nanoparticle conjugates,” Phys. Rev. B 79(23), 233309 (2009).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74(3), 033402 (2006).
[CrossRef]

Phys. Rev. D Part. Fields

P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D Part. Fields 3(4), 825–839 (1971).
[CrossRef]

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Figures (18)

Fig. 1
Fig. 1

Geometry of a concentric core-shell particle.

Fig. 2
Fig. 2

Array of plasmonic nanoparticles on a planarly multilayered medium.

Fig. 3
Fig. 3

Integration contours   C r and   C d (a) in complex   k ρ -plane and (b) in complex   k z -plane.

Fig. 4
Fig. 4

(a) Magnitude and (b) phase of the plarizability factor   ξ of a concentric nano core-shell dielectric-plasmonic particle of Fig. 1 vs. a/b for different wavelengths with SiO2 core and silver coating when b = 30 nm.

Fig. 5
Fig. 5

Magnitudes of   Γ 1 ( e ) ,   Γ 1 ( h ) , and   Γ 2 ( e ) of a concentric nano core-shell dielectric-plasmonic particle of Fig. 1 vs. a/b with SiO2 core and silver coating when b = 30 nm and   λ 0 = 500 nm.

Fig. 6
Fig. 6

A three layer substrate with SiO2 (   ε r = 2.2-j0.01) slab of thickness 0 .16   λ 0 , GaAs-AlGaAs (   ε r = 8-j0.1) slab of thickness 0 .3   λ 0 , and gold (   ε r = −2.28-j3.81) slab of thickness 0 .4   λ 0 (at operating wavelength of   λ 0 = 500 nm).

Fig. 7
Fig. 7

Total spectral reflection coefficients vs. modified contour parameter t for (a)   TE z and (b)   TM z modes from the entire substrate via the exact formulation and CI method.

Fig. 9
Fig. 9

Total spectral reflection coefficients vs. modified contour parameter t for (a)   TE z and (b)   TM z modes in the GaAs-AlGaAs layer via the exact formulation and CI method.

Fig. 8
Fig. 8

Total spectral transmission coefficients vs. modified contour parameter t for (a)   TE z and (b)   TM z modes in the GaAs-AlGaAs layer via the exact formulation and CI method.

Fig. 10
Fig. 10

Magnitude of total spatial reflection coefficients for (a)   TE z and (b)   TM z modes from the entire substrate via the exact integration and CI method.

Fig. 12
Fig. 12

Magnitude of total spatial reflection coefficients for (a)   TE z and (b)   TM z modes for the GaAs-AlGaAs layer via the exact integration and CI method.

Fig. 13
Fig. 13

(a) Configuration of three plasmonic nanoparticles. (b) Normalized   | E x | via the array (deposited on the layered substrate) using exact integration and CI method.

Fig. 11
Fig. 11

Magnitude of total spatial transmission coefficients for (a)   TE z and (b)   TM z modes for the GaAs-AlGaAs layer via the exact integration and CI method.

Fig. 14
Fig. 14

(a) Configuration of three unit electric dipoles (with different polarizations) above the layered substrate shown in Fig. 6, (b) DMCI result, and (c) FDTD result for the normalized   | E z | 2 (dB) at the middle of the GaAs-AlGaAs layer.

Fig. 16
Fig. 16

(a) Configuration of eight plasmonic nanoparticles and a z-directed unit electric dipole at the center above the layered substrate shown in Fig. 6, (b) DMCI result, and (c) FDTD result for the normalized   | E z | 2 (dB) at the middle of the GaAs-AlGaAs layer.

Fig. 15
Fig. 15

(a) Configuration of nine unit electric dipoles above the layered substrate shown in Fig. 6, (b) DMCI result, and (c) FDTD result for the normalized   | E z | 2 (dB) at the middle of the GaAs-AlGaAs layer.

Fig. 17
Fig. 17

(a) A periodic array of 100 plasmonic nanoparticles above the substrate of Fig. 6 and (b)   | E z | 2 (dB) at the middle of the GaAs-AlGaAs layer. It is normalized to the case that no nanoparticle exists.

Fig. 18
Fig. 18

(a) An aperiodic array of 100 plasmonic nanoparticles above the substrate of Fig. 6 and (b)   | E z | 2 (dB) at the middle of the GaAs-AlGaAs layer. It is normalized to the case that no nanoparticle exists.

Tables (3)

Tables Icon

Table 1 Complex Terms for the Total Reflection Coefficients of the Entire Substrate

Tables Icon

Table 3 Complex Terms for the Total Reflection Coefficients of the GaAs-AlGaAs Layer

Tables Icon

Table 2 Complex Terms for the Total Transmission Coefficients of the GaAs-AlGaAs Layer

Equations (45)

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E i = p = 0 q = p p [ a p q N p q ( 1 ) + b p q M p q ( 1 ) ]         E s = p = 0 q = p p [ Γ p ( e ) a p q N p q ( 3 ) + Γ p ( h ) b p q M p q ( 3 ) ] .
Γ p ( e ) = U p ( e ) U p ( e ) j V p ( e )
U p ( e ) = [ j p ( k c a ) j p ( k s a ) y p ( k s a ) 0 j p d ( k c a ) / ε c j p d ( k s a ) / ε s y p d ( k s a ) / ε s 0 0 j p ( k s b ) y p ( k s b ) j p ( k m b ) 0 j p d ( k s b ) / ε s y p d ( k s b ) / ε s j p d ( k m b ) / ε m ] .
J 0 = ξ E t o t a l         ξ = 6 π ω ε m k m 3 Γ 1 ( e ) .
E ( r ) = j ω μ ( I + k 2 ) . J 0 exp ( j k r ) 4 π r         H ( r ) = × J 0 exp ( j k r ) 4 π r
J 0 = x J x + y J y + z J z         I = x x + y y + z z .
J 0 p ( r p ) = ξ p { E e x t . ( r p ) + q = 1 , q p N E d i p . q ( r p ) + E r e f . e x t . ( r p ) + q = 1 N E r e f . q ( r p ) } .
exp ( j k r ) r = + d k ρ k ρ j 2 k z H 0 ( 2 ) ( k ρ ρ ) exp ( j k z | z z ' | )
H 0 ( 2 ) ( k ρ ρ ) = 1 π + d k x 1 k y exp ( j k x ( x x ' ) j k y | y y ' | ) .
E i x q ( r ) = 1 8 π ω ε i { J x q ( ω 2 μ i ε i + 2 x 2 ) + J y q 2 x y + J z q 2 x z } × + d k ρ k ρ k i z H 0 ( 2 ) ( k ρ ρ q ) T i T M [ exp ( j k i z | z z q | ) R i T M exp ( j k i z ( z z q + 2 d i ) ) ]
E i y q ( r ) = 1 8 π ω ε i { J x q 2 y x + J y q ( ω 2 μ i ε i + 2 y 2 ) + J z q 2 y z } × + d k ρ k ρ k i z H 0 ( 2 ) ( k ρ ρ q ) T i T E [ exp ( j k i z | z z q | ) + R i T E exp ( j k i z ( z z q + 2 d i ) ) ]
E i z q ( r ) = 1 8 π ω ε i { J x q 2 z x + J y q 2 z y + J z q ( ω 2 μ i ε i + 2 z 2 ) } × + d k ρ k ρ k i z H 0 ( 2 ) ( k ρ ρ q ) T i T M [ exp ( j k i z | z z q | ) + R i T M exp ( j k i z ( z z q + 2 d i ) ) ]
H i x q ( r ) = j 8 π { J y q z J z q y } × + d k ρ k ρ k i z H 0 ( 2 ) ( k ρ ρ q ) T i T E [ exp ( j k i z | z z q | ) R i T E exp ( j k i z ( z z q + 2 d i ) ) ]
H i y q ( r ) = j 8 π { J x q z + J z q x } × + d k ρ k ρ k i z H 0 ( 2 ) ( k ρ ρ q ) T i T M [ exp ( j k i z | z z q | ) + R i T M exp ( j k i z ( z z q + 2 d i ) ) ]
H i z q ( r ) = j 8 π { J x q y J y q x } × + d k ρ k ρ k i z H 0 ( 2 ) ( k ρ ρ q ) T i T E [ exp ( j k i z | z z q | ) + R i T E exp ( j k i z ( z z q + 2 d i ) ) ]
T i T M = T 1 T M exp ( j k 1 z d 1 ) exp ( j k i z d i 1 ) × l = 1 i 1 { exp ( j k l z ( d l d l 1 ) ) t l , l + 1 T M 1 + r l , l + 1 T M R l + 1 T M exp ( j 2 k l + 1 z ( d l + 1 d l ) ) }
R i T M = r i , i + 1 T M + R i + 1 T M exp ( j 2 k i + 1 z ( d i + 1 d i ) ) 1 + r i , i + 1 T M R i + 1 T M exp ( j 2 k i + 1 z ( d i + 1 d i ) )
t i , i + 1 T M = 2 ε i + 1 k i z ε i + 1 k i z + ε i k i + 1 z           r i , i + 1 T M = ε i + 1 k i z ε i k i + 1 z ε i + 1 k i z + ε i k i + 1 z .
t i , i + 1 T E = 2 μ i + 1 k i z μ i + 1 k i z + μ i k i + 1 z           r i , i + 1 T E = μ i + 1 k i z μ i k i + 1 z μ i + 1 k i z + μ i k i + 1 z .
F ( r ) = + d k ρ f ( k z ) k ρ j 2 k z H 0 ( 2 ) ( k ρ ρ ) exp ( j k z | z z ' | ) ,
f ( k z ) = n a n exp ( k z b n ) ,
F ( r ) = + d k ρ n a n exp ( k z b n ) k ρ j 2 k z H 0 ( 2 ) ( k ρ ρ ) exp ( j k z ( z z ' ) ) = n a n + d k ρ k ρ j 2 k z H 0 ( 2 ) ( k ρ ρ ) exp ( j k z ( z z ' j b n ) ) = n a n exp ( j k R n ) R n
R n = ( x x ' ) 2 + ( y y ' ) 2 + ( z z ' j b n ) 2 .
T i = f ( k 1 z , k 2 z , , k i z )           R i = g ( k i z , k i + 1 z , , k N z ) .
k j z 2 = k j 2 k ρ 2 ,
k j z 2 = k j 2 k i 2 + k i z 2 .
T i T M ( k i z ) = l α i l exp ( k i z β i l )           T i T E ( k i z ) = n α i n ' exp ( k i z β i n ' )
T i T M R i T M ( k i z ) = m γ i m exp ( k i z δ i m )           T i T E R i T E ( k i z ) = o γ i o ' exp ( k i z δ i o ' )
E i x q ( r ) = j 4 π ω ε i { J x q ( ω 2 μ i ε i + 2 x 2 ) + J y q 2 x y + J z q 2 x z } × [ l α i l exp ( j k i P i l q ) P i l q m γ i m exp ( j k i Q i m q ) Q i m q ]
E i y q ( r ) = j 4 π ω ε i { J x q 2 y x + J y q ( ω 2 μ i ε i + 2 y 2 ) + J z q 2 y z } × [ n α i n ' exp ( j k i P i n q ' ) P i n q ' + o γ i o ' exp ( j k i Q i o q ' ) Q i o q ' ]
E i z q ( r ) = j 4 π ω ε i { J x q 2 z x + J y q 2 z y + J z q ( ω 2 μ i ε i + 2 z 2 ) } × [ l α i l exp ( j k i P i l q ) P i l q + m γ i m exp ( j k i Q i m q ) Q i m q ]
H i x q ( r ) = 1 4 π { J y q z + J z q y } [ n α i n ' exp ( j k i P i n q ' ) P i n q ' o γ i o ' exp ( j k i Q i o q ' ) Q i o q ' ]
H i y q ( r ) = 1 4 π { J x q z J z q x } [ l α i l exp ( j k i P i l q ) P i l q + m γ i m exp ( j k i Q i m q ) Q i m q ]
H i z q ( r ) = 1 4 π { J x q y + J y q x } [ n α i n ' exp ( j k i P i n q ' ) P i n q ' + o γ i o ' exp ( j k i Q i o q ' ) Q i o q ' ]
P i l q = ρ q 2 + ( z z q j β i l ) 2           P i n q ' = ρ q 2 + ( z z q j β i n ' ) 2
Q i m q = ρ q 2 + ( z z q + 2 d i + j δ i m ) 2           Q i o q ' = ρ q 2 + ( z z q + 2 d i + j δ i o ' ) 2 .
k i z = k i [ j t + ( 1 t T ) ]           0 t T .
F ( t ) n = 1 N A n exp ( B n t )
F ( t m ) = F ( t 1 ) , F ( t 2 ) , , F ( t 2 N )
t m = T 2 N 1 ( m 1 )           m = 1 , 2 , , 2 N
[ F ( t N ) F ( t N 1 ) F ( t N + 1 ) F ( t N ) F ( t 1 ) F ( t 2 ) F ( t 2 N 1 ) F ( t 2 N 2 ) F ( t N ) ] [ C N C N 1 C 1 ] = [ F ( t N + 1 ) F ( t N + 2 ) F ( t 2 N ) ] ,
ρ N + C N ρ N 1 + C N 1 ρ N 2 + + C 1 = 0.
[ ρ 1 t 1 ρ 2 t 1 ρ 1 t 2 ρ 2 t 2 ρ N t 1 ρ N t 2 ρ 1 t N ρ 2 t N ρ N t N ] [ A 1 A 2 A N ] = [ F ( t 1 ) F ( t 2 ) F ( t N ) ] .
F ( k z ) n = 1 N α n exp ( β n k z )
α n = A n exp ( T B n 1 + j T )             β n = T B n k ( 1 + j T ) .

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