Abstract

The optical properties of a concentric nanometer-sized spherical shell comprised of an (active) 3-level gain medium core and a surrounding plasmonic metal shell are investigated. Current research in optical metamaterials has demonstrated that including lossless plasmonic materials to achieve a negative permittivity in a nano-sized coated spherical particle can lead to novel optical properties such as resonant scattering as well as transparency or invisibility. However, in practice, plasmonic materials have high losses at optical frequencies. It is observed that with the introduction of active materials, the intrinsic absorption in the plasmonic shell can be overcome and new optical properties can be observed in the scattering and absorption cross-sections of these coated nano-sized spherical shell particles. In addition, a “super” resonance is observed with a magnitude that is 103 greater than that for a tuned, resonant passive nano-sized coated spherical shell. This observation suggests the possibility of realizing a highly sub-wavelength laser with dimensions more than an order of magnitude below the traditional half-wavelength cavity length criteria. The operating characteristics of this coated nano-particle (CNP) laser are obtained numerically for a variety of configurations.

© 2007 Optical Society of America

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    [CrossRef]

2006 (9)

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006).
[CrossRef] [PubMed]

Ulf Leonhardt, "Optical conformal mapping," Science 312, 1777 (2006).
[PubMed]

G. W. Milton and N.-A. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London, Ser. A 462, 3027 (2006).
[CrossRef]

R. W. Ziolkowski and A. Erentok, "Metamaterial-based efficient electrically small antennas," IEEE Trans Antennas Propag. 54, 2113 (2006).
[CrossRef]

L. R. Hirsch and A. M. Gobin, "Metal nanoshells," Annals of Biomedical Engineering 34, 15 (2006).

A. Alù, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557 (2006).
[CrossRef] [PubMed]

K. Okamoto, S. Vyawahare, and A. Scherer, "Surface-plasmon enhanced bright emission from CdSe quantum-dot nanocrystals," J. Opt. Soc. Am. B 23, 1674 (2006).
[CrossRef]

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev and V. M. Shalaev, "Enhancement of surface plasmons in an Ag aggregate by optical gain in a dielectric medium," Opt. Lett. 31, 3022 (2006).
[CrossRef] [PubMed]

2005 (6)

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535 (2005).
[CrossRef]

A. W. H. Lin, N. J. Halas, and R. A. Drezek, "Optically tunable nanoparticle contrast agents for early cancer detection: model-based analysis of gold nanoshells," J. Biomed. Opt. 10, 064035 (2005)
[CrossRef]

R. W. Ziolkowski and A. D. Kipple, "Reciprocity between the effects of resonant scattering and enhanced radiated power by electrically small antennas in the presence of nested metamaterial shells," Phys. Rev. E 72, 036602 (2005).
[CrossRef]

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

A. Alù and N. Engheta, "Achieving transparency with plasmonic and metamaterials coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

2004 (3)

N. K. Grady, N. J. Halas, and P. Norlander, "Influence of dielectric function properties on the optical response of plasmonic resonant metallic nanoparticles," Chem. Phys. Lett. 399, 167 (2004).
[CrossRef]

I. Avrutsky, "Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain," Phys. Rev. B 70, 155416 (2004).
[CrossRef]

N. M. Lawandy, "Localized surface plasmon singularities in amplifying media," Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

2003 (2)

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

R. W. Ziolkowski and A. D. Kipple, "Application of double negative materials to increase the power radiated by electrically small antennas," IEEE Trans Antennas Propag. 51, 2626 (2003).
[CrossRef]

2002 (1)

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma and C. J. Humphreys, "Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms," J. Appl. Phys. 91, 367 (2002).
[CrossRef]

2001 (1)

J. B. Jackson and N. J. Halas, "Silver nanoshells: variations in morphologies and optical properties," J. Phys. Chem. B 105, 2743 (2001).
[CrossRef]

1999 (1)

R. D. Averitt, S. L. Westcott, and N. J Halas, "Linear optical properties of gold nanoshells," J. Opt. Soc. Am. B. 16, 1824 (1999).
[CrossRef]

1990 (1)

E. Desurvire, "Study of the complex atomic susceptibility of erbium-doped fiber amplifiers," J. Lightwave Technol. 8, 1517 (1990).
[CrossRef]

1982 (1)

M. Kerker and C. G. Blatchford, "Elastic scattering and absorption, and surface-enhanced Raman scattering by concentric spheres comprised of a metallic and dielectric region," Phys. Rev. B 26, 4052 (1982).
[CrossRef]

1972 (1)

P.B. Johnson and R.W. Christy, "Optical constants of the nobel metals," Phys. Rev. B 6,4370 (1972).
[CrossRef]

1968 (1)

V. G. Veselago, "The elctrodynamics of substances with simulataneously negative values of ε and μ," Sov. Phys. Uspekhi 10, 509 (1968).
[CrossRef]

1951 (1)

A. L. Aden and M. Kerker, "Scattering of electromagnetic waves from two concentric spheres," J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Adegoke, J.

Aden, A. L.

A. L. Aden and M. Kerker, "Scattering of electromagnetic waves from two concentric spheres," J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Alù, A.

A. Alù, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557 (2006).
[CrossRef] [PubMed]

A. Alù and N. Engheta, "Achieving transparency with plasmonic and metamaterials coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

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

Averitt, R. D.

R. D. Averitt, S. L. Westcott, and N. J Halas, "Linear optical properties of gold nanoshells," J. Opt. Soc. Am. B. 16, 1824 (1999).
[CrossRef]

Avrutsky, I.

I. Avrutsky, "Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain," Phys. Rev. B 70, 155416 (2004).
[CrossRef]

Bahoura, M.

Bergman, D. J.

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Blatchford, C. G.

M. Kerker and C. G. Blatchford, "Elastic scattering and absorption, and surface-enhanced Raman scattering by concentric spheres comprised of a metallic and dielectric region," Phys. Rev. B 26, 4052 (1982).
[CrossRef]

Christy, R.W.

P.B. Johnson and R.W. Christy, "Optical constants of the nobel metals," Phys. Rev. B 6,4370 (1972).
[CrossRef]

Chryssou, C. E.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma and C. J. Humphreys, "Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms," J. Appl. Phys. 91, 367 (2002).
[CrossRef]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006).
[CrossRef] [PubMed]

Desurvire, E.

E. Desurvire, "Study of the complex atomic susceptibility of erbium-doped fiber amplifiers," J. Lightwave Technol. 8, 1517 (1990).
[CrossRef]

Drachev, V. P.

Drezek, R. A.

A. W. H. Lin, N. J. Halas, and R. A. Drezek, "Optically tunable nanoparticle contrast agents for early cancer detection: model-based analysis of gold nanoshells," J. Biomed. Opt. 10, 064035 (2005)
[CrossRef]

Engheta, N.

A. Alù, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557 (2006).
[CrossRef] [PubMed]

A. Alù and N. Engheta, "Achieving transparency with plasmonic and metamaterials coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535 (2005).
[CrossRef]

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

Erentok, A.

R. W. Ziolkowski and A. Erentok, "Metamaterial-based efficient electrically small antennas," IEEE Trans Antennas Propag. 54, 2113 (2006).
[CrossRef]

A. Erentok and R. W. Ziolkowski, "A hybrid optimization method to analyze metamaterial-based electrically small antennas," IEEE Trans Antennas Propag. (to be published).

Gobin, A. M.

L. R. Hirsch and A. M. Gobin, "Metal nanoshells," Annals of Biomedical Engineering 34, 15 (2006).

Grady, N. K.

N. K. Grady, N. J. Halas, and P. Norlander, "Influence of dielectric function properties on the optical response of plasmonic resonant metallic nanoparticles," Chem. Phys. Lett. 399, 167 (2004).
[CrossRef]

Halas, N. J

R. D. Averitt, S. L. Westcott, and N. J Halas, "Linear optical properties of gold nanoshells," J. Opt. Soc. Am. B. 16, 1824 (1999).
[CrossRef]

Halas, N. J.

A. W. H. Lin, N. J. Halas, and R. A. Drezek, "Optically tunable nanoparticle contrast agents for early cancer detection: model-based analysis of gold nanoshells," J. Biomed. Opt. 10, 064035 (2005)
[CrossRef]

N. K. Grady, N. J. Halas, and P. Norlander, "Influence of dielectric function properties on the optical response of plasmonic resonant metallic nanoparticles," Chem. Phys. Lett. 399, 167 (2004).
[CrossRef]

J. B. Jackson and N. J. Halas, "Silver nanoshells: variations in morphologies and optical properties," J. Phys. Chem. B 105, 2743 (2001).
[CrossRef]

Hirsch, L. R.

L. R. Hirsch and A. M. Gobin, "Metal nanoshells," Annals of Biomedical Engineering 34, 15 (2006).

Hole, D. E.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma and C. J. Humphreys, "Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms," J. Appl. Phys. 91, 367 (2002).
[CrossRef]

Humphreys, C. J.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma and C. J. Humphreys, "Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms," J. Appl. Phys. 91, 367 (2002).
[CrossRef]

Jackson, J. B.

J. B. Jackson and N. J. Halas, "Silver nanoshells: variations in morphologies and optical properties," J. Phys. Chem. B 105, 2743 (2001).
[CrossRef]

Johnson, P.B.

P.B. Johnson and R.W. Christy, "Optical constants of the nobel metals," Phys. Rev. B 6,4370 (1972).
[CrossRef]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006).
[CrossRef] [PubMed]

Kenyon, A. J.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma and C. J. Humphreys, "Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms," J. Appl. Phys. 91, 367 (2002).
[CrossRef]

Kerker, M.

M. Kerker and C. G. Blatchford, "Elastic scattering and absorption, and surface-enhanced Raman scattering by concentric spheres comprised of a metallic and dielectric region," Phys. Rev. B 26, 4052 (1982).
[CrossRef]

A. L. Aden and M. Kerker, "Scattering of electromagnetic waves from two concentric spheres," J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Kipple, A. D.

R. W. Ziolkowski and A. D. Kipple, "Reciprocity between the effects of resonant scattering and enhanced radiated power by electrically small antennas in the presence of nested metamaterial shells," Phys. Rev. E 72, 036602 (2005).
[CrossRef]

R. W. Ziolkowski and A. D. Kipple, "Application of double negative materials to increase the power radiated by electrically small antennas," IEEE Trans Antennas Propag. 51, 2626 (2003).
[CrossRef]

Lawandy, N. M.

N. M. Lawandy, "Localized surface plasmon singularities in amplifying media," Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

Lin, A. W. H.

A. W. H. Lin, N. J. Halas, and R. A. Drezek, "Optically tunable nanoparticle contrast agents for early cancer detection: model-based analysis of gold nanoshells," J. Biomed. Opt. 10, 064035 (2005)
[CrossRef]

Milton, G. W.

G. W. Milton and N.-A. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London, Ser. A 462, 3027 (2006).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006).
[CrossRef] [PubMed]

Nicorovici, N.-A. P.

G. W. Milton and N.-A. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London, Ser. A 462, 3027 (2006).
[CrossRef]

Noginov, M. A.

Norlander, P.

N. K. Grady, N. J. Halas, and P. Norlander, "Influence of dielectric function properties on the optical response of plasmonic resonant metallic nanoparticles," Chem. Phys. Lett. 399, 167 (2004).
[CrossRef]

O’Reilly, E. P.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Okamoto, K.

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

Pitt, C. W.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma and C. J. Humphreys, "Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms," J. Appl. Phys. 91, 367 (2002).
[CrossRef]

Protsenko, I. E.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Ritzo, B. A.

Salandrino, A.

Samoilov, V. N.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Scherer, A.

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

Sharma, N.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma and C. J. Humphreys, "Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms," J. Appl. Phys. 91, 367 (2002).
[CrossRef]

Shimizu-Iwayama, T.

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma and C. J. Humphreys, "Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms," J. Appl. Phys. 91, 367 (2002).
[CrossRef]

Small, C. E.

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006).
[CrossRef] [PubMed]

Stockman, M. I.

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Uskov, A. V.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The elctrodynamics of substances with simulataneously negative values of ε and μ," Sov. Phys. Uspekhi 10, 509 (1968).
[CrossRef]

Vyawahare, S.

Westcott, S. L.

R. D. Averitt, S. L. Westcott, and N. J Halas, "Linear optical properties of gold nanoshells," J. Opt. Soc. Am. B. 16, 1824 (1999).
[CrossRef]

Zaimidoroga, O. A.

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Zhu, G.

Ziolkowski, R. W.

R. W. Ziolkowski and A. Erentok, "Metamaterial-based efficient electrically small antennas," IEEE Trans Antennas Propag. 54, 2113 (2006).
[CrossRef]

R. W. Ziolkowski and A. D. Kipple, "Reciprocity between the effects of resonant scattering and enhanced radiated power by electrically small antennas in the presence of nested metamaterial shells," Phys. Rev. E 72, 036602 (2005).
[CrossRef]

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535 (2005).
[CrossRef]

R. W. Ziolkowski and A. D. Kipple, "Application of double negative materials to increase the power radiated by electrically small antennas," IEEE Trans Antennas Propag. 51, 2626 (2003).
[CrossRef]

A. Erentok and R. W. Ziolkowski, "A hybrid optimization method to analyze metamaterial-based electrically small antennas," IEEE Trans Antennas Propag. (to be published).

Annals of Biomedical Engineering (1)

L. R. Hirsch and A. M. Gobin, "Metal nanoshells," Annals of Biomedical Engineering 34, 15 (2006).

Appl. Phys. Lett. (1)

N. M. Lawandy, "Localized surface plasmon singularities in amplifying media," Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

Chem. Phys. Lett. (1)

N. K. Grady, N. J. Halas, and P. Norlander, "Influence of dielectric function properties on the optical response of plasmonic resonant metallic nanoparticles," Chem. Phys. Lett. 399, 167 (2004).
[CrossRef]

IEEE Trans Antennas Propag. (3)

R. W. Ziolkowski and A. Erentok, "Metamaterial-based efficient electrically small antennas," IEEE Trans Antennas Propag. 54, 2113 (2006).
[CrossRef]

A. Erentok and R. W. Ziolkowski, "A hybrid optimization method to analyze metamaterial-based electrically small antennas," IEEE Trans Antennas Propag. (to be published).

R. W. Ziolkowski and A. D. Kipple, "Application of double negative materials to increase the power radiated by electrically small antennas," IEEE Trans Antennas Propag. 51, 2626 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535 (2005).
[CrossRef]

J. Appl. Phys. (3)

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

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[CrossRef]

A. J. Kenyon, C. E. Chryssou, C. W. Pitt, T. Shimizu-Iwayama, D. E. Hole, N. Sharma and C. J. Humphreys, "Luminescence from erbium-doped silicon nanocrystals in silica: Excitation mechanisms," J. Appl. Phys. 91, 367 (2002).
[CrossRef]

J. Biomed. Opt. (1)

A. W. H. Lin, N. J. Halas, and R. A. Drezek, "Optically tunable nanoparticle contrast agents for early cancer detection: model-based analysis of gold nanoshells," J. Biomed. Opt. 10, 064035 (2005)
[CrossRef]

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[CrossRef]

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J. Opt. Soc. Am. B. (1)

R. D. Averitt, S. L. Westcott, and N. J Halas, "Linear optical properties of gold nanoshells," J. Opt. Soc. Am. B. 16, 1824 (1999).
[CrossRef]

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J. B. Jackson and N. J. Halas, "Silver nanoshells: variations in morphologies and optical properties," J. Phys. Chem. B 105, 2743 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

I. E. Protsenko, A. V. Uskov, O. A. Zaimidoroga, V. N. Samoilov, and E. P. O’Reilly, "Dipole nanolaser," Phys. Rev. A 71, 063812 (2005).
[CrossRef]

Phys. Rev. B (3)

I. Avrutsky, "Surface plasmons at nanoscale relief gratings between a metal and a dielectric medium with optical gain," Phys. Rev. B 70, 155416 (2004).
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[CrossRef]

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R. W. Ziolkowski and A. D. Kipple, "Reciprocity between the effects of resonant scattering and enhanced radiated power by electrically small antennas in the presence of nested metamaterial shells," Phys. Rev. E 72, 036602 (2005).
[CrossRef]

A. Alù and N. Engheta, "Achieving transparency with plasmonic and metamaterials coatings," Phys. Rev. E 72, 016623 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

D. J. Bergman and M. I. Stockman, "Surface plasmon amplification by stimulated emission of radiation: Quantum generation of coherent surface plasmons in nanosystems," Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

G. W. Milton and N.-A. P. Nicorovici, "On the cloaking effects associated with anomalous localized resonance," Proc. R. Soc. London, Ser. A 462, 3027 (2006).
[CrossRef]

Science (3)

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977 (2006).
[CrossRef] [PubMed]

Ulf Leonhardt, "Optical conformal mapping," Science 312, 1777 (2006).
[PubMed]

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V. G. Veselago, "The elctrodynamics of substances with simulataneously negative values of ε and μ," Sov. Phys. Uspekhi 10, 509 (1968).
[CrossRef]

Other (8)

N. M. Lawandy, "Nano-particle plasmonics in active media," in Complex Mediums VI: Light and Complexity, edited by M. W. McCall, G. Dewar, and M. A. Noginov, Proc. SPIE 5924, 5924OG (2005).
[CrossRef]

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M. J. Weber, Handbook of Laser Wavelengths (CRC Press LLC, 1999).

E. Desurvire, Erbium Doped-fiber Amplifiers (John Wiley and Sons, New York, 1994).

R. W. Ziolkowski, "Metamaterial-based antennas: Research and developments," IEICE Trans. Electron. E89-C, 1267 (2006).
[CrossRef]

S. Arslanagic, R. W. Ziolkowski, and O. Breinbjerg, "Hertzian dipole excitation of higher order resonant modes in electrically small nested metamaterial shells: Source and scattering results," in Proceedings of the IV International Workshop on Electromagnetic Wave Scattering - EWS, (Gebze Institute of Technology, Gebze, Turkey, 2006) pp 8.9-8.14.

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

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Figures (23)

Fig. 1.
Fig. 1.

Dependence of the terms in the scattering coefficients as a function of the radii ratio for a Ag-SiO2 CNP, (a). TE coefficient, (b). TM coefficient, (c). TE coefficient denominator, and (d). TM coefficient denominator. In d) both lossless (red, solid curve) and lossy (blue, dashed curve) bulk Ag results are given.

Fig. 2.
Fig. 2.

Wavelength tunability of the TM resonance of the Ag-SiO2 CNP by varying the radii ratio.

Fig. 3.
Fig. 3.

Size dependence of the permittivity of gold.

Fig. 4.
Fig. 4.

Size dependence of the permittivity of silver.

Fig. 5.
Fig. 5.

The effects that different Au models have on the efficiencies for the Au-SiO2 passive CNPs are compared. Drude, bulk, and size dependent models of the Au are shown. (a) Comparison of the normalized efficiencies to show the location of the resonances, (b) Comparison of the unnormalized efficiencies to show the dominance of the Drude results, and (c) Comparison of the unnormalized bulk and size dependent efficiencies to show that the size dependent, i.e., the most physical nano-scale model, results produce the lowest level, largest bandwidth resonance.

Fig. 6.
Fig. 6.

The effects that different Ag models have on the efficiencies for the Ag-SiO2 passive CNPs are compared. Drude, bulk, and size dependent models of the Ag are shown. (a) Comparison of the normalized efficiencies to show the location of the resonances, (b) Comparison of the unnormalized efficiencies to show the dominance of the Drude results, and (c) Comparison of the unnormalized bulk and size dependent efficiencies to show that the size dependent, i.e., the most physical nano-scale model, results produce the lowest level, largest bandwidth resonance.

Fig. 7.
Fig. 7.

The real and imaginary parts of the rare-earth ion doped silica susceptibility, with the parameters em =5.8×104 cm -1 and abs =5.3×104 cm -1 as the pump power ratio, P, is varied.

Fig. 8.
Fig. 8.

Comparisons of the contributions of the scattering and absorption efficiencies demonstrate that the total efficiency in passive Au-SiO2 and Ag-SiO2 CNPs is dominated by the absorption.

Fig. 9.
Fig. 9.

Absorption efficiencies for the Au-SiO2 CNPs for several values of the loss/gain parameter k.

Fig. 10.
Fig. 10.

Scattering efficiency for the Au-SiO2 CNPs for several values of the loss/gain parameter k.

Fig. 11.
Fig. 11.

The absorption and scattering efficiencies for an Au-SiO2 CNP with k slightly beyond critical. The narrowing of the width of these efficiencies is immediately apparent.

Fig. 12.
Fig. 12.

Comparison of the optical gain constant values of (a) Au, and (b) Ag, that are required to overcome the passive CNP losses and to achieve the super-resonant state. Shown is the Log (base 10) of the absolute value of the total efficiency as a function of the optical gain parameter k.

Fig. 13.
Fig. 13.

Contour and surface plots of the scattering efficiency and the absorption efficiency as functions of n and k.

Fig. 14.
Fig. 14.

Energy stored in the active Au-SiO2 CNP as a function of the gain parameter k.

Fig. 15.
Fig. 15.

The total electric and magnetic field distributions in the near-field region of the CNP with an active-SiO2 core and an Au nano-shell for several values of the optical gain parameter k.

Fig. 16.
Fig. 16.

Plots of the near-field distribution of the field components Eθ and Hϕ for the CNP with an active-SiO2 core and an Au nano-shell show that the dipole contributions dominate their behavior.

Fig. 17.
Fig. 17.

A plot of the total stored energy in the Au-SiO2 CNP as a function of n and k.

Fig. 18.
Fig. 18.

Scattering and absorption efficiencies for the CNP with the Au shell and the rare-earth-SiO2 core for the pump power ratio P = 100.

Fig. 19.
Fig. 19.

Scattering and absorption efficiencies for the CNP with the Ag shell and the rare-earth-SiO2 core for various values of the pump power ratio P.

Fig. 20.
Fig. 20.

The normalized total efficiency as a function of the pump power ratio P for the Ag-SiO2 CNP having a rare-earth core.

Fig. 21.
Fig. 21.

The total stored energy in the Ag-SiO2 CNP with the rare-earth core as a function of the pump power ratio.

Fig. 22.
Fig. 22.

The total electric and magnetic field distributions in the near-field region of the CNP with a rare-earth-SiO2 core and an Ag nano-shell for several values of the pump power ratio P. Super resonance occurs at P = 4.6.

Fig. 23.
Fig. 23.

Plots of the near-field distribution of the field components Eθ and Hϕ for the CNP with a rare-earth-SiO2 core and an Ag nano-shell show that the dipole contributions dominate their behavior.

Tables (1)

Tables Icon

Table 1. Gold and Silver material model constants

Equations (34)

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P scat = Re { 1 2 S [ E s × H s * ] n̂dS }
P abs = Re { 1 2 S [ E tot × H tot * ] n̂dS }
σ scat = P scat I inc = 2 π β o 2 n ( 2 n + 1 ) ( a n 2 + b n 2 )
σ abs = P abs I inc = 2 π β o 2 n ( 2 n + 1 ) ( Re { a n } + a n 2 + Re { b n } + b n 2 )
σ ext = σ scat + σ abs
Q scat = σ scat πr 2 2
Q abs = σ abs πr 2 2
Q ext = Q scat + Q abs
[ M ] [ C ] = [ M TE 0 0 M TM ] [ A TE B TM ] = [ f TE f TM ] = [ F ]
a n TE = det [ TE ( f TE ) ] det [ M TE ]
b n TM = det [ TM ( f TM ) ] det [ M TM ]
ε ω R = ε Drude ω R + χ IntBand ( ω )
ε Drude ω R = 1 ω p 2 Γ ( R ) 2 + ω 2 + i Γ ( R ) 2 ω p 2 ω ( Γ ( R ) 2 + ω 2 )
Γ ( R ) = Γ + A V F R
ε = n 2 k 2 + i 2 kn
P H = ε 0 ( 1 + χ H ) E signal ε 0 n 2 E signal
P ion = ε 0 χ ion E signal
P T = P H + P ion
χ ion ( λ ) = χ ion ( λ ) ion ( λ )
χ T ( λ ) = χ H ( λ ) + χ ion ( λ )
χ ion ( λ ) = n λ 2 π [ σ e ( λ ) N ¯ 2 σ a ( λ ) N ¯ 1 ]
χ ion ( λ ) = n λ 2 π [ σ e ( λ ) N ¯ 2 σ a ( λ ) N ¯ 1 ]
N ¯ 1 = N 1 + P , N ¯ 2 = NP 1 + P
σ e ( λ ) = 1 π P . V . σ e ( ω ) ω ω
σ a ( λ ) = 1 π P . V . σ a ( λ ) ω ω
W E = ℜe { V [ 1 2 ω ( ωε ) ( E R 2 + E θ 2 + E ϕ 2 ) ] dV }
W H = ℜe { V [ 1 2 ω ( ωμ ) ( H R 2 + H θ 2 + H ϕ 2 ) ] dV }
W E Core = ℜe { ω ( ωε 1 ) πr 2 E 0 2 ( β 2 β * 2 ) n = 1 ( 2 n + 1 ) [ A 1 TECore Λ jj ( n ) ( βr ) + B 1 TMCore { ( n + 1 2 n + 1 ) Λ jj ( n 1 ) ( βr ) + ( n 2 n + 1 ) Λ jj ( n + 1 ) ( βr ) } ] β = β 1 r = r 1 }
W M Core = ℜe { ω ( ωμ 1 ) ε 1 2 μ 1 2 πr 2 E 0 2 ( β 2 β * 2 ) n = 1 ( 2 n + 1 ) [ B 1 TMCore Λ jj ( n ) ( βr ) + A 1 TECore { ( n + 1 2 n + 1 ) Λ jj ( n 1 ) ( βr ) + ( n 2 n + 1 ) Λ jj ( n + 1 ) ( βr ) } ] β = β 1 r = r 1 }
W E Shell = ℜe { ω ( ωε 2 ) πr 2 E 0 2 ( β 2 β * 2 ) n = 1 ( 2 n + 1 ) [ A 1 TEShell Λ jj ( n ) ( βr ) + A 2 TEShell Λ yy ( n ) ( βr ) + B 1 TMShell { ( n + 1 2 n + 1 ) Λ jj ( n 1 ) ( βr ) + ( n 2 n + 1 ) Λ jj ( n + 1 ) ( βr ) } + B 2 TMShell { ( n + 1 2 n + 1 ) Λ yy ( n 1 ) ( βr ) + ( n 2 n + 1 ) Λ yy ( n + 1 ) ( βr ) } + 2 Im { A 3 TEShell Λ jy ( n ) ( βr ) + B 3 TMShell { ( n + 1 2 n + 1 ) Λ jy ( n 1 ) ( βr ) + ( n 2 n + 1 ) Λ jy ( n + 1 ) ( βr ) } } ] β = β 2 r = r 1 β = β 2 r = r 2 }
W M Shell = ℜe { ω ( ωμ 2 ) ε 2 2 πr 2 E 0 2 μ 2 2 ( β 2 β * 2 ) n = 1 ( 2 n + 1 ) [ A 1 TEShell { ( n + 1 2 n + 1 ) Λ jj ( n 1 ) ( βr ) + ( n 2 n + 1 ) Λ jj ( n + 1 ) ( βr ) } + A 2 TEShell { ( n + 1 2 n + 1 ) Λ yy ( n 1 ) ( βr ) + ( n 2 n + 1 ) Λ yy ( n + 1 ) ( βr ) } + B 1 TMShell Λ jj ( n ) ( βr ) + B 2 TMShell Λ yy ( n ) ( βr ) + 2 Im { A 3 TEShell { ( n + 1 2 n + 1 ) Λ jy ( n 1 ) ( βr ) + ( n 2 n + 1 ) Λ jy ( n + 1 ) ( βr ) } + B 3 TMShell Λ jy ( n + 1 ) ( βr ) } ] β = β 2 r = r 2 β = β 2 r = r 2 }
Λ uv ( n ) ( βr ) = ( β * u n v * n 1 βu n 1 v * n )
Λ uv ( n + 1 ) ( βr ) = ( β * u n + 1 v * n βu n v * n + 1 )
Λ uv ( n 1 ) ( βr ) = ( β * u n 1 v * n 2 βu n 2 v * n 1 )

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