Abstract

For periodically corrugated nanowire cross sections, such that the polar-angle dependence of the radius is r=r0[1+uNcos(Nφ)], we calculate both the resonant values of metal permittivity ε and the corresponding plasmonic eigenfunctions. For sufficiently small perturbation amplitudes, NuN1, these fundamental characteristics admit full-scale analytical analysis revealing nontrivial plasmonic properties. For NuN>1, the analytical analysis is supplemented by numerical simulations; they show nonlinearly growing redshifts of the main plasmonic resonances with increasing modulation periodicity N and the amplitude uN.

© 2012 Optical Society of America

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  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]
  2. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
    [CrossRef]
  3. R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
    [CrossRef]
  4. 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, 193–204 (2010).
    [CrossRef]
  5. N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10, 631–636 (2011).
    [CrossRef]
  6. R. Jin, Y. W. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng, “Photoinduced conversion of silver nanospheres to nanoprisms,” Science 294, 1901–1903 (2001).
    [CrossRef]
  7. V. Klimov, Nanoplasmonics (Pan Stanford, 2011).
  8. L. Nolvotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2007).
  9. J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
    [CrossRef]
  10. J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
    [CrossRef]
  11. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11, 735–745 (2003).
    [CrossRef]
  12. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
    [CrossRef]
  13. I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107, 6269–6275 (2003).
    [CrossRef]
  14. S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
    [CrossRef]
  15. G. Laurent, N. Felidj, J. Aubard, and G. Levi, “Evidence of multipolar excitations in surface enhanced Raman scattering,” Phys. Rev. B 71, 045430 (2005).
    [CrossRef]
  16. F. Ouyang and M. Isaacson, “Surface plasmon excitation of objects with arbitrary shape and dielectric constant,” Philos. Mag. B 60, 481–492 (1989).
    [CrossRef]
  17. I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72, 155412 (2005).
    [CrossRef]
  18. The importance of the curvature parameter comes from fact that a number of general judgements of [17] about the ε spectrum refer to convex particles, i.e., to κ>0.
  19. L. D. Landau and E. M. Lifshits, Quantum Mechanics(Pergamon, 1977), Chap. 12.
  20. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
    [CrossRef]
  21. P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today 2(1), 18–29 (2007).
    [CrossRef]

2011

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10, 631–636 (2011).
[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, 193–204 (2010).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

2009

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

2007

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today 2(1), 18–29 (2007).
[CrossRef]

2006

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

2005

G. Laurent, N. Felidj, J. Aubard, and G. Levi, “Evidence of multipolar excitations in surface enhanced Raman scattering,” Phys. Rev. B 71, 045430 (2005).
[CrossRef]

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72, 155412 (2005).
[CrossRef]

2003

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11, 735–745 (2003).
[CrossRef]

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107, 6269–6275 (2003).
[CrossRef]

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]

2001

R. Jin, Y. W. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng, “Photoinduced conversion of silver nanospheres to nanoprisms,” Science 294, 1901–1903 (2001).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

1989

F. Ouyang and M. Isaacson, “Surface plasmon excitation of objects with arbitrary shape and dielectric constant,” Philos. Mag. B 60, 481–492 (1989).
[CrossRef]

Alivisatos, A. P.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10, 631–636 (2011).
[CrossRef]

Andrews, S. R.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Aubard, J.

G. Laurent, N. Felidj, J. Aubard, and G. Levi, “Evidence of multipolar excitations in surface enhanced Raman scattering,” Phys. Rev. B 71, 045430 (2005).
[CrossRef]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[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, 193–204 (2010).
[CrossRef]

Barrera, R. G.

I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107, 6269–6275 (2003).
[CrossRef]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

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]

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, 193–204 (2010).
[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, 193–204 (2010).
[CrossRef]

Cao, Y. W.

R. Jin, Y. W. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng, “Photoinduced conversion of silver nanospheres to nanoprisms,” Science 294, 1901–1903 (2001).
[CrossRef]

Coronado, E.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

El-Sayed, I. H.

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today 2(1), 18–29 (2007).
[CrossRef]

El-Sayed, M. A.

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today 2(1), 18–29 (2007).
[CrossRef]

Felidj, N.

G. Laurent, N. Felidj, J. Aubard, and G. Levi, “Evidence of multipolar excitations in surface enhanced Raman scattering,” Phys. Rev. B 71, 045430 (2005).
[CrossRef]

Fredkin, D. R.

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72, 155412 (2005).
[CrossRef]

Garcia-Vidal, F. J.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

Giessen, H.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10, 631–636 (2011).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Hecht, B.

L. Nolvotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2007).

Hentschel, M.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10, 631–636 (2011).
[CrossRef]

Herz, E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Isaacson, M.

F. Ouyang and M. Isaacson, “Surface plasmon excitation of objects with arbitrary shape and dielectric constant,” Philos. Mag. B 60, 481–492 (1989).
[CrossRef]

Jain, P. K.

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Au nanoparticles target cancer,” Nano Today 2(1), 18–29 (2007).
[CrossRef]

Jin, R.

R. Jin, Y. W. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng, “Photoinduced conversion of silver nanospheres to nanoprisms,” Science 294, 1901–1903 (2001).
[CrossRef]

Jun, Y. C.

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, 193–204 (2010).
[CrossRef]

Kelly, K. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

R. Jin, Y. W. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng, “Photoinduced conversion of silver nanospheres to nanoprisms,” Science 294, 1901–1903 (2001).
[CrossRef]

Klimov, V.

V. Klimov, Nanoplasmonics (Pan Stanford, 2011).

Kottmann, J. P.

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshits, Quantum Mechanics(Pergamon, 1977), Chap. 12.

Laurent, G.

G. Laurent, N. Felidj, J. Aubard, and G. Levi, “Evidence of multipolar excitations in surface enhanced Raman scattering,” Phys. Rev. B 71, 045430 (2005).
[CrossRef]

Levi, G.

G. Laurent, N. Felidj, J. Aubard, and G. Levi, “Evidence of multipolar excitations in surface enhanced Raman scattering,” Phys. Rev. B 71, 045430 (2005).
[CrossRef]

Lifshits, E. M.

L. D. Landau and E. M. Lifshits, Quantum Mechanics(Pergamon, 1977), Chap. 12.

Liu, N.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10, 631–636 (2011).
[CrossRef]

Ma, R. M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Maier, S. A.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

Martin, O. J. F.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

J. P. Kottmann and O. J. F. Martin, “Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires,” Appl. Phys. B 73, 299–304 (2001).
[CrossRef]

Martin-Moreno, L.

S. A. Maier, S. R. Andrews, L. Martin-Moreno, and F. J. Garcia-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97, 176805 (2006).
[CrossRef]

Mayergoyz, I. D.

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72, 155412 (2005).
[CrossRef]

Mirkin, C. A.

R. Jin, Y. W. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng, “Photoinduced conversion of silver nanospheres to nanoprisms,” Science 294, 1901–1903 (2001).
[CrossRef]

Narimanov, E. E.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Noginov, M. A.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Noguez, C.

I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107, 6269–6275 (2003).
[CrossRef]

Nolvotny, L.

L. Nolvotny and B. Hecht, Principles of Nano-Optics(Cambridge University, 2007).

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Ouyang, F.

F. Ouyang and M. Isaacson, “Surface plasmon excitation of objects with arbitrary shape and dielectric constant,” Philos. Mag. B 60, 481–492 (1989).
[CrossRef]

Podolskiy, V. A.

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef]

Sarychev, A. K.

Schatz, G. C.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

R. Jin, Y. W. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng, “Photoinduced conversion of silver nanospheres to nanoprisms,” Science 294, 1901–1903 (2001).
[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, 193–204 (2010).
[CrossRef]

Schultz, S.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

Shalaev, V. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11, 735–745 (2003).
[CrossRef]

Smith, D. R.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, “Plasmon resonances of silver nanowires with a nonregular cross section,” Phys. Rev. B 64, 235402 (2001).
[CrossRef]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Sosa, I. O.

I. O. Sosa, C. Noguez, and R. G. Barrera, “Optical properties of metal nanoparticles with arbitrary shapes,” J. Phys. Chem. B 107, 6269–6275 (2003).
[CrossRef]

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]

Stout, S.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Suteewong, T.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Tang, M. L.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nat. Mater. 10, 631–636 (2011).
[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, 193–204 (2010).
[CrossRef]

Wiesner, U.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Zhang, X.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
[CrossRef]

Zhang, Z.

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72, 155412 (2005).
[CrossRef]

Zhao, L. L.

K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003).
[CrossRef]

Zheng, J. G.

R. Jin, Y. W. Cao, C. A. Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng, “Photoinduced conversion of silver nanospheres to nanoprisms,” Science 294, 1901–1903 (2001).
[CrossRef]

Zhu, G.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[CrossRef]

Appl. Phys. B

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Figures (5)

Fig. 1.
Fig. 1.

Three harmonically corrugated cross sections corresponding to Eq. (1): (a) N=2 and u2=0.1, (b) N=5 and u5=0.1, and (c) N=10 and u10=0.4. The dotted lines show the nonperturbed circular shape. Figure 1(a) illustrates additionally the introduction of the polar coordinate system.

Fig. 2.
Fig. 2.

Three representative polar diagrams for the above specified functions σj±(φ) (arbitrary units): (a) even dipole function σ1+ for N=3; (b) odd dipole function σ1+ for N=3; and (c) even quadrupole function σ2+ for N=4. The dotted lines show the cross section shape for N=3, u3=0.1 [Figs. 2(a) and 2(b)] and N=4, u4=0.4 [Fig. 2(c). The signs “+” and “” indicate the charges of the petals.

Fig. 3.
Fig. 3.

Six lowest branches of ε(uN) for N=10. Five of them, with j=1 to 5, show initial linear decrease, while the last (dashed) branch shows a quadratic behavior for u100. The branch 1 is dipolar one. The open circles in the inset show the dependence ε(NuN) for the lowest branch 5 and NuN1.5, and the straight dotted line is the prediction of the perturbation theory.

Fig. 4.
Fig. 4.

Dependences εN/2(uN) and ε1(uN) for N=4, 10, and 20. The open circles are numerical data and the dashed lines are quadratic fits.

Fig. 5.
Fig. 5.

Dependences σN/2(φ) for N=10: line 1 corresponds to the perturbation theory, and lines 2 and 3 are calculated numerically for uN=0.2 and 0.7, respectively.

Equations (13)

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r=r0[1+uNcos(Nφ)],
LK(r,r)σ(r)dl=Λσ(r),r,rL,
K(r,r)=n·(rr)π(rr)2
02πK(φ,φ)σ(φ)dφ=Λσ(φ),
K(φ,φ)=r2rrcosψrφrsinψπ(r2+r22rrcosψ),
K=uuuφsinψ2π(1cosψ).
K=uNπ{cos[φ+(N1)φ]+2cos[2φ+(N2)φ]++(N1)cos[(N1)φ+φ]+N2cos(Nφ)}.
σ=m=1N1amcos(mφ).
uNaN1=Λa12uNaN2=Λa2=(N2)uNa2=ΛaN2(N1)uNa1=ΛaN1.
Λj±=±uNj(Nj)aNj=±(Nj)/jaj.
σj±(φ)=cos(jφ)±(Nj)/jcos[(Nj)φ].
ΛN/2=NuN/2,σN/2=cos(Nφ/2),
τj±(φ)=cos(jφ)±j/(Nj)cos[(Nj)φ],

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