Abstract

Using the effective-index approximation we show that touching spherical metal surfaces form a broadband omnidirectional absorber of gap surface plasmons (GSP), concentrating all GSP waves travelling within a certain radius at the point of contact (at which the field intensity tends to infinity even in the presence of metal absorption) and representing thereby a two-dimensional analogue of an optical black-hole realized without use of meta materials. The developed wave analysis is supplemented with the geometrical optics (adiabatic) description providing explicit expressions for the critical radius (radius of the event horizon) and buildup of field enhancement along ray trajectories.

© 2011 Optical Society of America

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  1. D. A. Genov, S. Zhang, and X. Zhang, Nat. Phys. 5, 687 (2009).
    [CrossRef]
  2. E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
    [CrossRef]
  3. Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
    [CrossRef]
  4. D. A. Genov, Nat. Photon. 5, 76 (2011).
    [CrossRef]
  5. D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
    [CrossRef]
  6. I. I. Smolyaninov, New J. Phys. 5, 147 (2003).
    [CrossRef]
  7. A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 105, 266807 (2010).
    [CrossRef]
  8. S. I. Bozhevolnyi and K. V. Nerkararyan, Opt. Lett. 34, 2039 (2009).
    [CrossRef] [PubMed]
  9. L. D. Landau and E. M. Lifshitz, Quantum Mechanics(Elsevier Science, 2004).
  10. M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
    [CrossRef] [PubMed]
  11. M. Born and E. Wolf, Principles of Optics (Cambridge, 1999).
  12. E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

2011 (1)

D. A. Genov, Nat. Photon. 5, 76 (2011).
[CrossRef]

2010 (3)

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 105, 266807 (2010).
[CrossRef]

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

2009 (3)

S. I. Bozhevolnyi and K. V. Nerkararyan, Opt. Lett. 34, 2039 (2009).
[CrossRef] [PubMed]

D. A. Genov, S. Zhang, and X. Zhang, Nat. Phys. 5, 687 (2009).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

2004 (1)

M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

2003 (1)

I. I. Smolyaninov, New J. Phys. 5, 147 (2003).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge, 1999).

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

S. I. Bozhevolnyi and K. V. Nerkararyan, Opt. Lett. 34, 2039 (2009).
[CrossRef] [PubMed]

Cai, B. G.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Cheng, Q.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Cui, T. J.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Fernández-Domínguez, A. I.

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 105, 266807 (2010).
[CrossRef]

Genov, D. A.

D. A. Genov, Nat. Photon. 5, 76 (2011).
[CrossRef]

D. A. Genov, S. Zhang, and X. Zhang, Nat. Phys. 5, 687 (2009).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

Jiang, W. X.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Kildishev, A. V.

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics(Elsevier Science, 2004).

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics(Elsevier Science, 2004).

Maier, S. A.

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 105, 266807 (2010).
[CrossRef]

Narimanov, E. E.

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Nerkararyan, K. V.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

Pendry, J. B.

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 105, 266807 (2010).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov, New J. Phys. 5, 147 (2003).
[CrossRef]

Stockman, M. I.

M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge, 1999).

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, Nat. Phys. 5, 687 (2009).
[CrossRef]

Zhang, X.

D. A. Genov, S. Zhang, and X. Zhang, Nat. Phys. 5, 687 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

E. E. Narimanov and A. V. Kildishev, Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Nat. Photon. (2)

D. A. Genov, Nat. Photon. 5, 76 (2011).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

Nat. Phys. (1)

D. A. Genov, S. Zhang, and X. Zhang, Nat. Phys. 5, 687 (2009).
[CrossRef]

New J. Phys. (2)

I. I. Smolyaninov, New J. Phys. 5, 147 (2003).
[CrossRef]

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, New J. Phys. 12, 063006 (2010).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

M. I. Stockman, Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

A. I. Fernández-Domínguez, S. A. Maier, and J. B. Pendry, Phys. Rev. Lett. 105, 266807 (2010).
[CrossRef]

Other (3)

L. D. Landau and E. M. Lifshitz, Quantum Mechanics(Elsevier Science, 2004).

M. Born and E. Wolf, Principles of Optics (Cambridge, 1999).

E. D. Palik, Handbook of Optical Constants of Solids(Academic, 1985).

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Figures (3)

Fig. 1
Fig. 1

Geometry of the considered configuration formed by touching metal spheres embedded in dielectric, with ε m and ε d being their respective susceptibilities.

Fig. 2
Fig. 2

GSP ray trajectories: (a) the polar system of coordinates along with the distance b of ray launch from outside the contact area and (b) ray trajectories calculated for a 100 μm -radius gold sphere in contact with a plane surface and the light wavelength of 800 nm using tabular gold constants [12].

Fig. 3
Fig. 3

The critical launch distance and upper limit for the sphere radius versus the wavelength for gold surfaces.

Equations (13)

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2 E z ρ 2 + 1 ρ E z ρ + 1 ρ 2 2 E z φ 2 + 2 E z z 2 + ε d ( m ) k 0 2 E z = 0 ,
E z ( ρ , φ , z ) = F ( ρ ) Z ( z , ρ ) e i n φ ; n = 0 , ± 1 , ± 2 , ... .
2 Z z 2 + [ ε d ( m ) k 0 2 q 2 ( ρ ) ] Z = 0 ,
2 F ρ 2 + 1 ρ F ρ n 2 ρ 2 F + q 2 ( ρ ) F = 0 .
q 2 ( ρ ) k 2 + 2 k r w ( ρ ) k 2 + 4 k r R ρ 2 ; k = k 0 ε d , r = ε d ( ε d ε m ) ε m .
ξ 2 2 F ξ 2 + ξ F ξ + ( ξ 2 ( i μ n ) 2 ) F = 0 ; ξ = k ρ , μ n 2 = 4 k r R n 2 > 0 .
E z n ( ξ , φ ) ξ 1 exp [ i ( n φ + μ n ) ln ξ ] ; ξ 2 μ n 2 ,
q ( ρ ) ρ ( φ ) sin α = γ ,
d ρ d φ = ρ b ρ 2 + 4 r R k b 2 ,
ρ ( φ ) = { β / sinh ( β φ b ) , b < b cr , β = b cr 2 b 2 β / sin ( β φ b ) , b > b cr , β = b 2 b cr 2 ,
δ = 1 q 2 | d q d s | 1 ,
Γ ( φ > φ 0 ) φ 0 φ exp { ( 3 β b k b cr 2 ε 2 b ε ) · ( φ φ 0 ) } ,
6 b cr 2 b 2 k b cr 2 > ε ε .

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