Abstract

Using the analytical description of channel plasmon polaritons (CPPs) developed recently [Opt. Lett. 34, 2039 (2009) ], we consider the adiabatic CPP nanofocusing in V grooves with linearly decreasing groove angles, deriving closed-form expressions for local field enhancements. Calculations at telecom wavelengths predict the possibility of reaching the intensity enhancements exceeding 1200 for realistic groove tapers cut into gold. Our conclusions are in good agreement with the results of previous investigations.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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2010 (1)

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

2009 (4)

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

E. Verhagen, M. Spasenović, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

H. Choi, D. F. P. Pile, S. Nam, G. Bartal, and X. Zhang, Opt. Express 17, 7519 (2009).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbesen, Nano Lett. 9, 1278 (2009).
[CrossRef] [PubMed]

2008 (2)

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

S. I. Bozhevolnyi and J. Jung, Opt. Express 16, 2676 (2008).
[CrossRef] [PubMed]

2007 (4)

M. Yan and M. Qiu, J. Opt. Soc. Am. B 24, 2333 (2007).
[CrossRef]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nano Lett. 7, 880 (2007).
[CrossRef] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, Nano Lett. 7, 2784 (2007).
[CrossRef] [PubMed]

K. Vernon, D. K. Gramotnev, and D. F. P. Pile, J. Appl. Phys. 101, 104312 (2007).
[CrossRef]

2006 (2)

2005 (1)

D. K. Gramotnev, J. Appl. Phys. 98, 104302 (2005).
[CrossRef]

2004 (1)

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

1997 (1)

K. V. Nerkararyan, Phys. Lett. A 237, 103 (1997).
[CrossRef]

Albrecht, M.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, Nano Lett. 7, 2784 (2007).
[CrossRef] [PubMed]

Andreani, L. C.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Bartal, G.

Bek, A.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Bozhevolnyi, S. I.

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

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbesen, Nano Lett. 9, 1278 (2009).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

S. I. Bozhevolnyi and J. Jung, Opt. Express 16, 2676 (2008).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nano Lett. 7, 880 (2007).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, Opt. Express 14, 9467 (2006).
[CrossRef] [PubMed]

E. Moreno, F. J. García-Vidal, S. G. Rodrigo, L. Martín-Moreno, and S. I. Bozhevolnyi, Opt. Lett. 31, 3447 (2006).
[CrossRef] [PubMed]

Candeloro, P.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Choi, H.

Das, G.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

De Angelis, F.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Devaux, E.

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbesen, Nano Lett. 9, 1278 (2009).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nano Lett. 7, 880 (2007).
[CrossRef] [PubMed]

Di Fabrizio, E.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Ebbesen, T. W.

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbesen, Nano Lett. 9, 1278 (2009).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nano Lett. 7, 880 (2007).
[CrossRef] [PubMed]

Elsaesser, T.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, Nano Lett. 7, 2784 (2007).
[CrossRef] [PubMed]

Galli, M.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

García-Vidal, F. J.

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbesen, Nano Lett. 9, 1278 (2009).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. García-Vidal, S. G. Rodrigo, L. Martín-Moreno, and S. I. Bozhevolnyi, Opt. Lett. 31, 3447 (2006).
[CrossRef] [PubMed]

Gramotnev, D. K.

K. Vernon, D. K. Gramotnev, and D. F. P. Pile, J. Appl. Phys. 101, 104312 (2007).
[CrossRef]

D. K. Gramotnev, J. Appl. Phys. 98, 104302 (2005).
[CrossRef]

Jung, J.

Kuipers, L.

E. Verhagen, M. Spasenović, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Laluet, J. -Y.

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nano Lett. 7, 880 (2007).
[CrossRef] [PubMed]

Lazzarino, M.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Liberale, C.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Lienau, C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, Nano Lett. 7, 2784 (2007).
[CrossRef] [PubMed]

Maksymov, I.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Martín-Moreno, L.

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbesen, Nano Lett. 9, 1278 (2009).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. García-Vidal, S. G. Rodrigo, L. Martín-Moreno, and S. I. Bozhevolnyi, Opt. Lett. 31, 3447 (2006).
[CrossRef] [PubMed]

Moreno, E.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. García-Vidal, S. G. Rodrigo, L. Martín-Moreno, and S. I. Bozhevolnyi, Opt. Lett. 31, 3447 (2006).
[CrossRef] [PubMed]

Nam, S.

Neacsu, C. C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, Nano Lett. 7, 2784 (2007).
[CrossRef] [PubMed]

Nerkararyan, K. V.

Palik, E. D.

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

Patrini, M.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Pile, D. F. P.

H. Choi, D. F. P. Pile, S. Nam, G. Bartal, and X. Zhang, Opt. Express 17, 7519 (2009).
[CrossRef] [PubMed]

K. Vernon, D. K. Gramotnev, and D. F. P. Pile, J. Appl. Phys. 101, 104312 (2007).
[CrossRef]

Polman, A.

E. Verhagen, M. Spasenović, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Qiu, M.

Raschke, M. B.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, Nano Lett. 7, 2784 (2007).
[CrossRef] [PubMed]

Rodrigo, S. G.

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbesen, Nano Lett. 9, 1278 (2009).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Moreno, F. J. García-Vidal, S. G. Rodrigo, L. Martín-Moreno, and S. I. Bozhevolnyi, Opt. Lett. 31, 3447 (2006).
[CrossRef] [PubMed]

Ropers, C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, Nano Lett. 7, 2784 (2007).
[CrossRef] [PubMed]

Spasenovic, M.

E. Verhagen, M. Spasenović, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Stockman, M. I.

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

Verhagen, E.

E. Verhagen, M. Spasenović, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Vernon, K.

K. Vernon, D. K. Gramotnev, and D. F. P. Pile, J. Appl. Phys. 101, 104312 (2007).
[CrossRef]

Volkov, V. S.

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbesen, Nano Lett. 9, 1278 (2009).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nano Lett. 7, 880 (2007).
[CrossRef] [PubMed]

Yan, M.

Zhang, X.

J. Appl. Phys. (2)

D. K. Gramotnev, J. Appl. Phys. 98, 104302 (2005).
[CrossRef]

K. Vernon, D. K. Gramotnev, and D. F. P. Pile, J. Appl. Phys. 101, 104312 (2007).
[CrossRef]

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

Nano Lett. (3)

V. S. Volkov, S. I. Bozhevolnyi, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nano Lett. 7, 880 (2007).
[CrossRef] [PubMed]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, Nano Lett. 7, 2784 (2007).
[CrossRef] [PubMed]

V. S. Volkov, S. I. Bozhevolnyi, S. G. Rodrigo, L. Martín-Moreno, F. J. García-Vidal, E. Devaux, and T. W. Ebbesen, Nano Lett. 9, 1278 (2009).
[CrossRef] [PubMed]

Nat. Nanotechnol. (1)

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, Nat. Nanotechnol. 5, 67 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Lett. A (1)

K. V. Nerkararyan, Phys. Lett. A 237, 103 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

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

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martín-Moreno, and F. J. García-Vidal, Phys. Rev. Lett. 100, 023901 (2008).
[CrossRef] [PubMed]

E. Verhagen, M. Spasenović, A. Polman, and L. Kuipers, Phys. Rev. Lett. 102, 203904 (2009).
[CrossRef] [PubMed]

Other (1)

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 tapered V-groove configuration.

Fig. 2
Fig. 2

Fundamental CPP mode field magnitude distributions calculated at the wavelength of 1550 nm for different groove angles: θ = ( a ) 30 ° , (b) 20 ° , (c) 15 ° , (d) 10 ° , and (e) 5 ° .

Fig. 3
Fig. 3

Field enhancement dependences calculated for relatively short tapers of different lengths and two light wavelengths using Eq. (3). Vertical dashed lines indicate the positions of taper terminations.

Equations (8)

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

E z ( x , y , | z | < w ( y ) 2 ) A ( x ) k | r | y θ ( x ) exp ( k | r | y θ ( x ) ) exp ( i 0 x β ( u ) d u ) ,
k = 2 π λ ε d ,     r = ε d ( ε d ε m ) ε m ,     β ( x ) = k 1 + ( r / θ ( x ) ) 2 ,
P ( x ) = 3 16 ω ε d ( k | r | ) 2 | A ( x ) | 2 θ ( x ) β ( x ) [ θ 2 ( x ) θ cr 2 ] exp ( γ ( x ) ) ,
β ( x ) = β ( x ) + i β ( x ) ,     ε m = ε m + i ε m ,    
θ cr = 2 3 ε d ε m ,     γ ( x ) = 2 0 x β ( u ) d u .
Γ ( x ) = | A ( x ) A ( 0 ) | 2 = θ ( x ) 2 + | r | 2 θ 0 2 + | r | 2 θ 0 2 ( θ 0 2 θ cr 2 ) θ ( x ) 2 ( θ ( x ) 2 θ cr 2 ) exp ( γ ( x ) ) ,
γ ( x ) = k ε m ε m L | r | θ 0 ln | θ 0 θ ( x ) | r | + | r | 2 + θ ( x ) 2 | r | + | r | 2 + θ 0 2 | .
Γ ( x ) θ 0 3 16 | r | 3 [ 2 | r | θ ( x ) ] 4 k ( ε m / ε m ) ( L | r | / θ 0 ) .

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