Abstract

Using the effective-index approximation along with the explicit expression for the propagation constant of gap surface plasmons established recently [Opt. Express 16, 2676 (2008) ], we derive closed-form expressions for channel plasmon polariton (CPP) modes supported by V grooves cut into metal. The CPP field distributions and mode characteristics are calculated for the air–gold configuration. The results obtained are found to be in good agreement with the results of previous numerical simulations.

© 2009 Optical Society of America

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References

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2009 (1)

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 (1)

2007 (2)

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]

2006 (3)

2005 (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

2004 (1)

D. K. Gramotnev and D. F. P. Pile, Appl. Phys. Lett. 85, 6323 (2004).
[CrossRef]

2002 (1)

I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
[CrossRef]

1977 (1)

1974 (1)

1969 (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Bozhevolnyi, S. I.

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]

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, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[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]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Burns, W. K.

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]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

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]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Economou, E. N.

E. N. Economou, Phys. Rev. 182, 539 (1969).
[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, F. J. García-Vidal, S. G. Rodrigo, L. Martín-Moreno, and S. I. Bozhevolnyi, Opt. Lett. 31, 3447 (2006).
[CrossRef] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev and D. F. P. Pile, Appl. Phys. Lett. 85, 6323 (2004).
[CrossRef]

Hocker, G. B.

Jung, J.

Kogelnik, H.

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]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Maradudin, A. A.

I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
[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, F. J. García-Vidal, S. G. Rodrigo, L. Martín-Moreno, and S. I. Bozhevolnyi, Opt. Lett. 31, 3447 (2006).
[CrossRef] [PubMed]

Merzbacher, E.

E. Merzbacher, Quantum Mechanics (Wiley, 1998).

Moreno, E.

Novikov, I. V.

I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
[CrossRef]

Palik, E. D.

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

Pile, D. F. P.

D. K. Gramotnev and D. F. P. Pile, Appl. Phys. Lett. 85, 6323 (2004).
[CrossRef]

Qiu, M.

Ramaswamy, V.

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

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]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Yan, M.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. K. Gramotnev and D. F. P. Pile, Appl. Phys. Lett. 85, 6323 (2004).
[CrossRef]

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

Nano Lett. (2)

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

Nature (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen, Nature 440, 508 (2006).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (1)

E. N. Economou, Phys. Rev. 182, 539 (1969).
[CrossRef]

Phys. Rev. B (1)

I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).
[CrossRef]

Phys. Rev. Lett. (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, Phys. Rev. Lett. 95, 046802 (2005).
[CrossRef] [PubMed]

Other (3)

E. Merzbacher, Quantum Mechanics (Wiley, 1998).

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

Plasmonic Nanoguides and Circuits, S.I.Bozhevolnyi, ed. (Pan Stanford, 2008).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic of the V-groove configuration under consideration. (b) CPP mode depth profiles for the first three modes calculated using Eq. (7).

Fig. 2
Fig. 2

(a)–(c) Fundamental and (d) second CPP mode field magnitude distributions calculated for different groove angles: (a),(c),(d) θ = 25 ° and (b) 35°, and wavelengths: (a),(b) λ = 1.55 1.55 and (c),(d) 1.033 μ m . All panels have a lateral size of 6 μ m .

Fig. 3
Fig. 3

Fundamental CPP mode depth profiles calculated with the FEM for two waveguide configurations having the same waveguide parameter V cpp = 1.34 π [14] and the depth profile given by Eq. (7).

Equations (9)

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Δ E z + ε d ( m ) k 0 2 E z = 0     with     k 0 = ω c = 2 π λ ,
E z ( x , y , z ) = Y ( y ) Z ( y , z ) exp ( i β x ) ,
2 Z z 2 + [ ε d ( m ) k 0 2 q 2 ( y ) ] Z = 0 ,
2 Y y 2 + [ q 2 ( y ) β 2 ] Y = 0 ,
q 2 ( y ) k 2 + 2 k r w ( y ) ,     k = k 0 ε d ,     r = ε d ( ε d ε m ) ε m ,
d 2 Y d y 2 + [ 2 k r θ y + k 2 β 2 ] Y = 0.
β n = k 1 + [ r θ ( n + 1 ) ] 2 ,     n = 0 , 1 , 2 , ,
Y n ( y ) = exp [ k | r | y θ ( n + 1 ) ] ν = 0 n α ν y ν + 1 ,     with     α ν + 1 = 2 α ν k | r | θ ( ν n ) ( ν + 1 ) ( ν + 2 ) ( n + 1 ) ,
V cpp = 4 π d ε d | ε d ε m | λ θ | ε m | > 2 2 .

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