Abstract

Using the N-order finite-difference time-domain (FDTD) method, we show that optical resonances of the bowtie nanoaperture (BNA) are due to the combination of a guided mode inside the aperture and Fabry–Perot modes along the metal thickness. The resonance of lower energy, which leads to the well-known light confinement in the gap zone, occurs at the cutoff wavelength of the fundamental guided mode. No plasmon resonance is directly involved in the generation of the light hot spot. We also define a straightforward relationship between the resonance wavelengths of the BNA and its geometrical parameters. This brings a simple tool for the optimization of the BNA design.

© 2010 Optical Society of America

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  1. T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkeland, and V. Sandogdhar, Phys. Rev. Lett. 95, 200801(2005).
    [CrossRef] [PubMed]
  2. D. P. Fromm, A. Sundaramurthy, P. J. Schuk, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
    [CrossRef]
  3. K. Sendur and W. Challener, J. Microsc. 210, 279 (2003).
    [CrossRef] [PubMed]
  4. E. X. Jin and X. Xu, Appl. Phys. Lett. 86, 111106 (2005).
    [CrossRef]
  5. E. X. Jin and X. Xu, Appl. Phys. B 84, 3 (2006).
    [CrossRef]
  6. L. Wang and X. Xu, J. Microsc. 229, 483 (2008).
    [CrossRef] [PubMed]
  7. R. Guo, E. C. Kinzel, Y. Li, S. M. Uppuluri, A. Raman, and X. Xu, Opt. Express 18, 4961 (2010).
    [CrossRef] [PubMed]
  8. H. Guo, T. P. Meyrath, T. Zentgraf, N. Liu, L. Fu, H. Schweizer, and H. Giessen, Opt. Express 16, 7756 (2008).
    [CrossRef] [PubMed]
  9. F. I. Baida, D. V. Labeke, G. Granet, A. Moreau, and A. Belkhir, Appl. Phys. B 79, 1 (2004).
    [CrossRef]
  10. F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, Phys. Rev. B 74, 205419 (2006).
    [CrossRef]

2010 (1)

2008 (2)

2006 (2)

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, Phys. Rev. B 74, 205419 (2006).
[CrossRef]

E. X. Jin and X. Xu, Appl. Phys. B 84, 3 (2006).
[CrossRef]

2005 (2)

E. X. Jin and X. Xu, Appl. Phys. Lett. 86, 111106 (2005).
[CrossRef]

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkeland, and V. Sandogdhar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

2004 (2)

D. P. Fromm, A. Sundaramurthy, P. J. Schuk, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

F. I. Baida, D. V. Labeke, G. Granet, A. Moreau, and A. Belkhir, Appl. Phys. B 79, 1 (2004).
[CrossRef]

2003 (1)

K. Sendur and W. Challener, J. Microsc. 210, 279 (2003).
[CrossRef] [PubMed]

Baida, F. I.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, Phys. Rev. B 74, 205419 (2006).
[CrossRef]

F. I. Baida, D. V. Labeke, G. Granet, A. Moreau, and A. Belkhir, Appl. Phys. B 79, 1 (2004).
[CrossRef]

Belkhir, A.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, Phys. Rev. B 74, 205419 (2006).
[CrossRef]

F. I. Baida, D. V. Labeke, G. Granet, A. Moreau, and A. Belkhir, Appl. Phys. B 79, 1 (2004).
[CrossRef]

Burger, S.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkeland, and V. Sandogdhar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Challener, W.

K. Sendur and W. Challener, J. Microsc. 210, 279 (2003).
[CrossRef] [PubMed]

Fromm, D. P.

D. P. Fromm, A. Sundaramurthy, P. J. Schuk, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Fu, L.

Giessen, H.

Granet, G.

F. I. Baida, D. V. Labeke, G. Granet, A. Moreau, and A. Belkhir, Appl. Phys. B 79, 1 (2004).
[CrossRef]

Guo, H.

Guo, R.

Hakanson, U.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkeland, and V. Sandogdhar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Henkeland, C.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkeland, and V. Sandogdhar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Jin, E. X.

E. X. Jin and X. Xu, Appl. Phys. B 84, 3 (2006).
[CrossRef]

E. X. Jin and X. Xu, Appl. Phys. Lett. 86, 111106 (2005).
[CrossRef]

Kalkbrenner, T.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkeland, and V. Sandogdhar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Kino, G.

D. P. Fromm, A. Sundaramurthy, P. J. Schuk, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Kinzel, E. C.

Labeke, D. V.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, Phys. Rev. B 74, 205419 (2006).
[CrossRef]

F. I. Baida, D. V. Labeke, G. Granet, A. Moreau, and A. Belkhir, Appl. Phys. B 79, 1 (2004).
[CrossRef]

Lamrous, O.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Li, Y.

Liu, N.

Meyrath, T. P.

Moerner, W. E.

D. P. Fromm, A. Sundaramurthy, P. J. Schuk, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Moreau, A.

F. I. Baida, D. V. Labeke, G. Granet, A. Moreau, and A. Belkhir, Appl. Phys. B 79, 1 (2004).
[CrossRef]

Raman, A.

Sandogdhar, V.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkeland, and V. Sandogdhar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Schadle, A.

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkeland, and V. Sandogdhar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

Schuk, P. J.

D. P. Fromm, A. Sundaramurthy, P. J. Schuk, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Schweizer, H.

Sendur, K.

K. Sendur and W. Challener, J. Microsc. 210, 279 (2003).
[CrossRef] [PubMed]

Sundaramurthy, A.

D. P. Fromm, A. Sundaramurthy, P. J. Schuk, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Uppuluri, S. M.

Wang, L.

L. Wang and X. Xu, J. Microsc. 229, 483 (2008).
[CrossRef] [PubMed]

Xu, X.

R. Guo, E. C. Kinzel, Y. Li, S. M. Uppuluri, A. Raman, and X. Xu, Opt. Express 18, 4961 (2010).
[CrossRef] [PubMed]

L. Wang and X. Xu, J. Microsc. 229, 483 (2008).
[CrossRef] [PubMed]

E. X. Jin and X. Xu, Appl. Phys. B 84, 3 (2006).
[CrossRef]

E. X. Jin and X. Xu, Appl. Phys. Lett. 86, 111106 (2005).
[CrossRef]

Zentgraf, T.

Appl. Phys. B (2)

E. X. Jin and X. Xu, Appl. Phys. B 84, 3 (2006).
[CrossRef]

F. I. Baida, D. V. Labeke, G. Granet, A. Moreau, and A. Belkhir, Appl. Phys. B 79, 1 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

E. X. Jin and X. Xu, Appl. Phys. Lett. 86, 111106 (2005).
[CrossRef]

J. Microsc. (2)

K. Sendur and W. Challener, J. Microsc. 210, 279 (2003).
[CrossRef] [PubMed]

L. Wang and X. Xu, J. Microsc. 229, 483 (2008).
[CrossRef] [PubMed]

Nano Lett. (1)

D. P. Fromm, A. Sundaramurthy, P. J. Schuk, G. Kino, and W. E. Moerner, Nano Lett. 4, 957 (2004).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (1)

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Phys. Rev. Lett. (1)

T. Kalkbrenner, U. Hakanson, A. Schadle, S. Burger, C. Henkeland, and V. Sandogdhar, Phys. Rev. Lett. 95, 200801(2005).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Scheme of the BNA. The BNA geometrical parameter dimensions are defined by the lateral size D, the gap size G, the bow angle θ, and the metal thickness h.

Fig. 2
Fig. 2

Normalized electric-field intensity spectrum calculated (3D-FDTD simulations) in the near field at 5 nm beyond the gap. We set D = 275 nm , θ = 45 o , G = 55 nm , and h = 800 nm .

Fig. 3
Fig. 3

Transmission spectrum ( | E | ) of the BNA as a function of the metal-layer thickness obtained through homemade 3D-FDTD code ( D = 275 nm , θ = 45 o , G = 55 nm , and h varies from 100 to 770 nm ).

Fig. 4
Fig. 4

Spectral density of the infinitely long bowtie waveguide made in gold with the same geometrical parameters of Fig. 2. Insets, intensity distributions ( | E | 0.8 ) of the two first modes.

Fig. 5
Fig. 5

Intensity distributions ( | E | 0.4 ) in the transversal plane x z : (a) λ = 1311 nm , (b) λ = 918 nm , and (c) λ = 580 nm corresponding to the FP 0 , FP 2 , and FP 4 peaks of Fig. 2, respectively.

Fig. 6
Fig. 6

Cutoff wavelength of the fundamental mode (a) as a function of G and (b) as a function of the natural logarithm of G, when D = 305 nm . (c) Cutoff wavelength of the fundamental mode as a function of D when G is fixed to 55 nm . The dashed curves in (b) and (c) correspond to Eq. (1) with parameters given in Table 1.

Tables (1)

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Table 1 Parameters of Eq. (1) for the Five Metals

Equations (1)

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λ c ( G , D ) = α D + β ln ( G ) + δ D ln ( G ) + γ ,

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