Abstract

A practical technique by which a strongly confined and strongly enhanced optical near-field can be created on a metallic probe-tip is investigated. The technique uses an I-shaped aperture in a pyramidal structure formed on a thick metallic screen. The pyramidal structure divided into two sections by the I-shaped aperture and one of them is used as a tapered metallic probe. A surface plasmon polariton (SPP), which is excited and enhanced in the I-shaped aperture, propagates along the side surface of the aperture and pyramidal structure and illuminate the probe-tip. Scattering of optical waves by this structure is solved numerically using a volume integral equation by a generalized minimum residual method and fast Fourier transformation. It is shown that a strongly localized and strongly enhanced optical field is created at the tip of this metallic probe by SPPs. The fundamental characteristics of the localized and enhanced optical near-field on the probe-tip are investigated.

© 2006 Optical Society of America

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References

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Appl. Phys. Lett.

H. F. Frey, F. Keilmann, A. Kriele, and R. Guckenberger, "Enhancing the resolution of scanning near-field optical microscopy by a metal tip grown on an aperture probe," Appl. Phys. Lett. 81, 5030-5032 (2002).
[CrossRef]

K. Tanaka and M. Tanaka, "Simulation of nanometric optical circuits based on surface plasmon polariton gap waveguide," Appl. Phys. Lett. 82, 1158-1160 (2003).
[CrossRef]

K. Tanaka, M. Tanaka and T. Sugiyama, "Metallic tip-probe providing high intensity and small spot size with a small background light in near-field optics," Appl. Phys. Lett. 87, 151116 (2005).
[CrossRef]

F. Zenhausern, M. P. O'Boyle, and H. K. Wickramasinghe, "Apertureless near-field optical microscope," Appl. Phys. Lett. 65, 1623-1625 (1994).
[CrossRef]

O. J. F. Martin, and C. Girard, "Controlling and tuning strong optical field gradients at a local probe microscope tip apex," Appl. Phys. Lett. 70, 705-707 (1997).
[CrossRef]

IEEE Trans on MTT

P. Zwamborn and P. M. van den Berg, "The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems," IEEE Trans on MTT 40, 1757-1766 (1992).
[CrossRef]

J. Appl. Phys.

K. Tanaka and M. Tanaka, "Simulation of confined and enhanced optical near-fields for an I-shaped aperture in a pyramidal structure on a thick metallic screen," J. Appl. Phys. 95, 3765-3771 (2004).
[CrossRef]

J. Microsc.

E. Oesterschulze, G. Georgiev, M. Muller-Weigand, A. Vollkopf, and O. Rudow, "Transmission line probe based on a bow-tie antenna," J. Microsc. 202, 39-44 (2001).
[CrossRef] [PubMed]

K. Tanaka and M. Tanaka, "Simulation of an aperture in the thick metallic screen that gives high intensity and small spot size using surface plasmon polariton," J. Microsc. 210, 294-300 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Opt. Comm.

K. Tanaka and M. Tanaka, "Optimized computer-aided design of I-shaped subwavelength aperture for high intensity and small spot size," Opt. Comm. 233, 231-244 (2004).
[CrossRef]

Opt. Commun.

O. Rudow, A. Vollkopf, M. Muller-Weigand, G. Georgiev and E. Oesterschulze, "Theoretical investigation of a coaxial probe concept for scanning near-field microscopy," Opt. Commun. 189, 187-192 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

L. Novotony, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

A. Naber, D. Molenda, U. C. Fischer, H.-J. Maas, C. Höppener, N. Lu, and H. Fuchs, "Enhanced light confinement in a near-field optical probe with a triangular aperture," Phys. Rev. Lett. 89, 210801- 210804 (2002).
[CrossRef] [PubMed]

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

Science

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Carcia-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Other

D. W. Pohl and D. Courjon, eds., Near-Field Optics (Kluwer Academic, Dordrecht; Boston, 1993).

M. Ohtsu and H. Hori, Near-Field Nano-Optics (Kluwer Academic/Plenum Publishers, New York, 1999).
[CrossRef]

S. Kawata, M. Ohtsu, and M. Irie, eds., Nano-Optics (Springer, Tokyo, 2002).

R. Barrett, T. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the solution of linear systems: building blocks for iterative methods (SIAM, New York, 1994).
[CrossRef]

E. K. Miller, L. Medgyesi-Mitschnag and E. H. Newsman, ed., Computational electromagnetics frequency-domain method of moments (IEEE Press, New York, 1992).

G. S. Smith, An introduction to classical electromagnetic radiation (Cambridge University New York, 1997).

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Figures (11)

Fig. 1.
Fig. 1.

Geometry of the problem.

Fig. 2.
Fig. 2.

Two-dimensional optical intensity distributions on the (a) y-z and (b) x-z planes. The positions of the planes are shown by the broken lines in the upper insets. The intensity scale-range normalized by the incident intensity is 0 - 80. (λ=573 nm, ε1= -12.4 - j0.85).

Fig. 3.
Fig. 3.

Two-dimensional optical intensity distributions just above the probe-tip on planes parallel to the x-y plane and placed at positions (a) k 0 z=k 0 w + k 0 h + 0.05 and (b) k 0 z=k 0 w + k 0 h + 0.15. The intensity scale-range normalized by the incident intensity is 0-1000. (λ=573 nm, ε1= -12.4 - j0.85).

Fig. 4.
Fig. 4.

Two-dimensional intensity distributions of the (a) x-component, (b) y-component, and (c) z-component of the total electric field just above the probe-tip on plane parallel to the x-y plane placed at k 0 z = k 0 w + k 0 h + 0.05. The normalized intensity scale-range is 0-1000. (λ=573 nm, ε1= -12.4 - j0.85).

Fig. 5.
Fig. 5.

Two-dimensional optical intensity distributions on the (a) y-z and (b) x-z planes. The positions of the planes are shown by the broken lines in the upper insets. The normalized intensity scale-range is 0 - 80 in (a) and (b). (c) Two-dimensional optical intensity distribution just above probe-tip on plane parallel to the x-y plane and placed at a position k 0 z = k 0 w + k 0 h + 0.05. The normalized intensity scale-range is 0-1000 in (c). (λ=573 nm, ε1= -12.4 - j0.85).

Fig. 6.
Fig. 6.

Two-dimensional optical intensity distributions on the (a) y-z and (b) x-z planes. The positions of the planes are shown by the broken lines in the upper insets. The normalized intensity scale-range is 0-80 in (a) and (b). (c) Two-dimensional optical intensity distribution just above probe-tip on plane parallel to the x-y plane and placed at a position k 0 z=k 0 w + k 0 h + 0.05. The normalized intensity scale-range is 0-1000 in (c). (λ=573 nm, ε1= -12.4 - j0.85).

Fig. 7.
Fig. 7.

Two-dimensional optical intensity distributions on the (a) y-z and (b) x-z planes. The positions of the planes are shown by the broken lines in the upper insets. The normalized intensity scale-range is 0-40 in (a) and (b). (c) Two-dimensional optical intensity distribution just above probe-tip on plane parallel to the x-y plane and placed at a position k 0 z=k 0 w + k 0 h + 0.05. The normalized intensity scale-range is 0-1000 in (c). (λ=573 nm, ε1= -12.4 - j0.85).

Fig. 8.
Fig. 8.

Two-dimensional optical intensity distributions on the (a) y-z and (b) x-z planes. The positions of the planes are shown by the broken lines in the upper insets. The normalized intensity scale-range is 0-80 in (a) and (b). (c) Two-dimensional optical intensity distribution just above probe-tip on plane parallel to the x-y plane and placed at a position k 0 z=k 0 w + k 0 h + 0.05. The normalized intensity scale-range is 0-1000 in (c). (λ=488 nm, ε1= -34.5 - j8.5).

Fig. 9.
Fig. 9.

Two-dimensional optical intensity distributions on the (a) y-z and (b) x-z planes. The positions of the planes are shown by the broken lines in the upper insets. The normalized intensity scale-range is 0-12 in (a) and (b). (c) Two-dimensional optical intensity distribution just above probe-tip on plane parallel to the x-y plane and placed at a position k 0 z=k 0 w + k 0 h + 0.05. The normalized intensity scale-range is 0-30 in (c). (λ=1300 nm, ε1= -7.2-j20.5).

Fig. 10.
Fig. 10.

Cross section of the screen and pyramidal structure on the x-z plane used (a) in Figs. 2–9, and (b) that used in Fig. 11.

Fig. 11.
Fig. 11.

Two-dimensional optical intensity distributions on the (a) y-z and (b) x-z planes. The positions of the planes are shown by the broken lines in the upper insets. The normalized intensity scale-range is 0-80 in (a) and (b). (c) Two-dimensional optical intensity distribution just above probe-tip on plane parallel to the x-y plane and placed at a position k 0 z=k 0 w + k 0 h + 0.05. The normalized intensity scale-range is 0-1000 in (c). (λ=573 nm, ε1= -12.4 - j0.85).

Equations (7)

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E i ( x ) = D ( x ) ε r ( x ) ( k 0 2 + ) A ( x )
A ( x ) = ( 1 ε 0 ) V [ ( ε r ( x ' ) ε 0 ) ε r ( x ' ) ] G ( x x ' ) D ( x ' ) dv '
G ( x x ' ) = exp ( j k 0 x x ' ) ( 4 π x x ' ) .
E i ( x ) = E 0 W 0 W ( z ) exp [ ( z ) ] { i x + i z j [ 1 + γ 2 ( z ) ] 1 2 γ ( x ) exp [ ( z ) ] }
× exp [ ( x 2 + y 2 ) W 2 ( z ) ] exp { j k 0 ( x 2 + y 2 ) [ 2 R ( z ) ] } } exp ( j k 0 z ) ,
W ( z ) = W 0 [ 1 + γ 2 ( z ) ] 1 2 , ψ ( z ) = Tan 1 γ ( z ) , R ( z ) = z [ 1 + 1 γ 2 ( z ) ] ,
γ ( z ) = 2 z ( k 0 W 0 2 ) , γ ( x ) = 2 x ( k 0 W 0 2 ) ,

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