Abstract

Families of fractals are investigated as near-field aperture shapes. They are shown to have multiple transmission resonances associated with their multiple length scales. The higher iterations exhibit enhanced transmission, and spatial resolution exceeding the first order. Near-field enhancements of greater than 400 times the incident intensity and resolutions of better than λ/20 have been shown with apertures modeled after third iteration prefractals. Enhancements as large as 1011 have been shown, when compared with conventional square apertures that produce the same spot size. The effects of the complex permittivity values of the metal film are also addressed.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett. (2)

J.A. Matteo, D.P. Fromm, Y. Yuen, P.J. Schuck, W.E. Moerner, L. Hesselink, �??Spectral analysis of strongly enhanced visible light transmission through single C-shaped nanoapertures,�?? Appl. Phys. Lett. 26, 648-50 (2004).
[CrossRef]

L. Xiangang, T. Ishihara, �??Surface plasmon resonant interference nanolithography technique,�?? Appl. Phys. Lett. 84, 4780-2 (2004).
[CrossRef]

Electron. Lett. (1)

C. Puente, J. Romeu, R. Pous, X. Garcia, F. Benitez, �??Fractal multiband antenna based on the Sierpinski gasket,�?? Electron. Lett. 32, 1-2 (1996).
[CrossRef]

IEEE Antennas and Propagation Magazine (2)

D. H. Werner, S. Ganguly, �??An overview of fractal antenna engineering research,�?? IEEE Antennas and Propagation Magazine 45, 38-57 (2003).
[CrossRef]

C.M. Furse, �??Faster than Fourier - ultra-efficient time-to-frequency domain conversions for FDTD,�?? IEEE Antennas and Propagation Magazine 42, 24-34 (2000).
[CrossRef]

IEEE Trans. on Antennas and Propagation (1)

J.P. Gianvittorio, J. Romeu, S. Blanch, Y. Rahmat-Samii, �??Self-similar prefractal frequency selective surfaces for multiband and dual-polarized applications,�?? IEEE Trans. on Antennas and Propagation 51, 3088-96 (2003).
[CrossRef]

J. of Appl. Phys. (1)

Y. Leviatan, �??Study of near-zone fields of a small aperture,�?? J. of Appl. Phys. 60, 1577-83 (1986).
[CrossRef]

J. of Microsc. (1)

F. Demming, J. Jersch, S. Klein, K. Dickman, �??Coaxial scanning near-field optical microscope tips: an alternative for conventional tips with high transmission efficiency?,�?? J. of Microsc. 201, 383-7 (2001).
[CrossRef]

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

Jpn. J. Appl. Phys. (3)

X. Shi, L. Hesselink, �??Mechanisms for enhancing power throughput from planar nano-apertures for nearfield optical data storage,�?? Jpn. J. Appl. Phys. 41, 1632-5 (2001).
[CrossRef]

K. Tanaka, M. Oumi, T. Niwa, S. Ichihara, Y. Mitsuoka, K. Nakajima, T. Ohkubo, H. Hosaka, K. Itao, �??High spatial resolution and throughput potential of an optical head with a triangular aperture for nearfield optical data storage,�?? Jpn. J. Appl. Phys. 42, 1113-17 (2003).
[CrossRef]

E.X. Jin, X.F. Xu, �??Finite-difference time-domain studies on optical transmission through planar nanoapertures in a metal film,�?? Jpn. J. Appl. Phys. 43, 407-17 (2004).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

K. J. Vinoy, K.A. Jose, K. K. Varadan, V. V. Varadan, �??Hilbert curve fractal antenna: a small resonant antenna for VHF/UHF applications,�?? Microwave Opt. Technol. Lett. 29, 215-19 (2001).
[CrossRef]

Nature (2)

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, �??Extraordinary optical transmission through sub-wavelength hole arrays,�?? Nature 391, 667-9 (1998).
[CrossRef]

J. K. Trautman, J. J. Macklin, L. E. Brus, E. Betzig, �??Near-field spectroscopy of single molecules a at room temperature,�?? Nature 369, 40-2 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. (1)

H. A. Bethe, �??Theory of diffraction by small holes,�?? Phys. Rev. 66, 163 (1944).
[CrossRef]

Phys. Rev. Lett. (1)

F.J. Garcia-Vidal, H.J. Lezec, T.W. Ebbesen, L. Martin-Moreno, �??Multiple paths to enhance optical transmission through a single subwavelength slit ,�?? Phys. Rev. Lett. 90, 213901 (2003).
[CrossRef] [PubMed]

Other (4)

K.J. Falconer, Fractal Geometry: Mathematical Foundations and Applications (Wiley, Chichester, 2003).

L. Sun, L. Hesselink, �??Topology visualization of the optical power flow through a novel, C-shaped nanoaperture,�?? IEEE TCVG Conference, Austin TX 2004 (to be published).

V.M. Shalaev, Optical properties of nanostructured random media (Springer, New York, 2001).

D.H. Werner, R. Mittra, Frontiers in Electromagnetics (IEEE Press, New York, 2000).

Supplementary Material (2)

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» Media 2: AVI (2172 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

First three iterations of a). Hilbert Curve, b). Purina Fractal, c). Sierpinski Triangle, and d). Sierpinski Carpet.

Fig. 2.
Fig. 2.

Caculated broadband spectral transmission efficiency of apertures modeled after the first three iterations of a). Hilbert Curve b). Purina Fractal, and c.) Sierpinski Carpet.

Fig. 3.
Fig. 3.

Calculated electric field distributions of the first three iterations of the Hilbert fractal family at their resonant wavelengths. The second (c.) and third (d.) order resonance of the third iteration fractal aperture is shown.

Fig. 4.
Fig. 4.

Animation of the transverse power flow at the input face of the second order resonance of the third iteration Hilbert fractal (3,2). The minimum feature size (d) is set to 54nm, and the wavelength is 1µm. Pseudocolor plot is of the relative intensity for unit input, and the vector flow diagram is of the in plane power flow (Sx,Sy). (2.29MB)

Fig. 5.
Fig. 5.

Animation of the transverse power flow at the input face of the third order resonance of the third iteration Hilbert fractal (3,3). The minimum feature size (d) is set to 18.5nm, and the wavelength is 1µm. Pseudocolor plot is of the relative intensity for unit input, and the vector flow diagram is of the in plane power flow (Sx,Sy). (2.12MB)

Fig. 6.
Fig. 6.

Distribution of Igain and confinement factor values for apertures modeled after the second and third iterations of the Purina Fractal (diamonds), Sierpinski Carpet (squares), and Hilbert Curve(triangles). Square apertures (black line) providing the same spot size are shown for comparison.

Fig. 7.
Fig. 7.

Near-field intensity distribution at resonance for the Hilbert (3,2) aperture in a). 100nm thick Ag film, and b). 100nm thick PEC film

Equations (5)

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T . E . ( λ ) = n = 1 n max P n trans ( λ ) A * P inc ( λ )
PT = trans S dA P inc * A aperture
I gain = FWHM E 2 dA E inc 2 * A FWHM
CF = λ 1 2 ( X FWHM + Y FWHM )
D = log ( N ) log ( S )

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