OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 2 — Jan. 24, 2005
  • pp: 636–647
« Show journal navigation

Fractal extensions of near-field aperture shapes for enhanced transmission and resolution

J. A. Matteo and L. Hesselink  »View Author Affiliations


Optics Express, Vol. 13, Issue 2, pp. 636-647 (2005)
http://dx.doi.org/10.1364/OPEX.13.000636


View Full Text Article

Acrobat PDF (351 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

1. Introduction

Illumination through sub-wavelength apertures in opaque films is one method for achieving resolution smaller than the diffraction limit [1

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

]. Many different methods have been used to overcome the rapid falloff of transmission with decreasing aperture size. Most of these methods rely either on engineering the shape of the aperture [2

2. X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano-apertures for near-field optical data storage,” Jpn. J. Appl. Phys. 41, 1632–5 (2001). [CrossRef]

5

5. K. Tanaka, M. Oumi, T. Niwa, S. Ichihara, Y. Mitsuoka, K. Nakajima, T. Ohkubo, H. Hosaka, and 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]

], or the spacing of an aperture array [6

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

,7

7. T. Thio, K.M. Pellerin, R.A. Linke, H.J. Lezec, and T.W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–4 (2001). [CrossRef]

]. Both methods are able to greatly enhance sub-wavelength transmission, but due to their distinctly different mechanisms for eliciting this effect, they naturally lend themselves to different types of practical application. Single sub-wavelength apertures have been shown to collect light from an area no larger than (λ)2, and therefore benefit from diffraction limited illumination [8

8. L. Sun and L. Hesselink, “Topology visualization of the optical power flow through a novel, C-shaped nano-aperture,” IEEE TCVG Conference, Austin TX 2004 (to be published).

]. Aperture arrays, on the other hand, require several wavelength-sized periods of structure in order to operate optimally [9

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

], and require a widely expanded incident beam. In many applications, diffraction limited illumination is not feasible. Conversely, many applications require high powers, so that illuminating an entire aperture array may be prohibitively inefficient. Therefore, a versatile structure, capable of collecting light from an area ranging from the diffraction limit out to several wavelengths would be a valuable asset in bridging the gap between single nano-apertures and aperture arrays. Fractals, by definition, are multifaceted structures that exhibit self-similarity in their geometric structure. Unlike Euclidean objects, they are defined by an iterative rule, rather than a formula [10

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

]. Each successive iteration of this rule introduces a new length scale which provides an additional degree of freedom in engineering resonant structures. The self-similar, multi-resonant features of fractal geometries have been exploited in designing microwave antennas with broadband behavior, large gain, and sub-wavelength size [11

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

,12

12. C. Puente, J. Romeu, R. Pous, X. Garcia, and F. Benitez, “Fractal multiband antenna based on the Sierpinski gasket,” Electron. Lett. 32, 1–2 (1996). [CrossRef]

]. They have also been used to make frequency selective surfaces with behavior analogous to photonic crystals, in a far more compact structure [13

13. J.P. Gianvittorio, J. Romeu, S. Blanch, and 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]

]. These results represent far-field microwave results, however, and do not address the issues of field confinement and enhancement which are of crucial importance in near-field optics. In the optical regime, random fractal aggregates of metal particles have been shown to produce the immense local fields needed for surface enhanced Raman spectroscopy (SERS) [14

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

]. This is verification that fractal structures are able to produce a strong confinement and enhancement of the optical near-field. Due to their random nature, however, these structures cannot be engineered to have precise spectral properties, nor can the location of the enhancement be accurately controlled. Interestingly, several of the different aperture shapes used to obtain enhanced transmission very closely resemble the first or second iterations in different families of fractals [2

2. X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano-apertures for near-field optical data storage,” Jpn. J. Appl. Phys. 41, 1632–5 (2001). [CrossRef]

,5

5. K. Tanaka, M. Oumi, T. Niwa, S. Ichihara, Y. Mitsuoka, K. Nakajima, T. Ohkubo, H. Hosaka, and 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]

,15

15. A. Moreau, G. Granet, F.I. Baida, and D. Van Labeke,”Light transmission by subwavelength square coaxial aperture arrays in metallic films,” Opt. Express 11, 1131–6 (2003). [CrossRef] [PubMed]

]. Figure 1 shows the first few iterations of the Hilbert, Purina, Sierpinski Triangle and Sierpinski Carpet fractal families, respectively.

Fig. 1. First three iterations of a). Hilbert Curve, b). Purina Fractal, c). Sierpinski Triangle, and d). Sierpinski Carpet.

In this letter, we present numerical studies demonstrating that the fractal’s ability to simultaneously exploit both shape and spacing can be used with nano-apertures to increase near-field resolution and enhance transmission. By carefully choosing the fractal family and iteration, as well as including the dispersive properties of metals at optical and infrared frequencies, it is possible to design a structure that combines both the efficient collection and spectral control exhibited in the microwave regime with the highly localized near-field distributions of the fractal aggregates, all into one compact structure. Many of these fractal aperture structures are capable of outperforming many of the conventional optical nano-aperture shapes.

2. FDTD results

2.1 Spectral analysis

Finite Difference Time Domain electromagnetic modeling is used to examine the spectral behavior and to map out the transmitted near field profiles of the higher iterations of these families of fractals. This method has proven to be a useful and accurate tool in designing and predicting the behavior of sub-wavelength metal structures [2

2. X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano-apertures for near-field optical data storage,” Jpn. J. Appl. Phys. 41, 1632–5 (2001). [CrossRef]

,16

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

]. In the case of spectral characterization, an aperture can be viewed as a resonant structure. Its resonance peak is the wavelength at which its transmission function is highest. For two apertures of the same size, the aperture with the longer resonance wavelength will have greater resolution potential, because, due to the scalability of Maxwell’s equations, its size can be reduced to have the same resonance wavelength as the other, albeit at a smaller physical size. An excellent example of this is the C-aperture which has been shown to greatly outperform a square aperture of the same area and a square aperture modeled to produce the same near-field spot size, because its resonant wavelength occurs at a much longer wavelength [16

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

]. In this study, the spectral transmission properties of the first three iterations of several families of fractals are modeled. An incident modulated Gaussian pulse with its spectral content spanning the visible and mid-IR wavelengths is used to probe the structures, and the Fourier transform of the time response of each aperture is used to calculate its spectral transmission properties or transmission efficiency function. For computational efficiency, this value is calculated as a running sum at discrete wavelengths as described in [17

17. 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]

], and averaged at several common probe locations throughout the transmission region. It is normalized to the cross-sectional area of the aperture and the spectral power distribution of the incident pulse.

T.E.(λ)=n=1nmaxPntrans(λ)A*Pinc(λ)
(1)

In each case, the minimum feature size of the aperture (d) is fixed at 140nm. These apertures are placed in an infinitesimally thin perfectly electrically conducting screen (PEC), in order to avoid probing thickness or material resonances. These effects are incorporated at a later stage of the design process and are addressed later in this paper. Figure 2 shows the results of these initial, broadband simulations. A notation is introduced here where (n,m) represents the mth order resonance of the nth fractal iteration.

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.

As the iteration number increases, two effects occur. First, a new resonance appears at a longer wavelength. Second, some of the resonances that exist for the earlier iterations become stronger or narrower (Δλ/λ). This allows the fractal structure to be of use in two regimes. In the case where the existing resonances are enhanced, the fractal structure can be used to increase transmission by collecting photons from a larger area. It is essentially a method of cascading similar apertures in an intelligent fashion in order to localize the fields to a central spot, while suppressing sidelobes. The degree to which this is achieved depends heavily on the fractal family that is chosen. This mode of operation is of particular interest where diffraction limited resolution is not possible, and one wants to collect the incident light in a more efficient manner. It is also feasible to operate at the new, higher order resonances that appear at longer wavelengths. These apertures can be rescaled to be resonant at a shorter wavelength, despite having a smaller physical size.

2.2 Near-field distribution

Simply decreasing the physical size of the aperture isn’t a sufficient condition for stating that it enhances near-field resolution. In order to quantitatively investigate the resolution of different aperture configurations, it is necessary to look at the transmitted near-field intensity patterns at resonance. Some of these families of fractals are very efficient in suppressing sidelobes, and are capable of producing a near field spot that is much smaller than the physical size of the aperture. Others, despite exhibiting enhanced transmission, distribute the transmitted light throughout the structure. Therefore, it is necessary to calculate the near-field distribution for each iteration, at each resonance order, to verify the confinement of the transmitted light. In order to make accurate comparisons of aperture performance, the apertures were rescaled to tune each of the resonances found in Fig. 2, to 1µm. This was achieved through an iterative process of narrowing the spectral range, increasing the resolution of the FDTD mesh, and introducing a finite 100nm film thickness. Once the dimensions are set, monochromatic excitation at 1µm is used to calculate the steady-state near-field distribution at a distance of d/2 away from the aperture, where d is the aperture’s minimum feature size. Figures 3(a) and 3(b) show the calculated near-field distribution for apertures modeled after the first two iterations of the Hilbert fractal at a distance of d/2 away from the metal surface. In each case the intensity gain was calculated at d/2, where d is the minimum feature size of the aperture. This distance was chosen because it marks the edge of the confined near-zone described by Leviatan, in which the fields remain largely collimated [18

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

,19

19. X.L. Shi and L. Hesselink, “0,” J. Opt. Soc. Am. B 21, 1305–17 (2004). [CrossRef]

]. Beyond this region the fields rapidly diverge. Note that the aperture in Fig. 3(b) is a symmetric version of the C-aperture which has been shown numerically and experimentally to provide five to six orders of magnitude enhancements in transmission over conventional square apertures [16

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

]. Figures 3(c) and 3(d) show the near-field distributions for the second and third order resonances of the third iteration Hilbert fractal aperture.

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. 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. 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)

PT=transSdAPinc*Aaperture
(2)

Due to the fact that the near-field spot sizes of these apertures can be much smaller than their overall physical size, a more appropriate figure of merit is that of intensity gain, defined as,

Igain=FWHME2dAEinc2*AFWHM
(3)

which is essentially the average intensity enhancement within the near-field spot (FWHM). Also, due to the varying field distributions of the different fractal families and resonances, quantitative comparison of spot sizes is not entirely straightforward. For this reason confinement factor is defined as a figure of merit describing spot size,

CF=λ12(XFWHM+YFWHM)
(4)

where XFWHM and YFWHM are the full width half maximum sizes of the near-field spot in the x and y directions respectively. Figure 6 shows a distribution plot of the intensity gain and confinement factor for some of the higher fractal aperture iterations.

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.

It can be seen from this graph that the Hilbert fractal family produces the highest intensity gain of the shapes studied (Igain=441), and the Purina Fractal produces the smallest near-field spot size (FWHM=λ/20.04). Although much far-field work has been done in the microwave regime based on the Sierpinski Carpet structure [13

13. J.P. Gianvittorio, J. Romeu, S. Blanch, and 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]

,21

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

], our studies show that this fractal family is not of particular use in the near-field. Its higher iterations are able to enhance transmission, but the structure is inefficient in suppressing side-lobes, and in all of the iterations and resonance orders investigated here, the intensity is widely distributed throughout the aperture. The solid line shown is the transmission value for conventional square apertures producing the same spot size as the fractal apertures. Comparing the two values shows the enhancement factor of the fractal aperture shapes which can reach 1011 at λ/20. Numerical models of a C-aperture have been reported which is able to achieve λ/10 resolution and a very large intensity gain of 138.5 [19

19. X.L. Shi and L. Hesselink, “0,” J. Opt. Soc. Am. B 21, 1305–17 (2004). [CrossRef]

]. It can be seen that this is a highly optimized version of the second order Hilbert curve, and similar methods can also be employed to further optimize the higher iteration fractal aperture shapes presented above.

2.3 Real metal analysis

Due to the broad treatment of the many different geometric resonances, and the dispersive behavior of metallic materials, the effects of metallic optical properties have been ignored until this point. A method has been presented for locating the multiple resonances of the fractal structures and determining their confinement capabilities. Once a proper fractal family and iteration has been chosen, as well as an operating wavelength, the optical properties of the metal must be taken into account in order to accurately determine the dimensions of the aperture and to assess the performance. A Drude model can be used to fit the complex permittivity function of a metal at optical and infrared frequencies. As a demonstration of this method, the second order, third iteration Hilbert fractal aperture (3,2) can be designed to be resonant for a 100nm thick Ag film at 1µm. A least squares fitting method has been used to fit the real and imaginary values of the permittivity function of Ag in the wavelength range of 750nm-1250nm to 0.2% error. The Drude parameters used are εinf=3.810, τc=8.96×10-15 s, and ωp=6.79×1015 rad/s for the long wavelength permittivity, relaxation time, and plasma frequency, respectively. An incident pulse simulation is first done to locate the new, shifted resonance of the aperture in the Ag film. The aperture is then rescaled accordingly, and a monochromatic illumination study is carried out. Figure 7 shows the near-field distribution at d/2 for this aperture in comparison with the ideal, lossless case.

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

The near-field distribution of the aperture in the silver film is quite similar to that of the PEC film, with a slightly higher background, and an approximately 50% lower intensity gain (31.3 vs. 61.6). This degradation in signal, however, is accompanied by a significant improvement in resolution (56.4nm×63.7nm vs. 83.8nm×101.4nm). This is due to the fact that incorporation of the optical constants of the silver film caused a red shift in the resonant wavelength of the aperture. This requires that the aperture must be made smaller in size than an aperture in a PEC film in order to be in resonance at 1µm. Also, note that since the size parameter d is reduced, so also is the distance at which these measurements are made (d/2). This example verifies that the non-idealities of real metals at optical and infrared frequencies can be taken into account to design a fractal aperture with high transmission for given experimental conditions.

3. Fractal choice

Numerous families of fractals exist, many of which can be used for enhanced near-field transmission. The fractal families studied here were chosen because they are well-known classical examples of fractals but they are by no means exhaustive. A family of fractals can be defined by a seed structure, and an iterative rule. Depending on the structure one starts with, and the rule one defines for successive iterations, widely varying structures can result. With so many options, it can be very difficult to choose which fractal family to use. Two properties are frequently used to describe a fractal’s geometry, which can be of use in choosing a fractal family. The first property used to describe fractals is fractal dimension defined as [22

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

],

D=log(N)log(S)
(5)

4. Conclusion

Fractal apertures provide two potential advantages over conventional near-field apertures. By increasing the resonance wavelength, while maintaining a small near-field spot size, these apertures are able to enhance resolution while being illuminated with diffraction limited beams. Also, by efficiently suppressing sidelobes, light can be collected from a larger area within the diffraction limited illumination beam and provide enhanced transmission into a more intense near-field spot. Depending on the application, the desired performance, and the fabrication limits, a proper fractal family and iteration number can be chosen. Apertures of low lacunarity are beneficial to use because they are able to tightly confine light in the near-field. Fractal based aperture shapes have been shown to produce near-field spot sizes smaller than λ/20, and enhancements of over 400 times the incident intensity. It is worth noting that these results represent preliminary results with classical fractal shapes. This class of structures introduces another degree of engineering freedom which allows for numerous methods of further optimization. With its ability to enhance transmission while confining light to sub-wavelength dimensions, the fractal aperture represents a new class of versatile, highly-efficient near-field probes with potential extensions and improvements on the use of nano-apertures for nano-lithography [23

23. L. Xiangang and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84, 4780–2 (2004). [CrossRef]

], data storage [5

5. K. Tanaka, M. Oumi, T. Niwa, S. Ichihara, Y. Mitsuoka, K. Nakajima, T. Ohkubo, H. Hosaka, and 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]

], and single molecule studies [24

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

].

Acknowledgments

The authors would like to acknowledge the Wallenberg Global Learning Network for their support of this research.

References and links

1.

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

2.

X. Shi and L. Hesselink, “Mechanisms for enhancing power throughput from planar nano-apertures for near-field optical data storage,” Jpn. J. Appl. Phys. 41, 1632–5 (2001). [CrossRef]

3.

X. Shi, L. Hesselink, and R. L. Thornton, “Ultrahigh light transmission through a C-shaped nanoaperture,” Opt. Lett. 28, 1320–22 (2003). [CrossRef] [PubMed]

4.

F. Demming, J. Jersch, S. Klein, and 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]

5.

K. Tanaka, M. Oumi, T. Niwa, S. Ichihara, Y. Mitsuoka, K. Nakajima, T. Ohkubo, H. Hosaka, and 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]

6.

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

7.

T. Thio, K.M. Pellerin, R.A. Linke, H.J. Lezec, and T.W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–4 (2001). [CrossRef]

8.

L. Sun and L. Hesselink, “Topology visualization of the optical power flow through a novel, C-shaped nano-aperture,” IEEE TCVG Conference, Austin TX 2004 (to be published).

9.

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

10.

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

11.

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

12.

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

13.

J.P. Gianvittorio, J. Romeu, S. Blanch, and 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]

14.

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

15.

A. Moreau, G. Granet, F.I. Baida, and D. Van Labeke,”Light transmission by subwavelength square coaxial aperture arrays in metallic films,” Opt. Express 11, 1131–6 (2003). [CrossRef] [PubMed]

16.

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

17.

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]

18.

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

19.

X.L. Shi and L. Hesselink, “0,” J. Opt. Soc. Am. B 21, 1305–17 (2004). [CrossRef]

20.

E.X. Jin and X.F. Xu, “Finite-difference time-domain studies on optical transmission through planar nano-apertures in a metal film,” Jpn. J. Appl. Phys. 43, 407–17 (2004). [CrossRef]

21.

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

22.

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

23.

L. Xiangang and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84, 4780–2 (2004). [CrossRef]

24.

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

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(350.5730) Other areas of optics : Resolution

ToC Category:
Research Papers

History
Original Manuscript: November 10, 2004
Revised Manuscript: January 6, 2005
Published: January 24, 2005

Citation
Joseph Matteo and L. Hesselink, "Fractal extensions of near-field aperture shapes for enhanced transmission and resolution," Opt. Express 13, 636-647 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-2-636


Sort:  Journal  |  Reset  

References

  1. H. A. Bethe, �??Theory of diffraction by small holes,�?? Phys. Rev. 66, 163 (1944). [CrossRef]
  2. 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]
  3. X. Shi, L. Hesselink, and R. L. Thornton, �??Ultrahigh light transmission through a C-shaped nanoaperture,�?? Opt. Lett. 28, 1320-22 (2003). [CrossRef] [PubMed]
  4. 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]
  5. 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]
  6. 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]
  7. T. Thio, K.M. Pellerin, R.A. Linke, H.J. Lezec, T.W. Ebbesen, �??Enhanced light transmission through a single subwavelength aperture,�?? Opt. Lett. 26, 1972-4 (2001). [CrossRef]
  8. 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).
  9. 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]
  10. K.J. Falconer, Fractal Geometry: Mathematical Foundations and Applications (Wiley, Chichester, 2003).
  11. 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]
  12. 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]
  13. 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]
  14. V.M. Shalaev, Optical properties of nanostructured random media (Springer, New York, 2001).
  15. A. Moreau, G. Granet, F.I. Baida ,D. Van Labeke,�??Light transmission by subwavelength square coaxial aperture arrays in metallic films,�?? Opt. Express 11, 1131-6 (2003). [CrossRef] [PubMed]
  16. 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]
  17. 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]
  18. Y. Leviatan, �??Study of near-zone fields of a small aperture,�?? J. of Appl. Phys. 60, 1577-83 (1986). [CrossRef]
  19. X.L. Shi, L. Hesselink, �??Design of a C aperture to achieve lambda /10 resolution and resonant transmission,�?? J. Opt. Soc. Am. B 21, 1305-17 (2004). [CrossRef]
  20. 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]
  21. D. H. Werner, S. Ganguly, �??An overview of fractal antenna engineering research,�?? IEEE Antennas and Propagation Magazine 45, 38-57 (2003). [CrossRef]
  22. D.H. Werner, R. Mittra, Frontiers in Electromagnetics (IEEE Press, New York, 2000).
  23. L. Xiangang, T. Ishihara, �??Surface plasmon resonant interference nanolithography technique,�?? Appl. Phys. Lett. 84, 4780-2 (2004). [CrossRef]
  24. 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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material


» Media 1: AVI (2354 KB)     
» Media 2: AVI (2172 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited