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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 6 — Mar. 15, 2010
  • pp: 5854–5860
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Polarization dependence and independence of near-field enhancement through a subwavelength circle hole

Zu-Bin Li, Wen-Yuan Zhou, Xiang-Tian Kong, and Jian-Guo Tian  »View Author Affiliations


Optics Express, Vol. 18, Issue 6, pp. 5854-5860 (2010)
http://dx.doi.org/10.1364/OE.18.005854


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Abstract

By setting a metal rod or tooth-type structures in a single subwavelength hole, its near-field can be strongly enhanced. The near-field enhancement has strong polarization dependence when the structure in hole is twofold symmetric. Only the polarization along the longitudinal side of the metal rod or tooth-type structure can lead to strongest enhancement, which is attributed to the resonance of the localized surface plasmon. However, if the structure in hole is fourfold symmetric, the near-field enhancement is free from the polarization.

© 2010 OSA

It is generally known that light transmission through a subwavelength aperture is very poor according to the diffraction theory [1

1. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944). [CrossRef]

]. This diffraction limits the manipulation and the applications of light at the subwavelength scale, such as the near-field optical scanning microscope, optical imaging and optical storage. In 1998, T. W. Ebbesen et al reported the enhanced transmission (ET) through subwavelength hole arrays [2

2. 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(6668), 667–669 (1998). [CrossRef]

]. By the periodic structure of hole arrays, the surface plasmon is resonant with the incident light, which leads to the ET at certain wavelengths. After then, ET through a single aperture was found if it was surrounded by period structures, such as dimples or grooves [3

3. D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen, “Beyond the Bethe Limit: Tunable enhanced light transmission through a single sub-wavelength aperture,” Adv. Mater. 11(10), 860–862 (1999). [CrossRef]

5

5. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]

]. These findings attracted a lot of interests and many new results were reported about the ET. Some applications were designed according to these works and ET brought a lot of exciting results in other research fields. However, these structures are difficult to fabricate and this may be disadvantageous for the application of ET.

Recently, some works on H-shaped (or I-shaped) aperture [6

6. E. X. Jin and X. Xu, “Finitte-Difference Time-Domain studies on optical transmission through planar nano-apertures in a metal film,” Jpn. J. Appl. Phys. 43(1), 407–417 (2004). [CrossRef]

10

10. 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(15), 151116 (2005). [CrossRef]

] and bowtie aperture [11

11. E. X. Jin and X. Xu, “Enhanced optical near field from a bowtie aperture,” Appl. Phys. Lett. 88(15), 153110 (2006). [CrossRef]

14

14. H. Guo, T. P. Meyrath, T. Zentgraf, N. Liu, L. Fu, H. Schweizer, and H. Giessen, “Optical resonances of bowtie slot antennas and their geometry and material dependence,” Opt. Express 16(11), 7756–7766 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-7756. [CrossRef] [PubMed]

] reported higher near-field enhancement and smaller light spot than normal hole, which are very useful to enhance the near-field resolution and have been applied in near field imaging [15

15. K. Tanaka, M. Tanaka, and K. Katayama, “Simulation of near-field scanning optical microscopy using a plasmonic gap probe,” Opt. Express 14(22), 10603–10613 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-22-10603. [CrossRef] [PubMed]

17

17. N. Murphy-DuBay, L. Wang, E. C. Kinzel, S. M. V. Uppuluri, and X. Xu, “Nanopatterning using NSOM probes integrated with high transmission nanoscale bowtie aperture,” Opt. Express 16(4), 2584–2589 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-4-2584. [CrossRef] [PubMed]

], nanolithography [18

18. L. Wang, S. M. Uppuluri, E. X. Jin, and X. Xu, “Nanolithography using high transmission nanoscale bowtie apertures,” Nano Lett. 6(3), 361–364 (2006). [CrossRef] [PubMed]

,19

19. N. Murphy-DuBay, L. Wang, and X. Xu, “Nanolithography using high transmission nanoscale ridge aperture probe,” Appl. Phys., A Mater. Sci. Process. 93(4), 881–884 (2008). [CrossRef]

], and the vertical cavity surface emitting lasers [20

20. Z. Rao, L. Hesselink, and J. S. Harris, “High-intensity bowtie-shaped nano-aperture vertical-cavity surface-emitting laser for near-field optics,” Opt. Lett. 32(14), 1995–1997 (2007). [CrossRef] [PubMed]

,21

21. Z. Rao, L. Hesselink, and J. S. Harris, “High transmission through ridge nano-apertures on Vertical-Cavity Surface-Emitting Lasers,” Opt. Express 15(16), 10427–10438 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-16-10427. [CrossRef] [PubMed]

]. These structured apertures may be easier to fabricate to obtain ET for many application purposes than the bull’s eye structure in Ref [5

5. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]

].

In this letter, we study the near-field enhancement of this structured aperture and focus our attention on their polarization properties. We design some structured circle holes in Ag film and employ the finite-difference time-domain (FDTD) method to simulate the near-field intensity transmitting through them. As shown in Fig. 1
Fig. 1 (a) A bare hole in silver film. Two structured holes (b) with a rod and (c) with two teeth.
, our samples are subwavelength holes with radius r = 100 nm and thickness h = 150 nm, which are set to default for comparison. We set a rod in the center of the hole (shortened as rod-hole) and two tooth-type structures on the side of the hole (shortened as tooth-hole). The length and the width of the rod and teeth are denoted as lr and wr, lt and wt respectively. The thicknesses of the rod or the teeth are set equal to the thickness of the silver film. In fact, some works have reported about the field enhancement by a scatter structure in the hole [22

22. F. J. García de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10(25), 1475–1484 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-25-1475. [PubMed]

,23

23. K. Tanaka, H. Hosaka, K. Itao, M. Oumi, T. Niwa, T. Miyatani, Y. Mitsuoka, K. Nakajima, and T. Ohkubo, “Improvements in near-field optical performance using localized surface plasmon excitation by a scatterer-formed aperture,” Appl. Phys. Lett. 83(6), 1083–1085 (2003). [CrossRef]

], partly similar to the rod-hole. And the tooth-hole refers to the H-hole. However, the main idea of our paper is focus on the polarization properties and for this purpose, both holes are set as circle shape to prevent the polarization influence of the hole.

A home-made 3D FDTD code is used to simulate the fields transmitted through these structured holes. The simulation space is 1.2 × 1.2 × 0.3 μm3 and the constant space step is Δx = Δy = Δz = 2.5 nm. A plane incident pulse wave illuminates samples perpendicularly alone the z direction, with linear polarization. The detection plane is 50 nm away from the output surface of the film and parallel to the x-y plane sized as 0.4 × 0.4 μm2 which is larger enough than the size of the hole to ensure main fields through out can be detected. We just try to simulate a practical case such as a near-filed imaging process or an optical storage process. So we use a detection plane with small distance from the output surface. The transmitted electromagnetic fields of all mesh points on the detection plane are recorded and Fourier transformed to frequency domain. Then the transmitted intensity on the detection can be calculated by the electromagnetic fields and integrated by all mesh points on the detection plane for every frequency. The normalized intensity spectrum can be obtained by normalizing the transmitted intensity by the incident intensity calculated by the same process. By using this method, we can obtain the spectrum information by only once simulation and it is not necessary to calculate the data wavelength by wavelength. The permittivity of Ag is given by the Lorentz-Drude model. The parameters can be obtained from Ref [24

24. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef]

], which are coincident with the experimental data [25

25. D. W. Lynch, and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic, Orlando, Fla., 1985).

] well. By using the polarization vector, the Lorentz-Drude model can be transformed to time-domain and discretized [26

26. J. L. Young and R. O. Nelson, “A Summary and Systematic Analysis of FDTD Algorithms for Linearly Dispersive Media,” IEEE Antennas Propag. Mag. 43(4), 61–126 (2001). [CrossRef]

].

The normalized intensity spectra of these two structured holes are shown in Fig. 2
Fig. 2 Normalized intensity spectra of the two structured holes for x- and y-polarization, and a bare hole without any structure. The geometric parameters are wr = wt = 40 nm, lr = 120 nm, and lt = 60 nm. These parameters are set as default.
. It is clear that there are strong enhancements peak when the polarization is along the longitudinal side of the rod and the teeth, i.e. x-polarization. However, for the incidence with y-polarization, there are only very week enhancements for the two types of the holes. The peaks are at 861 nm and 845 nm for the rod-hole and the tooth-hole respectively. If comparing with the results of a bare hole, the normalized intensities of the structured hole at peaks are 56.8 times and 38.9 times enhanced for the rod-hole and the tooth-hole respectively. The enhancement is not very high because the geometric parameters of the holes are not optimized. The rod-hole and tooth-hole used in Fig. 2 are just the typical ones but not the best ones. Among the simulations we have ever done, the best enhancement is about 705 times, which is obtained by a tooth-hole with h = 150 nm, r = 60 nm, lt = 50 nm, and wt = 20 nm. In fact, if the parameters are adjusted finely, stronger enhancement can be achieved.

From the plots of the electric field distribution, we can see clearly the field enhancement, as shown in Fig. 3
Fig. 3 |E| (a.u.) field distributions of the rod-hole and the tooth-hole. (a) and (c) are on the output surface, (b) and (d) are on the detection plane. The incidences are the peak wavelengths.
. On the metal output surface, in Figs. 3(a) and 3(c), the fields are extraordinarily enhanced at the sharp edges of the rod and the teeth and show a very strong localized effect. However, if propagating a little distance away, the fields dump quickly and are diffracted to spots. This localized property is remarkable and we wonder if it is associated with the localized surface plasmon (LSP).

As is well known, the nano-scaled metal particles can excite LSP on their surface, which leads to strong near-field enhancement. We think that it may be the same way to obtain the near-field enhancement through the structured holes. The enhancement peaks of the holes for x- and y-polarization are just attributed to the longitudinal and transverse plasmon resonances respectively. The two-tooth structure acts like two coupled nanorods [27

27. J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelley, and T. Mallouk, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B 71(23), 235420 (2005). [CrossRef]

], whose LSP resonance is very similar to an isolated nanorod. In Fig. 2(a), the spectra of the rod-hole and the tooth-hole are very similar and the peaks are almost at the same position. Actually, the LSP resonance peak is determined by the length of the nanorod along the polarization direction if other parameters are the same. As a coupled structure, we can consider the two teeth as one rod. So if 2lt = lr, the peaks of the rod-hole and the tooth-hole will be very close to each other. Furthermore, we simulated the normalized intensity spectra for different rod and teeth lengths, which are shown in Fig. 4
Fig. 4 (a) Normalized intensity spectra of (a) the rod-hole and (b) the tooth-hole with different lengths. The inset in (a) is the peak wavelength as a function of the aspect ratio of the rod.
. And the peak wavelength as a function of the aspect ratio (defined by the length divided by the width) is shown in the inset of Fig. 4(a). The rule of these results is coincident with the LSP resonance of the metal nanorod well [28

28. S. Link, M. B. Mohamed, and M. A. El-Sayed, “Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant,” J. Phys. Chem. B 103(16), 3073–3077 (1999). [CrossRef]

,29

29. A. Brioude, X. C. Jiang, and M. P. Pileni, “Optical properties of gold nanorods: DDA simulations supported by experiments,” J. Phys. Chem. B 109(27), 13138–13142 (2005). [CrossRef]

], which confirms our supposition of the origin of the near-field ET of these structured holes. In addition, the resonance wavelength tuned by the rod or teeth length maybe present more usefulness. Modifying the length of the rod or teeth, one can control or choose the resonance wavelength which can obtain strongest enhancement. Then a filter or a switch may be achieved.

As its own property, the excitation of the LSP is strongly dependent on the polarization of the incident light. Similarly, the excitation of the LSP resonance by the nanorod presents strong polarization dependence too [30

30. A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velázquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Noguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74(24), 245425 (2006). [CrossRef]

,31

31. C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111(10), 3806–3819 (2007). [CrossRef]

]. It is easy to deduce that the structured holes should present a similar property of polarization dependence. We define the polarization angle θ by the polarization direction with respect to the x-axis. As shown in Fig. 5
Fig. 5 Normalized intensity spectra of (a) the rod-hole and (b) the tooth-hole for different polarization angles.
, as the angle changes, one peak decreases even disappears and the other peak becomes strong. This is because that there are two LSP resonance modes (transverse mode and the longitudinal mode) when the polarization is parallel or perpendicular to the long side of the rod or teeth, which leads to two peaks at different wavelengths. The LSP resonance will change between the two modes when the polarization changes.

This polarization dependence of the near-field enhancement through the structured subwavelength holes may be very useful for some applications. We can use it to choose the incidence with certain polarization or choose the wavelength which can transmit through. However, if the polarization is not necessary, the polarization dependence may be a disadvantage for some applications, such as near-field imaging and optical storage. One must adjust the polarization angle to get the best effect. A design of structured hole with polarization independence may be very helpful for polarization independent devices.

At first, let us analyze the polarization dependence of the transmitted intensity by very elementary optical theory. According to the superposition principle, we know that two lights with perpendicular polarizations can be superposed simply if they have not phase difference. So we can treat an incidence with polarization angle θ as two waves with x-polarization and y-polarization respectively. Then the incident intensity can be expressed as

I=Ix+Iy=Icos2θ+Isin2θ.
(1)

The transmittivity Tθ can be obtained

Tθ=Ixout+IyoutIin.
(2)

If we define the transmittivities of x- and y-polarization components as Tx and Ty, the output intensity components areIxout=IxinTx=IinTxcos2θ andIyout=IyinTy=IinTysin2θ. So we obtain the transmittivity of light with any polarization angle

Tθ=Txcos2θ+Tysin2θ.
(3)

As a linear system, the transmittivities Tx and Ty are invariable for any incident intensity. Thus if we know the transmittivities of a certain incident wavelength for the x- and y-polarization, we can obtain the transmittivity of any polarization angle by using Eq. (3). In Fig. 6(a)
Fig. 6 (a) Normalized intensity as a function of polarization angle calculated by Eq. (3) and FDTD simulation at the peak wavelength. (b) Normalized intensity spectra calculated by Eq. (3) and FDTD simulation at θ = 30°.
, we show the normalized intensity calculated by Eq. (3) and directly by FDTD simulation as a function of the polarization angle. The incident wavelengths are 861 nm for the rod-hole and 845 for the tooth-hole respectively. The figure shows clearly that the results by Eq. (3) and by FDTD are coincident very well. Especially, we calculate the spectra under polarization angle θ = 30° by Eq. (3) and FDTD as an example, which are shown in Fig. 6(b). We can see clearly that the spectra lines almost overlap with each other.

From Eq. (3), we can deduce that if Tx = Ty, then Tθ = Tx = Ty is independent of polarization angle θ. So if we design some structure in the hole which can realize the same transmittivity at x- and y-polarization, the transmittivity through this structured hole will be independent of the polarization and present an equal value. It is obvious that the fourfold rotational symmetric structure can realize this easily. Then we design two holes, a cross-hole and a four-tooth-hole, as show in the insets of Fig. 7
Fig. 7 Normalized intensity spectra of (a) cross-hole and (b) four-tooth-hole for θ = 0°, 30°, and 45° respectively. The geometric parameters of the cross and the teeth are set equal to that of the rod and teeth in Fig. 2.
and we simulate their normalized intensity spectra under the incident waves with polarization angle θ = 0°, 30°, and 45° respectively. As shown in Fig. 7, we can see clearly that the three spectra for different polarization angles are almost the same. The only little difference is at the peak. We think that this may be attributed to the error of FDTD simulation. In spite of the little difference, the transmitted light through the cross-hole and the four-tooth-hole realize the polarization independence for the near-field enhancement. These structures and their original idea may be practical for some polarization independent devices.

As a conclusion, we present the near-field enhancement through structured subwavelength holes and their polarization properties by using of FDTD simulation. By setting some effective structures, a rod or two teeth in the holes, the near-field of the holes can be extraordinarily enhanced. We attribute this enhancement to the LSP excited by the rod and the teeth. The enhancement of the rod-hole and the tooth-hole exhibits very strong polarization dependence, which is determined by the property of the LSP directly. Starting from a basic optical theory, we find a simple way to design some polarization independent structures, i.e. cross-hole and four-tooth-hole. The intensity spectra of these two holes for different polarization angles almost overlap together and the polarization independence is realized. These results may be useful for some polarization dependence and independence applications.

Acknowledgements

This research is supported by the Chinese National Key Basic Research Special Fund (No. 2006CB921703), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20070055087), and Tianjin Natural Science Foundation (No. 09JCYBJC01600).

References and links

1.

H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944). [CrossRef]

2.

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(6668), 667–669 (1998). [CrossRef]

3.

D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen, “Beyond the Bethe Limit: Tunable enhanced light transmission through a single sub-wavelength aperture,” Adv. Mater. 11(10), 860–862 (1999). [CrossRef]

4.

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(24), 1972–1974 (2001). [CrossRef]

5.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297(5582), 820–822 (2002). [CrossRef] [PubMed]

6.

E. X. Jin and X. Xu, “Finitte-Difference Time-Domain studies on optical transmission through planar nano-apertures in a metal film,” Jpn. J. Appl. Phys. 43(1), 407–417 (2004). [CrossRef]

7.

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(7), 3765–3771 (2004). [CrossRef]

8.

K. Tanaka and M. Tanaka, “Optimized computer-aided design of I-shaped subwavelength aperture for high intensity and small spot size,” Opt. Commun. 233(4-6), 231–244 (2004). [CrossRef]

9.

E. X. Jin and X. Xu, “Obtaining super resolution light spot using surface plasmon assisted sharp ridge nanoaperture,” Appl. Phys. Lett. 86(11), 111106 (2005). [CrossRef]

10.

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(15), 151116 (2005). [CrossRef]

11.

E. X. Jin and X. Xu, “Enhanced optical near field from a bowtie aperture,” Appl. Phys. Lett. 88(15), 153110 (2006). [CrossRef]

12.

E. X. Jin and X. Xu, “Plasmonic effects in near-field optical transmission enhancement through a single bowtie-shaped aperture,” Appl. Phys. B 84(1-2), 3–9 (2006). [CrossRef]

13.

L. Wang and X. Xu, “Spectral resonance of nanoscale bowtie apertures in visible wavelength,” Appl. Phys., A Mater. Sci. Process. 89(2), 293–297 (2007). [CrossRef]

14.

H. Guo, T. P. Meyrath, T. Zentgraf, N. Liu, L. Fu, H. Schweizer, and H. Giessen, “Optical resonances of bowtie slot antennas and their geometry and material dependence,” Opt. Express 16(11), 7756–7766 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-7756. [CrossRef] [PubMed]

15.

K. Tanaka, M. Tanaka, and K. Katayama, “Simulation of near-field scanning optical microscopy using a plasmonic gap probe,” Opt. Express 14(22), 10603–10613 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-22-10603. [CrossRef] [PubMed]

16.

L. Wang and X. Xu, “High transmission nanoscale bowtie-shaped aperture probe for near-field optical imaging,” Appl. Phys. Lett. 90(26), 261105 (2007). [CrossRef]

17.

N. Murphy-DuBay, L. Wang, E. C. Kinzel, S. M. V. Uppuluri, and X. Xu, “Nanopatterning using NSOM probes integrated with high transmission nanoscale bowtie aperture,” Opt. Express 16(4), 2584–2589 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-4-2584. [CrossRef] [PubMed]

18.

L. Wang, S. M. Uppuluri, E. X. Jin, and X. Xu, “Nanolithography using high transmission nanoscale bowtie apertures,” Nano Lett. 6(3), 361–364 (2006). [CrossRef] [PubMed]

19.

N. Murphy-DuBay, L. Wang, and X. Xu, “Nanolithography using high transmission nanoscale ridge aperture probe,” Appl. Phys., A Mater. Sci. Process. 93(4), 881–884 (2008). [CrossRef]

20.

Z. Rao, L. Hesselink, and J. S. Harris, “High-intensity bowtie-shaped nano-aperture vertical-cavity surface-emitting laser for near-field optics,” Opt. Lett. 32(14), 1995–1997 (2007). [CrossRef] [PubMed]

21.

Z. Rao, L. Hesselink, and J. S. Harris, “High transmission through ridge nano-apertures on Vertical-Cavity Surface-Emitting Lasers,” Opt. Express 15(16), 10427–10438 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-16-10427. [CrossRef] [PubMed]

22.

F. J. García de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10(25), 1475–1484 (2002), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-25-1475. [PubMed]

23.

K. Tanaka, H. Hosaka, K. Itao, M. Oumi, T. Niwa, T. Miyatani, Y. Mitsuoka, K. Nakajima, and T. Ohkubo, “Improvements in near-field optical performance using localized surface plasmon excitation by a scatterer-formed aperture,” Appl. Phys. Lett. 83(6), 1083–1085 (2003). [CrossRef]

24.

A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef]

25.

D. W. Lynch, and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in Handbook of Optical Constants of Solids, E.D. Palik, ed. (Academic, Orlando, Fla., 1985).

26.

J. L. Young and R. O. Nelson, “A Summary and Systematic Analysis of FDTD Algorithms for Linearly Dispersive Media,” IEEE Antennas Propag. Mag. 43(4), 61–126 (2001). [CrossRef]

27.

J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. García de Abajo, B. K. Kelley, and T. Mallouk, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B 71(23), 235420 (2005). [CrossRef]

28.

S. Link, M. B. Mohamed, and M. A. El-Sayed, “Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant,” J. Phys. Chem. B 103(16), 3073–3077 (1999). [CrossRef]

29.

A. Brioude, X. C. Jiang, and M. P. Pileni, “Optical properties of gold nanorods: DDA simulations supported by experiments,” J. Phys. Chem. B 109(27), 13138–13142 (2005). [CrossRef]

30.

A. Oliver, J. A. Reyes-Esqueda, J. C. Cheang-Wong, C. E. Román-Velázquez, A. Crespo-Sosa, L. Rodríguez-Fernández, J. A. Seman, and C. Noguez, “Controlled anisotropic deformation of Ag nanoparticles by Si ion irradiation,” Phys. Rev. B 74(24), 245425 (2006). [CrossRef]

31.

C. Noguez, “Surface plasmons on metal nanoparticles: the influence of shape and physical environment,” J. Phys. Chem. C 111(10), 3806–3819 (2007). [CrossRef]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(240.6680) Optics at surfaces : Surface plasmons
(260.5430) Physical optics : Polarization

ToC Category:
Diffraction and Gratings

History
Original Manuscript: December 21, 2009
Revised Manuscript: January 26, 2010
Manuscript Accepted: January 27, 2010
Published: March 9, 2010

Citation
Zu-Bin Li, Wen-Yuan Zhou, Xiang-Tian Kong, and Jian-Guo Tian, "Polarization dependence and independence of near-field enhancement through a subwavelength circle hole," Opt. Express 18, 5854-5860 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-6-5854


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References

  1. H. A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66(7-8), 163–182 (1944). [CrossRef]
  2. 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(6668), 667–669 (1998). [CrossRef]
  3. D. E. Grupp, H. J. Lezec, T. Thio, and T. W. Ebbesen, “Beyond the Bethe Limit: Tunable enhanced light transmission through a single sub-wavelength aperture,” Adv. Mater. 11(10), 860–862 (1999). [CrossRef]
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