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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 16 — Aug. 3, 2009
  • pp: 13995–14000
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A theoretical re-examination of giant transmission of light through a metallic nano-slit surrounded with periodic grooves

Yanxia Cui and Sailing He  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 13995-14000 (2009)
http://dx.doi.org/10.1364/OE.17.013995


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Abstract

We show that the slit-to-groove distance for a maximal transmission through the nano-slit surrounded with periodic grooves cannot be predicted by the theory of constructive interference between the groove-generated surface plasmon wave (SPW) and the incident wave. A clear physical explanation is given for the dependence of the transmission on the slit-to-groove distance. It is shown that the influence to the transmission comes from three parts: the groove-generated SPW, the incident wave and the nano-slit-generated SPW. The groove-generated SPW is the main factor determining the local field distribution around the nano-slit opening. The influence of the incident wave is very weak when strong SPW is generated on the input surface by many periods of deep grooves. The nano-slit-generated SPW can also be considered as a disturbance to the light distribution on the input surface.

© 2009 OSA

1. Introduction

The phenomenon of extraordinary optical transmission (EOT) through metallic nano-aperture arrays was first observed by Ebbesen nearly a decade ago [1

1. 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]

], and has motivated quite many experimental and theoretical works since then. Such an EOT phenomenon can be applied in e.g. optoelectronic devices, biological sensing [2

2. M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003). [CrossRef] [PubMed]

] and plasmonic lithography [3

3. W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. 3(12), 733–737 (2008). [CrossRef] [PubMed]

]. Since transmission efficiency of an isolated nano-aperture in a metallic film is quite low [4

4. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12(25), 6106–6121 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-25-6106. [CrossRef] [PubMed]

], periodic grooves around the aperture on the input surface are widely used to enhance the transmission efficiency (see e.g [5–8

5. F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003). [CrossRef] [PubMed]

].). However, the physical mechanism of this phenomenon is still not fully explained. For example, one important issue is the dependence of the transmission on the distance between the nano-slit center and the nearest groove center, and this has been studied in Refs [7

7. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3629. [CrossRef] [PubMed]

]. and [8

8. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99(4), 043902 (2007). [CrossRef] [PubMed]

] using the theory of interference between the groove-generated surface plasmon wave and the incident wave. The authors studied different main field components (one is the electric field [7

7. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3629. [CrossRef] [PubMed]

] and the other is the magnetic field [8

8. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99(4), 043902 (2007). [CrossRef] [PubMed]

]) and found inconsistent conclusions, neither of which is correct, as one will see below in our study. We note that although the influence of the slit-to-groove distance on the transmission efficiency was frequently investigated for the problem of the nano-slit with one groove nearby [9–11

9. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’ Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006). [CrossRef]

], it is quite different from the case of the nano-slit surrounded with many periods of grooves and a comparison between them is also given below in our study. It should also be noted that the composite diffracted evanescent wave model used in Ref [7

7. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3629. [CrossRef] [PubMed]

]. (and [9

9. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’ Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006). [CrossRef]

]) has been questioned in Ref [11

11. F. J. Garcia-Vidal, S. G. Rodrigo, and L. Martin-Moreno, “Foundations of the composite diffracted evanescent wave model,” Nat. Phys. 2(12), 790–790 (2006). [CrossRef]

], but the correct mechanism of the transmission through a metallic slit surrounded with a large number of grooves has still not been given. Recently, the phenomenon of extraordinary transmission has also been studied at terahertz [12

12. T. H. Isaac, J. G. Rivas, J. R. Sambles, W. L. Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008). [CrossRef]

], microwave, acoustic frequencies and matter-waves. Thus we think it is necessary to clarify the physical mechanism of the slit-grooves problem to avoid some inaccurate future design in engineering. Here, through an extensive study of the transmission (field) property for different slit-to-groove distances in various scenarios, our work is aimed at explaining clearly the phenomenon of EOT through a nano-slit surrounded with periodic grooves.

2. Calculations and discussions

Fig. 1. Schematic diagram of the metallic nano-slit (centered at x = 0 with width Ws milled in a metallic film of thickness t) surrounded with N grooves (with period P, depth H and width Wg) on the input air-metal surface (located at z = 0) on each side.

Figure 1 shows the two-dimensional (2D) schematic diagram of a metallic nano-slit surrounded by periodic grooves (on the input surface) on both sides. A TM-polarized (the magnetic field is perpendicular to the x-z plane) plane wave impinges normally on the structure. The wavelength of the surface plasmon wave (SPW) is usually estimated by formula λsp=Re(λ0/εmεd/(εm+εd)) where εm and εd are the relative permittivities of the metal and the dielectric, respectively. The film is free-standing in the air and made of gold with permittivity εm = -24.1 + i1.51 [8

8. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99(4), 043902 (2007). [CrossRef] [PubMed]

] at wavelength λ0 = 800 nm. Then we obtain λsp ~ 780 nm. We define transmission efficiency η as the ratio of the integration of the z-component of the Poynting vector over the output aperture to that over the input aperture. All the numerical simulations are carried out with the finite-element method and the validity has been confirmed by comparing the results for the structures studied in Ref [4

4. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12(25), 6106–6121 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-25-6106. [CrossRef] [PubMed]

].

Fig. 2. (Color online) Transmission efficiency η through a 50 nm-width nano-slit for a groove structure with H = 60 nm, Wg = 250 nm, P = 720 nm and N = 12. (a) Curves of η ~L when t = 340 nm (thin solid, non-resonant) and t = 200 nm (thick solid, resonant). Field ∣Hy∣ (dashed) at point (0, -10 nm) is also shown for comparison. (b) Curves of η ~L when the grooves [with N = 12 (thick) or N = 1 (thin)] are only on the right side (dashed) and on both sides (solid) of the non-resonant nano-slit (t = 340 nm).

Before studying some other features for the curves of η ~L in Fig. 2(a), we investigate another simple case by removing one side (left side) of the grooves (called half-grating hereafter). To minimize the influence of the nano-slit, we choose a non-resonant nano-slit (t = 340 nm) to study. The relation of η ~L for the half-grating case when N = 12 is shown in Fig. 2(b) by the thick dashed curve, which oscillates sinusoidally with a period of about 780 nm (i.e., λsp) and a relatively small amplitude [about a quarter of that for the thin solid curve in Fig. 2 (a); the right vertical axis has a scale 4 times larger than the left vertical axis]. For example, transmission efficiency reaches a peak value of 4.3 at slit-to-groove distance L0 in the first period, and its corresponding field distribution ~Hy∣ is shown in Fig. 3(a). In Fig. 3(a) one sees that the surface wave is strongly confined to the grating interface. Because the number of the grooves is not infinite, the field confinement is the strongest at the center (x = 4.5 μm) of the grating and becomes much weaker at the grating edges. One can also see clearly that curve ∣Hy∣ ~x at line z = -10 nm [green curve in Fig. 3(a)] decreases (from an amplitude of 0.19 at the grating center) very quickly toward ± x directions with an oscillating period of P = 720 nm (groove period). However, if there is no groove on the input surface, the field is distributed as a SPW on the flat metal-air interface with a period of λsp ≈ 780 nm and a weak confinement effect [see the period (780 nm) and smaller intensity (lower than 0.1) on the left side of curve ∣Hy∣ ~x in Fig. 3(a)]. Since the nano-slit is opened in the flat metal-air interface region (x < 0, larger L corresponds to larger ∣x∣), the thick dashed curve η ~L in Fig. 2(b) has the properties of period 780 nm (λsp), low amplitude (due to weak confinement), and small damping, and such a periodic dependence of η on L also indicates that groove-generated SPW influences significantly the transmission.

Fig. 3. (Color online) Magnetic field distributions ∣Hy∣ for different situations (with N = 12) considered in Fig. 2(b). (a) L 0 = 545 nm for the half-grating case, (b-e) L 1 = 340 nm, L 2 = 530 nm, L 3 = 710 nm and L 4 = 950 nm for the whole-grating case. The green curves show the intensity of magnetic field on horizontal line z = -10 nm.

Now we come back to study the structure of Fig. 1 (called the whole-grating case hereafter). We redraw in Fig. 2(b) the relation of η ~L for the non-resonant nano-slit [i.e. the thin solid curve in Fig. 2(a)] by the thick solid curve, which has three main features: (a) it oscillates with a period of λsp ≈780 nm; (b) there are two sharp peaks in each period (e.g. η = 21.5 at L1 = 340 nm and η = 19.5 at L3 = 710 nm in the first period), whose transmission can be four times larger than that for the half-grating case (η = 4.3). There are also two valleys in each period (e.g. η = 6.4 at L2 = 530 nm and η = 1.2 at L4 = 950 nm in the first period); (c) the peaks decrease more quickly as compared with the half-grating case. For different slit-to-groove distances the field distributions are different on both the grating interface and the flat metal-air interface (between the left and right half-gratings; opened with the nano-slit) as shown in Fig. 3(b)–(e) for ∣Hy∣ distributions at the above two peaks and two valleys. For a minimal transmission situation (corresponding to slit-to-groove distance L2) shown in Fig. 3(c), the field distribution on the grating interface is the same as that on the grating interface for the half-grating case in Fig. 3(a), and an oscillation peak (but not large field intensity) is formed on the flat metal-air interface [also seen clearly in the middle square region of curve ∣Hy∣ ~x in Fig. 3(c)]. Since light has been confined to the center of the left and right half-gratings, the field confinement on the flat metal-air interface (including the nano-slit area) is quite weak after a quick drop along the grating interface [see Fig. 3(c)]. For the other minimal transmission situation (L = L4) shown in Fig. 3(e), the field distribution is very similar to that in Fig. 3(c), and the only difference is that there are three oscillations on the flat metal-air interface between the two half-gratings [a small one at the center and two large ones on the sides, seen from the enlarged inset for ∣Hy∣ ~x in Fig. 3(e)]. The small (or extremely small) amplitude at the center is the reason for the low transmission when L = L2 (or L = L4). For a maximum transmission situation (L = L1) shown in Fig. 3(b), the field distribution on the grating interface is no longer the same as that for the half-grating case. Instead, it is strongly confined at x = 0 (the opening position of the nano-slit) and an oscillation is formed between the nearest left and right grooves [see curve ∣Hy∣ ~x in the square region of Fig. 3(b), which is much stronger than that in Fig. 3(c)]. For the other maximum transmission situation (L = L3) shown in Fig. 3(d), the field distribution on the grating interface is quite similar to that in Fig. 3(b) except smaller amplitude and also three oscillations on the flat metal-air interface between the two half-gratings [see curve ∣Hy∣ ~x in Fig. 3(d)]. Due to the strong field confinement on the flat metal-air interface region opened with the nano-slit, the transmission for L = L1 (or L3) is quite high (and the peak drops quickly as L varies). In this situation, the left and right half-gratings work together as a whole grating with energy strongly concentrated around the whole-grating center (i.e. x = 0; note that all the bright spots in the flat metal-air interface region have higher field intensity than those on the grating interface). The flat metal-air interface between the two half-gratings supports some special interference pattern formed by two counter-propagating SPWs (of wavelength λsp) coming from the left and right half-gratings. This explains why the period of the curve η ~L is equal to λsp, instead of the groove period (P = 720nm). For a minimal transmission distance (L2 or L4), the SPWs generated by the left and right half-gratings are weakly coupled to each other and the centers of the confined energy (on both sides) are around the center of each half-grating (instead of x = 0). Thus, the field intensity at the nano-slit opening is much weaker than that around the center of each half-grating. In this situation, the left (right) half-grating seems to influence the transmission separately.

The authors of Ref [8

8. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99(4), 043902 (2007). [CrossRef] [PubMed]

]. proposed a magnetic field phase theory and argued that the maximal (or minimal) transmission through the nano-slit corresponds to constructive (or destructive) interference between the groove-generated SPW and the incident plane wave at the nano-slit center, which was realized by adjusting the slit-to-groove distance to L ≈0.5λsp (or Lλsp). According to their magnetic field phase theory, the maximal transmission should appear when L = 0.5λsp + sp (K is an integer) and there should be only one maximal transmission per period (λsp) for the curve η ~L. This conflicts with our results shown in Fig. 2(a) that there are two transmission peaks per period. Their mistake is that they predicted the optimal distance (L) of maximal transmission through a nano-slit surrounded with 33 pairs of grooves by using the excitation phase of the SPW of only one groove on one side of the nano-slit. In Fig. 2(b) we plot curve η ~L when only one groove is milled on one side of the nano-slit (i.e., half-grating with N = 1) with the thin dashed curve (i.e. the problem studied in Refs [9–11

9. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’ Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006). [CrossRef]

].). From this curve, one sees only one oscillation peak per period, which is completely different from the thick solid curve (for the whole-grating case when N = 12). The theory in Ref [8

8. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99(4), 043902 (2007). [CrossRef] [PubMed]

]. is not reliable as one sees clearly in Fig. 2(b) that the peak position for the thin dashed curve (corresponding to a maximal transmission distance according to the theory of Ref [8

8. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99(4), 043902 (2007). [CrossRef] [PubMed]

].) is around the valley of the thick solid curve (corresponding to an actually minimal transmission distance) for this special case. In addition, we plot in Fig. 2(b) curve η ~L (thin solid) for the whole-grating case when N = 1. Unlike the big difference between the thick solid curve (whole-grating) and the thick dashed curve (half-grating) in Fig. 2(b) for N = 12, this thin solid curve has similar features as the thin dashed curve (half-grating case with N = 1). This is due to lack of periodic effect of grooves in the formation of localized SPW when N = 1.

Another group experimentally found out in Ref [7

7. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3629. [CrossRef] [PubMed]

]. that for a nano-hole surrounded with 16 nano-ring grooves, the optimal distance from the nano-hole to the center of the nearest nano-ring is L = (K + 0.25)P, where K is an integer, and P is the groove period (quite close to λsp for their experimental sample). They explained this according to their analytical model — composite diffracted evanescent wave model (based on a simplified structure when the nano-hole is surrounded with only one nano-ring groove) that the scattered electric field (Ex) at the center of the groove was π/2 out of phase with respect to the incident plane wave. They ignored the periodic effect of the grooves and made the same mistake as the authors of Ref [8

8. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99(4), 043902 (2007). [CrossRef] [PubMed]

]. They did not study various experimental samples to check their conclusion. Note that the problems of 3D nano-hole and 2D nano-slit surrounded with grooves have similar properties due to similar physical mechanism. Our simulations show that for different groove structures the smallest slit-to-groove distance for maximal transmission varies quite much, instead of being fixed at 0.5λsp or 0.25λsp (or 0.25P). In Fig. 4, the thin curves show the normalized transmission efficiency (ηn) of light through the nano-slit as a function of distance L for four different sets of groove depth and width (with the same groove period). One can see clearly that the shapes of thin curves ηn ~L (including the positions of the peaks and valleys) are completely different (for the same P and same λsp) due to different local field distributions. We emphasize that for different groove structures the transmission is maximal when the surface energy center locates at the center of the whole structure (x = 0) and is minimal when the surface energy center locates at the center of each half-grating.

Fig. 4. Normalized transmission efficiency as L varies when the incident wave is a plane wave (thin curves) or two point sources at (± 11 μm, -10 nm) (thick curves). Here Ws = 50 nm, t = 340 nm (non-resonant case), P = 780 nm and N = 12. The groove depth and width are (a) H = 60 nm, Wg = 250 nm; (b) H = 60 nm, Wg = 400 nm; (c) H = 60 nm, Wg = 550 nm; (d) H = 10 nm, Wg = 250 nm.

3. Conclusions

Acknowledgments

This work is supported by the NSFC of China (60688401 and 60677047), National Basic Research Program of China (2004CB719800), Swedish Research Council (VR) and AOARD. The authors thank Prof. Y. Okuno, Dr. N. Fang, Dr. Y. Jin and Z. C. Wang for discussions.

References and links

1.

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]

2.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003). [CrossRef] [PubMed]

3.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. 3(12), 733–737 (2008). [CrossRef] [PubMed]

4.

Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12(25), 6106–6121 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-25-6106. [CrossRef] [PubMed]

5.

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003). [CrossRef] [PubMed]

6.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13(3), 429–432 (2002). [CrossRef]

7.

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3629. [CrossRef] [PubMed]

8.

O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99(4), 043902 (2007). [CrossRef] [PubMed]

9.

G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O’ Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006). [CrossRef]

10.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006). [CrossRef]

11.

F. J. Garcia-Vidal, S. G. Rodrigo, and L. Martin-Moreno, “Foundations of the composite diffracted evanescent wave model,” Nat. Phys. 2(12), 790–790 (2006). [CrossRef]

12.

T. H. Isaac, J. G. Rivas, J. R. Sambles, W. L. Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008). [CrossRef]

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

ToC Category:
Diffraction and Gratings

History
Original Manuscript: July 7, 2009
Revised Manuscript: July 22, 2009
Manuscript Accepted: July 24, 2009
Published: August 3, 2009

Citation
Yanxia Cui and Sailing He, "A theoretical re-examination of giant transmission of light through a metallic nano-slit surrounded with periodic grooves," Opt. Express 17, 13995-14000 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13995


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References

  1. 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]
  2. M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, “Zero-mode waveguides for single-molecule analysis at high concentrations,” Science 299(5607), 682–686 (2003). [CrossRef] [PubMed]
  3. W. Srituravanich, L. Pan, Y. Wang, C. Sun, D. B. Bogy, and X. Zhang, “Flying plasmonic lens in the near field for high-speed nanolithography,” Nat. Nanotechnol. 3(12), 733–737 (2008). [CrossRef] [PubMed]
  4. Y. Xie, A. R. Zakharian, J. V. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12(25), 6106–6121 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-25-6106 . [CrossRef] [PubMed]
  5. F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple paths to enhance optical transmission through a single subwavelength slit,” Phys. Rev. Lett. 90(21), 213901 (2003). [CrossRef] [PubMed]
  6. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13(3), 429–432 (2002). [CrossRef]
  7. H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12(16), 3629–3651 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-16-3629 . [CrossRef] [PubMed]
  8. O. T. A. Janssen, H. P. Urbach, and G. W. ’t Hooft, “Giant optical transmission of a subwavelength slit optimized using the magnetic field phase,” Phys. Rev. Lett. 99(4), 043902 (2007). [CrossRef] [PubMed]
  9. G. Gay, O. Alloschery, B. Viaris de Lesegno, C. O' Dwyer, J. Weiner, and H. J. Lezec, “The optical response of nanostructured surfaces and the composite diffracted evanescent wave model,” Nat. Phys. 2(4), 262–267 (2006). [CrossRef]
  10. P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2(8), 551–556 (2006). [CrossRef]
  11. F. J. Garcia-Vidal, S. G. Rodrigo, and L. Martin-Moreno, “Foundations of the composite diffracted evanescent wave model,” Nat. Phys. 2(12), 790–790 (2006). [CrossRef]
  12. T. H. Isaac, J. G. Rivas, J. R. Sambles, W. L. Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008). [CrossRef]

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Fig. 4.
 

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