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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 18 — Sep. 4, 2006
  • pp: 8037–8042
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Periodic dielectric bars assisted enhanced transmission and directional light emission from a single subwavelength slit

Zu-Bin Li, Jian-Guo Tian, Wen-Yuan Zhou, Wei-Ping Zang, and Chunping Zhang  »View Author Affiliations


Optics Express, Vol. 14, Issue 18, pp. 8037-8042 (2006)
http://dx.doi.org/10.1364/OE.14.008037


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Abstract

The transmission from a single subwavelength slit in a metal film with periodic dielectric bars on its surfaces has been analyzed numerically by the finite-difference time-domain method. Results show that the role of the periodic dielectric bars is just the same as that of the periodic grooves directly on the surfaces. With the modulations of dielectric bars on the input and output surfaces of the metal film, light transmission through the subwavelength slit is enhanced extraordinarily and confined to directional emission. The CDEW model is employed to explain the mechanism of the transmission enhancement and directional emission caused by the periodic dielectric bars.

© 2006 Optical Society of America

It is generally known that light transmission through a subwavelength aperture is very poor and diffracted to all directions according to the standard diffraction theory. Recently, extraordinarily enhanced transmission was observed through a single subwavelength aperture in a metal film if surrounded by periodic corrugations on the illuminating side [1

1 . 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 – 1974 ( 2001 ). [CrossRef]

]. With periodic grooves on the output side of the metal film, the transmission was confined to be a beaming light from a single hole or directional emission from a single slit [2

2 . 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 , 820 – 822 ( 2002 ). [CrossRef] [PubMed]

]. These findings attracted a lot of interest because of their extensive potential applications such as optimized probe for near-field microscopy [3

3 . T. Thio , H.J. Lezec , and T.W. Ebbesen , “ Strongly enhanced optical transmission through subwavelength holes in metal films ,” Physica B 279 , 90 – 93 ( 2000 ). [CrossRef]

], near-field optical data readout systems [4–5

4 . G. Gbur , H. F. Schouten , and T. D. Visser , “ Achieving superresolution in near-field optical data readout systems using surface plasmons ,” Appl. Phys. Lett. 87 , 191105 ( 2005 ). [CrossRef]

], near-field imaging [6

6 . K. Ishihara , T. Ikari , H. Minamide , J. Shikata , K. Ohashi , H. Yokoyama , and H. Ito , “ Terahertz near-field imaging using enhanced transmission through a single subwavelength aperture ,” Jpn. J. Appl. Phys. 44 , L929 – L931 ( 2005 ). [CrossRef]

], and micro-aperture laser [7

7 . S. Shinada , J. Hashizume , and F. Koyama , “ Surface plasmon resonance on microaperture vertical-cavity surface-emitting laser with metal grating ,” Appl. Phys. Lett. 83 , 836 – 838 ( 2003 ). [CrossRef]

]. Furthermore, enhanced transmission and beaming light were also reported from annular aperture with grooves surrounded [8–10

8 . H. Caglayan , I. Bulu , and E. Ozbay , “ Extraordinary grating-coupled microwave transmission through a subwavelength annular aperture ,” Opt. Express 13 , 1666 – 1671 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1666 . [CrossRef] [PubMed]

]. Besides these aperture-groove structures, beaming light from a nanoslit surrounded by metallic heterostructures [11

11 . B. Wang and G. P. Wang , “ Directional beaming of light from a nanoslit surrounded by metallic heterostructures ,” Appl. Phys. Lett. 88 , 013114 ( 2006 ). [CrossRef]

] and enhanced transmission from an aperture in a multilayered metallic film [12

12 . A. V. Zayats and I. I. Smolyaninov , “ High-optical-throughput individual nanoscale aperture in a multilayered metallic film ,” Opt. Lett. 31 , 398 – 400 ( 2006 ). [CrossRef] [PubMed]

] were reported very recently.

Fig. 1. Sketch maps of a slit in a metal film with periodic dielectric bars (a) on the input surface and (b) on the output surface.

In this letter, we change the dielectric film in structures of Ref. [13–14

13 . Z.-B. Li , J.-G. Tian , Z.-B. Liu , W.-Y. Zhou , and C.-P. Zhang , “ Enhanced light transmission through a single subwavelength aperture in layered films consisting of metal and dielectric ,” Opt. Express 13 , 9071 – 9077 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-22-9071 . [CrossRef] [PubMed]

] to periodic dielectric bars with subwavelength width and analyze the transmission from subwavelength slits in these new structures numerically by finite-difference time-domain (FDTD) method. The sketch maps are shown in Fig. 1. In our simulation, we use metal Ag and its permittivity is given by Drude model: ε (ω) = 1 - [ωp2/(ω 2 + iωγ)] with ωp = 1.346 × 1016 rad/s and γ = 9.617 × 1013 rad/s. The geometry of the metal film is fixed for comparison [2

2 . 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 , 820 – 822 ( 2002 ). [CrossRef] [PubMed]

] and simplicity as thickness h Ag = 300 nm and slit width w = 40 nm. The slit is surrounded by 2Ndi dielectric bars and the dielectric is supposed to be isotropic, and without dispersion and absorption. Referred to the results in our works [13–14

13 . Z.-B. Li , J.-G. Tian , Z.-B. Liu , W.-Y. Zhou , and C.-P. Zhang , “ Enhanced light transmission through a single subwavelength aperture in layered films consisting of metal and dielectric ,” Opt. Express 13 , 9071 – 9077 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-22-9071 . [CrossRef] [PubMed]

], Ndi is set to be 5. A TM polarized plane wave is incident perpendicularly on the structures. The dielectric bars will be put on the input or output surface of the metal film respectively to discuss their effects on the transmission enhancement or directional light emission.

At first, we put dielectric bars on the input surface of the metal film and the output surface is smooth [see Fig. 1(a)]. Under this condition, the transmission through the slit is totally determined by the dielectric bars on the input surface. In Fig. 2, we show area-normalized transmission spectra of three structures in metal films: a bare slit without any structure on its surfaces, a slit with dielectric bars on the input surface, and a slit with periodic grooves on the input surface. The parameters of the dielectric bars are period pdi = 500 nm, height hdi = 100 nm, width wdi = 40 nm, refractive index n = 2.0, and these parameters are set to be default if not mentioned additionally. The slit-groove metal structure has ±5 grooves directly on the input surface with period of 500 nm, width of 40nm, and depth of 60 nm.

Fig. 2. Area-normalized transmission spectra of a bare slit (red line), a slit with dielectric bars (green line) and a slit with periodic grooves (blue line). All three slits are in the same metal film with thickness of 300 nm and slit width of 40 nm. The spectra are normalized by the fraction of the surface occupied by the slit.

From Fig. 2, we can see clearly that the transmission through the subwavelength slit in our structure is extraordinarily enhanced by the modulation of the periodic dielectric bars on the input surface of the metal film. Compared with the enhancement caused by grooves directly on the metal surface with same period and width, the peak enhancement by the dielectric bars is stronger and the peak wavelength is a little longer. However, despite these small differences, the properties of their transmission peaks are very similar, and we suppose that the periodic dielectric bars play the same role in the transmission enhancement through the subwavelength slit as what the periodic grooves do.

Although the resonant excitation of surface plasmons was used widely to explain the mechanism of transmission enhancement, it doesn’t fit our result obtained from the structure of metal slit and dielectric bars. As we know, the frequency of the surface plasmon is determined by the permittivities of the metal and the dielectric at the interface. However, with large difference of dielectric properties (n = 1 for air grooves and n = 2 for dielectric bars), the resonant wavelengths of the slit with grooves and the slit with dielectric bars are very close (see Fig. 2). This cannot be explained by the surface plasmons model. In this letter, the CDEW (composite diffracted evanescent waves) model presented by Lezec and Thio [18

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

] is employed to explain the mechanism of transmission enhancement. In the CDEW model, the transmission enhancement is due to the constructive interference of composite diffracted evanescent waves generated by subwavelength features on the surface. Just as shown in Fig. 3, when light illuminates on the metal-dielectric structure, it will be diffracted into evanescent waves by subwavelength-scaled dielectric bars. These composite evanescent waves propagate to the slit and interfere with the light incident directly on the slit, leading to field enhancement when the interference is constructive at selected wavelength. Based on the CDEW model, the stronger enhancement and the little longer peak wavelength can be explained easily. The stronger enhancement is because the dielectric bars are transparent, which affect little on the propagation of evanescent waves from far side. And the longer peak wavelength is caused by the increase of the effective refractive index neff at the interface of the dielectric bars and the metal film {see Eq. (4) in Ref. [18

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

]}.

Fig. 3. The schematic diagram of transmission enhancement by CDEW model.

In Fig. 5 are shown Tmax and λmax as a function of n. As n increases, Tmax increases first and then decreases. This is because that when n increases, the diffractive ability of the dielectric bars increases, leading to more evanescent waves and stronger transmission enhancement. However, larger n leads to stronger reflection at the dielectric surface, which weakens the contribution to enhancement from dielectric bars far away from the slit. These two contrary processes act together and lead to this variation finally. λmax increases as n increases, which is due to the increase of the effective refractive index neff at the interface.

Fig. 4. (a) Normalized transmittance and (b) wavelength at peak as a function of the height of dielectric bars. Other parameters of the dielectric bars are set as default.
Fig. 5. (a) Normalized transmittance and (b) wavelength at peak as a function of the refractive index of dielectric bars. Other parameters of the dielectric bars are set as default.
Fig. 6. Area-normalized transmission spectra of a bare slit (red line) and a slit with metal bars on the input surface (blue line). The metal bars have a period of 500 nm, height of 40 nm and width of 40 nm.

As a comparison, we change the dielectric bars to metal bars and simulate the transmission. As shown in Fig. 6, the transmission through the slit with periodic metal bars is also enhanced, but the enhancement is quite low. Actually, the evanescent waves can also be generated by the diffraction of the metal bars, but the metal bars interrupt the propagation of the evanescent waves and block the contributions to the enhancement from bars out of the first pair. Thus the enhancement by metal bars is mostly due to the first pair of bars. The enhancement factor of the transmission peak in Fig. 6 is 3.4, which is very similar to the result obtained from slit with only one pair of grooves [19

19 . A. P. Hibbins , J. R. Sambles , and C. R. Lawrence , “ Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate ,” Appl. Phys. Lett. 81 , 4661 – 4663 ( 2002 ). [CrossRef]

].

From results above, we know that the transmission through a subwavelength slit is extraordinarily enhanced by the modulation of the periodic dielectric bars on the input surface. As we already knew [14

14 . Z.-B. Li , J.-G. Tian , W.-Y. Zhou , Z.-B. Liu , W.-P Zang , and C.-P. Zhang , “ Highly directional emission from a subwavelength slit in metal-dielectric layered films ,” Chin. Phys. Lett. 23 , 1207 – 1210 ( 2006 ). [CrossRef]

], the features on the output surface can modulate the distribution of the light transmitted through the slit. We simulate the field distributions through the slit with periodic dielectric bars on the output surface under different parameters, which are shown in Fig. 7. The grooves [see Fig. 1(b)] on the input surface of the metal film have period of 500 nm, width of 40 nm and depth of 60 nm. The incident light is 500 nm if not mentioned especially. From the plots in Fig. 7, we can see clearly that the transmission through the slit is confined to directional emission by the modulation of the dielectric bars on the output surface. The plot of pdi = 400 nm presents a beaming light emission. Just same as the effect of dielectric film with grooves [14

14 . Z.-B. Li , J.-G. Tian , W.-Y. Zhou , Z.-B. Liu , W.-P Zang , and C.-P. Zhang , “ Highly directional emission from a subwavelength slit in metal-dielectric layered films ,” Chin. Phys. Lett. 23 , 1207 – 1210 ( 2006 ). [CrossRef]

], the dielectric bars diffract the evanescent waves (which are generated by the diffraction of the subwavelength slit) into propagating waves and these diffracted waves interferes with each other leading to the beaming light or directional emission. However, it must be noticed that the dielectric bars are of very small width compared with the incident wavelength and the bar period. Thus the variation of the dielectric parameters will not affect the field distribution too much. As shown in Fig. 7, although the incident wavelength, period, refractive index, and height of the dielectric bars vary greatly, the distributions of output fields vary much slowly, especially compared with the results modulated by the dielectric film [14

14 . Z.-B. Li , J.-G. Tian , W.-Y. Zhou , Z.-B. Liu , W.-P Zang , and C.-P. Zhang , “ Highly directional emission from a subwavelength slit in metal-dielectric layered films ,” Chin. Phys. Lett. 23 , 1207 – 1210 ( 2006 ). [CrossRef]

].

In conclusion, we have analyzed numerically the properties of the transmission from a single subwavelength slit in a metal film with periodic dielectric bars on the input and output surface respectively by the FDTD method. Results show that the transmission is strongly enhanced by the modulation of the dielectric bars on the input surface, and confined to beaming light or directional emission by the modulation of the dielectric bars on the output surface. The dielectric bars play the same role as the periodic grooves directly on the surfaces. We employ the CDEW model to explain the mechanism of the transmission enhancement and the directional emission. The structure with periodic dielectric particles is very efficient to obtain strong transmission enhancement. And we think our results will be very helpful for the applications of subwavelength optical devices.

Fig. 7. Patterns of light emitting from the slit under different incident wavelength and parameters of dielectric bars. Other parameters are set as default.

Acknowledgement

This research is supported by Science & Technology Development Project of Tianjin (grant 033104311), the Preparatory Project of the National Key Fundamental Research Program (grant 2004CCA04400), and the Program for Changjiang Scholars and Innovative Research Team in University.

References and links

1 .

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 – 1974 ( 2001 ). [CrossRef]

2 .

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 , 820 – 822 ( 2002 ). [CrossRef] [PubMed]

3 .

T. Thio , H.J. Lezec , and T.W. Ebbesen , “ Strongly enhanced optical transmission through subwavelength holes in metal films ,” Physica B 279 , 90 – 93 ( 2000 ). [CrossRef]

4 .

G. Gbur , H. F. Schouten , and T. D. Visser , “ Achieving superresolution in near-field optical data readout systems using surface plasmons ,” Appl. Phys. Lett. 87 , 191105 ( 2005 ). [CrossRef]

5 .

C. H. Gan and G. Gbur , “ Strategies for employing surface plasmons in near-field optical readout systems ,” Opt. Express 14 , 2385 – 2397 ( 2006 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-6-2385 . [CrossRef] [PubMed]

6 .

K. Ishihara , T. Ikari , H. Minamide , J. Shikata , K. Ohashi , H. Yokoyama , and H. Ito , “ Terahertz near-field imaging using enhanced transmission through a single subwavelength aperture ,” Jpn. J. Appl. Phys. 44 , L929 – L931 ( 2005 ). [CrossRef]

7 .

S. Shinada , J. Hashizume , and F. Koyama , “ Surface plasmon resonance on microaperture vertical-cavity surface-emitting laser with metal grating ,” Appl. Phys. Lett. 83 , 836 – 838 ( 2003 ). [CrossRef]

8 .

H. Caglayan , I. Bulu , and E. Ozbay , “ Extraordinary grating-coupled microwave transmission through a subwavelength annular aperture ,” Opt. Express 13 , 1666 – 1671 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1666 . [CrossRef] [PubMed]

9 .

M. J. Lockyear , A. P. Hibbins , and J. R. Sambles , “ Microwave transmission through a single subwavelength annular aperture in a metal plate ,” Phys. Rev. Lett. 94 , 193902 ( 2005 ). [CrossRef] [PubMed]

10 .

H. Caglayan , I. Bulu , and E. Ozbay , “ Beaming of electromagnetic waves emitted through a subwavelength annular aperture ,” J. Opt. Soc. Am. 23 , 419 – 422 ( 2006 ). [CrossRef]

11 .

B. Wang and G. P. Wang , “ Directional beaming of light from a nanoslit surrounded by metallic heterostructures ,” Appl. Phys. Lett. 88 , 013114 ( 2006 ). [CrossRef]

12 .

A. V. Zayats and I. I. Smolyaninov , “ High-optical-throughput individual nanoscale aperture in a multilayered metallic film ,” Opt. Lett. 31 , 398 – 400 ( 2006 ). [CrossRef] [PubMed]

13 .

Z.-B. Li , J.-G. Tian , Z.-B. Liu , W.-Y. Zhou , and C.-P. Zhang , “ Enhanced light transmission through a single subwavelength aperture in layered films consisting of metal and dielectric ,” Opt. Express 13 , 9071 – 9077 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-22-9071 . [CrossRef] [PubMed]

14 .

Z.-B. Li , J.-G. Tian , W.-Y. Zhou , Z.-B. Liu , W.-P Zang , and C.-P. Zhang , “ Highly directional emission from a subwavelength slit in metal-dielectric layered films ,” Chin. Phys. Lett. 23 , 1207 – 1210 ( 2006 ). [CrossRef]

15 .

E. Moreno , F. J. Garcia-Vidal , and L. Martin-Moreno , “ Enhanced transmission and beaming of light via photonic crystal surface modes ,” Phys. Rev. B 69 , 121402 (R) ( 2004 ). [CrossRef]

16 .

P. Kramper , M. Agio , C. M. Soukoulis , A. Birner , F. Muller , R. B. Wehrspohn , U. Gosele , and V. Sandoghdar , “ Highly directional emission from photonic crystal waveguides of subwavelength width ,” Phys. Rev. Lett. 92 , 113903 ( 2004 ). [CrossRef] [PubMed]

17 .

S. K. Morrison and Y. S. Kivshar , “ Engineering of directional emission from photonic-crystal waveguides ,” Appl. Phys. Lett. 86 , 081110 ( 2005 ). [CrossRef]

18 .

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

19 .

A. P. Hibbins , J. R. Sambles , and C. R. Lawrence , “ Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate ,” Appl. Phys. Lett. 81 , 4661 – 4663 ( 2002 ). [CrossRef]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(240.6690) Optics at surfaces : Surface waves

ToC Category:
Diffraction and Gratings

History
Original Manuscript: May 15, 2006
Revised Manuscript: June 26, 2006
Manuscript Accepted: July 21, 2006
Published: September 1, 2006

Citation
Zu-Bin Li, Jian-Guo Tian, Wen-Yuan Zhou, Wei-Ping Zang, and Chunping Zhang, "Periodic dielectric bars assisted enhanced transmission and directional light emission from a single subwavelength slit," Opt. Express 14, 8037-8042 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-18-8037


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References

  1. 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, 1972-1974 (2001). [CrossRef]
  2. 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, 820-822 (2002). [CrossRef] [PubMed]
  3. T. Thio, H.J. Lezec, and T.W. Ebbesen, "Strongly enhanced optical transmission through subwavelength holes in metal films," Physica B 279, 90-93 (2000). [CrossRef]
  4. G. Gbur, H. F. Schouten, and T. D. Visser, "Achieving superresolution in near-field optical data readout systems using surface plasmons," Appl. Phys. Lett. 87, 191105 (2005). [CrossRef]
  5. C. H. Gan and G. Gbur, "Strategies for employing surface plasmons in near-field optical readout systems," Opt. Express 14, 2385-2397 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-6-2385. [CrossRef] [PubMed]
  6. K. Ishihara, T. Ikari, H. Minamide, J. Shikata, K. Ohashi, H. Yokoyama, and H. Ito, "Terahertz near-field imaging using enhanced transmission through a single subwavelength aperture," Jpn. J. Appl. Phys. 44, L929-L931 (2005). [CrossRef]
  7. S. Shinada, J. Hashizume, and F. Koyama, "Surface plasmon resonance on microaperture vertical-cavity surface-emitting laser with metal grating," Appl. Phys. Lett. 83, 836-838 (2003). [CrossRef]
  8. H. Caglayan, I. Bulu, and E. Ozbay, "Extraordinary grating-coupled microwave transmission through a subwavelength annular aperture," Opt. Express 13, 1666-1671 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1666. [CrossRef] [PubMed]
  9. M. J. Lockyear, A. P. Hibbins, and J. R. Sambles, "Microwave transmission through a single subwavelength annular aperture in a metal plate," Phys. Rev. Lett. 94, 193902 (2005). [CrossRef] [PubMed]
  10. H. Caglayan, I. Bulu, and E. Ozbay, "Beaming of electromagnetic waves emitted through a subwavelength annular aperture," J. Opt. Soc. Am. 23, 419-422 (2006). [CrossRef]
  11. B. Wang and G. P. Wang, "Directional beaming of light from a nanoslit surrounded by metallic heterostructures," Appl. Phys. Lett. 88, 013114 (2006). [CrossRef]
  12. A. V. Zayats and I. I. Smolyaninov, "High-optical-throughput individual nanoscale aperture in a multilayered metallic film," Opt. Lett. 31, 398-400 (2006). [CrossRef] [PubMed]
  13. Z.-B. Li, J.-G. Tian, Z.-B. Liu, W.-Y. Zhou, and C.-P. Zhang, "Enhanced light transmission through a single subwavelength aperture in layered films consisting of metal and dielectric," Opt. Express 13, 9071-9077 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-22-9071. [CrossRef] [PubMed]
  14. Z.-B. Li, J.-G. Tian, W.-Y. Zhou, Z.-B. Liu, W.-P Zang, and C.-P. Zhang, "Highly directional emission from a subwavelength slit in metal-dielectric layered films," Chin. Phys. Lett. 23, 1207-1210 (2006). [CrossRef]
  15. <jrn>. E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402(R) (2004).</jrn> [CrossRef]
  16. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muller, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar, "Highly directional emission from photonic crystal waveguides of subwavelength width," Phys. Rev. Lett. 92, 113903 (2004). [CrossRef] [PubMed]
  17. S. K. Morrison and Y. S. Kivshar, "Engineering of directional emission from photonic-crystal waveguides," Appl. Phys. Lett. 86, 081110 (2005). [CrossRef]
  18. H. J. Lezec and T. Thio, "Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays," Opt. Express 12, 3629-3651 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3629. [CrossRef] [PubMed]
  19. A. P. Hibbins, J. R. Sambles, and C. R. Lawrence, "Gratingless enhanced microwave transmission through a subwavelength aperture in a thick metal plate," Appl. Phys. Lett. 81, 4661-4663 (2002). [CrossRef]

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