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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 14 — Jul. 6, 2009
  • pp: 11730–11738
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Regular and anomalous Extraordinary Optical Transmission at the THz-gap

S.A. Kuznetsov, M. Navarro-Cía, V.V. Kubarev, A.V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla  »View Author Affiliations


Optics Express, Vol. 17, Issue 14, pp. 11730-11738 (2009)
http://dx.doi.org/10.1364/OE.17.011730


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Abstract

In this paper Anomalous Extraordinary Transmission (ET) is reported for s-polarization of low loss doubly periodic subwavelength hole arrays patterned on polypropylene (PP) substrates by conventional contact photolithography at the so-called THz-gap (1–10 THz). The unexpected enhanced transmittance for s-polarization (i.e. without spoof plasmons) was previously numerically demonstrated in subwavelength slits arrays. However, subsequently no experimental work has been devoted to this unexpected Extraordinary Transmission neither in subwavelength slits nor in subwavelength holes. Here, numerical study and experimental results of the Anomalous ET and the symmetric and antisymmetric transmittance modes associated with the already well-known p-polarization ET are shown alongside a systematically analysis of the frequency peaks as a function of hole size for both incident polarizations.

© 2009 Optical Society of America

1. Introduction

The band between 1 THz and 10 THz (0.3–0.03 mm), so-called Terahertz-gap, is a region of the spectrum where many molecular excitations, such as rotations and vibrations, happen. Moreover, THz electromagnetic waves can penetrate through several optical opaque materials and biological tissues, and thus allow their use for imaging in both security and medical applications. Therefore, this range has a huge potential not only for physical characterization, but for chemical analysis as well.

Extensive experimental research of EOT in microwaves [17

17. M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, “Enhanced Gain by Double-Periodic Stacked Subwavelength Hole Array,” IEEE Microwave Wireless Compon. Lett. 17, 831–833(2007). [CrossRef]

], millimeter-waves [12

12. M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, I. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimetre-wave transmission through subwavelength hole arrays,” Opt. Lett. 292500–2502 (2004). [CrossRef] [PubMed]

] and optics [7

7. T. W. Ebbesen, H. J. Lezec, H. Ghaemi, T. Thio, and P. A. Wolf, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

] has been carried out, but few analyses [18

18. J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306-1-4 (2003). [CrossRef]

20

20. A. K. Azad, Y. Zhao, W. Zhang, and M. He, “Effect of dielectric properties of metals on terahertz transmission in subwavelength hole arrays,” Opt. Lett. 31, 2637–2639 (2006). [CrossRef] [PubMed]

] have been devoted to the so-called THz-gap. A couple of these papers was dedicated to perforated doped semiconductor [18

18. J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306-1-4 (2003). [CrossRef]

,19

19. E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75, 235305-1-5 (2007). [CrossRef]

], whereas the other one dealt with perforated metallic plates and provides a deep investigation of the influence of the dielectric properties of metals [20

20. A. K. Azad, Y. Zhao, W. Zhang, and M. He, “Effect of dielectric properties of metals on terahertz transmission in subwavelength hole arrays,” Opt. Lett. 31, 2637–2639 (2006). [CrossRef] [PubMed]

].

Nevertheless, this is not the whole of the story. In 2006 a paper was published showing numerically EOT for s-polarization (i.e. without spoof plasmons) in subwavelength slit arrays lying over a thin dielectric layer, which plays a key role for the unexpected enhancement [21

21. E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006). [CrossRef]

]. Here we report for the first time the experimental realization at the THz-gap of this anomalous high transmittance. Similar results but in millimeter wave range can be found in [22

22. M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo, and V. Lomakin, “Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays,” Opt. Express 15, 1107–1114 (2007). [CrossRef] [PubMed]

] despite this feature was not claimed. Also, Ulrich reported analogous resonances but for inductive grid with propagating holes [5

5. R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Inf. Phys. 7, 37–55, (1967). [CrossRef]

].

This paper demonstrates experimentally the anomalous EOT for s-polarized excitation (electric field along the short periodicity, Ex). Also, it triggers intensive discussion on design, low-cost manufacture and measurement of EOT doubly periodic subwavelength hole arrays in metallic surfaces on/over Polypropylene substrates within THz-gap. Furthermore, experimental verification of both symmetric and antisymmetric modes, that were not previously reported in this THz cutoff range, as well as analysis of hole size dependence of transmittance are presented.

2. “THz-performance” of polypropylene substrates and design of THz-EOT prototypes

At terahertz frequencies typical topological sizes of EOT-structures become of the order of ~10–100µm that is very suitable for creating a topological micro-pattern by a well-tailored contact photolithography technique (CPhLT) employed in the semiconductor industry. The key problem of non-self-bearing THz-structures is the lack of appropriate low absorbing and low dispersive substrates fitting for CPhLT. It should be noted that frequently used polyimide-based (PI-based) substrates obtained by high-quality PI-film growing from a liquid phase due to spin coating and subsequent thermal annealing processes are considered to be ideal for CPhLT; PI has high stiffness, minimal inner and surface defects and its thickness can be accurately controlled. However, the fundamental drawback of PI limiting its use in THz-applications is absorption which is undesirably high even at small values of thickness (a few microns). In comparison with PI, polypropylene (PP) and polyethylene (PE) exhibit in general drastically smaller losses and dispersion within the THz-band which, along with their relative cheapness and commercial availability makes them very promising substrate materials for applied THz-sciences and engineering. Unlike PE, PP is considered to be a more “technological” material due to its higher mechanical fastness, melting temperature and better chemical adhesion. In our recent works we have successfully adapted CPhLT for creating PP-based mesh filters and metasurfaces for millimetre and submillimetre waves (f≈45–500 GHz) [23

23. M. Aznabet, M. Navarro-Cía, S. A. Kuznetsov, A. V. Gelfand, N. I. Fedorinina, Yu. G. Goncharov, M. Beruete, O. El Mrabet, and M. Sorolla, “Polypropylene-substrate-based SRR- and CSRR- metasurfaces for submillimeter waves,” Opt. Express 16, 18312–18319 (2008). [CrossRef] [PubMed]

]. In this work we extended CPhLT for fabricating structures with smaller scale topologies – topologies of EOT hole arrays with EOT-resonance at frequencies ~2–3 THz. The main drawback of commercial PP (as well as PE) follows from its production technology – extrusion from a hot liquid melt of polymeric microgranules that may lead to uncontrollable deviation of thickness (up to 20%) and increase number of film microdefects. In particular, the latter effect is manifested, as we show below, in the appearance of microhillocks on the PP-film surface with typical height of a microgranule size. On average the microhillocks do not deteriorate THz-transmission of the film, but may result in some deviation of the topological dimensions of the microstructures fabricated by CPhLT due to a loose contact between the film and the photo-mask.

Figure 1 presents the results of wideband Fourier-transform THz-characterization of some commercial PP-films with different thickness (the values are pointed in the insets). The case of 4µm-thick PI-film is shown in Fig. 1(a) for comparison. The data overlap the band 1.5–21 THz and were obtained using the vacuum FT-spectrometer “Bruker IFS 66v/s” (spectral resolution ~0.1 cm-1) under “room temperature” measurement conditions. The results show high transmittance of PP-films for moderate values of thickness (8–40µm). Derived from the presented graphs the averaged values of PP’s optical constants (for the points far from molecular absorption bands at 398, 459 and 529 cm-1) are close to the following: refractive index n≈1.5±0.02, loss tangent tgδ≈1-1.5·10-3. The constants exhibit very small frequency dispersion within the investigated THz-band; a slight difference is revealed for film samples from different PP-suppliers: e.g. our 39µm-PP-sample exhibits higher values of n and tgδ than the 40µm-one, which is clearly seen from position and magnitude of Fabry-Perot resonances in spectral transmission (s-polarization 1(c)).

Fig. 1. Optical properties of PP-films at terahertz frequencies. THz-transmittance of 4µm-thick PI-film (a) is shown for comparison. Dashed lines with numbers (b, c) indicate positions of most intensive PP absorption lines. Note that we use the abscissas in both wavenumber (bottom in cm-1) and frequency (top in THz) units.

To fabricate terahertz EOT hole array prototypes discussed in this paper we have chosen a 20µm-thick PP-film estimated to be a compromise between the requirements of thickness minimization (to decrease dielectric losses) and appropriate stiffness (acceptable for employed CPhLT procedures), see details in Fig. 2. In addition, a microscopic study revealed fewer granularity of such a film compared to close in parameters 15µm-thick PP-film from our set of available thicknesses. The design parameters for 20µm-PP-based asymmetric EOT hole arrays were chosen to set the EOT-resonances at 2 and 2.6 THz (not far from the low-frequency end of the instrumentation band) that defined the following values: transversal periodicities dx=47.5 µm and dy=113 µm, hole diameter a=40.1 µm, aluminum metallization thickness t=0.5 µm (a unit cell is shown in Fig. 2(a)). It is well-known that asymmetric prototypes (prototypes with different dielectrics in each interface) have a worst performance in terms of transmittance [14

14. V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71, 235117-1-10 (2005). [CrossRef]

,24

24. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200, 1–7 (2001). [CrossRef]

] since SPP-like waves excited in either side of the metal have different frequencies and therefore, the perfect matching between them is lost, yielding to less transmittance. In consequence, a doubly periodic subwavelength hole array has been designed to minimize in somehow this problem.

Fig. 2. (a): Geometry of hole array unit cell. Note that the PP is not perforated (b, c): Microscope images of 20µm-PP-film-backed hole arrays (prototype #3) illustrating inherent granularity (surface roughness) of low-cost commercial PP-films. The case (b) corresponds to focusing on the nearest PP surface, the case (c) - focusing on the top of microhillocks.

Table 1. Key information of fabricated prototypes

table-icon
View This Table

CPhLT, whose stages are described in [23

23. M. Aznabet, M. Navarro-Cía, S. A. Kuznetsov, A. V. Gelfand, N. I. Fedorinina, Yu. G. Goncharov, M. Beruete, O. El Mrabet, and M. Sorolla, “Polypropylene-substrate-based SRR- and CSRR- metasurfaces for submillimeter waves,” Opt. Express 16, 18312–18319 (2008). [CrossRef] [PubMed]

], was used to fabricate four hole array prototypes with 50 mm clear aperture diameter. For two of them before thermal deposition of Al onto PP an auxiliary thin (20nm-thick) layer of Titanium (Ti) was created by magnetron sputtering to study enhancement of surface adhesion of Al to PP. Our technological experiments show that without good adhesion Al can flake away at the points of PP-film microhillocks that degrades selective properties of fabricated microstructures. In our case Ti-inclusive prototypes are devoid of such a drawback. However their manufacturing required to increase duration of a CPhLT’s chemical etching stage results in slight augmentation of holes diameter a. The Table 1 resumes key information on four fabricated prototypes including measured values of actual hole diameter a. Figures 2(b)(c) illustrate the microscopic structure of the fabricated samples by the example of the prototype #3. The images were obtained by optical microscopy in the “light reflection” regime with enhanced phase contrast. Light illumination and observer position correspond to the side of the PP-film (the Al-layer is located beneath the film). It is clearly seen the aforementioned residual granularity of low-cost commercial PP (Fig. 2(b)). The typical value of the microhillock height measured by refocusing from PP surface onto the microhillock’s apex (Fig. 2(c)) appeared to be 8 µm. Presence of diffused background scattering in Fig. 2(c) points out at nonideal smoothness of the film.

3. Numerical and measurement results

Fig. 3. Transmittance for p-polarzation (red curves) and s-polarization (blue curves) measurements. Dotted lines in the insets correspond to numerical results. Prototypes without Ti-layer: (a) hole diameter a=39.75 µm, (b) a=40.95 µm; Prototypes with Ti-layer: (c) a=41.35 µm, (d) a=43.10 µm. To guide the eye, black arrow indicate Wood’s anomaly linked with the large periodicity in the interface air-metal.

Measurements were performed using the vacuum FT-spectrometer “Bruker IFS 66v/s”. The frequency dependent THz intensity of the prototypes for both incident polarizations in the whole bandwidth is plotted in Fig. 3, whereas a zoom of the experimental Extraordinary Transmission peaks along with simulation results are displayed in corresponding insets of Fig. 3.

Fig. 4. (a) Cross-sectional views of the unit cell just in the middle of the hole of the electric field (arrows) - only in the left hand side panel - and x-component of the electric field Ex (color map), in the vicinity of the structure with geometrical parameters as prototype 1 under s-polarization. (b, c) Cross-sectional view of the electric field (arrows) and z-component of the electric field Ez (color map), in the vicinity of the structure under p-polarization: (b) lower frequency peak - antisymmetric coupling, (c) higher frequency peak - symmetric coupling.

For s-polarization (blue curves) EOT is not expected unless a thin dielectric slab on top of the metallic layer is placed [21

21. E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006). [CrossRef]

] as in our prototypes. This anomalous maximum within the cutoff zone - the cutoff frequency of a single hole of radius 20.5 µm is fco=4.3 THz or 2.85 THz when is loaded with air or PP respectively - is around 2.55 THz in all prototypes with relatively high intensity values of 0.30, 0.38, 0.42, and 0.57 respectively and the Wood anomaly of the interface air-metal is around 6.3 THz for this case. The electric field distribution at the xz- and yz-planes corresponding to this anomalous peak is rendered in Fig. 4(a), where arrows point at the direction of the E-field, whereas color map illustrate the proportional magnitude of the x-component of it (y- and z-components are negligible. The z-component is only noticeable at the edge of the holes, see arrows). The incoming plane wave seems to just accommodate to the holes so as to pass through them which are in accordance with Ref. 21 for subwavelength slit arrays.

In the case of p-polarization (incident electric field along the large periodicity of the hole array), Ey (red curves), the low frequency resonant response is originated from the antisymmetric combination of the two SPP-like modes associated with the two interfaces of the structure (so-called Short Range-SPP-like mode, SR-SPP-like mode), Fig. 4(b). This is straightforwardly derived from the opposite colours at each face of the metal layer in Fig. 4(b). Intensity of each prototypes is 0.41, 0.44, 0.57 and 0.62 corresponding to hole diameter a=39.75, 40.95, 41.35 and 43.10 µm. Note that for both polarizations, the peak reaches similar amplitude values. The other resonance feature observed below Wood’s anomalies within the cutoff region is caused by the corresponding symmetric combination (so-called Long Range-SPP-like mode, LR-SPP-like mode), Fig. 4(c). In this case, intensity values are 0.16, 0.18, 0.20 and 0.26 in that order. These measurements agree well with numerical results, where small discrepancies could be attributed to differences between the parameters used to model metals and PP-film and the real ones. Besides, in Figs. 4(b) and 4(c), where the field distribution at the yz incident plane is depicted (arrows point at the direction of the E-field, whereas color maps illustrate the proportional magnitude of the z-component of it), it is as well highlighted the higher confinement to the metal of the SR-SPP-like mode in opposition to LR-SPP-like mode, since the z-component of the electric field Ez associated with the surface wave prolongs significantly within the air region.

5. Conclusion

Fig. 5. Peak frequency as a function of the hole diameter; (black) lower frequency resonance, (red) higher frequency resonance, (gray) and (pink) for numerical results in that order. The dotted lines are guides to the eyes.

Acknowledgements

This work was supported by Spanish Government and E.U. Feder under contracts Consolider “Engineering Metamaterials” CSD2008-00066 and TEC2008-06871-C02-01.

References and links

1.

J. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London A 79, 399–416 (1907). [CrossRef]

2.

E. H. Synge, “A suggested model for extending microscopic resolution into the ultra-microscopic region,” Philos. Mag. 3, 356–362 (1928).

3.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500Å resolution microscope,” Ultramicroscopy 13, 227–231 (1984). [CrossRef]

4.

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

5.

R. Ulrich, “Far-infrared properties of metallic mesh and its complementary structure,” Inf. Phys. 7, 37–55, (1967). [CrossRef]

6.

C. C. Chen, “Transmission of Microwave Through Perforated Flat Plates of Finite Thickness,” IEEE Trans. Microwave Theory Tech. 21, 1–7, (1973). [CrossRef]

7.

T. W. Ebbesen, H. J. Lezec, H. Ghaemi, T. Thio, and P. A. Wolf, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

8.

M.M.J. Treacy, “Dynamical diffraction in metallic optical gratings,” Appl. Phys. Lett. 75, 606–608 (1999). [CrossRef]

9.

J.A. Porto, F.J. García-Vidal, and J.B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999). [CrossRef]

10.

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

11.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

12.

M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, I. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, “Enhanced millimetre-wave transmission through subwavelength hole arrays,” Opt. Lett. 292500–2502 (2004). [CrossRef] [PubMed]

13.

M. Sarrazin, J. P. Vigneron, and J. M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415-1-8 (2003). [CrossRef]

14.

V. Lomakin and E. Michielssen, “Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs,” Phys. Rev. B 71, 235117-1-10 (2005). [CrossRef]

15.

D. R. Jackson, A. A. Oliner, T. Zhao, and J. T. Williams, “Beaming of light at broadside through a subwavelength hole: Leaky wave model and open stopband effect,” Radio Sci. 40, 1–12 (2005). [CrossRef]

16.

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science 305, 847–848 (2004). [CrossRef] [PubMed]

17.

M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, “Enhanced Gain by Double-Periodic Stacked Subwavelength Hole Array,” IEEE Microwave Wireless Compon. Lett. 17, 831–833(2007). [CrossRef]

18.

J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, “Enhanced transmission of THz radiation through subwavelength holes,” Phys. Rev. B 68, 201306-1-4 (2003). [CrossRef]

19.

E. Hendry, M. J. Lockyear, J. Gómez Rivas, L. Kuipers, and M. Bonn, “Ultrafast optical switching of the THz transmission through metallic subwavelength hole arrays,” Phys. Rev. B 75, 235305-1-5 (2007). [CrossRef]

20.

A. K. Azad, Y. Zhao, W. Zhang, and M. He, “Effect of dielectric properties of metals on terahertz transmission in subwavelength hole arrays,” Opt. Lett. 31, 2637–2639 (2006). [CrossRef] [PubMed]

21.

E. Moreno, L. Martín-Moreno, and F. J. García-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006). [CrossRef]

22.

M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo, and V. Lomakin, “Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays,” Opt. Express 15, 1107–1114 (2007). [CrossRef] [PubMed]

23.

M. Aznabet, M. Navarro-Cía, S. A. Kuznetsov, A. V. Gelfand, N. I. Fedorinina, Yu. G. Goncharov, M. Beruete, O. El Mrabet, and M. Sorolla, “Polypropylene-substrate-based SRR- and CSRR- metasurfaces for submillimeter waves,” Opt. Express 16, 18312–18319 (2008). [CrossRef] [PubMed]

24.

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200, 1–7 (2001). [CrossRef]

25.

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers“Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85, 4316–4318 (2004). [CrossRef]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(240.6690) Optics at surfaces : Surface waves
(040.2235) Detectors : Far infrared or terahertz
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Diffraction and Gratings

History
Original Manuscript: March 25, 2009
Revised Manuscript: May 7, 2009
Manuscript Accepted: June 3, 2009
Published: June 26, 2009

Citation
S. A. Kuznetsov, M. Navarro-Cía, V. V. Kubarev, A. V. Gelfand, M. Beruete, I. Campillo, and M. Sorolla, "Regular and anomalous extraordinary optical transmission at the THz-gap," Opt. Express 17, 11730-11738 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-11730


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References

  1. J. Rayleigh, "On the dynamical theory of gratings," Proc. R. Soc. London A 79, 399-416 (1907). [CrossRef]
  2. E. H. Synge, "A suggested model for extending microscopic resolution into the ultra-microscopic region," Philos. Mag. 3, 356-362 (1928).
  3. A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500Å resolution microscope," Ultramicroscopy 13, 227-231 (1984). [CrossRef]
  4. H. A. Bethe, "Theory of diffraction by small holes," Phys. Rev. 66, 163-182 (1944). [CrossRef]
  5. R. Ulrich, "Far-infrared properties of metallic mesh and its complementary structure," Inf. Phys. 7, 37-55, (1967). [CrossRef]
  6. C. C. Chen, "Transmission of Microwave Through Perforated Flat Plates of Finite Thickness," IEEE Trans. Microwave Theory Tech. 21, 1-7, (1973). [CrossRef]
  7. T. W. Ebbesen, H. J. Lezec, H. Ghaemi, T. Thio, and P. A. Wolf, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998). [CrossRef]
  8. M.M.J. Treacy, "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett. 75, 606-608 (1999). [CrossRef]
  9. J.A. Porto, F.J. García-Vidal, J.B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999). [CrossRef]
  10. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martín-Moreno, F. J. García-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002). [CrossRef] [PubMed]
  11. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114-1117 (2001). [CrossRef] [PubMed]
  12. M. Beruete, M. Sorolla, I. Campillo, J. S. Dolado, I. Martín-Moreno, J. Bravo-Abad, and F. J. García-Vidal, "Enhanced millimetre-wave transmission through subwavelength hole arrays," Opt. Lett. 292500-2502 (2004). [CrossRef] [PubMed]
  13. M. Sarrazin, J. P. Vigneron and J. M. Vigoureux, "Role of Wood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67, 085415 (2003). [CrossRef]
  14. V. Lomakin and E. Michielssen, "Enhanced transmission through metallic plates perforated by arrays of subwavelength holes and sandwiched between dielectric slabs," Phys. Rev. B 71, 235117 (2005). [CrossRef]
  15. D. R. Jackson, A. A. Oliner, T. Zhao, and J. T. Williams, "Beaming of light at broadside through a subwavelength hole: Leaky wave model and open stopband effect," Radio Sci. 40, 1-12 (2005). [CrossRef]
  16. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004). [CrossRef] [PubMed]
  17. M. Beruete, I. Campillo, J. E. Rodríguez-Seco, E. Perea, M. Navarro-Cía, I. J. Núñez-Manrique, and M. Sorolla, "Enhanced Gain by Double-Periodic Stacked Subwavelength Hole Array," IEEE Microwave Wireless Compon. Lett. 17, 831-833 (2007). [CrossRef]
  18. J. Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201306 (2003). [CrossRef]
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