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.

Early study of transmission through subwavelength holes has its origin at the beginning of 20th century [1]. Later on, Synge [2] proposed the use of a small aperture close to the sample surface to overcome the diffraction limit, but it was not applied until mid 80’s in the development of near-field scanning optical microscopy [3] using arrays of subwavelength holes. Contrary to Bethe’s theoretical model [4] of the 40’s, these arrays gave rather significant enhanced transmission. In parallel, microwave transmission through periodically perforated thin metallic plates had been studied since 60’s. [5, 6]. However, it was Ebbesen et al. [7] who paid particular attention to the high transmittance peaks observed at optical wavelengths within the cutoff defined by the aperture size of perforated plates, namely Extraordinary Optical Transmission (EOT) (it is worth noting that also anomalous high transmittance was reported in subwavelength slit arrays [8,9] and a subwavelength slot in corrugated surfaces [10], but from now on, we will not deal with them). This enhancement was successfully explained in terms of Surface Plamons Polaritons (SPPs), but subsequent analytical results under Perfect Conductor condition [11] and experimental results in perforated aluminum plates at millimeter-waves [12], where metals no longer support SPPs, brought some doubts about the physics underlying the EOT. Therefore, explanations based on Wood’s anomaly [13,14] and leaky waves formalism started to become important [15]. Finally, Pendry et al. [16] found that perforated periodically subwavelength holes change the effective electric permeability of the metal, in such a way that it behaves as an electron plasma, being also consistent with the far-field reflection and dispersion experiments. They termed the wave supported in that structured surface as spoof plasmon.

Extensive experimental research of EOT in microwaves [17], millimeter-waves [12] and optics [7] has been carried out, but few analyses [1820] have been devoted to the so-called THz-gap. A couple of these papers was dedicated to perforated doped semiconductor [18,19], whereas the other one dealt with perforated metallic plates and provides a deep investigation of the influence of the dielectric properties of metals [20].

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

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]. 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.

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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 [14,24] 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.

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Tables Icon

Table 1. Key information of fabricated prototypes

CPhLT, whose stages are described in [23], 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

We perform numerical simulations using the commercially available 3D electromagnetic solver CST Microwave StudioTM, which is based upon Finite Integration Time Domain Method (FITD). We simulate a unit cell as shown in Fig. 2(a) with periodic boundary conditions in the directions perpendicular to the direction of propagation thus ensuring a correct periodic continuation of the structure. Along the propagation direction (z-axis), open boundary conditions are employed. A Drude model for metals is used: the plasma frequency for aluminium is ωp=2.243×1016 rad/s and the collision frequency chosen is γ=3.4×1014 Hz. The skin depth is δsd=(2/(µωσ))1/2 where µ is the magnetic permeability which is 4π×10-7 H/m in our case, and σ is the conductivity. Thus, for ω=6.28×1012 and 3.14×1013 rad/s (1 and 5 THz), the skin depth for Al is approximately 81.4 and 36.4 nm respectively. These values assure that the coupling between either face of EOT surface is through the subwavelength hole rather than evanescent waves through the metal within our frequency range. The dielectric constant of the PP was taken as εr=2.25 with loss tangent tgδ=0.001, according to the experimental characterization of the previous section. Finally, a tetrahedral mesh was used and the desired linear equation system solver accuracy in terms of the relative residual normal was chosen as 10-9 and reached in all simulations.

 

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.

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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.

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

The experimental dependence on the size of the hole is plotted in Fig. 5 (dark blue dots for s-polarization, and black and red dots for usual EOT excitation), and is in accordance with similar studies, as well as numerical results (blue, and gray and pink dots for anomalous and common EOT respectively). As it was previously reported for subwavelength hole arrays in the visible [25], the increase of the size of the holes shifts the resonance frequencies related to SR- and LR-SPP-like modes toward lower frequencies, although this is more pronounced for the SR-like mode case. An intuitive idea is based on the fact that the bigger the hole, the lower the frequency cutoff. Therefore, the spectrum governed by the subwavelength holes, that is, the EOT, may shift to allow transmission, but Wood’s anomalies must remain in the same frequency since it depends on the lattice constant. As a result of the last fact, and recalling that the LR-like mode emerge close to air-metal Wood’s anomaly minimum, this explain the less pronounced shift undergone by the LR-like mode. With regards to the anomalous EOT peak, its behaviour seems to follow LR-like mode because of its emergence near the air-metal Wood’s anomaly as Ref. 21 suggests.

5. Conclusion

Anomalous Extraordinary Optical Transmission in subwavelength hole arrays deposited over a PP-substrate is experimentally demonstrated at the so-called THz-gap. Contrary to standard EOT which is explained by the so-called spoof plasmons substantiated both in free-standing and dielectric embedded structures, this EOT for s-polarization arises from surface waves supported by the thin PP layer (that is, in dielectric embedded structures). As a point of interest, we have experimentally found that the amplitude the anomalous peak is similar to the amplitude of the standard EOT SR-SPP-like mode. This result is based on the design and manufacture by contact photolithography of a low-cost but accurate Extraordinary Transmission doubly periodic subwavelength hole array within the so-called THz-gap. Moreover, particular attention is paid to wideband characterization of the PP-substrate used. Both symmetric and antisymmetric modes of the usual EOT are reported and experimental results agree well with numerical analysis and with literature devoted to EOT in other frequencies ranges. These results could find application in the design of novel THz and optical devices like filters and polarisers.

 

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.

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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]  

References

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  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]
  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 (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]

2008 (1)

2007 (3)

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]

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 (2007).
[CrossRef]

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]

2006 (2)

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]

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]

2005 (2)

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]

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]

2004 (3)

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

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]

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]

2003 (2)

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]

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]

2002 (1)

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]

2001 (2)

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]

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]

1999 (2)

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

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]

1998 (1)

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]

1984 (1)

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

1973 (1)

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

1967 (1)

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

1944 (1)

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

1928 (1)

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

1907 (1)

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

Azad, A. K.

Aznabet, M.

Beruete, M.

Bethe, H. A.

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

Bonn, M.

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 (2007).
[CrossRef]

Bravo-Abad, J.

Campillo, I.

Chen, C. C.

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

Degiron, A.

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]

Devaux, E.

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]

Dolado, J. S.

Ebbesen, T. W.

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]

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]

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]

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]

El Mrabet, O.

Falcone, F.

Fedorinina, N. I.

García-Vidal, F. J.

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]

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]

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

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]

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]

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]

García-Vidal, F.J.

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]

Gelfand, A. V.

Ghaemi, H.

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]

Gómez Rivas, J.

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 (2007).
[CrossRef]

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]

Goncharov, Yu. G.

Haring Bolivar, P.

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]

Harootunian, A.

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

He, M.

Hendry, E.

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 (2007).
[CrossRef]

Isaacson, M.

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

Jackson, D. R.

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]

Kim, T. J.

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]

Krishnan, A.

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]

Kuipers, L.

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 (2007).
[CrossRef]

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]

Kurz, H.

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]

Kuznetsov, S. A.

Lewis, A.

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

Lezec, H. J.

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]

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]

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]

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]

Linke, R. A.

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]

Lockyear, M. J.

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 (2007).
[CrossRef]

Lomakin, V.

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]

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]

Martín-Moreno, I.

Martín-Moreno, L.

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]

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

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]

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]

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]

Michielssen, E.

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]

Moreno, E.

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]

Muray, A.

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

Navarro-Cía, M.

Núñez-Manrique, I. J.

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]

Oliner, A. A.

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]

Pellerin, K. M.

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]

Pendry, J.

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]

Pendry, J. B.

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

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]

Pendry, J.B.

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]

Perea, E.

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]

Porto, J.A.

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]

Rayleigh, J.

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

Rodríguez-Seco, J. E.

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]

Sarrazin, M.

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]

Schotsch, C.

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]

Segerink, F. B.

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]

Sorolla, M.

Synge, E. H.

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

Thio, T.

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]

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]

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]

Treacy, M.M.J.

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

Ulrich, R.

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

van der Molen, K. L.

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Figures (5)

Fig. 1.
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.

Fig. 2.
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.

Fig. 3.
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.

Fig. 4.
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.

Fig. 5.
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.

Tables (1)

Tables Icon

Table 1. Key information of fabricated prototypes

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