Selective enhanced resonances of two asymmetric terahertz nano resonators

doi:10.1364/OE.20.025644

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Selective enhanced resonances of two asymmetric terahertz nano resonators

Young-Mi Bahk, Jae-Wook Choi, Jisoo Kyoung, Hyeong-Ryeol Park, Kwang Jun Ahn, and Dai-Sik Kim »View Author Affiliations

Optics Express, Vol. 20, Issue 23, pp. 25644-25653 (2012)
http://dx.doi.org/10.1364/OE.20.025644

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– Abstract
1. Introduction
2. Samples and methods
3. Results and discussion
4. Conclusion
– References and links

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Abstract

We studied the electromagnetic interaction between two asymmetric terahertz nano resonators, rectangular holes which have a few hundred micron lengths but nanoscale widths. We report that the dominant resonant transmission of the structures can be modulated by the horizontal distance between two rectangles due to the different oscillation strength of the asymmetric coupling at two different resonance frequencies. Our results are significant for an optimum design of rectangular holes in terahertz frequency regime for applications such as sensitive nanoparticle detection and terahertz filters.

1. Introduction

The transmission characteristics of electromagnetic (EM) waves through various sub-wavelength holes have been studied theoretically and experimentally since the extraordinary optical transmission (EOT) phenomenon was reported over a decade ago by Ebbesen et al. [1

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

–5

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

]. It has been shown that the interaction between individual elements in an array structure strongly affects the resonance properties, resulting in spectral peak position shifts and the linewidth changes relative to that of a single structure [6

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt. 7(2), S90–S96 (2005). [CrossRef]

–10

M. Shalaby, H. Merbold, M. Peccianti, L. Razzari, G. Sharma, T. Ozaki, R. Morandotti, T. Feurer, A. Weber, L. Heyderman, B. Patterson, and H. Sigg, “Concurrent field enhancement and high transmission of THz radiation in nanoslit arrays,” Appl. Phys. Lett. 99(4), 041110 (2011). [CrossRef]

]. Since then, strongly coupled systems with various geometries have attracted considerable attention in the past few years in a wide spectral range from terahertz (THz) to visible frequencies [11

B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008). [CrossRef] [PubMed]

–22

A. Artar, A. A. Yanik, and H. Altug, “Multispectral plasmon induced transparency in coupled meta-atoms,” Nano Lett. 11(4), 1685–1689 (2011). [CrossRef] [PubMed]

]. Furthermore, by breaking the geometrical symmetry of the coupled structure, new electromagnetic properties, such as achieving resonances with high-quality factors and directional scattering and chirality, were observed due to asymmetric mutual interaction [23

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007). [CrossRef] [PubMed]

–30

E. Hendry, R. V. Mikhaylovskiy, L. D. Barron, M. Kadodwala, and T. J. Davis, “Chiral electromagnetic fields generated by arrays of nanoslits,” Nano Lett. 12(7), 3640–3644 (2012). [CrossRef] [PubMed]

Recently, we have already studied, theoretically and experimentally, the longitudinal [31

H.-R. Park, Y.-M. Bahk, K. J. Ahn, Q. H. Park, D.-S. Kim, L. Martín-Moreno, F. J. García-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano 5(10), 8340–8345 (2011). [CrossRef] [PubMed]

] and transverse [32

Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D.-S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett. 106(1), 013902 (2011). [CrossRef] [PubMed]

] coupling between identical THz nano resonators, which are hundreds of microns long rectangular holes with nanosized widths. According to these works, the resonance properties strongly depend on the distances which control the coupling strength. In particular, for the transverse coupling, a closely packed periodic array of rectangular holes was found to exhibit ultra-broadband transmission due to the strong interaction between the rectangles. To understand the physical origin of these collective behaviors of extended systems, such as chains and arrays, a better understanding of the constituent coupling between two single holes is necessary.

In this work, we investigate transmission characteristics of coupled two THz nano resonators transversely aligned. For symmetric structures, the transmission resonance reveals oscillatory behavior depending on the horizontal distance between the rectangles. Furthermore, we consider two asymmetric structures to distinguish the coupling effects which affect each resonance differently. Compared with transmissions of symmetric structures, asymmetric systems show modulations of the transmissions at two resonant frequencies, caused by locally modified coupling strengths depending on the distance. We interpret our experimental results by using a fully analytical model based on coupled-mode formalism.

2. Samples and methods

We have fabricated pairs of rectangular holes in a 200-nm-thick gold film deposited onto a silicon (Si) substrate with a thickness of 500 μm, as illustrated in Fig. 1(a) . The horizontal distance between two rectangles, d, was varied from 200 μm down to 2 μm. Symmetric samples are rectangular hole pairs which have an equal length of 100 μm and a fixed width of 300 nm. Asymmetric samples are formed by rectangles with two different lengths of 150 μm and 100 μm and the same width of 350 nm. In order to obtain high signal-to-noise ratio, our samples consist of six (nine) vertically aligned two asymmetric (symmetric) rectangles with a separation (center to center) of 160 μm (110 μm), in which the vertical coupling is negligible. Figure 1(b) shows scanning electron microscope (SEM) images of symmetric (left) and asymmetric (right) rectangles with a distance of 100 μm, patterned by electron beam lithography using a negative photoresist and the single layer lift-off process.

Fig. 1 (a) Geometry of a pair of THz nano resonators. The structure consists of two rectangular holes in a 200-nm-thick gold film on a 500-μm-thick Si substrate. The two rectangles have the same or different lengths and the same widths. The samples are illuminated by horizontally polarized light with normal incidence. (b) SEM images of two symmetric (left) and asymmetric (right) THz nano resonators with a distance of 100 μm. Symmetric resonators have lengths l₁ = l₂ = 100 μm and a width w = 300 nm. Asymmetric case have l₁ = 150 μm and l₂ = 100 μm with width of 350 nm. (c) Schematic of THz time-domain spectroscopy setup. Electro-optic sampling method is used to measure the THz time domain signals.

We perform THz time-domain spectroscopy (THz-TDS) to measure transmitted amplitudes through various samples in the frequency range from 0.3 THz to 1 THz [33

M. Exter, C. Fattinger, and D. Grischkowsky, “Terahertz time-domain spectroscopy of water vapor,” Opt. Lett. 14(20), 1128–1130 (1989). [CrossRef] [PubMed]

, 34

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro‐optic field detectors,” Appl. Phys. Lett. 68(21), 2924–2926 (1996). [CrossRef]

]. As shown in Fig. 1(c), a single-cycle THz pulse of about 2 ps duration is generated from a 2 kV cm⁻¹ biased semi-insulating gallium arsenide, GaAs emitter illuminated by a femtosecond Ti:sapphire laser pulse of 150 fs duration, centered at a wavelength of 780 nm with a repetition rate of 76 MHz and the average power of 600 mW. The generated THz pulse is collected and focused using off-axis parabolic mirrors and the diameter of THz spot is about 3 mm. Samples are located at the THz focus center, and the transmitted THz waves are focused onto an electro-optic detection crystal (500-μm-thick zinc telluride, ZnTe (110)) for detecting the horizontal electric field. The THz-TDS system is capable of detecting the transmitted signal through subwavelength holes due to a high signal-to-noise ratio (SNR) (up to 10,000:1). We only consider the case of normal incidence, and the electric field of the incident wave is polarized along the short edge of the rectangle. The transmission properties of the samples are experimentally characterized by the normalized transmitted amplitude defined as

T = \frac{| E_{s a m p l e} (ω) |}{| E_{r e f} (ω) |},

(1)

where E_sample and E_ref are in respective the transmitted electric field amplitude through the sample and only the Si substrate which are covered by a 1 mm by 1 mm aluminum reference aperture. To obtain the near-field enhancement factor of the rectangular hole, we determine the ratios of total area covered by the holes to the reference aperture area. We can assume that the 1 mm aperture is enough to have essentially the same electric field as the incident filed. Dividing the normalized transmitted amplitude T with the coverage ratio, the near-field enhancement factor is obtained from the far-field measurement by Kirchhoff formalism [35

J. S. Kyoung, M. A. Seo, H. R. Park, K. J. Ahn, and D. S. Kim, “Far field detection of terahertz near field enhancement of sub-wavelength slits using Kirchhoff integral formalism,” Opt. Commun. 283(24), 4907–4910 (2010). [CrossRef]

, 36

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009). [CrossRef]

3. Results and discussion

3.1 Single terahertz nano resonators

We begin with the investigation of transmission properties of single THz nano resonators. Figure 2(a) shows experimental results of the transmission through two kinds of single resonators with the fixed width of 350 nm and different lengths of 150 μm and 100 μm. SEM images of these samples are shown in the inset of same figure. The maximum of transmission through two samples show about 4.3% and 2.6% even though the ratios of total area covered by the holes are 0.03% and 0.02%, respectively. This is because the field inside rectangular hole with nano-sized width can be enhanced up to two orders of magnitude higher than the incident field [37

H. R. Park, Y. M. Park, H. S. Kim, J. S. Kyoung, M. A. Seo, D. J. Park, Y. H. Ahn, K. J. Ahn, and D. S. Kim, “Terahertz nanoresonators: giant field enhancement and ultrabroadband performance,” Appl. Phys. Lett. 96(12), 121106 (2010). [CrossRef]

]. The resonance frequency is approximately the cutoff waveguide frequency, ~c/(2n_effl), where n_eff is the effective refractive index of the substrate [38

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95(10), 103901 (2005). [CrossRef] [PubMed]

, 39

J. H. Kang, J.-H. Choe, D. S. Kim, and Q. H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17(18), 15652–15658 (2009). [CrossRef] [PubMed]

]. Normalized-to-area amplitudes obtained by the numerical calculations based on the modal expansion are shown in Fig. 2(b) and in good agreement with the experimental results. The normalized-to-area amplitude is the average enhancement of electric field inside the aperture [32

, 38

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95(10), 103901 (2005). [CrossRef] [PubMed]

]. The discrepancy between the experimental and theoretical spectra may be caused by several reasons such as sample imperfections (gold roughness and structure profile) and the perfect electrical conductor (PEC) approximation in the calculations.

Fig. 2 (a) Normalized transmitted amplitude spectra measured through two types of single THz nano resonators with different lengths l = 150 μm and 100 μm, the same width w = 350 nm. SEM images of the samples are shown in the inset. The scale bar is 30 μm. (b) Normalized-to-area amplitudes as the same presented in Fig. 2(a) are calculated using the modal expansion.

3.2 Coupled-mode formalism

To understand transmission properties of two rectangular holes, we have applied a theoretical coupled-mode formalism based on the modal expansion of the EM fields in the different regions of the structure. A detailed account of theoretical formalism can be found in references [5

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

, 40

J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93(22), 227401 (2004). [CrossRef] [PubMed]

]. The modeling of the system ends up with solving a 4 by 4 matrix for

E_{α}^{I}

and

E_{α}^{I I I}

which are the modal amplitudes of the electric field at the input and output sides of the α^th (α = 1, 2) aperture, respectively:

(\begin{matrix} G_{11}^{I} - Σ_{1} & - G_{1}^{V} & G_{12}^{I} & 0 \\ - G_{1}^{V} & G_{11}^{I I I} - Σ_{1} & 0 & G_{12}^{I I I} \\ G_{21}^{I} & 0 & G_{22}^{I} - Σ_{2} & - G_{2}^{V} \\ 0 & G_{21}^{I I I} & - G_{2}^{V} & G_{22}^{I I I} - Σ_{2} \end{matrix}) (\begin{matrix} E_{1}^{I} \\ E_{1}^{I I I} \\ E_{2}^{I} \\ E_{2}^{I I I} \end{matrix}) = (\begin{matrix} I_{1} \\ 0 \\ I_{2} \\ 0 \end{matrix}) .

(2)

In this equation, the magnitudes

Σ_{α}

and

G_{α}^{V}

are defined as

Σ_{α} = Y_{α} / \tan (q_{z}^{α} h)

and

G_{α}^{V} = Y_{α} / \sin (q_{z}^{α} h),

respectively,

Y_{α} = q_{z}^{α} / k_{0}

where

k_{0} = 2 π / λ

and

q_{z}^{α} = \sqrt{k_{0}^{2} - {(π / l_{α})}^{2}}

is the propagation constant of the fundamental TE mode inside the holes, is the admittance of the plane wave. is related to the bouncing back and forth of the EM fields inside an object α and

G_{α}^{V}

reflects the coupling between the EM fields at the two sides of the object.

I_{α} = 4 \sqrt{2} / i π

represents the direct illumination over the object α. The terms

G_{α β}^{I, I I I}

take into account the EM coupling between the rectangles α and β, occurring at the two interfaces of the structure:

\begin{array}{l} G_{α β}^{I, I I I} = \frac{i}{{(2 π)}^{2}} \frac{w_{β} l_{β}}{2} \iint d k_{x} d k_{y} \frac{k_{x}^{2} + k_{I, I I I z}^{2}}{k_{0} k_{I, I I I z}} F_{α} (k_{x}, k_{y}) F_{β} (k_{x}, k_{y}) e^{- i k_{x} (x_{β} - x_{α})} e^{- i k_{y} (y_{β} - y_{α})} \\ F_{α} (k_{x}, k_{y}) = \sin c (\frac{w_{α} k_{x}}{2}) [\sin c (\frac{π}{2} + \frac{l_{α} k_{y}}{2}) + \sin c (\frac{π}{2} - \frac{l_{α} k_{y}}{2})], \end{array}

(3)

where

k_{I, I I I z}^{} = \sqrt{ε_{I, I I I} k_{0}^{2} - k_{x}^{2} - k_{y}^{2}}

and l_α and w_α are the length and width, and (x_α, y_α) is the position of the rectangle α. These propagators take into account that the point in object β emits EM radiation which can be collected by object α (

G_{α α}^{I, I I I}

is related to the self-illumination of the hole.). Notice that

Re (G_{α β}^{I, I I I})

result from the coupling of the fundamental TE mode with evanescent modes at the two regions and

Im (G_{α β}^{I, I I I})

from the radiative modes. When the thickness h of metal film is very thin (

q_{z}^{α} h < < 1

G_{α}^{V},

Σ_{α}^{},

and

G_{α α}^{I, I I I}

can be approximated to

G_{α}^{V} \approx \frac{λ}{2 π h} > > 1, ​ Σ_{α}^{} \approx G_{α}^{V}, \frac{G_{22}^{I, I I I}}{G_{11}^{I, I I I}} \approx \frac{w_{2} l_{2}}{w_{1} l_{1}},

(4)

so that at each resonance the modal amplitudes of the transmitted electric field at two apertures simplify to

| E_{1}^{I I I} | \approx \frac{| I_{1} |}{2 Im (G_{11}^{a v e} + G_{12}^{a v e})} and | E_{2}^{I I I} | \approx \frac{| I_{2} |}{2 Im (G_{22}^{a v e} + G_{21}^{a v e})},

(5)

where

G_{α β}^{a v e} = \frac{G_{α β}^{I} + G_{α β}^{I I I}}{2}

is the averaged EM coupling at input and output sides. When we compare the transmitted electric field of a non-coupled single rectangular hole

| E_{α}^{I I I} | \approx \frac{| I_{α} |}{2 Im (G_{α α}^{a v e})},

the above equations demonstrate clearly that coupling effect on the transmission at resonance is governed by the imaginary part of the EM coupling

G_{α β}^{a v e}

[32

]. The interference of the radiated field in the far-field region makes the transmission to be effectively enhanced (

Im (G_{α β}^{a v e}) < 0

) or reduced (

Im (G_{α β}^{a v e}) > 0

), depending on the distance between two holes.

3.3 Two symmetric terahertz nano resonators

We investigate the symmetric coupling in pairs of THz nano resonators. The symmetric system consists of two identical rectangular holes with width w = 300 nm and length l = 100 μm. We fabricated a set of seven samples with different distance d which were varied from 200 μm down to 5 μm, as shown in the left column of Fig. 3(a) . Notice that the nanometer scale width of the resonators enables reaching a few micrometer distance which is a deep subwavelength distance (d = 5 μm ~λ_res / 100). It allows us to realize the strong coupling effects. The experimentally acquired transmitted amplitude spectra for these different samples are presented in the middle column. The magnitude of the transmission peak slightly decreases and returns to increase as the distance is reduced from 200 μm to 80 μm. For the sample with the smallest distance (d = 5 μm), however, the resonant transmitted amplitude dramatically reduces due to the strong interaction between two nano resonators. The calculated total normalized-to-area amplitudes are shown in the right column for a comparison. The discrepancy between the experimental and theoretical spectra can be caused by the calculation based on PEC approximation, as mentioned before. Nevertheless the spectral features and tendencies observed in the experimental results are well reproduced by the theoretical calculations.

Fig. 3 (a) Experimental and calculated transmission spectra of two symmetric THz nano resonators with different distances. SEM images of the corresponding structures are shown in the left column. The middle column shows the measured spectra. The right column shows the calculated total normalized-to-area amplitude for the corresponding d. (b) Evolution of the transmission resonance amplitude normalized by that of a single rectangular hole.

To investigate the evolution of the symmetric coupling behavior, we have normalized the maximum transmitted amplitude of each sample by that of a single nano resonator, (see Fig. 3(b)). A distance-dependent coupling effect is clearly observable when using the normalization: one would expect that the normalized maximum transmission is 2 for two non-coupled resonators. First concentrating on the overall tendency of the maximum transmission, the resonance transmission is not a monotonic function of d. The origin of the non-monotonic behavior can be traced to the oscillatory and slowly decaying trend of EM coupling,

I m (G_{12}^{a v e})

[32

]. Specifically, the total resonant transmission through the pair of rectangles for d = 100 μm is enhanced 3 times more than that of a single hole. It means that the maximum transmission through each resonator of the pair increases by a factor 1.5 due to the EM coupling with respect to that of a single hole. When d < 100 μm, the transmission is decreasing as d is reduced and the normalized transmission is smaller than 2 times of single hole case for d < 50 μm. This short-range interaction can be understood by the strong overlapping of two large transmission cross-sections characterizing rectangular holes with extremely large aspect ratio.

3.4 Two asymmetric terahertz nano resonators

Next, we investigate transmission properties of asymmetric THz nano resonator pairs. The sample structures consist of two rectangular holes with different lengths, l₁ = 150 μm and l₂ = 100 μm but a same width w = 350 nm. The respective resonant frequencies of these rectangles are located at 0.4 THz and 0.6 THz, as demonstrated in Fig. 2. The left column of Fig. 4(a) shows the SEM images of different samples with the decreasing d, from 200 μm down to 2 μm. The measured spectra are shown in the middle column of the figure. When the distance between two holes is sufficiently large for weak coupling (d = 200 μm), the transmission spectrum shows two well-separated resonances centered at about 0.4 THz (I) and 0.6 THz (II). As the distance is decreased from 200 μm, 170 μm and 130 μm, the only resonance II slightly decreases and returns to increase. For d = 100 μm and 80 μm, it is seen that the resonance II is more enhanced while the resonance I is slightly reduced, so that the resonance II is dominant. By further decreasing d down to 2 μm, the resonance II is drastically suppressed, and the resonance I is more enhanced, resulting in a dominant resonance at 0.4 THz. The strong coupling in the asymmetric system leads to the suppression of higher frequency resonance. As a result, the dominant resonance in the asymmetric system can be modulated and chosen by varying the distance between two nano resonators. The modulation nature of the observed results is confirmed by theoretical calculations, which is in good agreement with the experimental results (see the right column of Fig. 4(a)). In Fig. 4(b), we show the transmission peak at two different resonances normalized by the respective maximum transmission through a single hole, as a function of d. As expected, the maximum transmissions at two resonances have oscillatory behavior as changing the distance. However, more enhanced resonance oscillation amplitude at the resonance II is clearly observed, while the resonance oscillation amplitude at the resonance I is not so much changed. This is because the high frequency resonance can be excited at the long rectangular hole, while it is difficult to excite the low frequency resonance at the short rectangular hole due to the asymmetric coupling effect. Furthermore, the in-phase (out-of-phase) excitation of two rectangular holes can enhance (reduce) the maximum transmission of the high frequency resonance with changing of the distance. Remarkably, at the resonance II the transmitted amplitude reaches up to about 2 times when compared to the case of a single hole. It leads to the change of the dominant resonance from the resonance I to the resonance II.

Fig. 4 (a) Transmission spectra for two asymmetric THz nano resonators in dependence on the distances d. SEM images (left column), the measured spectra (middle column), and the theoretical calculations (right column) of the corresponding structures are shown in the figure. (b) Evolution of the two resonant transmission normalized by the respective maximum transmission of a single resonator as a function of d.

To interpret the modification of the oscillation strength at two resonance frequencies, the EM coupling between two holes

Im (G_{α β}^{a v e})

normalized by

Im (G_{α α}^{a v e})

are plotted as a function of the distance in Fig. 5 . The oscillatory and slowly decaying trend and the period of the coupling terms at two resonances are similar with the change of maximum transmission plotted in Fig. 4(b). As we mentioned before, the negative (positive) of

Im (G_{α β}^{a v e})

is accompanied by the enhanced (suppressed) transmission. In addition, a strong oscillation is observed at resonance II, while the oscillation at resonance I has a much weaker amplitude. Particularly, when the distance is decreasing down to the short-range interaction regime,

Im (G_{12}^{a v e})

increases up to 2 times of self-energy of single hole,

Im (G_{11}^{a v e})

, which leads to the suppression of the resonance I. As a results, the asymmetric oscillation strength of the EM coupling leads to the modulation of the dominant resonance peak.

Fig. 5 Evolution of imaginary parts of the averaged EM coupling between two holes,

G_{α β}^{a v e} = \frac{G_{α β}^{I} + G_{α β}^{I I I}}{2}

calculated at resonance I and resonance II.

4. Conclusion

In conclusion, we have experimentally and theoretically demonstrated the coupling effects in symmetric and asymmetric terahertz nano resonator pairs. For the symmetric case, we obtained an optimum distance for the maximum resonant transmission through two coupled rectangular holes. In addition, the resonant transmission shows an oscillatory behavior with the distance between two holes, due to the oscillatory electromagnetic coupling. By breaking the symmetry of the structure, the oscillation strengths at two different resonances can be modified, showing that the oscillation amplitude at the higher (lower) frequency resonance is enhanced (suppressed). These results lead to the modulation and interchange of the dominant resonance peak. Our findings provide valuable insight into the design and optimization of rectangular holes with desirable optical properties, such as maximum enhanced electric fields.

Acknowledgment

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (SRC, No: 2008-0062255) (GRL, No: K20815000003) (Others, No: 2010-0029648, 2011-0019170, 2011-0020209), the Global Frontier R&D Program on Center for Multiscale Energy System, and Hi Seoul Science / Humanities Fellowship from Seoul Scholarship Foundation. We would like to thank Prof. Paul C. M. Planken, Prof. Aurèle J. L. Adam, and Nishant Kumar (TU Delft) for discussions about near-field.

References and links

1.	T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
2.	J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]
3.	J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys. 2(2), 120–123 (2006). [CrossRef]
4.	C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007). [CrossRef] [PubMed]
5.	F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]
6.	A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt. 7(2), S90–S96 (2005). [CrossRef]
7.	Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett. 96(23), 233901 (2006). [CrossRef] [PubMed]
8.	A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite arrays of slits,” Phys. Rev. B 76(23), 235430 (2007). [CrossRef]
9.	A. Mary, S. G. Rodrigo, L. Martín-Moreno, and F. J. García-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76(19), 195414 (2007). [CrossRef]
10.	M. Shalaby, H. Merbold, M. Peccianti, L. Razzari, G. Sharma, T. Ozaki, R. Morandotti, T. Feurer, A. Weber, L. Heyderman, B. Patterson, and H. Sigg, “Concurrent field enhancement and high transmission of THz radiation in nanoslit arrays,” Appl. Phys. Lett. 99(4), 041110 (2011). [CrossRef]
11.	B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008). [CrossRef] [PubMed]
12.	P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett. 8(4), 1174–1178 (2008). [CrossRef] [PubMed]
13.	I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009). [CrossRef] [PubMed]
14.	H. Fischer and O. J. F. Martin, “Retardation-induced plasmonic blinking in coupled nanoparticles,” Opt. Lett. 34(3), 368–370 (2009). [CrossRef] [PubMed]
15.	D. S. Kim, J. Heo, S. H. Ahn, S. W. Han, W. S. Yun, and Z. H. Kim, “Real-space mapping of the strongly coupled plasmons of nanoparticle dimers,” Nano Lett. 9(10), 3619–3625 (2009). [CrossRef] [PubMed]
16.	V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010). [CrossRef] [PubMed]
17.	N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl. 49(51), 9838–9852 (2010). [CrossRef] [PubMed]
18.	M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett. 10(7), 2721–2726 (2010). [CrossRef] [PubMed]
19.	R. Taubert, R. Ameling, T. Weiss, A. Christ, and H. Giessen, “From near-field to far-field coupling in the third dimension: retarded interaction of particle plasmons,” Nano Lett. 11(10), 4421–4424 (2011). [CrossRef] [PubMed]
20.	D. Weber, P. Albella, P. Alonso-González, F. Neubrech, H. Gui, T. Nagao, R. Hillenbrand, J. Aizpurua, and A. Pucci, “Longitudinal and transverse coupling in infrared gold nanoantenna arrays: long range versus short range interaction regimes,” Opt. Express 19(16), 15047–15061 (2011). [CrossRef] [PubMed]
21.	N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011). [CrossRef] [PubMed]
22.	A. Artar, A. A. Yanik, and H. Altug, “Multispectral plasmon induced transparency in coupled meta-atoms,” Nano Lett. 11(4), 1685–1689 (2011). [CrossRef] [PubMed]
23.	V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007). [CrossRef] [PubMed]
24.	A. Christ, Y. Ekinci, H. H. Solak, N. A. Gippius, S. G. Tikhodeev, and O. J. F. Martin, “Controlling the fano interference in a plasmonic lattice,” Phys. Rev. B 76(20), 201405 (2007). [CrossRef]
25.	A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8(8), 2171–2175 (2008). [CrossRef] [PubMed]
26.	C.-Y. Chen, I.-W. Un, N.-H. Tai, and T.-J. Yen, “Asymmetric coupling between subradiant and superradiant plasmonic resonances and its enhanced sensing performance,” Opt. Express 17(17), 15372–15380 (2009). [CrossRef] [PubMed]
27.	Z. Liu and G. Jin, “Phase effects in the enhanced transmission through compound subwavelength rectangular hole arrays,” J. Appl. Phys. 106(6), 063122–063126 (2009). [CrossRef]
28.	T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4(5), 312–315 (2010). [CrossRef]
29.	T. Shegai, S. Chen, V. D. Miljković, G. Zengin, P. Johansson, and M. Käll, “A bimetallic nanoantenna for directional colour routing,” Nat Commun 2, 481 (2011). [CrossRef] [PubMed]
30.	E. Hendry, R. V. Mikhaylovskiy, L. D. Barron, M. Kadodwala, and T. J. Davis, “Chiral electromagnetic fields generated by arrays of nanoslits,” Nano Lett. 12(7), 3640–3644 (2012). [CrossRef] [PubMed]
31.	H.-R. Park, Y.-M. Bahk, K. J. Ahn, Q. H. Park, D.-S. Kim, L. Martín-Moreno, F. J. García-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano 5(10), 8340–8345 (2011). [CrossRef] [PubMed]
32.	Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D.-S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett. 106(1), 013902 (2011). [CrossRef] [PubMed]
33.	M. Exter, C. Fattinger, and D. Grischkowsky, “Terahertz time-domain spectroscopy of water vapor,” Opt. Lett. 14(20), 1128–1130 (1989). [CrossRef] [PubMed]
34.	Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro‐optic field detectors,” Appl. Phys. Lett. 68(21), 2924–2926 (1996). [CrossRef]
35.	J. S. Kyoung, M. A. Seo, H. R. Park, K. J. Ahn, and D. S. Kim, “Far field detection of terahertz near field enhancement of sub-wavelength slits using Kirchhoff integral formalism,” Opt. Commun. 283(24), 4907–4910 (2010). [CrossRef]
36.	M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009). [CrossRef]
37.	H. R. Park, Y. M. Park, H. S. Kim, J. S. Kyoung, M. A. Seo, D. J. Park, Y. H. Ahn, K. J. Ahn, and D. S. Kim, “Terahertz nanoresonators: giant field enhancement and ultrabroadband performance,” Appl. Phys. Lett. 96(12), 121106 (2010). [CrossRef]
38.	F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett. 95(10), 103901 (2005). [CrossRef] [PubMed]
39.	J. H. Kang, J.-H. Choe, D. S. Kim, and Q. H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express 17(18), 15652–15658 (2009). [CrossRef] [PubMed]
40.	J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93(22), 227401 (2004). [CrossRef] [PubMed]

OCIS Codes
(260.5740) Physical optics : Resonance
(300.6495) Spectroscopy : Spectroscopy, teraherz
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Spectroscopy

History
Original Manuscript: July 24, 2012
Revised Manuscript: October 22, 2012
Manuscript Accepted: October 23, 2012
Published: October 29, 2012

Citation
Young-Mi Bahk, Jae-Wook Choi, Jisoo Kyoung, Hyeong-Ryeol Park, Kwang Jun Ahn, and Dai-Sik Kim, "Selective enhanced resonances of two asymmetric terahertz nano resonators," Opt. Express 20, 25644-25653 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-23-25644

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References

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998). [CrossRef]
J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004). [CrossRef] [PubMed]
J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys.2(2), 120–123 (2006). [CrossRef]
C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007). [CrossRef] [PubMed]
F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys.82(1), 729–787 (2010). [CrossRef]
A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt.7(2), S90–S96 (2005). [CrossRef]
Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.96(23), 233901 (2006). [CrossRef] [PubMed]
A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite arrays of slits,” Phys. Rev. B76(23), 235430 (2007). [CrossRef]
A. Mary, S. G. Rodrigo, L. Martín-Moreno, and F. J. García-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B76(19), 195414 (2007). [CrossRef]
M. Shalaby, H. Merbold, M. Peccianti, L. Razzari, G. Sharma, T. Ozaki, R. Morandotti, T. Feurer, A. Weber, L. Heyderman, B. Patterson, and H. Sigg, “Concurrent field enhancement and high transmission of THz radiation in nanoslit arrays,” Appl. Phys. Lett.99(4), 041110 (2011). [CrossRef]
B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett.101(14), 143902 (2008). [CrossRef] [PubMed]
P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett.8(4), 1174–1178 (2008). [CrossRef] [PubMed]
I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett.103(21), 213902 (2009). [CrossRef] [PubMed]
H. Fischer and O. J. F. Martin, “Retardation-induced plasmonic blinking in coupled nanoparticles,” Opt. Lett.34(3), 368–370 (2009). [CrossRef] [PubMed]
D. S. Kim, J. Heo, S. H. Ahn, S. W. Han, W. S. Yun, and Z. H. Kim, “Real-space mapping of the strongly coupled plasmons of nanoparticle dimers,” Nano Lett.9(10), 3619–3625 (2009). [CrossRef] [PubMed]
V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010). [CrossRef] [PubMed]
N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl.49(51), 9838–9852 (2010). [CrossRef] [PubMed]
M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett.10(7), 2721–2726 (2010). [CrossRef] [PubMed]
R. Taubert, R. Ameling, T. Weiss, A. Christ, and H. Giessen, “From near-field to far-field coupling in the third dimension: retarded interaction of particle plasmons,” Nano Lett.11(10), 4421–4424 (2011). [CrossRef] [PubMed]
D. Weber, P. Albella, P. Alonso-González, F. Neubrech, H. Gui, T. Nagao, R. Hillenbrand, J. Aizpurua, and A. Pucci, “Longitudinal and transverse coupling in infrared gold nanoantenna arrays: long range versus short range interaction regimes,” Opt. Express19(16), 15047–15061 (2011). [CrossRef] [PubMed]
N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011). [CrossRef] [PubMed]
A. Artar, A. A. Yanik, and H. Altug, “Multispectral plasmon induced transparency in coupled meta-atoms,” Nano Lett.11(4), 1685–1689 (2011). [CrossRef] [PubMed]
V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007). [CrossRef] [PubMed]
A. Christ, Y. Ekinci, H. H. Solak, N. A. Gippius, S. G. Tikhodeev, and O. J. F. Martin, “Controlling the fano interference in a plasmonic lattice,” Phys. Rev. B76(20), 201405 (2007). [CrossRef]
A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008). [CrossRef] [PubMed]
C.-Y. Chen, I.-W. Un, N.-H. Tai, and T.-J. Yen, “Asymmetric coupling between subradiant and superradiant plasmonic resonances and its enhanced sensing performance,” Opt. Express17(17), 15372–15380 (2009). [CrossRef] [PubMed]
Z. Liu and G. Jin, “Phase effects in the enhanced transmission through compound subwavelength rectangular hole arrays,” J. Appl. Phys.106(6), 063122–063126 (2009). [CrossRef]
T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics4(5), 312–315 (2010). [CrossRef]
T. Shegai, S. Chen, V. D. Miljković, G. Zengin, P. Johansson, and M. Käll, “A bimetallic nanoantenna for directional colour routing,” Nat Commun2, 481 (2011). [CrossRef] [PubMed]
E. Hendry, R. V. Mikhaylovskiy, L. D. Barron, M. Kadodwala, and T. J. Davis, “Chiral electromagnetic fields generated by arrays of nanoslits,” Nano Lett.12(7), 3640–3644 (2012). [CrossRef] [PubMed]
H.-R. Park, Y.-M. Bahk, K. J. Ahn, Q. H. Park, D.-S. Kim, L. Martín-Moreno, F. J. García-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5(10), 8340–8345 (2011). [CrossRef] [PubMed]
Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D.-S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106(1), 013902 (2011). [CrossRef] [PubMed]
M. Exter, C. Fattinger, and D. Grischkowsky, “Terahertz time-domain spectroscopy of water vapor,” Opt. Lett.14(20), 1128–1130 (1989). [CrossRef] [PubMed]
Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro‐optic field detectors,” Appl. Phys. Lett.68(21), 2924–2926 (1996). [CrossRef]
J. S. Kyoung, M. A. Seo, H. R. Park, K. J. Ahn, and D. S. Kim, “Far field detection of terahertz near field enhancement of sub-wavelength slits using Kirchhoff integral formalism,” Opt. Commun.283(24), 4907–4910 (2010). [CrossRef]
M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics3(3), 152–156 (2009). [CrossRef]
H. R. Park, Y. M. Park, H. S. Kim, J. S. Kyoung, M. A. Seo, D. J. Park, Y. H. Ahn, K. J. Ahn, and D. S. Kim, “Terahertz nanoresonators: giant field enhancement and ultrabroadband performance,” Appl. Phys. Lett.96(12), 121106 (2010). [CrossRef]
F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95(10), 103901 (2005). [CrossRef] [PubMed]
J. H. Kang, J.-H. Choe, D. S. Kim, and Q. H. Park, “Substrate effect on aperture resonances in a thin metal film,” Opt. Express17(18), 15652–15658 (2009). [CrossRef] [PubMed]
J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett.93(22), 227401 (2004). [CrossRef] [PubMed]

Ahn, K. J.
Ahn, S. H.
Ahn, Y. H.
Aizpurua, J.
Albella, P.
Alivisatos, A. P.
Alonso-González, P.
Altug, H.
Ameling, R.
Artar, A.
Auguié, B.
Bahk, Y. M.
Bahk, Y.-M.
Barnes, W. L.
Barron, L. D.
Bitzer, A.
Bravo-Abad, J.
Chang, W.-S.
Chen, C.-Y.
Chen, S.
Choe, J.-H.
Choi, S. S.
Christ, A.
Davis, T. J.
Degiron, A.
Ebbesen, T. W.
Ekinci, Y.
Eng, L. M.
Exter, M.
Fattinger, C.
Fedotov, V. A.
Fernández-Domínguez, A. I.
Feurer, T.
Fischer, H.
Frimmer, M.
Garcia-Vidal, F. J.
García-Vidal, F. J.
Genet, C.
Ghaemi, H. F.
Giessen, H.
Gippius, N. A.
Grischkowsky, D.
Gui, H.
Halas, N. J.
Han, S. W.
Hendry, E.
Hentschel, M.
Heo, J.
Heyderman, L.
Hillenbrand, R.
Hofmann, H. F.
Jin, G.
Johansson, P.
Kadodwala, M.
Kadoya, Y.
Käll, M.
Kang, J. H.
Kim, D. S.
Kim, D.-S.
Kim, H. S.
Kim, Z. H.
Koenderink, A. F.
Koo, S. M.
Kosako, T.
Kuipers, L.
Kuo, P.
Kyoung, J. S.
Lal, S.
Lezec, H. J.
Link, S.
Litz, M.
Liu, N.
Liu, Z.
Martin, O. J. F.
Martin-Moreno, L.
Martín-Moreno, L.
Mary, A.
Merbold, H.
Mikhaylovskiy, R. V.
Miljkovic, V. D.
Morandotti, R.
Moreno, E.
Nagao, T.
Neubrech, F.
Nordlander, P.
Olk, P.
Ozaki, T.
Papasimakis, N.
Park, D. J.
Park, G. S.
Park, H. R.
Park, H.-R.
Park, N. K.
Park, Q. H.
Park, Y. M.
Patterson, B.
Peccianti, M.
Pendry, J. B.
Planken, P. C. M.
Plum, E.
Porto, J. A.
Prosvirnin, S. L.
Przybilla, F.
Pucci, A.
Qiu, M.
Razzari, L.
Renger, J.
Rodrigo, S. G.
Rose, M.
Ruan, Z.
Saliba, M.
Seo, M. A.
Sersic, I.
Shalaby, M.
Sharma, G.
Shegai, T.
Sigg, H.
Solak, H. H.
Suwal, O. K.
Tai, N.-H.
Taubert, R.
Thio, T.
Tikhodeev, S. G.
Tsai, D. P.
Un, I.-W.
Verhagen, E.
Vogelgesang, R.
Walther, M.
Weber, A.
Weber, D.
Weiss, T.
Wenzel, M. T.
Wolff, P. A.
Wu, Q.
Yanik, A. A.
Yen, T.-J.
Yun, W. S.
Zengin, G.
Zhang, X.-C.
Zheludev, N. I.

ACS Nano

H.-R. Park, Y.-M. Bahk, K. J. Ahn, Q. H. Park, D.-S. Kim, L. Martín-Moreno, F. J. García-Vidal, and J. Bravo-Abad, “Controlling terahertz radiation with nanoscale metal barriers embedded in nano slot antennas,” ACS Nano5(10), 8340–8345 (2011). [CrossRef] [PubMed]

Angew. Chem. Int. Ed. Engl.

N. Liu and H. Giessen, “Coupling effects in optical metamaterials,” Angew. Chem. Int. Ed. Engl.49(51), 9838–9852 (2010). [CrossRef] [PubMed]

Appl. Phys. Lett.

M. Shalaby, H. Merbold, M. Peccianti, L. Razzari, G. Sharma, T. Ozaki, R. Morandotti, T. Feurer, A. Weber, L. Heyderman, B. Patterson, and H. Sigg, “Concurrent field enhancement and high transmission of THz radiation in nanoslit arrays,” Appl. Phys. Lett.99(4), 041110 (2011). [CrossRef]
Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro‐optic field detectors,” Appl. Phys. Lett.68(21), 2924–2926 (1996). [CrossRef]
H. R. Park, Y. M. Park, H. S. Kim, J. S. Kyoung, M. A. Seo, D. J. Park, Y. H. Ahn, K. J. Ahn, and D. S. Kim, “Terahertz nanoresonators: giant field enhancement and ultrabroadband performance,” Appl. Phys. Lett.96(12), 121106 (2010). [CrossRef]

Chem. Rev.

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev.111(6), 3913–3961 (2011). [CrossRef] [PubMed]

J. Appl. Phys.

Z. Liu and G. Jin, “Phase effects in the enhanced transmission through compound subwavelength rectangular hole arrays,” J. Appl. Phys.106(6), 063122–063126 (2009). [CrossRef]

J. Opt. A, Pure Appl. Opt.

A. Degiron and T. W. Ebbesen, “The role of localized surface plasmon modes in the enhanced transmission of periodic subwavelength apertures,” J. Opt. A, Pure Appl. Opt.7(2), S90–S96 (2005). [CrossRef]

Nano Lett.

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nanoparticles,” Nano Lett.8(4), 1174–1178 (2008). [CrossRef] [PubMed]
M. Hentschel, M. Saliba, R. Vogelgesang, H. Giessen, A. P. Alivisatos, and N. Liu, “Transition from isolated to collective modes in plasmonic oligomers,” Nano Lett.10(7), 2721–2726 (2010). [CrossRef] [PubMed]
R. Taubert, R. Ameling, T. Weiss, A. Christ, and H. Giessen, “From near-field to far-field coupling in the third dimension: retarded interaction of particle plasmons,” Nano Lett.11(10), 4421–4424 (2011). [CrossRef] [PubMed]
E. Hendry, R. V. Mikhaylovskiy, L. D. Barron, M. Kadodwala, and T. J. Davis, “Chiral electromagnetic fields generated by arrays of nanoslits,” Nano Lett.12(7), 3640–3644 (2012). [CrossRef] [PubMed]
A. Artar, A. A. Yanik, and H. Altug, “Multispectral plasmon induced transparency in coupled meta-atoms,” Nano Lett.11(4), 1685–1689 (2011). [CrossRef] [PubMed]
D. S. Kim, J. Heo, S. H. Ahn, S. W. Han, W. S. Yun, and Z. H. Kim, “Real-space mapping of the strongly coupled plasmons of nanoparticle dimers,” Nano Lett.9(10), 3619–3625 (2009). [CrossRef] [PubMed]
A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett.8(8), 2171–2175 (2008). [CrossRef] [PubMed]

Nat Commun

T. Shegai, S. Chen, V. D. Miljković, G. Zengin, P. Johansson, and M. Käll, “A bimetallic nanoantenna for directional colour routing,” Nat Commun2, 481 (2011). [CrossRef] [PubMed]

Nat. Photonics

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics4(5), 312–315 (2010). [CrossRef]
M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics3(3), 152–156 (2009). [CrossRef]

Nat. Phys.

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. García-Vidal, L. Martín-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nat. Phys.2(2), 120–123 (2006). [CrossRef]

Nature

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007). [CrossRef] [PubMed]
T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998). [CrossRef]

Opt. Commun.

J. S. Kyoung, M. A. Seo, H. R. Park, K. J. Ahn, and D. S. Kim, “Far field detection of terahertz near field enhancement of sub-wavelength slits using Kirchhoff integral formalism,” Opt. Commun.283(24), 4907–4910 (2010). [CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

A. Christ, Y. Ekinci, H. H. Solak, N. A. Gippius, S. G. Tikhodeev, and O. J. F. Martin, “Controlling the fano interference in a plasmonic lattice,” Phys. Rev. B76(20), 201405 (2007). [CrossRef]
A. I. Fernández-Domínguez, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite arrays of slits,” Phys. Rev. B76(23), 235430 (2007). [CrossRef]
A. Mary, S. G. Rodrigo, L. Martín-Moreno, and F. J. García-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B76(19), 195414 (2007). [CrossRef]

Phys. Rev. Lett.

Z. Ruan and M. Qiu, “Enhanced transmission through periodic arrays of subwavelength holes: the role of localized waveguide resonances,” Phys. Rev. Lett.96(23), 233901 (2006). [CrossRef] [PubMed]
I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett.103(21), 213902 (2009). [CrossRef] [PubMed]
B. Auguié and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett.101(14), 143902 (2008). [CrossRef] [PubMed]
V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett.104(22), 223901 (2010). [CrossRef] [PubMed]
V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett.99(14), 147401 (2007). [CrossRef] [PubMed]
Y. M. Bahk, H. R. Park, K. J. Ahn, H. S. Kim, Y. H. Ahn, D.-S. Kim, J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, “Anomalous band formation in arrays of terahertz nanoresonators,” Phys. Rev. Lett.106(1), 013902 (2011). [CrossRef] [PubMed]
F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of light through a single rectangular hole,” Phys. Rev. Lett.95(10), 103901 (2005). [CrossRef] [PubMed]
J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett.93(22), 227401 (2004). [CrossRef] [PubMed]

Rev. Mod. Phys.

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys.82(1), 729–787 (2010). [CrossRef]

Science

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004). [CrossRef] [PubMed]

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