Terahertz near-field enhancement in narrow rectangular apertures on metal film

doi:10.1364/OE.17.012493

Terahertz near-field enhancement in narrow rectangular apertures on metal film

D. J. Park, S. B. Choi, Y. H. Ahn, F. Rotermund, I. B. Sohn, Chul Kang, M. S. Jeong, and D. S. Kim »View Author Affiliations

Optics Express, Vol. 17, Issue 15, pp. 12493-12501 (2009)
http://dx.doi.org/10.1364/OE.17.012493

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▸ Article Outline
– Abstract
1. Introduction
2. Sample preparation and experiments
3. Theory and discussion
4. Conclusions
– References and links

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Abstract

We report huge field accumulations in rectangular aperture arrays on thin metal film by using shape resonance in THz frequency region. A huge far-field transmission enhancement is observed in samples of various widths ranging from 10 µm to 1.8 µm which correspond to only an order of λ/100. Theoretical calculations based on vector diffraction theory indicates 230 times near-field enhancement in case of the 1.8 µm wide rectangular aperture. Transmission measurement through the single rectangular aperture shows that the shape resonance, not the periodicity, is mainly responsible for the transmission enhancement and the corresponding field enhancement.

1. Introduction

Accumulating electromagnetic field into various subwavelength structures such as single hole and array of holes [1

S. C. Hohng, D. S. Kim, Y. C. Yoon, V. Malyarchuk, C. Lienau, J. W. Park, K. H. Yoo, J. Kim, S. H. Han, and Q. H. Park, “Evolution of the near-field patterns into the far-field in surface plasmonic band gap nanostructures,” J. Korean Phys. Soc. 46 (2005).

–19

D. J. Park, S. B. Choi, Y. H. Ahn, Q. H. Park, and D. S. Kim, “Theoretical Study of terahertz Near-Field Enhancement Assisted by Shape Resonance in Rectangular Hole Arrays in Metal Films,” J. Korean Phys. Soc. 54, 7 (2009).

], single slit and array of slits [20

K. G. Lee and Q. H. Park, “Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits,” Phys. Rev. Lett. 95, 103902–103904 (2005). [CrossRef] [PubMed]

–34

D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93 (2008). [CrossRef]

], nano- or micro-particles [35

Y. B. Ji, E. S. Lee, J. S. Jang, and T. I. Jeon, “Enhancement of the detection of THz Sommerfeld wave using a conical wire waveguide,” Opt. Express 16 , 271–278 (2008). [CrossRef] [PubMed]

–39

T. Klar, M. Perner, S. Grosse, G. Von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998). [CrossRef]

], and nanowires, etc., has been the major issue in a wide spectral range from THz to visible frequencies. The reason why this phenomenon is widely investigated is that the field localization is closely connected to the field enhancement which has a critical importance in many practical applications such as near-field fabrication, metamaterials [40

R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16, 6537–6543 (2008). [CrossRef] [PubMed]

], superlensing [41

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Superlens,” Nano Lett. 7, 403–408 (2007). [CrossRef] [PubMed]

, 42

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef] [PubMed]

] and bio-sensing [43

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999). [CrossRef]

]. The problem lies behind is that many part of the incident electromagnetic waves are absorbed or scattered, so that only small part of the waves can be localized inside the subwavelength structures. This has been described well by H. A. Bethe [44

H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163 (1944). [CrossRef]

Recent investigations on the transmission enhancement through the subwavelength apertures or slits on the metal films have successfully addressed this issue. The resonance phenomena such as surface plasmon polariton excitation [2

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

, 20

K. G. Lee and Q. H. Park, “Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits,” Phys. Rev. Lett. 95, 103902–103904 (2005). [CrossRef] [PubMed]

, 29

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901 (2003). [CrossRef] [PubMed]

, 45

D. J. Park, S. B. Choi, K. J. Ahn, D. S. Kim, J. H. Kang, Q. H. Park, M. S. Jeong, and D. K. Ko, “Experimental verification of surface plasmon amplification on a metallic transmission grating,” Phys. Rev. B 77, 115451–115454 (2008).

], quasi-waveguide resonance, Fabry-Perot resonance [24

J. W. Lee, M. A. Seo, D. J. Park, S. C. Jeoung, Q. H. Park, C. Lienau, and D. S. Kim, “Terahertz transparency at Fabry-Perot resonances of periodic slit arrays in a metal plate: experiment and theory,” Opt. Express 14, 12637–12643 (2006). [CrossRef] [PubMed]

, 32

J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414–035415 (2007). [CrossRef]

], shape resonance [5

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. Lett. 95, 103901–103904 (2005). [CrossRef] [PubMed]

, 18

F. J. Garcia-Vidal, L. Martin-Moreno, E. Moreno, L. K. S. Kumar,, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411–153414 (2006). [CrossRef]

, 31

J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz Electromagnetic Wave Transmission through Random Arrays of Single Rectangular Holes and Slits in Thin Metallic Sheets,” Phys. Rev. Lett. 99, 137401–137404 (2007). [CrossRef] [PubMed]

], and the antenna resonance [38

J. Hao and G. W. Hanson, “Infrared and optical properties of carbon nanotube dipole antennas,” IEEE Trans. Nanotechnol. 5, 766–775 (2006). [CrossRef]

, 46

J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. G. de Abajo, B. K. Kelley, and T. Mallouk, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B 71, 235420–235413 (2005). [CrossRef]

–48

G. W. Bryant, F. J. Garcia de Abajo, and J. Aizpurua, “Mapping the Plasmon Resonances of Metallic Nanoantennas,” Nano Lett. 8, 631–636 (2008). [CrossRef] [PubMed]

] have made it possible to achieve both the field localization and the enhancement without losing significant energies. In general, the energy loss or the field localization factor is strongly related to how strong the resonance is. Recently perfect transmission in the subwavelength aperture has been demonstrated in THz frequency regime, where the shape resonance plays a crucial role [5

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. Lett. 95, 103901–103904 (2005). [CrossRef] [PubMed]

, 18

, 24

]. With the shape resonance, the field is localized near and inside the cavity, and the field enhancement factor is inversely proportional to coverage, β, which is defined by the fractional area of opening region. For instance, in the recent work by J. W. Lee et al. [24

, 31

], ~100% transmission was demonstrated successfully by using the random arrays of rectangles on aluminium film, with the coverage of 12% and the near-field enhancement factor of 8. On the other hand, the question still arises on whether we can make the coverage extremely small by reducing the width of the rectangular aperture even down to 1 µm while maintaining considerable amounts of transmission, and accordingly, whether we can achieve the field enhancement factors of more than 100.

In this report, we performed THz time-domain spectroscopies (THz-TDS) in single and arrays of rectangular apertures and observed the THz transmission enhancement in the samples with the coverage of less than 1%. We measured the THz transmission for a series of samples with various rectangular widths from 10 µm to 1.8 µm, which scales from λ/20 to λ/100. We found that 40~60% of the THz amplitude can be transmitted through the samples, regardless of their rectangular widths so that the corresponding near-field enhancement factor could reach as much as 200 for the sample of 1.8 µm width. Our observations have been confirmed by theoretical calculations based on Rayleigh wave expansion method which is an equivalent interpretation of the Kirchhoff’s diffraction integral in periodic structures. The transmission measurement through the single rectangular aperture repeats essentially the same result with those of the periodic samples, which confirms that the shape resonance, not the periodicity, is responsible for the transmission enhancement and the corresponding field enhancement.

2. Sample preparation and experiments

Periodic rectangular arrays were prepared on 17 µm thick Al kitchen foil, by using a femtosecond laser machining method [22

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, “Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors,” Opt. Express 15, 11781–11789 (2007). [CrossRef] [PubMed]

, 24

]. Rectangular arrays (6×6) have been punctured on this foil with widths of a=10 µm, 7 µm, and 5 µm, respectively, keeping the length of l=200 µm and unit cell size of 400×400 µm. The corresponding coverage of each sample is β=1.3%, 0.875%, 0.625%, respectively. A scanning electron microscopic image is shown in Fig. 1(a) for a rectangular aperture in the case of a=5 µm. The transmission spectra for these samples are measured by conventional THz-TDS setup as schematically shown in Fig. 1(b). A linearly polarized THz pulse is generated from InAs crystal, and then focused onto the samples with the 2 mm spot diameter by using a Tsurupica^TM THz lens (Broadband Inc. Japan). This pulse train is then refocused for the photoconductive antenna (based on Semi-insulating GaAs) detection. Time-traces of the transmitted THz electric fields are recorded by varying the time-delay between the probe beam and the THz pulse.

Fig. 1. (a) Scanning electron microscopy (SEM) image for sample with a=5 µm. Incident THz polarization is depicted as white arrow. (b) Schematic of THz-TDS experimental setup.

Figure 2(a) shows time traces of the measured THz field amplitude for the samples with a=10 µm, 7 µm, 5 µm, respectively (from top to bottom). The reference time trace is also shown at the bottom of the Fig. 2(a) by recording the field transmission through a 2.5×2.5 mm square aperture which corresponds to the total area of the sample. The peak amplitudes from the rectangular hole arrays are weaker than the reference by about 10 times. On the other hand, the signals show strong sinusoidal oscillations with Q-factor of ~10, which indicates the presence of the relatively sharp resonance. The spectrum of each THz time trace shown in Fig. 2(b) is taken by a Fast Fourier Transform (FFT) process, and normalized to the reference spectrum. As expected from the monochromatic oscillations in the time traces, there exists a well-defined resonance peak. For all of the samples, the peak position lies at ~0.63 THz, which is slightly smaller than the half-wavelength frequency of 0.75 THz in the case of 200 µm aperture length. This discrepancy suggests that the shape resonance is determined not only by the length of the aperture, but also by the other geometrical factors such as the aperture width and the film thickness. Similar result has been discussed recently both theoretically and experimentally [46

, 47

L. Novotny, “Effective Wavelength Scaling for Optical Antennas,” Phys. Rev. Lett. 98, 266802–266804 (2007). [CrossRef] [PubMed]

One of the most interesting observations is that the spectral maxima yield 0.4~0.6, even though the coverage has been dramatically reduced to 0.6% in the case of a=5 µm. The fluctuation in the transmission for the different samples originates from the sample imperfections rather than from the decreased rectangular width. Since the field enhancement factor is inversely proportional to the coverage, our result implies that almost 10 times near-field enhancement compared to the previous results is achievable [31

]. The detailed discussion will be presented in section 3. In other words, the enhancement factor is expected to reach as large as ~90 for the sample with a=5 µm.

Fig. 2. (a) Time-traces of transmitted field amplitudes for the rectangular width of 10 µm (magenta), 7 µm (blue), and 5 µm (red), respectively. Shown together is time-trace of the reference (black) through 2.5×2.5 mm aperture. (b) Fourier-transformed transmission amplitudes for the three samples in (a), normalized to the reference.

Motivated by the fact that the transmission does not change significantly with the decreasing widths of the aperture, we performed THz transmission through the structures far below the wavelength. Here, we are particularly interested in the dramatic field enhancement with the help of the shape resonance, by reducing the size of the width dramatically. We fabricated an array of rectangles on the 1.5 µm-thin films, with the width of 1.8 µm which corresponds to λ/100 scale. The length of the aperture is 120 µm. The pattern consists of 6×6 arrays of rectangular apertures with 240×240 µm sized unit cells. The resultant coverage β is 0.375% for this sample. As shown by the transmission spectrum in Fig 3, the amplitude at the transmission peak is observed at ~0.5, which is comparable to those of the previous samples with the larger widths. This indicates that the field can be efficiently accumulated inside the aperture creating highly concentrated electromagnetic fields. The field enhancement factor is supposed to exceed 200, at least 20 times higher than that of previous report [31

]. The spectral peak position is blue-shifted to ~1 THz which corresponds to the resonance frequency determined by the length of the aperture.

Fig. 3. Normalized Fourier-transformed transmission spectrum of the 120 µm long, 1.8 µm wide rectangle array.

This extraordinary field accumulation can be attributed to the shape resonance of the rectangular apertures, or the constructive interference between the scattered fields from each rectangle. The latter contribution, however, can be explicitly excluded when we perform the similar experiment using a single rectangular aperture instead of using the arrays. In Fig. 4, we show a transmission spectrum through a single aperture with 5 µmwide and 200 µm-long. The field amplitude shown here is normalized to that of 400×400 µm squared aperture, which is the size of the unit cell for the array samples. The geometrical effect from the reference aperture is negligible since the corresponding resonance (~0.36 THz) is far from the main resonance of interests. We also found that the transmission through the single aperture did not change significantly in terms of the amplitude as well as the spectral position. This result clearly confirms that the shape resonance effect dominate the field enhancement demonstrated throughout our experiments.

Fig. 4. Fourier-transformed amplitude spectrum of 5 µm width single rectangle, normalized by the reference spectrum which has passed through 400×400 µm square aperture.

3. Theory and discussion

We have performed theoretical calculations based on the Rayleigh wave expansion together with the waveguide mode expansion. The magnetic field components H_x, H_y , and H_z are given as follows for the reflection region (region I) and the transmission regions (region III), respectively, from Rayleigh wave expansion. [19

]

(H_{x}^{I}, H_{y}^{I}, H_{z}^{I}) = \sqrt{\frac{ε_{0}}{μ_{0}}} \underset{mn}{Σ} (G_{mn}^{x}, G_{mn}^{y}, G_{mn}^{z}) e^{i x_{mn} (z - \frac{h}{2})} \times e^{i (ϕ_{mn} - ω t)} + e^{ik (z - \frac{h}{2})},

(1)

(H_{x}^{III}, H_{y}^{III}, H_{z}^{III}) = \sqrt{\frac{ε_{0}}{μ_{0}}} \underset{mn}{Σ} (F_{mn}^{x}, F_{mn}^{y}, F_{mn}^{z}) e^{- i x_{mn} (z + \frac{h}{2})} \times e^{i (ϕ_{mn} - ω t)} .

(2)

G_mn ^(x,y,z) and F_mn ^(x,y,z) denotes the reflection and the transmission coefficients for each diffraction orders, respectively,

χ_{mn} = \sqrt{k^{2} - α_{m}^{2} - β_{n}^{2}}, ϕ_{mn} = α_{m} x + β_{n} y, α_{m} = 2 π m ⁄ d_{x}

, ϕ_mn =α_mx+β_ny, α_m =2πm/d_x, β_n =2πn/d_y , where d_x and d_y denotes periods along x and y directions, respectively, k denotes the incident wavevector, and h denotes the thickness of the metal film. The magnetic field components H_x, H_y , and H_z inside the rectangular aperture (region II) are given as follows from waveguide mode expansion:

H_{x}^{II} = 0

H_{y}^{II} = \frac{i μ}{k} \sqrt{\frac{ε_{0}}{μ_{0}}} \sin (\frac{π y}{l}) (A \frac{\sin μ z}{\sin (\frac{μ h}{2})} + B \frac{\cos μ z}{\cos (\frac{μ h}{2})})

H_{y}^{II} = \frac{i}{k} \frac{π}{l} \sqrt{\frac{ε_{0}}{μ_{0}}} \cos (\frac{π y}{l}) (- A \frac{\cos μ z}{\sin (\frac{μ h}{2})} + B \frac{\sin μ z}{\cos (\frac{μ h}{2})})

(3)

A and B denote the waveguide mode amplitudes, µ is a waveguide vector along z direction, defined as

μ = \sqrt{k^{2} - {(π ⁄ l)}^{2}}

, and l denotes the length of the rectangles. We assumed that the TE ₁₀ mode is dominant so that other waveguide modes can be neglected.

Applying boundary condition ∇×H⃗|_s=0 and Hⁱ _y =H^j _y at the each interface gives the coupled equations between A, B, G_mn ^(x,y,z) and F_mn ^(x,y,z). Solving these equations gives the entire electric and magnetic field components in the reflection and the transmission regions, as well as inside the waveguide. For example, the resultant E_x field component is given as follows:

E_{x} = \frac{\frac{i μ}{k π}}{(W_{x}^{2} + {(\frac{μ}{k π})}^{2}) + 2 W_{x} \frac{i μ}{k π} \cot μh} \underset{mn}{Σ} K_{mn} e^{i χ_{mn} (z - \frac{h}{2})} \times e^{i (ϕ_{mn} - ω t)},

(4)

where K_mn denotes overlap integral of the field inside the rectangle which is given as

K_{mn} = \frac{1}{d_{x} d_{y}} \int_{0}^{l} \int_{0}^{w} \sin \frac{πy}{l} e^{- i ϕ_{mn}} dxdy,

(5)

and W_x is given as

W_{x} = \frac{1}{2 l w} \underset{mn}{Σ} \frac{{χ_{mn}}^{2} + {α_{m}}^{2}}{χ_{mn} k} K_{mn} \int_{0}^{l} \int_{0}^{w} e^{i ϕ_{mn}} dxdy .

(6)

Since the χ_mn is imaginary unless m=n=0 at k<2 π/d_x , the far-field transmittance is simply determined by the zeroth order transmission coefficient, which is simply described as follows:

E_{far} = \frac{\frac{i μ}{k π}}{(W_{x}^{2} + {(\frac{μ}{kπ})}^{2}) + 2 W_{x} \frac{i μ}{kπ} \cot μh} \frac{2}{π} \frac{lw}{d_{x} d_{y}} e^{i (k_{0} z - ω t) \cdot}

(7)

It is easily found that the Eq. (7) is proportional to the coverage, β=wl/d_xd_y . On the other hands, the near-field at the center of the rectangular aperture, where the near-field has its maximum amplitude, is simply given as follows:

E_{near} (x = w ⁄ 2, y = l ⁄ 2, z = h ⁄ 2) = \frac{\frac{i μ}{k π}}{(W_{x}^{2} + {(\frac{μ}{kπ})}^{2}) + 2 W_{x} \frac{i μ}{kπ} \cot μh} e^{- i ωt .}

(8)

Since the infinite summation ∑_mn K_mn exp(iα_mw/2+iβ_nl/2) is simply a unity regardless of the periodicity, the length, and the width of the rectangles. Finally, the near-field amplitude can be extracted from the far-field transmittance as follows:

∣ \frac{E_{near}}{E_{far}} ∣ = 1 \times \frac{π}{2} \frac{d_{x} d_{y}}{wl}; E_{near} = \frac{π}{2} \frac{d_{x} d_{y}}{wl} ∣ E_{far} ∣ = \frac{π}{2} β^{- 1} ∣ E_{far} ∣ \cdot

(9)

This reproduces exactly the same result of the Kirchhoff’s diffraction integral formalism in the single aperture [49

A. Drezet, J. C. Woehl, and S. Huant, “Diffraction of light by a planar aperture in a metallic screen,” J. Math. Phys. 47 (2006). [CrossRef]

, 50

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, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon. 3, 152–156 (2009). [CrossRef]

]. Consequently, the near-field enhancement factor F is obtained by multiplying the far-field amplitude with the inverse-coverage β ^-1. These results are summarized in table 1 together with the experimentally measured far-field transmission amplitude t. As shown in the table, the estimated enhancement factors are more than 50, even reaches ~200 for the sample with 1.8 µm widths. We should like to note that the field intensity which is the square of the field amplitude, would exceed ~40,000.

Table 1. The coverage (β), measured transmission ampitude (t), and the enhancement factor (F) calculated by multiplying transmittance with coverage inverse for various rectangle width.

Rectangular Width (a)	Coverage (β)	Transmitted Amplitude (t)	Enhancement Factor (F)
10 µm	1%	0.34	53.38
7 µm	0.688%	0.55	125.4
5 µm	0.625%	0.58	145.7
1.8 µm	0.375%	0.48	200.9

Finally, in Fig. 5 we show the simulated near-field amplitude of the E_x field component, normalized to the incident field amplitude for each samples used in the experiment, i. e., for the 10 µm, 7 µm and 5 µm wide apertures on 17 µm thick film, and the 1.8 µm wide aperture on 1.5 µm thick film. The far-field transmission is also shown for comparison at the bottom of Fig. 5. The simulation result shows a reasonable agreement with the experimental result, which confirms the field enhancement factors of 150~430, for the series of geometries used in our experiments. The calculations show that the theoretical enhancement factors are 2~3 times higher than the experimental results. This is likely due to the imperfection of the sample (anisotropy, asymmetry, etc.), which causes the reduction in the far-field transmission. In this sense, the actual near-field enhancement could be much higher than what is estimated from the experimental results. It is also noticeable that the near-field spectrum in the simulation results replicates exactly the far-field spectrum found in the experiments.

Fig. 5. Calculated near-field transmission spectra are shown for the samples with the rectangular widths of 1 µm (black), 5 µm (blue), 7 µm (red), and 10 µm (magenta), respectively. Shown together at the bottom is the calculated far-field transmission spectrum for the 10 µm width sample (navy).

4. Conclusions

In conclusion, we have demonstrated that the huge THz field accumulation can be achieved with the help of the shape resonance of the extremely narrow, rectangular apertures on the thin metal film. The peak transmission was measured at around 60% regardless of the width of the aperture, which are only orders of λ/40 to λ/100. By considering both the coverages of the each sample and the measured far-field transmission, the field enhancement factors in near-field are estimated to be 53 to 200. The theoretical calculations based on the Rayleigh expansion methods are in good agreement with our experimental observations. We expect that these huge THz field enhancements would trigger various future researches such as THz-nonlinearity measurement, THz-controlled nano-optic devices and single molecule detection using THz wave.

Acknowledgments

This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (R11-2008-095-01000-0, R01-2008-000-20702-0), the Korea Research Foundation (KRF-2007-412-J04002), KICOS (Korea Foundation for International Cooperation of Science & Technology), the Research Council of the City of Seoul, and Ajou university research fellowship of 2008.

References and links

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13.	A. Bitzer and M. Walther, “Terahertz near-field imaging of metallic subwavelength holes and hole arrays,” Appl. Phys. Lett. 92, 231101–231103 (2008). [CrossRef]
14.	B. Gelmont, R. Parthasarathy, and T. Globus, “Edge effects in propagation of terahertz radiation in subwavelength periodic structures,” Semiconductors 42, 924–930 (2008). [CrossRef]
15.	A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Theory of light transmission through an array of rectangular holes,” Phys. Rev. B 76, 195414–195415 (2007). [CrossRef]
16.	C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, “Control of enhanced THz transmission through metallic hole arrays using nematic liquid crystal,” Opt. Express 13, 3921–3930 (2005). [CrossRef] [PubMed]
17.	H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express 13, 763–769 (2005). [CrossRef] [PubMed]
18.	F. J. Garcia-Vidal, L. Martin-Moreno, E. Moreno, L. K. S. Kumar,, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411–153414 (2006). [CrossRef]
19.	D. J. Park, S. B. Choi, Y. H. Ahn, Q. H. Park, and D. S. Kim, “Theoretical Study of terahertz Near-Field Enhancement Assisted by Shape Resonance in Rectangular Hole Arrays in Metal Films,” J. Korean Phys. Soc. 54, 7 (2009).
20.	K. G. Lee and Q. H. Park, “Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits,” Phys. Rev. Lett. 95, 103902–103904 (2005). [CrossRef] [PubMed]
21.	T. H. Isaac, J. G. Rivas, J. R. Sambles, W. L. Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77, 4 (2008). [CrossRef]
22.	M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, “Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors,” Opt. Express 15, 11781–11789 (2007). [CrossRef] [PubMed]
23.	E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, M. J. Hibbins, and Lockyear, “Optical Control over Surface-Plasmon-Polariton-Assisted THz Transmission through a Slit Aperture,” Phys. Rev. Lett. 100, 123901–123904 (2008). [CrossRef] [PubMed]
24.	J. W. Lee, M. A. Seo, D. J. Park, S. C. Jeoung, Q. H. Park, C. Lienau, and D. S. Kim, “Terahertz transparency at Fabry-Perot resonances of periodic slit arrays in a metal plate: experiment and theory,” Opt. Express 14, 12637–12643 (2006). [CrossRef] [PubMed]
25.	R. Parthasarathy, A. Bykhovski, B. Gelmont, T. Globus, N. Swami, and D. Woolard, “Enhanced Coupling of Subterahertz Radiation with Semiconductor Periodic Slot Arrays,” Phys. Rev. Lett. 98, 153906–153904 (2007). [CrossRef] [PubMed]
26.	Y. Todorov, I. Sagnes, I. Abram, and C. Minot, “Purcell Enhancement of Spontaneous Emission from Quantum Cascades inside Mirror-Grating Metal Cavities at THz Frequencies,” Phys. Rev. Lett. 99, 223603–223604 (2007). [CrossRef]
27.	Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88, 574031–574034 (2002). [CrossRef]
28.	N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534–537 (2005). [CrossRef] [PubMed]
29.	F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90, 213901 (2003). [CrossRef] [PubMed]
30.	I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B 65, 1654321–1654329 (2002). [CrossRef]
31.	J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, “Terahertz Electromagnetic Wave Transmission through Random Arrays of Single Rectangular Holes and Slits in Thin Metallic Sheets,” Phys. Rev. Lett. 99, 137401–137404 (2007). [CrossRef] [PubMed]
32.	J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, “Fabry-Perot tuning of the band-gap polarity in plasmonic crystals,” Phys. Rev. B 75, 035414–035415 (2007). [CrossRef]
33.	S. B. Choi, D. J. Park, D. S. Kim, M. S. Jeong, and C. C. Byeon, “Spatio-spectral measurement of a surface plasmon polariton in a gold nano-slit array,” J. Korean Phys. Soc. 53, 713–716 (2008). [CrossRef]
34.	D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, “Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders,” Appl. Phys. Lett. 93 (2008). [CrossRef]
35.	Y. B. Ji, E. S. Lee, J. S. Jang, and T. I. Jeon, “Enhancement of the detection of THz Sommerfeld wave using a conical wire waveguide,” Opt. Express 16 , 271–278 (2008). [CrossRef] [PubMed]
36.	K. Wang and D. M. Mittleman, “Dispersion of Surface Plasmon Polaritons on Metal Wires in the Terahertz Frequency Range,” Phys. Rev. Lett. 96, 157401–157404 (2006). [CrossRef] [PubMed]
37.	W. Zhu, A. Agrawal, H. Cao, and A. Nahata, “Generation of broadband radially polarized terahertz radiation directly on a cylindrical metal wire,” Opt. Express 16, 8433–8439 (2008). [CrossRef] [PubMed]
38.	J. Hao and G. W. Hanson, “Infrared and optical properties of carbon nanotube dipole antennas,” IEEE Trans. Nanotechnol. 5, 766–775 (2006). [CrossRef]
39.	T. Klar, M. Perner, S. Grosse, G. Von Plessen, W. Spirkl, and J. Feldmann, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249–4252 (1998). [CrossRef]
40.	R. Singh, E. Smirnova, A. J. Taylor, J. F. O’Hara, and W. Zhang, “Optically thin terahertz metamaterials,” Opt. Express 16, 6537–6543 (2008). [CrossRef] [PubMed]
41.	Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Superlens,” Nano Lett. 7, 403–408 (2007). [CrossRef] [PubMed]
42.	J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef] [PubMed]
43.	J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999). [CrossRef]
44.	H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163 (1944). [CrossRef]
45.	D. J. Park, S. B. Choi, K. J. Ahn, D. S. Kim, J. H. Kang, Q. H. Park, M. S. Jeong, and D. K. Ko, “Experimental verification of surface plasmon amplification on a metallic transmission grating,” Phys. Rev. B 77, 115451–115454 (2008).
46.	J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. G. de Abajo, B. K. Kelley, and T. Mallouk, “Optical properties of coupled metallic nanorods for field-enhanced spectroscopy,” Phys. Rev. B 71, 235420–235413 (2005). [CrossRef]
47.	L. Novotny, “Effective Wavelength Scaling for Optical Antennas,” Phys. Rev. Lett. 98, 266802–266804 (2007). [CrossRef] [PubMed]
48.	G. W. Bryant, F. J. Garcia de Abajo, and J. Aizpurua, “Mapping the Plasmon Resonances of Metallic Nanoantennas,” Nano Lett. 8, 631–636 (2008). [CrossRef] [PubMed]
49.	A. Drezet, J. C. Woehl, and S. Huant, “Diffraction of light by a planar aperture in a metallic screen,” J. Math. Phys. 47 (2006). [CrossRef]
50.	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, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photon. 3, 152–156 (2009). [CrossRef]

OCIS Codes
(180.0180) Microscopy : Microscopy
(260.3090) Physical optics : Infrared, far
(320.7160) Ultrafast optics : Ultrafast technology

ToC Category:
Diffraction and Gratings

History
Original Manuscript: April 28, 2009
Revised Manuscript: June 9, 2009
Manuscript Accepted: June 11, 2009
Published: July 8, 2009

Citation
D. J. Park, S. B. Choi, Y. H. Ahn, F. Rotermund, I. B. Sohn, Chul Kang, M. S. Jeong, and D. S. Kim, "Terahertz near-field enhancement in narrow rectangular apertures on metal film," Opt. Express 17, 12493-12501 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-15-12493

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References

S. C. Hohng, D. S. Kim, Y. C. Yoon, V. Malyarchuk, C. Lienau, J. W. Park, K. H. Yoo, J. Kim, S. H. Han, and Q. H. Park, "Evolution of the near-field patterns into the far-field in surface plasmonic band gap nano-structures," J. Korean Phys. Soc. 46,S205-S209 (2005).
T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelenght hole arrays," Nature 391, 667-669 (1998). [CrossRef]
P. Alitalo, S. Maslovski, and S. Tretyakov, "Near-field enhancement and imaging in double cylindrical polariton-resonant structures: Enlarging superlens," Phys. Lett. A 357, 397-400 (2006). [CrossRef]
W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface Plasmon Polaritons and Their Role in the Enhanced Transmission of Light Through Periodic Arrays of Subwavelength Holes in a Metal Film," Phys. Rev. Lett. 92, 107401 (2004). [CrossRef] [PubMed]
F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, "Transmission of Light through a Single Rectangular Hole," Phys. Rev. Lett. 95, 103901-103904 (2005). [CrossRef] [PubMed]
S. C. Hohng, Y. C. Yoon, D. S. Kim, V. Malyarchuk, R. Muller, C. Lienau, J. W. Park, K. H. Yoo, J. Kim, H. Y. Ryu, and Q. H. Park, "Light emission from the shadows: Surface plasmon nano-optics at near and far fields," Appl. Phys. Lett. 81, 3239 (2002). [CrossRef]
D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and C. Lienau, "Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures," Phys. Rev. Lett. 91, 143901 (2003). [CrossRef] [PubMed]
H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002). [CrossRef] [PubMed]
L. Martin-Moreno, F. J. Garcia-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]
Z. Ruan, and M. Qiu, "Enhanced Transmission through Periodic Arrays of Subwavelength Holes: The Role of Localized Waveguide Resonances," Phys. Rev. Lett. 96, 233901-233904 (2006). [CrossRef] [PubMed]
A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, "Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays," J. Opt. Soc. Am. B 24, 2545-2555 (2007). [CrossRef]
A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, "Extraordinary optical transmission through metallic films perforated with aperture arrays having short-range order," Opt. Express 16, 6267-6273 (2008). [CrossRef] [PubMed]
A. Bitzer, and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, 231101-231103 (2008). [CrossRef]
B. Gelmont, R. Parthasarathy, and T. Globus, "Edge effects in propagation of terahertz radiation in subwavelength periodic structures," Semiconductors 42, 924-930 (2008). [CrossRef]
A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, "Theory of light transmission through an array of rectangular holes," Phys. Rev. B 76, 195414-195415 (2007). [CrossRef]
C.-L. Pan, C.-F. Hsieh, R.-P. Pan, M. Tanaka, F. Miyamaru, M. Tani, and M. Hangyo, "Control of enhanced THz transmission through metallic hole arrays using nematic liquid crystal," Opt. Express 13, 3921-3930 (2005). [CrossRef] [PubMed]
H. Cao, A. Agrawal, and A. Nahata, "Controlling the transmission resonance lineshape of a single subwavelength aperture," Opt. Express 13, 763-769 (2005). [CrossRef] [PubMed]
F. J. Garcia-Vidal, L. Martin-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, "Transmission of light through a single rectangular hole in a real metal," Phys. Rev. B 74, 153411-153414 (2006). [CrossRef]
D. J. Park, S. B. Choi, Y. H. Ahn, Q. H. Park, and D. S. Kim, "Theoretical Study of terahertz Near-Field Enhancement Assisted by Shape Resonance in Rectangular Hole Arrays in Metal Films," J. Korean Phys. Soc. 54, 7 (2009).
K. G. Lee, and Q. H. Park, "Coupling of Surface Plasmon Polaritons and Light in Metallic Nanoslits," Phys. Rev. Lett. 95, 103902-103904 (2005). [CrossRef] [PubMed]
T. H. Isaac, J. G. Rivas, J. R. Sambles, W. L. Barnes, and E. Hendry, "Surface plasmon mediated transmission of subwavelength slits at THz frequencies," Phys. Rev. B 77, 4 (2008). [CrossRef]
M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, "Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors," Opt. Express 15, 11781-11789 (2007). [CrossRef] [PubMed]
E. Hendry, F. J. Garcia-Vidal, L. Martin-Moreno, J. G. Rivas, M. Bonn, A. P. Hibbins, and M. J. Lockyear, "Optical Control over Surface-Plasmon-Polariton-Assisted THz Transmission through a Slit Aperture," Phys. Rev. Lett. 100, 123901-123904 (2008). [CrossRef] [PubMed]
J. W. Lee, M. A. Seo, D. J. Park, S. C. Jeoung, Q. H. Park, C. Lienau, and D. S. Kim, "Terahertz transparency at Fabry-Perot resonances of periodic slit arrays in a metal plate: experiment and theory," Opt. Express 14, 12637-12643 (2006). [CrossRef] [PubMed]
R. Parthasarathy, A. Bykhovski, B. Gelmont, T. Globus, N. Swami, and D. Woolard, "Enhanced Coupling of Subterahertz Radiation with Semiconductor Periodic Slot Arrays," Phys. Rev. Lett. 98, 153906 (2007). [CrossRef] [PubMed]
Y. Todorov, I. Sagnes, I. Abram, and C. Minot, "Purcell Enhancement of Spontaneous Emission from Quantum Cascades inside Mirror-Grating Metal Cavities at THz Frequencies," Phys. Rev. Lett. 99, 223603-223604 (2007). [CrossRef]
Q. Cao, and P. Lalanne, "Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits," Phys. Rev. Lett. 88, 574031-574034 (2002). [CrossRef]
N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science 308, 534-537 (2005). [CrossRef] [PubMed]
F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, "Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit," Phys. Rev. Lett. 90, 213901 (2003). [CrossRef] [PubMed]
I. R. Hooper and J. R. Sambles, "Dispersion of surface plasmon polaritons on short-pitch metal gratings," Phys. Rev. B 65, 1654321-1654329 (2002). [CrossRef]
J. W. Lee, M. A. Seo, D. H. Kang, K. S. Khim, S. C. Jeoung, and D. S. Kim, "Terahertz Electromagnetic Wave Transmission through Random Arrays of Single Rectangular Holes and Slits in Thin Metallic Sheets," Phys. Rev. Lett. 99, 137401-137404 (2007). [CrossRef] [PubMed]
J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, "Fabry-Perot tuning of the band-gap polarity in plasmonic crystals," Phys. Rev. B 75, 035414-035415 (2007). [CrossRef]
S. B. Choi, D. J. Park, D. S. Kim, M. S. Jeong, and C. C. Byeon, "Spatio-spectral measurement of a surface plasmon polariton in a gold nano-slit array," J. Korean Phys. Soc. 53, 713-716 (2008). [CrossRef]
D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, "Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders," Appl. Phys. Lett. 93, 073109 (2008). [CrossRef]
Y. B. Ji, E. S. Lee, J. S. Jang, and T. I. Jeon, "Enhancement of the detection of THz Sommerfeld wave using a conical wire waveguide," Opt. Express 16, 271-278 (2008). [CrossRef] [PubMed]
K. Wang and D. M. Mittleman, "Dispersion of Surface Plasmon Polaritons on Metal Wires in the Terahertz Frequency Range," Phys. Rev. Lett. 96, 157401-157404 (2006). [CrossRef] [PubMed]
W. Zhu, A. Agrawal, H. Cao, and A. Nahata, "Generation of broadband radially polarized terahertz radiation directly on a cylindrical metal wire," Opt. Express 16, 8433-8439 (2008). [CrossRef] [PubMed]
J. Hao and G. W. Hanson, "Infrared and optical properties of carbon nanotube dipole antennas," IEEE Trans. Nanotechnol. 5, 766-775 (2006). [CrossRef]
T. Klar, M. Perner, S. Grosse, G. Von Plessen, W. Spirkl, and J. Feldmann, "Surface-plasmon resonances in single metallic nanoparticles," Phys. Rev. Lett. 80, 4249-4252 (1998). [CrossRef]
R. Singh, E. Smirnova, A. J. Taylor, J. F. O'Hara, and W. Zhang, "Optically thin terahertz metamaterials," Opt. Express 16, 6537-6543 (2008). [CrossRef] [PubMed]
Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, "Far-Field Optical Superlens," Nano Lett. 7, 403-408 (2007). [CrossRef] [PubMed]
J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999). [CrossRef]
H. A. Bethe, "Theory of Diffraction by Small Holes," Phys. Rev. 66, 163 (1944). [CrossRef]
D. J. Park, S. B. Choi, K. J. Ahn, D. S. Kim, J. H. Kang, Q. H. Park, M. S. Jeong, and D. K. Ko, "Experimental verification of surface plasmon amplification on a metallic transmission grating," Phys. Rev. B 77, 115451-115454 (2008).
J. Aizpurua, G. W. Bryant, L. J. Richter, F. J. G. de Abajo, B. K. Kelley, and T. Mallouk, "Optical properties of coupled metallic nanorods for field-enhanced spectroscopy," Phys. Rev. B 71, 235420 (2005). [CrossRef]
L. Novotny, "Effective Wavelength Scaling for Optical Antennas," Phys. Rev. Lett. 98, 266802-266804 (2007). [CrossRef] [PubMed]
G. W. Bryant, F. J. Garcia de Abajo, and J. Aizpurua, "Mapping the Plasmon Resonances of Metallic Nanoantennas," Nano Lett. 8, 631-636 (2008). [CrossRef] [PubMed]
A. Drezet, J. C. Woehl, and S. Huant, "Diffraction of light by a planar aperture in a metallic screen," J. Math. Phys. 47,072901.1-072901.10 (2006). [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, Q. H. Park, and D. S. Kim, "Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit," Nat. Photonics 3, 152-156 (2009). [CrossRef]

Appl. Phys. Lett.

S. C. Hohng, Y. C. Yoon, D. S. Kim, V. Malyarchuk, R. Muller, C. Lienau, J. W. Park, K. H. Yoo, J. Kim, H. Y. Ryu, and Q. H. Park, "Light emission from the shadows: Surface plasmon nano-optics at near and far fields," Appl. Phys. Lett. 81, 3239 (2002). [CrossRef]
A. Bitzer, and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, 231101-231103 (2008). [CrossRef]
D. J. Park, K. G. Lee, H. W. Kihm, Y. M. Byun, D. S. Kim, C. Ropers, C. Lienau, J. H. Kang, and Q. H. Park, "Near-to-far-field spectral evolution in a plasmonic crystal: Experimental verification of the equipartition of diffraction orders," Appl. Phys. Lett. 93, 073109 (2008). [CrossRef]

IEEE Trans. Nanotechnol.

J. Hao and G. W. Hanson, "Infrared and optical properties of carbon nanotube dipole antennas," IEEE Trans. Nanotechnol. 5, 766-775 (2006). [CrossRef]

J. Korean Phys. Soc.

S. B. Choi, D. J. Park, D. S. Kim, M. S. Jeong, and C. C. Byeon, "Spatio-spectral measurement of a surface plasmon polariton in a gold nano-slit array," J. Korean Phys. Soc. 53, 713-716 (2008). [CrossRef]
D. J. Park, S. B. Choi, Y. H. Ahn, Q. H. Park, and D. S. Kim, "Theoretical Study of terahertz Near-Field Enhancement Assisted by Shape Resonance in Rectangular Hole Arrays in Metal Films," J. Korean Phys. Soc. 54, 7 (2009).
S. C. Hohng, D. S. Kim, Y. C. Yoon, V. Malyarchuk, C. Lienau, J. W. Park, K. H. Yoo, J. Kim, S. H. Han, and Q. H. Park, "Evolution of the near-field patterns into the far-field in surface plasmonic band gap nano-structures," J. Korean Phys. Soc. 46,S205-S209 (2005).

J. Opt. Soc. Am. B

A. Agrawal, T. Matsui, Z. V. Vardeny, and A. Nahata, "Terahertz transmission properties of quasiperiodic and aperiodic aperture arrays," J. Opt. Soc. Am. B 24, 2545-2555 (2007). [CrossRef]

Nano Lett.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, "Far-Field Optical Superlens," Nano Lett. 7, 403-408 (2007). [CrossRef] [PubMed]
G. W. Bryant, F. J. Garcia de Abajo, and J. Aizpurua, "Mapping the Plasmon Resonances of Metallic Nanoantennas," Nano Lett. 8, 631-636 (2008). [CrossRef] [PubMed]

Nat. Photonics

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, Q. H. Park, and D. S. Kim, "Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit," Nat. Photonics 3, 152-156 (2009). [CrossRef]

Nature

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

Opt. Express

Phys. Lett. A

P. Alitalo, S. Maslovski, and S. Tretyakov, "Near-field enhancement and imaging in double cylindrical polariton-resonant structures: Enlarging superlens," Phys. Lett. A 357, 397-400 (2006). [CrossRef]

Phys. Rev.

H. A. Bethe, "Theory of Diffraction by Small Holes," Phys. Rev. 66, 163 (1944). [CrossRef]

Phys. Rev. B

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, "Theory of light transmission through an array of rectangular holes," Phys. Rev. B 76, 195414-195415 (2007). [CrossRef]

Phys. Rev. B

T. H. Isaac, J. G. Rivas, J. R. Sambles, W. L. Barnes, and E. Hendry, "Surface plasmon mediated transmission of subwavelength slits at THz frequencies," Phys. Rev. B 77, 4 (2008). [CrossRef]
I. R. Hooper and J. R. Sambles, "Dispersion of surface plasmon polaritons on short-pitch metal gratings," Phys. Rev. B 65, 1654321-1654329 (2002). [CrossRef]
J. E. Kihm, Y. C. Yoon, D. J. Park, Y. H. Ahn, C. Ropers, C. Lienau, J. Kim, Q. H. Park, and D. S. Kim, "Fabry-Perot tuning of the band-gap polarity in plasmonic crystals," Phys. Rev. B 75, 035414-035415 (2007). [CrossRef]
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