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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 15 — Jul. 20, 2009
  • pp: 12493–12501
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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, C. 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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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.

© 2009 Optical Society of America

1. Introduction

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

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

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

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

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

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

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

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

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

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

] and bio-sensing [43

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

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

].

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

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

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]

]. 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 TsurupicaTM 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

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

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

].

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.

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 Hx, Hy, and Hz are given as follows for the reflection region (region I) and the transmission regions (region III), respectively, from Rayleigh wave expansion. [19

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).

]

(HxI,HyI,HzI)=ε0μ0Σmn(Gmnx,Gmny,Gmnz)eixmn(zh2)×ei(ϕmnωt)+eik(zh2),
(1)
(HxIII,HyIII,HzIII)=ε0μ0Σmn(Fmnx,Fmny,Fmnz)eixmn(z+h2)×ei(ϕmnωt).
(2)

Gmn (x,y,z) and Fmn (x,y,z) denotes the reflection and the transmission coefficients for each diffraction orders, respectively, χmn=k2αm2βn2,ϕmn=αmx+βny,αm=2πmdx, ϕmn=αmx+βny, αm=2πm/dx, βn=2πn/dy, where dx and dy 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 Hx, Hy, and Hz inside the rectangular aperture (region II) are given as follows from waveguide mode expansion:

HxII=0
HyII=iμkε0μ0sin(πyl)(Asinμzsin(μh2)+Bcosμzcos(μh2))
HyII=ikπlε0μ0cos(πyl)(Acosμzsin(μh2)+Bsinμzcos(μh2))
(3)

A and B denote the waveguide mode amplitudes, µ is a waveguide vector along z direction, defined as μ=k2(πl)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 Hiy=Hjy at the each interface gives the coupled equations between A, B, Gmn (x,y,z) and Fmn (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 Ex field component is given as follows:

Ex=iμkπ(Wx2+(μkπ)2)+2WxiμkπcotμhΣmnKmneiχmn(zh2)×ei(ϕmnωt),
(4)

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

Kmn=1dxdy0l0wsinπyleiϕmndxdy,
(5)

and Wx is given as

Wx=12lwΣmnχmn2+αm2χmnkKmn0l0weiϕmndxdy.
(6)

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

Efar=iμkπ(Wx2+(μ)2)+2Wxiμcotμh2πlwdxdyei(k0zωt)·
(7)

It is easily found that the Eq. (7) is proportional to the coverage, β=wl/dxdy. 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:

Enear(x=w2,y=l2,z=h2)=iμkπ(Wx2+(μ)2)+2Wxiμcotμheiωt.
(8)

Since the infinite summation ∑mn Kmnexp(mw/2+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:

EnearEfar=1×π2dxdywl;Enear=π2dxdywlEfar=π2β1Efar·
(9)

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

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

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.

table-icon
View This Table

Finally, in Fig. 5 we show the simulated near-field amplitude of the Ex 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.

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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. B77, 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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