Abstract

We investigate the spectral transmission properties of conically tapered metallic apertures made in a split metallic plate using terahertz (THz) time-domain spectroscopy. The introduction of even a small gap between the two halves of the plate results in spectral broadening of the transmitted radiation due to a reduction of the cut-off effect. We find that the resulting transmission spectrum can be described as a weighted sum of the spectra associated with a tapered aperture and a parallel plate waveguide, with the gap spacing controlling the relative ratio. We further find that the field concentration properties of the aperture in a split plate are limited by the radiation leakage through the gap and propose a tapered shell structure to realize strong broadband field concentration. Using numerical simulations, we validate these observations and yield insight into the mode properties within the split tapered aperture.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
    [CrossRef]
  7. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. T. D. Nguyen, Z. V. Vardeny, and A. Nahata, “Concentration of terahertz radiation through a conically tapered aperture,” Opt. Express18(24), 25441–25448 (2010).
    [CrossRef] [PubMed]
  12. M. C. Schaafsma, H. Starmans, A. Berrier, and J. Gómez Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys.15(1), 015006 (2013).
    [CrossRef]
  13. S. Liu, Z. V. Vardeny, and A. Nahata, “Concentration of broadband terahertz radiation using a periodic array of conically tapered apertures,” Opt. Express21(10), 12363–12372 (2013).
    [CrossRef] [PubMed]
  14. A. Rusina, M. Durach, K. A. Nelson, and M. I. Stockman, “Nanoconcentration of terahertz radiation in plasmonic waveguides,” Opt. Express16(23), 18576–18589 (2008).
    [CrossRef] [PubMed]
  15. H. Zhan, R. Mendis, and D. M. Mittleman, “Superfocusing terahertz waves below λ/250 using plasmonic parallel-plate waveguides,” Opt. Express18(9), 9643–9650 (2010).
    [CrossRef] [PubMed]
  16. K. Iwaszczuk, A. Andryieuski, A. Lavrinenko, X.-C. Zhang, and P. U. Jepsen, “Terahertz field enhancement to the MV/cm regime in a tapered parallel plate waveguide,” Opt. Express20(8), 8344–8355 (2012).
    [CrossRef] [PubMed]
  17. B. Clark, M. P. Taylor, and H. D. Hallen, “Novel split-tip proximal probe for fabrication of nanometer-textured, in-plane oriented polymer films,” J. Vac. Sci. Technol. B28(4), 687–692 (2010).
    [CrossRef]
  18. M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  24. H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express13(3), 763–769 (2005).
    [CrossRef] [PubMed]
  25. C. A. Balanis, Advanced Engineering Electromagnetics (John Wiley, 1989).
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    [CrossRef]

2013 (3)

M. C. Schaafsma, H. Starmans, A. Berrier, and J. Gómez Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys.15(1), 015006 (2013).
[CrossRef]

S. Liu, Z. V. Vardeny, and A. Nahata, “Concentration of broadband terahertz radiation using a periodic array of conically tapered apertures,” Opt. Express21(10), 12363–12372 (2013).
[CrossRef] [PubMed]

R. Mueckstein, M. Navarro-Cía, and O. Mitrofanov, “Mode interference and radiation leakage in a tapered parallel plate waveguide for terahertz waves,” Appl. Phys. Lett.102(14), 141103 (2013).
[CrossRef]

2012 (2)

2010 (5)

2009 (3)

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

M. Awad, M. Nagel, and H. Kurz, “Tapered Sommerfeld wire terahertz near-field imaging,” Appl. Phys. Lett.94(5), 051107 (2009).
[CrossRef]

V. Astley, R. Mendis, and D. M. Mittleman, “Characterization of terahertz field confinement at the end of a tapered metal wire waveguide,” Appl. Phys. Lett.95(3), 031104 (2009).
[CrossRef]

2008 (2)

2006 (2)

2005 (1)

2004 (1)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

2001 (1)

2000 (1)

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

1997 (1)

K. V. Nerkararyan, “Superfocusing of a surface polariton in a wedge-like structure,” Phys. Lett. A237(1–2), 103–105 (1997).
[CrossRef]

1984 (1)

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett.44(7), 651–653 (1984).
[CrossRef]

Agrawal, A.

Andryieuski, A.

Antosiewicz, T. J.

Arbel, D.

Astley, V.

V. Astley, R. Mendis, and D. M. Mittleman, “Characterization of terahertz field confinement at the end of a tapered metal wire waveguide,” Appl. Phys. Lett.95(3), 031104 (2009).
[CrossRef]

Awad, M.

M. Awad, M. Nagel, and H. Kurz, “Tapered Sommerfeld wire terahertz near-field imaging,” Appl. Phys. Lett.94(5), 051107 (2009).
[CrossRef]

Babadjanyan, A. J.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

Berrier, A.

M. C. Schaafsma, H. Starmans, A. Berrier, and J. Gómez Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys.15(1), 015006 (2013).
[CrossRef]

Burresi, M.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Cao, H.

Chen, L.

Clark, B.

B. Clark, M. P. Taylor, and H. D. Hallen, “Novel split-tip proximal probe for fabrication of nanometer-textured, in-plane oriented polymer films,” J. Vac. Sci. Technol. B28(4), 687–692 (2010).
[CrossRef]

Denk, W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett.44(7), 651–653 (1984).
[CrossRef]

Durach, M.

Ginzburg, P.

Gómez Rivas, J.

M. C. Schaafsma, H. Starmans, A. Berrier, and J. Gómez Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys.15(1), 015006 (2013).
[CrossRef]

Grischkowsky, D.

Hallen, H. D.

B. Clark, M. P. Taylor, and H. D. Hallen, “Novel split-tip proximal probe for fabrication of nanometer-textured, in-plane oriented polymer films,” J. Vac. Sci. Technol. B28(4), 687–692 (2010).
[CrossRef]

Heideman, R.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Iwaszczuk, K.

Jang, J. S.

Jeon, T. I.

Jepsen, P. U.

Ji, Y. B.

Kampfrath, T.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Kim, S. H.

Kuipers, L.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Kurz, H.

M. Awad, M. Nagel, and H. Kurz, “Tapered Sommerfeld wire terahertz near-field imaging,” Appl. Phys. Lett.94(5), 051107 (2009).
[CrossRef]

Lanz, M.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett.44(7), 651–653 (1984).
[CrossRef]

Lavrinenko, A.

Lee, E. S.

Leinse, A.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Lipson, M.

Liu, S.

Margaryan, N. L.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

Mendis, R.

Mitrofanov, O.

R. Mueckstein, M. Navarro-Cía, and O. Mitrofanov, “Mode interference and radiation leakage in a tapered parallel plate waveguide for terahertz waves,” Appl. Phys. Lett.102(14), 141103 (2013).
[CrossRef]

O. Mitrofanov, C. C. Renaud, and A. J. Seeds, “Terahertz probe for spectroscopy of sub-wavelength objects,” Opt. Express20(6), 6197–6202 (2012).
[CrossRef] [PubMed]

Mittleman, D. M.

H. Zhan, R. Mendis, and D. M. Mittleman, “Superfocusing terahertz waves below λ/250 using plasmonic parallel-plate waveguides,” Opt. Express18(9), 9643–9650 (2010).
[CrossRef] [PubMed]

V. Astley, R. Mendis, and D. M. Mittleman, “Characterization of terahertz field confinement at the end of a tapered metal wire waveguide,” Appl. Phys. Lett.95(3), 031104 (2009).
[CrossRef]

Mueckstein, R.

R. Mueckstein, M. Navarro-Cía, and O. Mitrofanov, “Mode interference and radiation leakage in a tapered parallel plate waveguide for terahertz waves,” Appl. Phys. Lett.102(14), 141103 (2013).
[CrossRef]

Nagel, M.

M. Awad, M. Nagel, and H. Kurz, “Tapered Sommerfeld wire terahertz near-field imaging,” Appl. Phys. Lett.94(5), 051107 (2009).
[CrossRef]

Nahata, A.

Navarro-Cía, M.

R. Mueckstein, M. Navarro-Cía, and O. Mitrofanov, “Mode interference and radiation leakage in a tapered parallel plate waveguide for terahertz waves,” Appl. Phys. Lett.102(14), 141103 (2013).
[CrossRef]

Nelson, K. A.

Nerkararyan, K. V.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

K. V. Nerkararyan, “Superfocusing of a surface polariton in a wedge-like structure,” Phys. Lett. A237(1–2), 103–105 (1997).
[CrossRef]

Nguyen, T. D.

Orenstein, M.

Pohl, D. W.

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett.44(7), 651–653 (1984).
[CrossRef]

Renaud, C. C.

Rusina, A.

Schaafsma, M. C.

M. C. Schaafsma, H. Starmans, A. Berrier, and J. Gómez Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys.15(1), 015006 (2013).
[CrossRef]

Schoenmaker, H.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Seeds, A. J.

Shakya, J.

Starmans, H.

M. C. Schaafsma, H. Starmans, A. Berrier, and J. Gómez Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys.15(1), 015006 (2013).
[CrossRef]

Stockman, M. I.

Szoplik, T.

Taylor, M. P.

B. Clark, M. P. Taylor, and H. D. Hallen, “Novel split-tip proximal probe for fabrication of nanometer-textured, in-plane oriented polymer films,” J. Vac. Sci. Technol. B28(4), 687–692 (2010).
[CrossRef]

van Oosten, D.

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Vardeny, Z. V.

Wróbel, P.

Zhan, H.

Zhang, X.-C.

Appl. Phys. Lett. (4)

D. W. Pohl, W. Denk, and M. Lanz, “Optical stethoscopy: Image recording with resolution λ/20,” Appl. Phys. Lett.44(7), 651–653 (1984).
[CrossRef]

M. Awad, M. Nagel, and H. Kurz, “Tapered Sommerfeld wire terahertz near-field imaging,” Appl. Phys. Lett.94(5), 051107 (2009).
[CrossRef]

V. Astley, R. Mendis, and D. M. Mittleman, “Characterization of terahertz field confinement at the end of a tapered metal wire waveguide,” Appl. Phys. Lett.95(3), 031104 (2009).
[CrossRef]

R. Mueckstein, M. Navarro-Cía, and O. Mitrofanov, “Mode interference and radiation leakage in a tapered parallel plate waveguide for terahertz waves,” Appl. Phys. Lett.102(14), 141103 (2013).
[CrossRef]

J. Appl. Phys. (1)

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys.87(8), 3785–3788 (2000).
[CrossRef]

J. Vac. Sci. Technol. B (1)

B. Clark, M. P. Taylor, and H. D. Hallen, “Novel split-tip proximal probe for fabrication of nanometer-textured, in-plane oriented polymer films,” J. Vac. Sci. Technol. B28(4), 687–692 (2010).
[CrossRef]

New J. Phys. (1)

M. C. Schaafsma, H. Starmans, A. Berrier, and J. Gómez Rivas, “Enhanced terahertz extinction of single plasmonic antennas with conically tapered waveguides,” New J. Phys.15(1), 015006 (2013).
[CrossRef]

Opt. Express (10)

S. Liu, Z. V. Vardeny, and A. Nahata, “Concentration of broadband terahertz radiation using a periodic array of conically tapered apertures,” Opt. Express21(10), 12363–12372 (2013).
[CrossRef] [PubMed]

A. Rusina, M. Durach, K. A. Nelson, and M. I. Stockman, “Nanoconcentration of terahertz radiation in plasmonic waveguides,” Opt. Express16(23), 18576–18589 (2008).
[CrossRef] [PubMed]

H. Zhan, R. Mendis, and D. M. Mittleman, “Superfocusing terahertz waves below λ/250 using plasmonic parallel-plate waveguides,” Opt. Express18(9), 9643–9650 (2010).
[CrossRef] [PubMed]

K. Iwaszczuk, A. Andryieuski, A. Lavrinenko, X.-C. Zhang, and P. U. Jepsen, “Terahertz field enhancement to the MV/cm regime in a tapered parallel plate waveguide,” Opt. Express20(8), 8344–8355 (2012).
[CrossRef] [PubMed]

T. J. Antosiewicz, P. Wróbel, and T. Szoplik, “Magnetic field concentrator for probing optical magnetic metamaterials,” Opt. Express18(25), 25906–25911 (2010).
[CrossRef] [PubMed]

T. D. Nguyen, Z. V. Vardeny, and A. Nahata, “Concentration of terahertz radiation through a conically tapered aperture,” Opt. Express18(24), 25441–25448 (2010).
[CrossRef] [PubMed]

S. H. Kim, E. S. Lee, Y. B. Ji, and T. I. Jeon, “Improvement of THz coupling using a tapered parallel-plate waveguide,” Opt. Express18(2), 1289–1295 (2010).
[CrossRef] [PubMed]

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. Express16(1), 271–278 (2008).
[CrossRef] [PubMed]

O. Mitrofanov, C. C. Renaud, and A. J. Seeds, “Terahertz probe for spectroscopy of sub-wavelength objects,” Opt. Express20(6), 6197–6202 (2012).
[CrossRef] [PubMed]

H. Cao, A. Agrawal, and A. Nahata, “Controlling the transmission resonance lineshape of a single subwavelength aperture,” Opt. Express13(3), 763–769 (2005).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. Lett. A (1)

K. V. Nerkararyan, “Superfocusing of a surface polariton in a wedge-like structure,” Phys. Lett. A237(1–2), 103–105 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

Science (1)

M. Burresi, D. van Oosten, T. Kampfrath, H. Schoenmaker, R. Heideman, A. Leinse, and L. Kuipers, “Probing the magnetic field of light at optical frequencies,” Science326(5952), 550–553 (2009).
[CrossRef] [PubMed]

Other (3)

J. D. Jackson, Classical Electrodynamics (John Wiley, 1999), p. 832.

Z. B. Popović and B. D. Popović, Introductory Electromagnetics (Prentice Hall, 2000), p. 556.

C. A. Balanis, Advanced Engineering Electromagnetics (John Wiley, 1989).

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Figures (4)

Fig. 1
Fig. 1

Details of the experimental design. (a) Schematic diagram of the different aperture structures studied. Left: cross-section (top), top view (middle) and perspective view (bottom) of the reference TA with an input aperture diameter, D1 = 2.0 mm, an output aperture diameter, D2 = 400 μm and metal thickness, d = 3.0 mm. Right: cross-section (top), top view (middle) and perspective view (bottom) of the split TA with the same dimensions as the reference TA but split into two halves. The two halves of the aperture are separated by a variable gap spacing, g. (b) Photographs of the reference TA and the split TA (with g ≈0). (c) Schematic diagram of the THz time-domain spectroscopy system. A collimated THz beam was normally incident on the sample. The radiated electromagnetic wave was detected using a photoconductive device for coherent broadband THz detection.

Fig. 2
Fig. 2

The experimentally measured spectral transmission properties of the split TA structures. (a) Amplitude spectra, t(ν), of the split TAs as a function of the gap spacing, g, as well as for the incident pulse (measured without a sample), reference TA and a parallel plate waveguide with a gap of 10 μm. (b) Analytically calculated spectra using the spectral amplitude of the reference TA and parallel plates in (a). (c) Coupling coefficients used to model the spectra in (b). (d) Energy averaged over the input opening area, calculated from (a). The lines in (c) and (d) are only guides to the eye.

Fig. 3
Fig. 3

Numerical simulations of the field properties for split TAs and relevant stretched TAs. (a) Amplitude spectra t(ν) for split TAs with g = 0, 10, 30, 60 and 100 μm and the parallel plates with g = 10 μm. (b) Analytically calculated spectra using the spectral amplitude of the reference TA and parallel plates in (a). (c) Corresponding coefficients used in (b). The lines are only guides to the eye. (d) Transmitted field amplitude, t(ν), of the stretched TAs with various elongation, s. Inset: top view of the stretched TA with marked dimensions.

Fig. 4
Fig. 4

(a) Snapshot of the electric field magnitude in the vicinity of the output aperture of a split shell TA. The white region is metal modeled as perfect electrical conductor. (b) Transmission spectra for the split shell TA (60 µm gap), as well as the spectra associated with the split TA (60 µm gap) and the reference TA (from Fig. 3). (c) Electric field throughput concentration factor (FE) obtained by integrating the field on the input and output planes of the TA and normalized by the opening area of the corresponding input and output surfaces.

Equations (2)

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t( ν )= C 1 t 1 ( ν )+ C 2 t 2 ( ν ).
Ε N = | t( ν ) | 2 dν A

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