Abstract

We describe the optical concentration properties of periodic arrays of conically tapered metallic apertures measured using terahertz (THz) time-domain spectroscopy. As a first step in this process, we optimize the geometrical properties of individual apertures, keeping the output aperture diameter fixed, and find that the optimal taper angle is 30°. A consequence of increasing the taper angle is that the effective cutoff frequency red shifts, which can be readily explained using conventional waveguide theory. We then fabricate and measure the transmission properties of a periodic (hexagonal) array of optimized tapered apertures. In contrast to periodic arrays of subwavelength apertures in thin metal films, which are characterized by narrowband transmission resonances associated with the periodic spacing, here we observe broadband enhanced transmission above the effective cutoff frequency. Further enhancement in the concentration capabilities of the array can be achieved by tilting the apertures towards the array center, although the optical throughput of individual tapered apertures is reduced with increasing tilt angle. Finally, we discuss possible future directions that utilize cascaded structures, as a means for obtaining further enhancement in the amplitude of the transmitted THz radiation.

© 2013 OSA

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References

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  1. E. Betzig, M. Isaacson, and A. Lewis, “Collection mode near-field scanning optical microscopy,” Appl. Phys. Lett.51(25), 2088–2090 (1987).
    [CrossRef]
  2. S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun.150(1-6), 22–26 (1998).
    [CrossRef]
  3. J. Villatoro, D. Monzón-Hernández, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett.40(2), 106–107 (2004).
    [CrossRef]
  4. P. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express13(3), 801–820 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun.253(1-3), 118–124 (2005).
    [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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  18. T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B16(10), 1743–1748 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]

2013

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]

2012

2011

J. Beermann, T. Søndergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys.13(6), 063029 (2011).
[CrossRef]

2010

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton.4(1), 043504 (2010).
[CrossRef]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (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]

2009

H. Choi, D. F. P. Pile, S. Nam, G. Bartal, and X. Zhang, “Compressing surface plasmons for nano-scale optical focusing,” Opt. Express17(9), 7519–7524 (2009).
[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]

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

2008

2005

2004

M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

J. Villatoro, D. Monzón-Hernández, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett.40(2), 106–107 (2004).
[CrossRef]

2000

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]

1999

1998

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun.150(1-6), 22–26 (1998).
[CrossRef]

1987

E. Betzig, M. Isaacson, and A. Lewis, “Collection mode near-field scanning optical microscopy,” Appl. Phys. Lett.51(25), 2088–2090 (1987).
[CrossRef]

Agrawal, A.

Andryieuski, A.

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]

Baghdasaryan, K. S.

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun.253(1-3), 118–124 (2005).
[CrossRef]

Barclay, P.

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Bartal, G.

Beermann, J.

J. Beermann, T. Søndergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys.13(6), 063029 (2011).
[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]

Betzig, E.

E. Betzig, M. Isaacson, and A. Lewis, “Collection mode near-field scanning optical microscopy,” Appl. Phys. Lett.51(25), 2088–2090 (1987).
[CrossRef]

Blair, S.

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton.4(1), 043504 (2010).
[CrossRef]

Bozhevolnyi, S. I.

J. Beermann, T. Søndergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys.13(6), 063029 (2011).
[CrossRef]

Brener, I.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun.150(1-6), 22–26 (1998).
[CrossRef]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Cao, H.

Choi, H.

Davis, M.

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton.4(1), 043504 (2010).
[CrossRef]

Devaux, E.

J. Beermann, T. Søndergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys.13(6), 063029 (2011).
[CrossRef]

Diwekar, M.

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton.4(1), 043504 (2010).
[CrossRef]

Durach, M.

Ebbesen, T. W.

J. Beermann, T. Søndergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys.13(6), 063029 (2011).
[CrossRef]

T. Thio, H. F. Ghaemi, H. J. Lezec, P. A. Wolff, and T. W. Ebbesen, “Surface-plasmon-enhanced transmission through hole arrays in Cr films,” J. Opt. Soc. Am. B16(10), 1743–1748 (1999).
[CrossRef]

Ghaemi, H. F.

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]

Hecht, B.

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun.253(1-3), 118–124 (2005).
[CrossRef]

Hunsche, S.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun.150(1-6), 22–26 (1998).
[CrossRef]

Isaacson, M.

E. Betzig, M. Isaacson, and A. Lewis, “Collection mode near-field scanning optical microscopy,” Appl. Phys. Lett.51(25), 2088–2090 (1987).
[CrossRef]

Iwaszczuk, K.

Janunts, N. A.

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun.253(1-3), 118–124 (2005).
[CrossRef]

Jepsen, P. U.

Jun, Y. C.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Koch, M.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun.150(1-6), 22–26 (1998).
[CrossRef]

Kurz, H.

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

Lavrinenko, A.

Lewis, A.

E. Betzig, M. Isaacson, and A. Lewis, “Collection mode near-field scanning optical microscopy,” Appl. Phys. Lett.51(25), 2088–2090 (1987).
[CrossRef]

Lezec, H. J.

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.

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]

Mittleman, D. M.

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]

Monzón-Hernández, D.

J. Villatoro, D. Monzón-Hernández, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett.40(2), 106–107 (2004).
[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.

Nam, S.

Nelson, K. A.

Nerkararyan, K. V.

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun.253(1-3), 118–124 (2005).
[CrossRef]

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]

Nguyen, T. D.

Novikov, S. M.

J. Beermann, T. Søndergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys.13(6), 063029 (2011).
[CrossRef]

Nuss, M. C.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun.150(1-6), 22–26 (1998).
[CrossRef]

Painter, O.

Pile, D. F. P.

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]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Søndergaard, T.

J. Beermann, T. Søndergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys.13(6), 063029 (2011).
[CrossRef]

Srinivasan, K.

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.

Talavera, D.

J. Villatoro, D. Monzón-Hernández, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett.40(2), 106–107 (2004).
[CrossRef]

Thio, T.

Vardeny, Z. V.

Villatoro, J.

J. Villatoro, D. Monzón-Hernández, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett.40(2), 106–107 (2004).
[CrossRef]

White, J. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

Wolff, P. A.

Zhang, X.

Zhang, X.-C.

Appl. Phys. Lett.

E. Betzig, M. Isaacson, and A. Lewis, “Collection mode near-field scanning optical microscopy,” Appl. Phys. Lett.51(25), 2088–2090 (1987).
[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]

Electron. Lett.

J. Villatoro, D. Monzón-Hernández, and D. Talavera, “High resolution refractive index sensing with cladded multimode tapered optical fibre,” Electron. Lett.40(2), 106–107 (2004).
[CrossRef]

J. Appl. Phys.

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. Nanophoton.

M. Diwekar, S. Blair, and M. Davis, “Increased light gathering capacity of sub-wavelength conical metallic apertures,” J. Nanophoton.4(1), 043504 (2010).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Mater.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater.9(3), 193–204 (2010).
[CrossRef] [PubMed]

New J. Phys.

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]

J. Beermann, T. Søndergaard, S. M. Novikov, S. I. Bozhevolnyi, E. Devaux, and T. W. Ebbesen, “Field enhancement and extraordinary optical transmission by tapered periodic slits in gold films,” New J. Phys.13(6), 063029 (2011).
[CrossRef]

Opt. Commun.

S. Hunsche, M. Koch, I. Brener, and M. C. Nuss, “THz near-field imaging,” Opt. Commun.150(1-6), 22–26 (1998).
[CrossRef]

N. A. Janunts, K. S. Baghdasaryan, K. V. Nerkararyan, and B. Hecht, “Excitation and superfocusing of surface plasmon polaritons on a silver-coated optical fiber tip,” Opt. Commun.253(1-3), 118–124 (2005).
[CrossRef]

Opt. Express

Phys. Rev. Lett.

M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

Other

N. Marcuvitz, Waveguide Handbook, (New York: McGraw-Hill, 1951).

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

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic diagram of the different apertures structures studied. Top: cross-section of the reference aperture with an aperture diameter, Do = 400 μm and metal thickness, do = 75 μm. Middle left and bottom left: cross-section and top view, respectively, of a single tapered aperture with a variable taper full angle, α, and a fixed output aperture diameter, D2 = 400 μm. The taper angle determines the input aperture diameter, D1. The thickness of the metal disk is d = 3 mm. Middle right and bottom right: cross-section and top view, respectively, of the hexagonal lattice of tapered aperture arrays with nineteen apertures, fabricated normal to the disk surface, with a taper full angle, α’ = 30°, an output aperture diameter, D2 = 400 μm, and an input aperture diameter, D1’ = 2 mm. Once again, the thickness of the metal disk is d = 3 mm. (b) Photographs of the stainless steel tapered aperture array structure with 19 apertures, each with α’ = 30°. (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 an individual tapered aperture structure as a function of the taper full angle, α. (a) Spectra of the field amplitude concentration factor, fE(ν), with respect to α, as noted. (b) Electric field concentration maximum, fE, as a function of the taper angle, α.

Fig. 3
Fig. 3

Calculated fE(ν) spectra of single tapered apertures for various full taper angles, α, as given. The calculation is based on cylindrical waveguide theory as described in the text. The result for each α was scaled to match the experimental concentration amplitude shown in Fig. 2(a).

Fig. 4
Fig. 4

Numerical simulations of the field properties for individual tapered aperture structures. (a) The enhancement spectrum fE(ν) for a TA with α = 30° from simulation (red trace) and experiment (blue trace). (b) Field concentration factor maximum, fE, of the TAs with various α obtained from simulation (red dots); the experimental fE results from Fig. 2(b) are shown for comparison (blue dots).

Fig. 5
Fig. 5

The spectral amplitude concentration factors, fE(ν) measured for the tapered aperture array and a single TA having α = 30° full angle. Both spectra were normalized by the transmitted field of the same reference obtained from a single cylindrical aperture.

Fig. 6
Fig. 6

Numerical simulations of structures designed for tighter field focusing. (a) Schematic diagram of the hexagonal tapered aperture array with seven apertures, where the axes of the outer apertures were tilted with an inclination angle, θ. The reduced spacing of the output apertures, p2, is shown in the top view on left top, cross-section on left bottom and isometric view on the right. For all the apertures, the input diameter D1’ is 2 mm and the output diameter D2 is 400 μm. (b) A snapshot of the planar electric field distribution near the output surface. (c) Maximum value of fE calculated for an individual TA with tilted axes of different inclination angles, θ, for the two orthogonal THz field polarizations. (d) Spectra of field concentration intensity, σ(ν), of TA arrays for various θ as given. The inset shows the maximum σ value extracted from σ(ν) at various values of θ.

Fig. 7
Fig. 7

Schematic diagram for a proposed cascaded taper structure. (a) Cross-section of the structure. The diameter of the input aperture (2.4 mm) on the bottom layer is equal to the longest distance between the edges of the output apertures on the top layer. (b) Decomposition of the structure into two sections: Structure 1 consists of seven tapered apertures forming a hexagonal array with input aperture diameters of 2 mm, output aperture diameters of 400 μm and axis inclination angle of 18.4°; Structure 2 consists of a single tapered aperture with input aperture diameter of 2.4 mm, output aperture diameter of 400 μm and taper full angle of 36.9°.

Equations (3)

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f E ( ν )= t α ( ν ) t ref ( ν ) ,
λ res = P [ 4 3 ( i 2 +ij+ j 2 ) ] 1/2 n SPP ,
σ(ν)= f E (ν) 2 ,

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