Abstract

We demonstrate the extraordinary transmission of terahertz THz radiation through gratings of subwavelength apertures structured in indium antimonide InSb. This transmission can be attributed to the tunneling of surface plasmons polaritons which are excited in semiconductors at THz frequencies. By thermally controlling the permittivity of the grating the transmittance increases by more than one order of magnitude. This increase might be associated to the larger the skin depth in InSb at low temperatures, which gives rise to a larger effective size of the apertures.

© 2005 Optical Society of America

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    [CrossRef]
  2. H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, �??Surface plasmons enhance optical transmission through subwavelength holes,�?? Phys. Rev. B 58, 6779-6782 (1998).
    [CrossRef]
  3. 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 B 16, 1743-1748 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. W.-C. Liu, D.P. Tsai, �??Optical tunneling effect of surface plasmon polaritons and localized plasmon resonance,�?? Phys. Rev. B 65, 155423 (2002).
    [CrossRef]
  8. S.A. Darmanyan and A.V. Zayats, �??Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,�?? Phys. Rev. B 67, 035424 (2003).
    [CrossRef]
  9. M.M.J. Treacy, �??Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,�?? Phys. Rev. B 66, 195105 (2002).
    [CrossRef]
  10. H.J. Lezec and T. Thio, �??Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,�?? Opt. Express 12, 3629 (2004), <a href= " http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3629">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3629</a>
    [CrossRef] [PubMed]
  11. L. Martín-Moreno, F.J. García-Vidal, H.J. Lezec, A. Derigon, and T.W. Ebbesen, �??Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,�?? Phys. Rev. Lett. 90, 167401 (2003).
    [CrossRef] [PubMed]
  12. J.B. Pendry, L. Martín-Moreno, and F.J. García-Vidal, �??Mimicking surface plasmons with structured surfaces,�?? Science 305, 847 (2004).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. S.S. Akarca-Biyikli, I. Bulu, and E. Ozbay, �??Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture,�?? Appl. Phys. Lett. 85, 1098 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. J. Gómez Rivas, P. Haring Bolivar, and H. Kurz, �??Thermal switching of the enhanced transmission of THz radiation through sub-wavelength apertures,�?? Opt. Lett. 29, 1680 (2004).
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  21. The transmission efficiency in Refs. [18, 19, 20] was defined as the transmitted amplitude normalized by the fraction of the surface occupied by the apertures, in contrast to the definition adopted here which refers to the transmitted power.
  22. D.E. Grupp, H.J. Lezec, T.W. Ebbesen, K.M. Pellerin, and T. Thio, �??Crucial role of metal surface in enhanced transmission through subwavelength apertures,�?? Appl. Phys. Lett. 77, 1569-1571 (2000).
    [CrossRef]
  23. M. van Exter and D. Grischkowsky, �??Optical and electronic properties of doped silicon from 0.1 to 2 THz,�?? Appl. Phys. Lett. 56, 1694-1696 (1990).
    [CrossRef]
  24. O. Madelung, �??Physics of III-V compounds,�?? Chapter 4 (John Wiley & Sons, Inc., New York 1964).
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    [CrossRef]
  26. CrysTec GmbH, www.crystec.de
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    [CrossRef]
  28. J.A. Porto, F.J. Garc´ýa-Vidal, and J.B. Pendry, �??Transmission resonances on metallic gratings with very narrow slits,�?? Phys. Rev. Lett. 83, 2845 (1999).
    [CrossRef]
  29. S. Astilean, Ph. Lalanne, and M. Palamaru, �??Light transmission through metallic channels much smaller than the wavelength,�?? Opt. Comm. 175, 265 (2000).
    [CrossRef]
  30. H.E. Went, A.P. Hibbins, J.R. Sambles, C.R. Lawrence, and A.P. Crick, �??Selective transmission through very deep zero-order metallic gratings at microwave frequencies,�?? Appl. Phys. Lett. 77, 2789 (2000).
    [CrossRef]
  31. A.P. Hibbins, J.R. Sambles, C.R. Lawrence, and D.M. Robinson, �??Remarkable transmission of microwave through a wall of long metallic bricks,�?? Appl. Phys. Lett. 79, 2844 (2001).
    [CrossRef]
  32. Q. Cao and P. Lalanne, �??Negative Role of Surface Plasmons in the Transmission of Metallic Gratings with Very Narrow Slits,�?? Phys. Rev. Lett. 88, 057403 (2002).
    [CrossRef] [PubMed]
  33. S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, �??Horizontal and vertical surface resonances in transmission metallic gratings,�?? J. Opt. A 4, S154 (2002).
    [CrossRef]
  34. P. Lalanne, C. Sauvan, J.P. Hugonin, J.C. Rodier, and P. Chavel, �??Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,�?? Phys. Rev. B 68, 125404 (2003).
    [CrossRef]
  35. J.L. Adams, L.C. Botten, and R.C. McPhedran, �??The crossed lamellar transmission grating,�?? J. Optics 9, 91 (1978).
    [CrossRef]
  36. D.R. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, �??Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,�?? J. Opt. Soc. Am. B 7, 2006 (1990).
    [CrossRef]
  37. R.W. Wood, �??Anomalous diffraction gratings,�?? Phys. Rev. 48, 928 (1935).
  38. K.J.K. Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, and L. Kuipers, �??Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,�?? Phys. Rev. Lett. 92, 183901 (2004).
    [CrossRef] [PubMed]
  39. A. Degiron, H.J. Lezec, W.L. Barnes, and T.W. Ebbesen, �??Effects of hole depth on enhanced light transmission through subwavelength hole arrays,�?? Appl. Phys. Lett. 81, 4327 (2002).
    [CrossRef]
  40. H. Raether, �??Surface plasmons on smooth and rough surfaces and on gratings,�?? Springer Tracts in Modern Physics, vol. 111 (Springer-Verlag, Berlin 1988).
  41. L. Martín-Moreno and F.J. García-Vidal, �??Optical transmission through circular hole arrays in optically thick metal films,�?? Opt. Express 12, 3619 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3619">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3619</a>
    [CrossRef]
  42. J.D. Jackson, �??Classical electrodynamics,�?? thrid edition, Chapter 8 (John Wiley & íSons, Inc., New York 1999).

Appl. Phys. Lett.

M. Lockyear, A.P. Hibbins, J.R. Sambles, and C.R. Lawrence, �??Surface-topography induced enhanced transmission and directivity of microwave radiation through subwavelength circular metal aperture,�?? Appl. Phys. Lett. 84, 2040 (2004).
[CrossRef]

F. Miyamaru and M. Hangyo, �??Finite size effect of transmission property for metal hole arrays in subterahertz region,�?? Appl. Phys. Lett. 84, 2742 (2004).
[CrossRef]

S.S. Akarca-Biyikli, I. Bulu, and E. Ozbay, �??Enhanced transmission of microwave radiation in one-dimensional metallic gratings with subwavelength aperture,�?? Appl. Phys. Lett. 85, 1098 (2004).
[CrossRef]

D.E. Grupp, H.J. Lezec, T.W. Ebbesen, K.M. Pellerin, and T. Thio, �??Crucial role of metal surface in enhanced transmission through subwavelength apertures,�?? Appl. Phys. Lett. 77, 1569-1571 (2000).
[CrossRef]

M. van Exter and D. Grischkowsky, �??Optical and electronic properties of doped silicon from 0.1 to 2 THz,�?? Appl. Phys. Lett. 56, 1694-1696 (1990).
[CrossRef]

S.C. Howells and L.A. Schlie, �??Transient terahertz reflection spectroscopy of undoped InSb from 0.1 to 1.1 THz,�?? Appl. Phys. Lett. 69, 550 (1996).
[CrossRef]

H.E. Went, A.P. Hibbins, J.R. Sambles, C.R. Lawrence, and A.P. Crick, �??Selective transmission through very deep zero-order metallic gratings at microwave frequencies,�?? Appl. Phys. Lett. 77, 2789 (2000).
[CrossRef]

A.P. Hibbins, J.R. Sambles, C.R. Lawrence, and D.M. Robinson, �??Remarkable transmission of microwave through a wall of long metallic bricks,�?? Appl. Phys. Lett. 79, 2844 (2001).
[CrossRef]

A. Degiron, H.J. Lezec, W.L. Barnes, and T.W. Ebbesen, �??Effects of hole depth on enhanced light transmission through subwavelength hole arrays,�?? Appl. Phys. Lett. 81, 4327 (2002).
[CrossRef]

J. Opt. A

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, �??Horizontal and vertical surface resonances in transmission metallic gratings,�?? J. Opt. A 4, S154 (2002).
[CrossRef]

J. Opt. A: pure Appl. Opt.

S. Enoch, E. Popov, M. Neviere, and R. Reinisch, �??Enhanced light transmission by hole arrays,�?? J. Opt. A: pure Appl. Opt. 4, S83 (2002).
[CrossRef]

J. Opt. Soc. Am B

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 B 16, 1743-1748 (1999).
[CrossRef]

J. Opt. Soc. Am. B

J. Optics.

J.L. Adams, L.C. Botten, and R.C. McPhedran, �??The crossed lamellar transmission grating,�?? J. Optics 9, 91 (1978).
[CrossRef]

Nature

W.L. Barnes, A. Dereux, and T.W. Ebbesen, �??Surface plasmon subwavelength optics,�?? Nature 424, 824 (2003).
[CrossRef] [PubMed]

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

Opt. Comm.

S. Astilean, Ph. Lalanne, and M. Palamaru, �??Light transmission through metallic channels much smaller than the wavelength,�?? Opt. Comm. 175, 265 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

R.W. Wood, �??Anomalous diffraction gratings,�?? Phys. Rev. 48, 928 (1935).

Phys. Rev. B

P. Lalanne, C. Sauvan, J.P. Hugonin, J.C. Rodier, and P. Chavel, �??Perturbative approach for surface plasmon effects on flat interfaces periodically corrugated by subwavelength apertures,�?? Phys. Rev. B 68, 125404 (2003).
[CrossRef]

U. Schröter and D. Heitmann, �??Surface-plasmon-enhanced transmission through metallic gratings,�?? Phys. Rev. B 58, 15419 (1998).
[CrossRef]

Gómez Rivas, C. Schotsch, P. Haring Bolivar, and H. Kurz, �??Enhanced transmission of THz radiation through sub-wavelength holes,�?? Phys. Rev. B 68, 201306 (2003).
[CrossRef]

C. Janke, J. Gómez Rivas, C. Schotsch, L. Beckmann, P. Haring Bolivar, and H. Kurz, �??Optimization of the enhanced THz transmission through arrays of sub-wavelength apertures,�?? Phys. Rev. B 69, 205314 (2004).
[CrossRef]

H.F. Ghaemi, T. Thio, D.E. Grupp, T.W. Ebbesen, and H.J. Lezec, �??Surface plasmons enhance optical transmission through subwavelength holes,�?? Phys. Rev. B 58, 6779-6782 (1998).
[CrossRef]

W.-C. Liu, D.P. Tsai, �??Optical tunneling effect of surface plasmon polaritons and localized plasmon resonance,�?? Phys. Rev. B 65, 155423 (2002).
[CrossRef]

S.A. Darmanyan and A.V. Zayats, �??Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,�?? Phys. Rev. B 67, 035424 (2003).
[CrossRef]

M.M.J. Treacy, �??Dynamical diffraction explanation of the anomalous transmission of light through metallic gratings,�?? Phys. Rev. B 66, 195105 (2002).
[CrossRef]

Phys. Rev. Lett.

L. Martín-Moreno, F.J. García-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 (2001).
[CrossRef] [PubMed]

L. Martín-Moreno, F.J. García-Vidal, H.J. Lezec, A. Derigon, and T.W. Ebbesen, �??Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,�?? Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

J.A. Porto, F.J. Garc´ýa-Vidal, and J.B. Pendry, �??Transmission resonances on metallic gratings with very narrow slits,�?? Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

K.J.K. Koerkamp, S. Enoch, F.B. Segerink, N.F. van Hulst, and L. Kuipers, �??Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,�?? Phys. Rev. Lett. 92, 183901 (2004).
[CrossRef] [PubMed]

Q. Cao and P. Lalanne, �??Negative Role of Surface Plasmons in the Transmission of Metallic Gratings with Very Narrow Slits,�?? Phys. Rev. Lett. 88, 057403 (2002).
[CrossRef] [PubMed]

Science

J.B. Pendry, L. Martín-Moreno, and F.J. García-Vidal, �??Mimicking surface plasmons with structured surfaces,�?? Science 305, 847 (2004).
[CrossRef] [PubMed]

Springer Tracts in Modern Physics

H. Raether, �??Surface plasmons on smooth and rough surfaces and on gratings,�?? Springer Tracts in Modern Physics, vol. 111 (Springer-Verlag, Berlin 1988).

Other

J.D. Jackson, �??Classical electrodynamics,�?? thrid edition, Chapter 8 (John Wiley & íSons, Inc., New York 1999).

CrysTec GmbH, www.crystec.de

The transmission efficiency in Refs. [18, 19, 20] was defined as the transmitted amplitude normalized by the fraction of the surface occupied by the apertures, in contrast to the definition adopted here which refers to the transmitted power.

O. Madelung, �??Physics of III-V compounds,�?? Chapter 4 (John Wiley & Sons, Inc., New York 1964).

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Figures (8)

Fig. 1.
Fig. 1.

Absolute value of the real part (blue lines) and the imaginary part (green lines) of the complex permittivity of InSb versus the frequency calculated with the Drude model. The solid curves correspond to room temperature, while the dashed curves are the permittivity at 225 K.

Fig. 2.
Fig. 2.

Transmittance measurements through a slab of bulk InSb with a thickness of 100 µm. The squares are measurements at room temperature, while the circles correspond to measurements at 225 K. The solid curves are fits to the measurements using the values of the permittivity calculated with the Drude model.

Fig. 3.
Fig. 3.

Scanning electron microscope image of a grating of subwavelength apertures structured in InSb. The thickness of the the grating is 130 µm, the lattice constant 300 µm, and the lateral size of the apertures 65 µm.

Fig. 4.
Fig. 4.

Time-domain terahertz amplitude. The red curve corresponds to the setup response, while the blue curve is the transmission through a square grating of apertures structured in InSb. For clarity a vertical offset is introduced.

Fig. 5.
Fig. 5.

Transmittance through a grating of InSb at a temperature of 325 K. The dashed lines indicate the frequencies of theWood’s anomalies for a square grating with a lattice constant of 300 µm. The inset represents the power spectrum of the reference pulse.

Fig. 6.
Fig. 6.

(a) Transmittance through a grating of apertures with a lateral size of 65 µm structured in InSb. The transmittance is measured for different temperatures of the grating as indicated in the legenda. The inset represents the same measurements as a function of the wavelength. (b) Transmittance through a bulk piece of InSb with a thickness of 100 µm at different temperatures.

Fig. 7.
Fig. 7.

Temperature dependence of the resonance frequency (a) and of the maximum transmittance at the resonance (b). The inset of (a) represents the effective refractive index as a function of temperature and that of (b) is the effective aperture size.

Fig. 8.
Fig. 8.

Transmittance through silicon gratings with lattice constant of 400 µm and different apertures sizes. The red line corresponds to the transmittance through a grating with square apertures with a lateral size of 130 µm, while the blue and green lines are the transmittance through similar gratings with apertures sides of 110 and 70 µm respectively.

Tables (1)

Tables Icon

Table 1. Real ε′ and imaginary ε″ permittivities of InSb at 0.6 THz for different temperatures T. Also are listed the propagation length of SPPs δ SPP on flat interfaces between air and a material with permittivity ε=ε′+″, the skin depth of the material δ InSb, and the SPPs decay length into air δ air.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

ε ( ω ) = ε ( 1 ω p 2 ω 2 + τ 2 + i ω p 2 τ 1 ω ( ω 2 + τ 2 ) )
δ SPP 2 c 0 ω ( ε ' + 1 ε ' ) 3 2 ε ' 2 ε " ,
δ air c 0 ω ( ε ' + 1 ) 1 2 .
δ ln Sb c 0 ω ( ε ' + 1 ε ' 2 ) 1 2 .
v = c 0 l 2 + m 2 a 0 1 n eff ,

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