Abstract

In this paper we design and measure a metamaterial polarizing device working in the sub-terahertz range. The polarizer is based on a modified version of our previous miniaturized Stacked Hole Array (SHA) structure, an arrangement that combines Extraordinary Optical Transmission (EOT) and Left-Handed Metamaterial (LHM) propagation even under Fresnel illumination. Here, we use a self complementary screen by connecting the holes of an EOT structure. Importantly, EOT remains and simultaneously total reflection is obtained for the orthogonal component. Moreover, by computing the dispersion diagram, we demonstrate that LHM propagation can be achieved for the principal polarization within the stop band of the orthogonal component, which propagates in other bands as a standard forward wave. Finally, we check our conjectures by measuring the transmission and reflection coefficients of screens milled on a low-loss microwave substrate. Measurements have been taken for 1 to 6 stacked wafers and they show clearly that the stack acts as a polarizer with left-handed characteristic. Our results open the way to design of novel polarization control metamaterials at Terahertz wavelengths..

© 2007 Optical Society of America

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References

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  1. J. C. Bose, Collected Physical Papers (London: Longmans, Green, 1927).
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    [CrossRef]
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    [CrossRef]
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  14. 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, 1114-1117 (2001).
    [CrossRef] [PubMed]
  15. J. Rivas, C. Schotsch, P. H. Bolivar and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201-306 (2003).
  16. J. B. Pendry, L. Martín-Moreno, F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
    [CrossRef] [PubMed]
  17. D. R. Jackson, A. A. Oliner, T. Zhao and J. T. Williams, "Beaming of light at broadside through a subwavelength hole: Leaky wave model and open stopband effect," Radio Sci. 40, 1-12 (2005).
    [CrossRef]
  18. J. A. Porto, F. J. García-Vidal and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
    [CrossRef]
  19. M. M. J. Treacy, "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett. 75, 606-608 (1999)
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  20. J. B. Pendry, A. J. Holden, W. J. Stewart and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  21. J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  22. V. G. Veselago, "The Electrodynamics of Substances with simultaneously negative values of ∑ and μ," Sov. Phys. Usp. 10, 509-514 (1968).
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    [CrossRef] [PubMed]
  24. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  25. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
    [CrossRef] [PubMed]
  26. M. Beruete, M. Sorolla, and I. Campillo," Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays," Opt. Express 14, 5445-5455 (2006).
    [CrossRef] [PubMed]
  27. M. Beruete, I. Campillo, M. Navarro, F. Falcone, and M. Sorolla, "Molding left- or right-handed metamaterials by stacked cut-off metallic hole arrays," accepted in the IEEE Trans. Antennas Propag., special issue in honor of Prof. L. B. Felsen, (2007).
  28. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
    [CrossRef] [PubMed]
  29. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
    [CrossRef] [PubMed]
  30. M. Beruete, M. Sorolla, and I. Campillo," Inhibiting negative index of refraction by a band gap of stacked cut-off metallic hole arrays," IEEE Microwave Wirel. Compon. Lett. 17, 16-18 (2007).
    [CrossRef]
  31. M. Beruete, M. Sorolla, I. Campillo, and J. S. Dolado, "Increase of the transmission in cut-off metallic hole arrays," IEEE Microwave Wirel. Compon. Lett. 15, 116-118 (2005).
    [CrossRef]
  32. M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo and V. Lomakin, "Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays," Opt. Express,  151107-1114 (2007).
    [CrossRef]
  33. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, "Strong polarization in the optical transmission through elliptical nanohole arrays," Phys. Rev. Lett. 92, 037401-1-4 (2004).
    [CrossRef] [PubMed]
  34. F. J. García de Abajo, R. Gómez-Medina and J. J. Sáenz, "Full transmission through perfect-conductor subwavelength hole arrays," Phys. Rev. E 72, 016608-1-4 (2005).
    [CrossRef]
  35. M. Beruete, M. Navarro-Cía, I. Campillo, P. Goy, and M. Sorolla, "Quasioptical polarizer based on selfcomplementary sub-wavelength hole arrays," submitted to the IEEE Microwave and Wireless Components Letters.
  36. C. Dahl, P. Goy, and J. P. Kotthaus, "Magneto-Optical Millimeter-Wave Spectroscopy," G. Grüner, ed., in Millimeter and Submillimeter Wave Spectroscopy of Solids, Topics in Applied Physics, (Springer, 1998).

2007 (3)

M. Tonouchi, "Cutting-edge terahertz technology," Nature Photonics 1, 97-105 (2007).
[CrossRef]

M. Beruete, M. Sorolla, and I. Campillo," Inhibiting negative index of refraction by a band gap of stacked cut-off metallic hole arrays," IEEE Microwave Wirel. Compon. Lett. 17, 16-18 (2007).
[CrossRef]

M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo and V. Lomakin, "Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays," Opt. Express,  151107-1114 (2007).
[CrossRef]

2006 (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

M. Beruete, M. Sorolla, and I. Campillo," Left-handed extraordinary optical transmission through a photonic crystal of subwavelength hole arrays," Opt. Express 14, 5445-5455 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

2005 (2)

M. Beruete, M. Sorolla, I. Campillo, and J. S. Dolado, "Increase of the transmission in cut-off metallic hole arrays," IEEE Microwave Wirel. Compon. Lett. 15, 116-118 (2005).
[CrossRef]

D. R. Jackson, A. A. Oliner, T. Zhao and J. T. Williams, "Beaming of light at broadside through a subwavelength hole: Leaky wave model and open stopband effect," Radio Sci. 40, 1-12 (2005).
[CrossRef]

2004 (2)

2003 (1)

J. Rivas, C. Schotsch, P. H. Bolivar and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201-306 (2003).

2001 (2)

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, 1114-1117 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-796 (2001).
[CrossRef] [PubMed]

2000 (1)

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

1999 (3)

J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. A. Porto, F. J. García-Vidal and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

M. M. J. Treacy, "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett. 75, 606-608 (1999)
[CrossRef]

1998 (1)

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

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

1986 (1)

G. Zhang, J. Hu and J. Zhao, "Study of the FIR bandpass filters consisting of two resonant grids," Int. J. Infrared Millimeter Waves 7, 237-243 (1986).
[CrossRef]

1982 (1)

1973 (1)

C. C. Chen, "Transmission of microwave through perforated flat plates of finite thickness," IEEE Trans. Microwave Theory Tech. 21, 1-7 (1973).
[CrossRef]

1968 (1)

V. G. Veselago, "The Electrodynamics of Substances with simultaneously negative values of ∑ and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1967 (1)

R. Ulrich, "Far-infrared properties of metallic mesh and its complementary structure," Infrared Phys. 7, 37- 55 (1967).
[CrossRef]

1924 (1)

A. Glagolewa-Arkadiewa, "Short electromagnetic waves of wavelength up to 82 microns," Nature 2844, 640, (1924).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. M. J. Treacy, "Dynamical diffraction in metallic optical gratings," Appl. Phys. Lett. 75, 606-608 (1999)
[CrossRef]

IEEE Microwave Wirel. Compon. Lett. (2)

M. Beruete, M. Sorolla, and I. Campillo," Inhibiting negative index of refraction by a band gap of stacked cut-off metallic hole arrays," IEEE Microwave Wirel. Compon. Lett. 17, 16-18 (2007).
[CrossRef]

M. Beruete, M. Sorolla, I. Campillo, and J. S. Dolado, "Increase of the transmission in cut-off metallic hole arrays," IEEE Microwave Wirel. Compon. Lett. 15, 116-118 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

J. B. Pendry, A. J. Holden, D. J. Robbins and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

C. C. Chen, "Transmission of microwave through perforated flat plates of finite thickness," IEEE Trans. Microwave Theory Tech. 21, 1-7 (1973).
[CrossRef]

Infrared Phys. (1)

R. Ulrich, "Far-infrared properties of metallic mesh and its complementary structure," Infrared Phys. 7, 37- 55 (1967).
[CrossRef]

Int. J. Infrared Millimeter Waves (1)

G. Zhang, J. Hu and J. Zhao, "Study of the FIR bandpass filters consisting of two resonant grids," Int. J. Infrared Millimeter Waves 7, 237-243 (1986).
[CrossRef]

Nature (2)

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

A. Glagolewa-Arkadiewa, "Short electromagnetic waves of wavelength up to 82 microns," Nature 2844, 640, (1924).
[CrossRef]

Nature Photonics (1)

M. Tonouchi, "Cutting-edge terahertz technology," Nature Photonics 1, 97-105 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

J. Rivas, C. Schotsch, P. H. Bolivar and H. Kurz, "Enhanced transmission of THz radiation through subwavelength holes," Phys. Rev. B 68, 201-306 (2003).

Phys. Rev. Lett. (4)

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, 1114-1117 (2001).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, W. J. Stewart and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

J. A. Porto, F. J. García-Vidal and J. B. Pendry, "Transmission resonances on metallic gratings with very narrow slits," Phys. Rev. Lett. 83, 2845-2848 (1999).
[CrossRef]

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

Radio Sci. (1)

D. R. Jackson, A. A. Oliner, T. Zhao and J. T. Williams, "Beaming of light at broadside through a subwavelength hole: Leaky wave model and open stopband effect," Radio Sci. 40, 1-12 (2005).
[CrossRef]

Science (4)

J. B. Pendry, L. Martín-Moreno, F. J. Garcia-Vidal, "Mimicking Surface Plasmons with Structured Surfaces," Science 305, 847-848 (2004).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science 314, 977-980 (2006).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-796 (2001).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The Electrodynamics of Substances with simultaneously negative values of ∑ and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (11)

M. Beruete, I. Campillo, M. Navarro, F. Falcone, and M. Sorolla, "Molding left- or right-handed metamaterials by stacked cut-off metallic hole arrays," accepted in the IEEE Trans. Antennas Propag., special issue in honor of Prof. L. B. Felsen, (2007).

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-1-4 (2005).
[CrossRef] [PubMed]

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, "Strong polarization in the optical transmission through elliptical nanohole arrays," Phys. Rev. Lett. 92, 037401-1-4 (2004).
[CrossRef] [PubMed]

F. J. García de Abajo, R. Gómez-Medina and J. J. Sáenz, "Full transmission through perfect-conductor subwavelength hole arrays," Phys. Rev. E 72, 016608-1-4 (2005).
[CrossRef]

M. Beruete, M. Navarro-Cía, I. Campillo, P. Goy, and M. Sorolla, "Quasioptical polarizer based on selfcomplementary sub-wavelength hole arrays," submitted to the IEEE Microwave and Wireless Components Letters.

C. Dahl, P. Goy, and J. P. Kotthaus, "Magneto-Optical Millimeter-Wave Spectroscopy," G. Grüner, ed., in Millimeter and Submillimeter Wave Spectroscopy of Solids, Topics in Applied Physics, (Springer, 1998).

J. C. Bose, Collected Physical Papers (London: Longmans, Green, 1927).

P. F. Goldsmith, Quasioptical Systems - Gaussian Beam, Quasioptical Propagation, and Applications (IEEE Press, 1998).

S. Cornbleet, Microwave Optics-The Optics of Microwave Antenna Design (Academic Press, 1976).

J. D. Jackson, Classical Electrodynamics, (Wiley, New York, 1999).

D. Rittenhouse, "An optical problem, proposed by Mr. Hopkinson, and solved by Mr. Rittenhouse," Trans. Amer. Phil. Soc. 2, 201-206(1786).
[CrossRef]

Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1.

Schematic representation and unit cell of a rectangular EOT hole array (a) and self-complementary EOT polarizer (b). Parameters: dx = 2.7 mm, dy = 5.0 mm, a = 2.5 mm, s = 0.2 mm. The metal thickness is t = 0 and conductivity σ→∞.

Fig. 2.
Fig. 2.

Simulation results of the polarization dependent transmission (a) and reflection (b) coefficients (continuous trace for co-polar and dashed one for cross-polar) for a slit array along the y-axis, corresponding to the cuts made on the self-complementary structure (green), hole array (red) and for the proposed polarizer (blue). The dimensions of the analyzed structures are given in Fig. 1(a) for the slit array (removing the thin metal lines of width s) and for the hole array. Fig. 1(b) gives the dimensions of the polarizer. Plot of the conduction and displacement currents at the resonance enhanced transmission peak with vertically polarized (Ey) light. Hole array case (c) and polarizer (d). The E-field is depicted in a perpendicular cutting plane through the middle of a hole and the scale is normalized to the maximum in each case.

Fig. 3.
Fig. 3.

Dispersion diagram for the co-polar (continuous red line) and cross-polarization (dashed red line) corresponding to the parameters dx = 1.8 mm, dy = 3.4 mm, a = 1.2 mm, s = 0.2 mm (for nomenclature check caption of Fig. 1(b)). The metal thickness is t = 35 microns and Cu conductivity σ = 5.8∙107. The substrate has the next characteristics: dielectric permittivity ε = 2.43 and thickness h = 0.49 mm The longitudinal lattice of the stack is dz = 0.525 mm.

Fig. 4.
Fig. 4.

Frozen image extracted from the given animation where an impinging circular polarized wave (upper right side) is transmitted through the LHM-polarizer and a pure vertically polarized wave emerges at the output side of the device (bottom left side). [Media 1]

Fig. 5.
Fig. 5.

Picture of the quasioptical measurement set-up where operates our AB MILLIMETRE vector network analyzer and a picture of the fabricated prototype. A detail of the fine fabrication process is also given.

Fig. 6.
Fig. 6.

Magnitude of the transmission and reflection coefficient of one wafer: co-polar (a) and cross-polar component (b) Magnitude of the transmission coefficient for several stacked wafers: co-polar (c) and cross-polar component (d) Phase of the transmission coefficient for several stacked wafers: co-polar (e) and cross-polar component (f) Magnitude of the reflection coefficient for several stacked wafers: co-polar (g) and cross-polar component (h)

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