Abstract

We present experimental and numerical investigations of planar terahertz metamaterial structures designed to interact with the state of polarization. The dependence of metamaterial resonances on polarization results in unique amplitude and phase characteristics of the terahertz transmission, providing the basis for polarimetric terahertz devices. We highlight some potential applications for polarimetric devices and present simulations of a terahertz quarter-wave plate and a polarizing terahertz beam splitter. Although this work was performed at terahertz frequencies, it may find applications in other frequency ranges as well.

© 2009 Optical Society of America

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2008

F. Zhang, Q. Zhao, L. Kang, D. P. Gaillot, X. Zhao, J. Zhou, D. Lippens, “Magnetic control of negative permeability metamaterials based on liquid crystals,” Appl. Phys. Lett. 92, 193104 (2008).
[CrossRef]

H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials, “ Nat. Photonics 2, 295 (2008).
[CrossRef]

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef] [PubMed]

M. Iwanagaa, “Ultracompact waveplates: Approach from metamaterials,” Appl. Phys. Lett. 92, 153102 (2008).
[CrossRef]

C.-F. Hsieh, Y.-C. Lai, R.-P. Pan, C.-L. Pan, “Polarizing terahertz waves with nematic liquid crystals”, Opt. Lett. 33, 1174–1176 (2008).
[CrossRef] [PubMed]

Y. Yuan, C. Bingham, T. Tyler, S. Palit, T. H. Hand, W. J. Padilla, D. R. Smith, N. M. Jokerst, S. A. Cummer, “Dual-band planar electric metamaterial in the terahertz regime,” Opt. Express 16, 9746–9752 (2008).
[CrossRef] [PubMed]

2007

J. S. Tharp, B. A. Lail, B. A. Munk, G. D. Boreman, “Design and demonstration of an infrared meanderline phase retarder,” IEEE Trans. Antennas Propag. 55, 2983–2988 (2007).
[CrossRef]

N. Kanda, K. Konishi, M. Kuwata-Gonokami, “Terahertz wave polarization rotation with double layered metal grating of complimentary chiral patterns,” Opt. Express 15, 11117–11125 (2007).
[CrossRef] [PubMed]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

N. Wongkasem, A. Akyurtlu, K. A. Marx, Q. Dong, J. Li, W. D. Goodhue, “Development of chiral negative refractive index metamaterials for the terahertz frequency regime,” IEEE Trans. Antennas Propag. 55, 3052–3062 (2007).
[CrossRef]

C. Imhof, R. Zengerle, “Strong birefringence in left-handed metallic metamaterials,” Opt. Commun. 280, 213–216 (2007).
[CrossRef]

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

A. Degiron, J. J. Mock, D. R. Smith, “Modulating and tuning the response of metamaterials at the unit cell level,” Opt. Express 15, 1115–1127 (2007).
[CrossRef] [PubMed]

E. Kim, Y. R. Shen, W. Wu, E. Ponizovskaya, Z. Yu, A. M. Bratkovsky, S. Y. Wang, R. S. Williams, “Modulation of negative index metamaterials in the near-IR range,” Appl. Phys. Lett. 91, 173105 (2007).
[CrossRef]

R. Piesiewicz, T. Kleine-Ostmann, N. Krumbholz, D. Mittleman, M. Koch, J. Schoebel, T. Kurner, “Short-range ultra-broadband terahertz communications: Concepts and perspectives,” IEEE Antennas Propag. Mag. 49, 24–39 (2007).
[CrossRef]

B. M. Fischer, H. Helm, P. U. Jepsen, “Chemical recognition with broadband THz spectroscopy,” Proc. IEEE 95, 1592–1604 (2007).
[CrossRef]

2006

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
[CrossRef] [PubMed]

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

J. D. Baena, L. Jelinek, R. Marques, J. Zehentner, “Electrically small isotropic three-dimensional magnetic resonators for metamaterial design,” Appl. Phys. Lett. 88, 134108 (2006).
[CrossRef]

J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express 16, 1786–1795 (2006).
[CrossRef]

X. Xu, B. Quan, C. Gu, L. Wang, “Bianisotropic response of microfabricated metamaterials in the terahertz region,” J. Opt. Soc. Am. B 23, 1174–1180 (2006).
[CrossRef]

C.-F. Hsieh, R.-P. Pan, T.-T. Tang, H.-L. Chen, C.-L. Pan, “Voltage-controlled liquid-crystal terahertz phase shifter and quarter-wave plate”, Opt. Lett. 31, 1112–1114 (2006).
[CrossRef] [PubMed]

J.-B. Masson, G. Gallot, “Terahertz achromatic quarter-wave plate”, Opt. Lett. 31, 265–267 (2006).
[CrossRef] [PubMed]

A. K. Azad, J. M. Dai, W. L. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31, 634–636 (2006).
[CrossRef] [PubMed]

W. J. Padilla, D. R. Smith, D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23, 404–414 (2006).
[CrossRef]

J. F. O’Hara, J. M. O. Zide, A. C. Gossard, A. J. Taylor, R. D. Averitt, “Enhanced terahertz detection via ErAs : GaAs nanoisland superlattices,” Appl. Phys. Lett. 88, 251119 (2006).
[CrossRef]

2005

E. Castro-Camus, J. Lloyd-Hughes, M. B. Johnston, M. D. Fraser, H. H. Tan, C. Jagadish, “Polarization-sensitive terahertz detection by multicontact photoconductive receivers,” Appl. Phys. Lett. 86, 254102 (2005).
[CrossRef]

N. C. J. van der Valk, W. A. M. van der Marel, P. C. M. Planken, “Terahertz polarization imaging,” Opt. Letters 30, 2802–2804 (2005).
[CrossRef]

A. Agrawal, H. Cao, A. Nahata, “Excitation and scattering of surface plasmon-polaritons on structured metal films and their application to pulse shaping and enhanced transmission,” New J. Phys. 7, 2491-13 (2005).
[CrossRef]

W. Zhang, A. Potts, A. Papakostas, D. M. Bagnall, “Intensity modulation and polarization rotation of visible light by dielectric planar chiral metamaterials,” Appl. Phys. Lett. 86, 231905 (2005).
[CrossRef]

A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, Y. S. Kivshar, “Birefringent left-handed metamaterials and perfect lenses for vectorial fields,” New J. Phys. 7, 2201-9 (2005).
[CrossRef]

R. Shimano, H. Nishimura, T. Sato, “Frequency tunable circular polarization control of terahertz radiation,” Jpn. J. Appl. Phys. Part 2-Lett. And Express Lett. 44, L676–L678 (2005).
[CrossRef]

N. Amer, W. C. Hurlbut, B. J. Norton, Y. S. Lee, T. B. Norris, “Generation of terahertz pulses with arbitrary elliptical polarization,” Appl. Phys. Lett. 87, 221111 (2005).
[CrossRef]

2004

T. W. Crowe, T. Globus, D. L. Woolard, J. L. Hesler, “Terahertz sources and detectors and their application to biological sensing,” Philos. Trans. R. Soc. London Ser. A 362, 365–374 (2004).
[CrossRef]

2003

J. Xu, G. J. Ramian, J. F. Galan, P. G. Savvidis, A. M. Scopatz, R. R. Birge, J. Allen, K. W. Plaxco, “Terahertz circular dichroism spectroscopy: A potential approach to the in situ detection of life’s metabolic and genetic machinery,” Astrobiology 3, 489–504 (2003).
[CrossRef] [PubMed]

2002

B. Ferguson, X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
[CrossRef]

R. Marques, J. Martel, F. Mesa, F. Medina, “A new 2D isotropic left-handed metamaterial design: Theory and experiment,” Microwave Opt. Technol. Lett. 35, 405–408 (2002).
[CrossRef]

S. O’Brien, J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys.: Condens. Matter 146383–6394 (2002).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

1999

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

C. Winnewisser, F. Lewen, J. Weinzierl, H. Helm, “Transmission features of frequency-selective components in the far infrared determined by terahertz time-domain spectroscopy,” Appl. Opt. 38, 3961–3967 (1999).
[CrossRef]

1998

S. Hunsche, D. M. Mittleman, M. Koch, M. C. Nuss, “New dimensions in T-ray imaging,” IEEE Trans. Electron. E81c, 269–276 (1998).

1996

1995

Agrawal, A.

A. Agrawal, H. Cao, A. Nahata, “Excitation and scattering of surface plasmon-polaritons on structured metal films and their application to pulse shaping and enhanced transmission,” New J. Phys. 7, 2491-13 (2005).
[CrossRef]

Akyurtlu, A.

N. Wongkasem, A. Akyurtlu, K. A. Marx, Q. Dong, J. Li, W. D. Goodhue, “Development of chiral negative refractive index metamaterials for the terahertz frequency regime,” IEEE Trans. Antennas Propag. 55, 3052–3062 (2007).
[CrossRef]

Allen, J.

J. Xu, G. J. Ramian, J. F. Galan, P. G. Savvidis, A. M. Scopatz, R. R. Birge, J. Allen, K. W. Plaxco, “Terahertz circular dichroism spectroscopy: A potential approach to the in situ detection of life’s metabolic and genetic machinery,” Astrobiology 3, 489–504 (2003).
[CrossRef] [PubMed]

Amer, N.

N. Amer, W. C. Hurlbut, B. J. Norton, Y. S. Lee, T. B. Norris, “Generation of terahertz pulses with arbitrary elliptical polarization,” Appl. Phys. Lett. 87, 221111 (2005).
[CrossRef]

Andreev, G. O.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, S. Y. Cho, N. M. Jokerst, D. R. Smith, “Tuned permeability in terahertz split-ring resonators for devices and sensors,” Appl. Phys. Lett. 91, 062511 (2007).
[CrossRef]

Averitt, R. D.

H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials, “ Nat. Photonics 2, 295 (2008).
[CrossRef]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

J. F. O’Hara, J. M. O. Zide, A. C. Gossard, A. J. Taylor, R. D. Averitt, “Enhanced terahertz detection via ErAs : GaAs nanoisland superlattices,” Appl. Phys. Lett. 88, 251119 (2006).
[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
[CrossRef] [PubMed]

Azad, A. K.

H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials, “ Nat. Photonics 2, 295 (2008).
[CrossRef]

J. F. O’Hara, E. Smirnova, A. K. Azad, H. T. Chen, A. J. Taylor, “Effects of microstructure variations on macroscopic terahertz metafilm properties,” Act. Passive Electron. Compon. 2007, 49691 (2007).

A. K. Azad, J. M. Dai, W. L. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31, 634–636 (2006).
[CrossRef] [PubMed]

Baena, J. D.

J. D. Baena, L. Jelinek, R. Marques, J. Zehentner, “Electrically small isotropic three-dimensional magnetic resonators for metamaterial design,” Appl. Phys. Lett. 88, 134108 (2006).
[CrossRef]

Bagnall, D. M.

W. Zhang, A. Potts, A. Papakostas, D. M. Bagnall, “Intensity modulation and polarization rotation of visible light by dielectric planar chiral metamaterials,” Appl. Phys. Lett. 86, 231905 (2005).
[CrossRef]

Basov, D. N.

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
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J. Opt. Soc. Am. B

J. Phys.: Condens. Matter

S. O’Brien, J. B. Pendry, “Magnetic activity at infrared frequencies in structured metallic photonic crystals,” J. Phys.: Condens. Matter 146383–6394 (2002).
[CrossRef]

Jpn. J. Appl. Phys. Part 2-Lett. And Express Lett.

R. Shimano, H. Nishimura, T. Sato, “Frequency tunable circular polarization control of terahertz radiation,” Jpn. J. Appl. Phys. Part 2-Lett. And Express Lett. 44, L676–L678 (2005).
[CrossRef]

Microwave Opt. Technol. Lett.

R. Marques, J. Martel, F. Mesa, F. Medina, “A new 2D isotropic left-handed metamaterial design: Theory and experiment,” Microwave Opt. Technol. Lett. 35, 405–408 (2002).
[CrossRef]

Nat. Mater.

B. Ferguson, X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
[CrossRef]

Nat. Photonics

H.-T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, W. J. Padilla, “Experimental demonstration of frequency-agile terahertz metamaterials, “ Nat. Photonics 2, 295 (2008).
[CrossRef]

Nature

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
[CrossRef] [PubMed]

New J. Phys.

A. A. Zharov, N. A. Zharova, R. E. Noskov, I. V. Shadrivov, Y. S. Kivshar, “Birefringent left-handed metamaterials and perfect lenses for vectorial fields,” New J. Phys. 7, 2201-9 (2005).
[CrossRef]

A. Agrawal, H. Cao, A. Nahata, “Excitation and scattering of surface plasmon-polaritons on structured metal films and their application to pulse shaping and enhanced transmission,” New J. Phys. 7, 2491-13 (2005).
[CrossRef]

Opt. Express

A. Degiron, J. J. Mock, D. R. Smith, “Modulating and tuning the response of metamaterials at the unit cell level,” Opt. Express 15, 1115–1127 (2007).
[CrossRef] [PubMed]

J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express 16, 1786–1795 (2006).
[CrossRef]

Opt. Lett.

C.-F. Hsieh, R.-P. Pan, T.-T. Tang, H.-L. Chen, C.-L. Pan, “Voltage-controlled liquid-crystal terahertz phase shifter and quarter-wave plate”, Opt. Lett. 31, 1112–1114 (2006).
[CrossRef] [PubMed]

Opt. Commun.

C. Imhof, R. Zengerle, “Strong birefringence in left-handed metallic metamaterials,” Opt. Commun. 280, 213–216 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Letters

N. C. J. van der Valk, W. A. M. van der Marel, P. C. M. Planken, “Terahertz polarization imaging,” Opt. Letters 30, 2802–2804 (2005).
[CrossRef]

Philos. Trans. R. Soc. London Ser. A

T. W. Crowe, T. Globus, D. L. Woolard, J. L. Hesler, “Terahertz sources and detectors and their application to biological sensing,” Philos. Trans. R. Soc. London Ser. A 362, 365–374 (2004).
[CrossRef]

Phys. Rev. Lett.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, R. D. Averitt, “Dynamical electric and magnetic metamaterial response at terahertz frequencies,” Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef] [PubMed]

Phys. Rev. Lett.

N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[CrossRef] [PubMed]

Proc. IEEE

B. M. Fischer, H. Helm, P. U. Jepsen, “Chemical recognition with broadband THz spectroscopy,” Proc. IEEE 95, 1592–1604 (2007).
[CrossRef]

Science

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

R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef] [PubMed]

Other

M. S. Boybay, O. M. Ramahi, “Double Negative Metamaterials for Subsurface Detection,” Proceedings of the 29th Annual International Conference of the IEEE EMBS, 3485–3488 (2007).

J. Han, A. Lakhtakia, “Semiconductor split-ring resonators for thermally tunable, terahertz metamaterials,” archived in http://arxiv.org/abs/0808.3183 (2008).

J. D. Jackson, Classical Electrodynamics (Wiley Academic Press, 1998).

CST Microwave Studio, © 2008 CST—Computer Simulation Technology, Wellesley Hills, MA, USA. www.cst.com.

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[PubMed]

Melles Griot, Technical Literature on Optics, www.mellesgriot.com/pdf/Waveplate ApNote.pdf

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B. A. Munk, Frequency Selective Surfaces: Theory and Design (Wiley Interscience, 2000).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Geometry of (a) the circular split ring and (b) the elliptical split ring resonators showing some of the dimensions. The splits and metal line widths are all 2μm while the periodicity is 60μm. The measurement of the angle between the incident THz electric field relative to the major (horizontal) axis of the ellipse or circle is indicated in (b).

Fig. 2.
Fig. 2.

Electromagnetic modeling and experimental results of terahertz transmission spectra as a function of polarization angle. Modeling results for: (a) CSRR independent of angle, (d) ESRR at 0° (solid) and 90° (dashed). Normalized transmission amplitude and phase spectra at various angles for (b, c) CSRR and (e, f) ESRR respectively. (b, c) 0°, 24°, 45°, 72° and 90° and (e, f) 0° (oe-17-02-773-i001), 30° (oe-17-02-773-i002), 45° (oe-17-02-773-i003), 66° (oe-17-02-773-i004) and 90° (oe-17-02-773-i005). The polarization of the THz radiation for 0° and 90° is as indicated in (f). Vertical lines in (e, f) indicate the frequencies at which the vertical and horizontal metamaterial transmission amplitudes are equal.

Fig. 3.
Fig. 3.

(a) Transmission amplitude and (b) phase of the anisotropic metamaterial as a function of polarization angle for resonances at 0.79 THz (oe-17-02-773-i006), 1.94 THz (oe-17-02-773-i007), 0.59 THz (oe-17-02-773-i008) and 1.39 THz (oe-17-02-773-i009). (c) Transmission amplitude and (d) phase of the anisotropic metamaterial as a function of polarization angle at 0.65 THz (oe-17-02-773-i010), 1.06 THz (oe-17-02-773-i011) and 1.83 (oe-17-02-773-i012) THz. Symbols indicate measured data and curves show results from Eq. 2.

Fig. 4.
Fig. 4.

Multilayer electromagnetic transmission modeling of a THz quarter-wave plate based on the ESRR. (a) Amplitude spectra for a dielectric/metamaterial/GaAs/metamaterial/dielectric structure for 0° - horizontal (solid) and 90° - vertical (dashed) polarized waves. (b) Zoom in on the region enclosed by the dashed line in (a). (c) Phase difference spectra. (d) Zoom in on the region enclosed by the dashed line in (c). Inset: schematic diagram of the layered structure where the dielectric layer thickness is 36μm, GaAs thickness is 121μm and the dashed lines represents the location of the metamaterial layers.

Fig. 5.
Fig. 5.

Multilayer electromagnetic transmission modeling of a polarizing beamsplitter based on the ESRR. (a) Amplitude spectra for a dielectric/metamaterial/GaAs/dielectric structure for 0° -horizontal (solid) and 90° - vertical (dashed) polarized waves. (b) Zoom in on the region enclosed by the dashed line in (a). (c) Phase difference spectra. (d) Zoom in on the region enclosed by the dashed line in (c). Inset: schematic diagram of the layered structure where the dielectric layer thickness is 56μm, GaAs thickness is 50μm and the dashed line represents the location of the metamaterial layer.

Fig. 6.
Fig. 6.

THz time domain waveforms (a) through the GaAs reference, and through the anisotropic metamaterial at three different polarizations: (b) horizontal, (c) 45°, (d) vertical. Inset in (a): incident pulse.

Equations (2)

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E ( θ ) = T H cos ( θ ) exp ( i ϕ H ) h ̂ + T V sin ( θ ) exp ( i ϕ V ) V ̂
E ͂ ( θ ) = T H cos 2 ( θ ) exp ( i ϕ H ) + T V sin 2 ( θ ) exp ( i ϕ V ) .

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