Abstract

We present a method of coupling free-space terahertz radiation to intersubband transitions in semiconductor quantum wells using an array of meta-atoms. Owing to the resonant nature of the interaction between metamaterial and incident light and the field enhancement in the vicinity of the metal structure, the coupling efficiency of this method is very high and the energy conversion ratio from in-plane to z field reaches values on the order of 50%. To identify the role of different aspects of this coupling, we have used a custom-made finite-difference time-domain code. The simulation results are supplemented by transmission measurements on modulation-doped GaAs/AlGaAs parabolic quantum wells which demonstrate efficient strong light-matter coupling between meta-atoms and intersubband transitions for normal incident electromagnetic waves.

© 2011 OSA

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  1. Z. Schlesinger, J. C. M. Hwang, and J. S. J. Allen, “Subband-Landau-level coupling in a two-dimensional electron gas,” Phys. Rev. Lett. 50, 2098–2101 (1983).
    [CrossRef]
  2. J. S. Smith, L. C. Chiu, S. Margalit, A. Yariv, and A. Y. Cho, “A new infrared detector using electron emission from multiple quantum wells,” J. Vac. Sci. Technol. B 1, 376–378 (1983).
    [CrossRef]
  3. J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 22, 553–556 (1994).
    [CrossRef]
  4. M. Helm, The Basic Physics of Intersubband Transitions , vol. 62 of Semiconductors and Semimetals (Academic Press, 2000).
  5. L. C. West and S. J. Eglash, “First observation of an extremely large-dipole infrared transition within the conduction band of a GaAs quantum well,” Appl. Phys. Lett. 46, 1156–1158 (1985).
    [CrossRef]
  6. B. F. Levine, R. J. Malik, J. Walker, K. K. Choi, C. G. Bethea, D. A. Kleinman, and J. M. Vandenberg, “Strong 8.2μm infrared intersubband absorption in doped GaAs/AlAs quantum well waveguides,” Appl. Phys. Lett. 50, 273–275 (1987).
    [CrossRef]
  7. D. Heitmann, J. P. Kotthaus, and E. G. Mohr, “Plasmon dispersion and intersubband resonance at high wavevectors in Si(100) inversion layers,” Solid State Commun. 44, 715–718 (1982).
    [CrossRef]
  8. 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]
  9. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
    [CrossRef]
  10. N. Meinzer, M. Ruther, S. Linden, C. M. Soukoulis, G. Khitrova, J. Hendrickson, J. D. Olitzky, H. M. Gibbs, and M. Wegener, “Arrays of Ag split-ring resonators coupled to InGaAs single-quantum-well gain,” Opt. Express 18, 24140–24151 (2010).
    [CrossRef] [PubMed]
  11. Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102, 186402 (2009).
  12. M. Geiser, C. Walther, G. Scalari, M. Beck, M. Fischer, L. Nevou, and J. Faist, “Strong light-matter coupling at terahertz frequencies at room temperature in electronic LC resonators,” Appl. Phys. Lett. 97, 191107 (2010).
  13. K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
    [CrossRef]
  14. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method , 2nd ed. (Artech House, 2000).
  15. B. Engquist and A. Majda, “Absorbing boundary conditions for numerical simulation of waves,” Proc. Natl. Acad. Sci. USA 74, 1765–1766 (1977).
    [CrossRef] [PubMed]
  16. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
    [CrossRef]
  17. K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982).
    [CrossRef]
  18. R. W. Ziolkowski, “The incorporation of microscopical material models into the FDTD approach for ultrafast optical pulse simulations,” IEEE Trans. Antennas Propag. 45, 375–391 (1997).
    [CrossRef]
  19. B. Bidégaray, “Time discretizations for Maxwell-Bloch equations,” Numer. Methods Partial Differ. Eq. 19, 284–300 (2003).
    [CrossRef]
  20. R. Kersting, R. Bratschitsch, G. Strasser, K. Unterrainer, and J. N. Heyman, “Sampling a terahertz dipole transition with subcycle time resolution,” Opt. Lett. 25, 272–274 (2000).
    [CrossRef]
  21. R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, “Coherent terahertz emission from opticall pumped intersubband plasmons in parabolic quantum wells,” Appl. Phys. Lett. 76, 3501–3503 (2000).
    [CrossRef]
  22. J. Ulrich, R. Zobl, K. Unterrainer, G. Strasser, E. Gornik, K. D. Maranowski, and A. C. Gossard, “Temperature dependence of far-infrared electroluminescence in parabolic quantum wells,” Appl. Phys. Lett. 74, 3158–3160 (1999).
    [CrossRef]

2010

2008

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

2003

B. Bidégaray, “Time discretizations for Maxwell-Bloch equations,” Numer. Methods Partial Differ. Eq. 19, 284–300 (2003).
[CrossRef]

2000

R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, “Coherent terahertz emission from opticall pumped intersubband plasmons in parabolic quantum wells,” Appl. Phys. Lett. 76, 3501–3503 (2000).
[CrossRef]

R. Kersting, R. Bratschitsch, G. Strasser, K. Unterrainer, and J. N. Heyman, “Sampling a terahertz dipole transition with subcycle time resolution,” Opt. Lett. 25, 272–274 (2000).
[CrossRef]

1999

J. Ulrich, R. Zobl, K. Unterrainer, G. Strasser, E. Gornik, K. D. Maranowski, and A. C. Gossard, “Temperature dependence of far-infrared electroluminescence in parabolic quantum wells,” Appl. Phys. Lett. 74, 3158–3160 (1999).
[CrossRef]

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]

1997

R. W. Ziolkowski, “The incorporation of microscopical material models into the FDTD approach for ultrafast optical pulse simulations,” IEEE Trans. Antennas Propag. 45, 375–391 (1997).
[CrossRef]

1994

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 22, 553–556 (1994).
[CrossRef]

1987

B. F. Levine, R. J. Malik, J. Walker, K. K. Choi, C. G. Bethea, D. A. Kleinman, and J. M. Vandenberg, “Strong 8.2μm infrared intersubband absorption in doped GaAs/AlAs quantum well waveguides,” Appl. Phys. Lett. 50, 273–275 (1987).
[CrossRef]

1985

L. C. West and S. J. Eglash, “First observation of an extremely large-dipole infrared transition within the conduction band of a GaAs quantum well,” Appl. Phys. Lett. 46, 1156–1158 (1985).
[CrossRef]

1983

Z. Schlesinger, J. C. M. Hwang, and J. S. J. Allen, “Subband-Landau-level coupling in a two-dimensional electron gas,” Phys. Rev. Lett. 50, 2098–2101 (1983).
[CrossRef]

J. S. Smith, L. C. Chiu, S. Margalit, A. Yariv, and A. Y. Cho, “A new infrared detector using electron emission from multiple quantum wells,” J. Vac. Sci. Technol. B 1, 376–378 (1983).
[CrossRef]

1982

D. Heitmann, J. P. Kotthaus, and E. G. Mohr, “Plasmon dispersion and intersubband resonance at high wavevectors in Si(100) inversion layers,” Solid State Commun. 44, 715–718 (1982).
[CrossRef]

K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982).
[CrossRef]

1981

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

1977

B. Engquist and A. Majda, “Absorbing boundary conditions for numerical simulation of waves,” Proc. Natl. Acad. Sci. USA 74, 1765–1766 (1977).
[CrossRef] [PubMed]

1966

K. S. Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966).
[CrossRef]

1911

M. Geiser, C. Walther, G. Scalari, M. Beck, M. Fischer, L. Nevou, and J. Faist, “Strong light-matter coupling at terahertz frequencies at room temperature in electronic LC resonators,” Appl. Phys. Lett. 97, 191107 (2010).

1864

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102, 186402 (2009).

Allen, J. S. J.

Z. Schlesinger, J. C. M. Hwang, and J. S. J. Allen, “Subband-Landau-level coupling in a two-dimensional electron gas,” Phys. Rev. Lett. 50, 2098–2101 (1983).
[CrossRef]

Andrews, A. M.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102, 186402 (2009).

Beck, M.

M. Geiser, C. Walther, G. Scalari, M. Beck, M. Fischer, L. Nevou, and J. Faist, “Strong light-matter coupling at terahertz frequencies at room temperature in electronic LC resonators,” Appl. Phys. Lett. 97, 191107 (2010).

Bethea, C. G.

B. F. Levine, R. J. Malik, J. Walker, K. K. Choi, C. G. Bethea, D. A. Kleinman, and J. M. Vandenberg, “Strong 8.2μm infrared intersubband absorption in doped GaAs/AlAs quantum well waveguides,” Appl. Phys. Lett. 50, 273–275 (1987).
[CrossRef]

Bidégaray, B.

B. Bidégaray, “Time discretizations for Maxwell-Bloch equations,” Numer. Methods Partial Differ. Eq. 19, 284–300 (2003).
[CrossRef]

Bratschitsch, R.

R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, “Coherent terahertz emission from opticall pumped intersubband plasmons in parabolic quantum wells,” Appl. Phys. Lett. 76, 3501–3503 (2000).
[CrossRef]

R. Kersting, R. Bratschitsch, G. Strasser, K. Unterrainer, and J. N. Heyman, “Sampling a terahertz dipole transition with subcycle time resolution,” Opt. Lett. 25, 272–274 (2000).
[CrossRef]

Capasso, F.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 22, 553–556 (1994).
[CrossRef]

Chiu, L. C.

J. S. Smith, L. C. Chiu, S. Margalit, A. Yariv, and A. Y. Cho, “A new infrared detector using electron emission from multiple quantum wells,” J. Vac. Sci. Technol. B 1, 376–378 (1983).
[CrossRef]

Cho, A. Y.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 22, 553–556 (1994).
[CrossRef]

J. S. Smith, L. C. Chiu, S. Margalit, A. Yariv, and A. Y. Cho, “A new infrared detector using electron emission from multiple quantum wells,” J. Vac. Sci. Technol. B 1, 376–378 (1983).
[CrossRef]

Choi, K. K.

B. F. Levine, R. J. Malik, J. Walker, K. K. Choi, C. G. Bethea, D. A. Kleinman, and J. M. Vandenberg, “Strong 8.2μm infrared intersubband absorption in doped GaAs/AlAs quantum well waveguides,” Appl. Phys. Lett. 50, 273–275 (1987).
[CrossRef]

Colombelli, R.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102, 186402 (2009).

Eglash, S. J.

L. C. West and S. J. Eglash, “First observation of an extremely large-dipole infrared transition within the conduction band of a GaAs quantum well,” Appl. Phys. Lett. 46, 1156–1158 (1985).
[CrossRef]

Engquist, B.

B. Engquist and A. Majda, “Absorbing boundary conditions for numerical simulation of waves,” Proc. Natl. Acad. Sci. USA 74, 1765–1766 (1977).
[CrossRef] [PubMed]

Faist, J.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 22, 553–556 (1994).
[CrossRef]

M. Geiser, C. Walther, G. Scalari, M. Beck, M. Fischer, L. Nevou, and J. Faist, “Strong light-matter coupling at terahertz frequencies at room temperature in electronic LC resonators,” Appl. Phys. Lett. 97, 191107 (2010).

Fedotov, V. A.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Fischer, M.

M. Geiser, C. Walther, G. Scalari, M. Beck, M. Fischer, L. Nevou, and J. Faist, “Strong light-matter coupling at terahertz frequencies at room temperature in electronic LC resonators,” Appl. Phys. Lett. 97, 191107 (2010).

Geiser, M.

M. Geiser, C. Walther, G. Scalari, M. Beck, M. Fischer, L. Nevou, and J. Faist, “Strong light-matter coupling at terahertz frequencies at room temperature in electronic LC resonators,” Appl. Phys. Lett. 97, 191107 (2010).

Gibbs, H. M.

Gornik, E.

J. Ulrich, R. Zobl, K. Unterrainer, G. Strasser, E. Gornik, K. D. Maranowski, and A. C. Gossard, “Temperature dependence of far-infrared electroluminescence in parabolic quantum wells,” Appl. Phys. Lett. 74, 3158–3160 (1999).
[CrossRef]

Gossard, A. C.

J. Ulrich, R. Zobl, K. Unterrainer, G. Strasser, E. Gornik, K. D. Maranowski, and A. C. Gossard, “Temperature dependence of far-infrared electroluminescence in parabolic quantum wells,” Appl. Phys. Lett. 74, 3158–3160 (1999).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method , 2nd ed. (Artech House, 2000).

Heitmann, D.

D. Heitmann, J. P. Kotthaus, and E. G. Mohr, “Plasmon dispersion and intersubband resonance at high wavevectors in Si(100) inversion layers,” Solid State Commun. 44, 715–718 (1982).
[CrossRef]

Helm, M.

M. Helm, The Basic Physics of Intersubband Transitions , vol. 62 of Semiconductors and Semimetals (Academic Press, 2000).

Hendrickson, J.

Heyman, J. N.

Holden, A. J.

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]

Hutchinson, A. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 22, 553–556 (1994).
[CrossRef]

Hwang, J. C. M.

Z. Schlesinger, J. C. M. Hwang, and J. S. J. Allen, “Subband-Landau-level coupling in a two-dimensional electron gas,” Phys. Rev. Lett. 50, 2098–2101 (1983).
[CrossRef]

Kersting, R.

R. Kersting, R. Bratschitsch, G. Strasser, K. Unterrainer, and J. N. Heyman, “Sampling a terahertz dipole transition with subcycle time resolution,” Opt. Lett. 25, 272–274 (2000).
[CrossRef]

R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, “Coherent terahertz emission from opticall pumped intersubband plasmons in parabolic quantum wells,” Appl. Phys. Lett. 76, 3501–3503 (2000).
[CrossRef]

Khitrova, G.

Klang, P.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102, 186402 (2009).

Kleinman, D. A.

B. F. Levine, R. J. Malik, J. Walker, K. K. Choi, C. G. Bethea, D. A. Kleinman, and J. M. Vandenberg, “Strong 8.2μm infrared intersubband absorption in doped GaAs/AlAs quantum well waveguides,” Appl. Phys. Lett. 50, 273–275 (1987).
[CrossRef]

Kotthaus, J. P.

D. Heitmann, J. P. Kotthaus, and E. G. Mohr, “Plasmon dispersion and intersubband resonance at high wavevectors in Si(100) inversion layers,” Solid State Commun. 44, 715–718 (1982).
[CrossRef]

Levine, B. F.

B. F. Levine, R. J. Malik, J. Walker, K. K. Choi, C. G. Bethea, D. A. Kleinman, and J. M. Vandenberg, “Strong 8.2μm infrared intersubband absorption in doped GaAs/AlAs quantum well waveguides,” Appl. Phys. Lett. 50, 273–275 (1987).
[CrossRef]

Linden, S.

Majda, A.

B. Engquist and A. Majda, “Absorbing boundary conditions for numerical simulation of waves,” Proc. Natl. Acad. Sci. USA 74, 1765–1766 (1977).
[CrossRef] [PubMed]

Malik, R. J.

B. F. Levine, R. J. Malik, J. Walker, K. K. Choi, C. G. Bethea, D. A. Kleinman, and J. M. Vandenberg, “Strong 8.2μm infrared intersubband absorption in doped GaAs/AlAs quantum well waveguides,” Appl. Phys. Lett. 50, 273–275 (1987).
[CrossRef]

Maranowski, K. D.

J. Ulrich, R. Zobl, K. Unterrainer, G. Strasser, E. Gornik, K. D. Maranowski, and A. C. Gossard, “Temperature dependence of far-infrared electroluminescence in parabolic quantum wells,” Appl. Phys. Lett. 74, 3158–3160 (1999).
[CrossRef]

Margalit, S.

J. S. Smith, L. C. Chiu, S. Margalit, A. Yariv, and A. Y. Cho, “A new infrared detector using electron emission from multiple quantum wells,” J. Vac. Sci. Technol. B 1, 376–378 (1983).
[CrossRef]

Meinzer, N.

Mohr, E. G.

D. Heitmann, J. P. Kotthaus, and E. G. Mohr, “Plasmon dispersion and intersubband resonance at high wavevectors in Si(100) inversion layers,” Solid State Commun. 44, 715–718 (1982).
[CrossRef]

Müller, T.

R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, “Coherent terahertz emission from opticall pumped intersubband plasmons in parabolic quantum wells,” Appl. Phys. Lett. 76, 3501–3503 (2000).
[CrossRef]

Mur, G.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

Nevou, L.

M. Geiser, C. Walther, G. Scalari, M. Beck, M. Fischer, L. Nevou, and J. Faist, “Strong light-matter coupling at terahertz frequencies at room temperature in electronic LC resonators,” Appl. Phys. Lett. 97, 191107 (2010).

Olitzky, J. D.

Papasimakis, N.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Pendry, J. B.

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]

Prosvirnin, S. L.

N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351–354 (2008).
[CrossRef]

Robbins, D. J.

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]

Ruther, M.

Sagnes, I.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102, 186402 (2009).

Scalari, G.

M. Geiser, C. Walther, G. Scalari, M. Beck, M. Fischer, L. Nevou, and J. Faist, “Strong light-matter coupling at terahertz frequencies at room temperature in electronic LC resonators,” Appl. Phys. Lett. 97, 191107 (2010).

Schlesinger, Z.

Z. Schlesinger, J. C. M. Hwang, and J. S. J. Allen, “Subband-Landau-level coupling in a two-dimensional electron gas,” Phys. Rev. Lett. 50, 2098–2101 (1983).
[CrossRef]

Sirtori, C.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 22, 553–556 (1994).
[CrossRef]

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102, 186402 (2009).

Sivco, D. L.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 22, 553–556 (1994).
[CrossRef]

Smith, J. S.

J. S. Smith, L. C. Chiu, S. Margalit, A. Yariv, and A. Y. Cho, “A new infrared detector using electron emission from multiple quantum wells,” J. Vac. Sci. Technol. B 1, 376–378 (1983).
[CrossRef]

Soukoulis, C. M.

Stewart, W. J.

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]

Strasser, G.

R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, “Coherent terahertz emission from opticall pumped intersubband plasmons in parabolic quantum wells,” Appl. Phys. Lett. 76, 3501–3503 (2000).
[CrossRef]

R. Kersting, R. Bratschitsch, G. Strasser, K. Unterrainer, and J. N. Heyman, “Sampling a terahertz dipole transition with subcycle time resolution,” Opt. Lett. 25, 272–274 (2000).
[CrossRef]

J. Ulrich, R. Zobl, K. Unterrainer, G. Strasser, E. Gornik, K. D. Maranowski, and A. C. Gossard, “Temperature dependence of far-infrared electroluminescence in parabolic quantum wells,” Appl. Phys. Lett. 74, 3158–3160 (1999).
[CrossRef]

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102, 186402 (2009).

Taflove, A.

K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982).
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method , 2nd ed. (Artech House, 2000).

Todorov, Y.

Y. Todorov, A. M. Andrews, I. Sagnes, R. Colombelli, P. Klang, G. Strasser, and C. Sirtori, “Strong light-matter coupling in subwavelength metal-dielectric microcavities at terahertz frequencies,” Phys. Rev. Lett. 102, 186402 (2009).

Ulrich, J.

J. Ulrich, R. Zobl, K. Unterrainer, G. Strasser, E. Gornik, K. D. Maranowski, and A. C. Gossard, “Temperature dependence of far-infrared electroluminescence in parabolic quantum wells,” Appl. Phys. Lett. 74, 3158–3160 (1999).
[CrossRef]

Umashankar, K.

K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982).
[CrossRef]

Unterrainer, K.

R. Kersting, R. Bratschitsch, G. Strasser, K. Unterrainer, and J. N. Heyman, “Sampling a terahertz dipole transition with subcycle time resolution,” Opt. Lett. 25, 272–274 (2000).
[CrossRef]

R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, “Coherent terahertz emission from opticall pumped intersubband plasmons in parabolic quantum wells,” Appl. Phys. Lett. 76, 3501–3503 (2000).
[CrossRef]

J. Ulrich, R. Zobl, K. Unterrainer, G. Strasser, E. Gornik, K. D. Maranowski, and A. C. Gossard, “Temperature dependence of far-infrared electroluminescence in parabolic quantum wells,” Appl. Phys. Lett. 74, 3158–3160 (1999).
[CrossRef]

Vandenberg, J. M.

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Figures (3)

Fig. 1
Fig. 1

Artistic view of the situation. a) The THz pulse is normally incident on the meta-surface. The QW is located underneath. b) Cut through the structure along the xz plane at the position indicated by the dashed line in a. The arrows indicate the electric field lines at resonance. This provides the z component necessary for efficient coupling to ISBs.

Fig. 2
Fig. 2

a) Layout of the MM. The size of the unit cell is a × b = 40 × 40μm. b,c) Simulated z component of the electric field just beneath the MM for different polarizations of the incident pulse. The polarization is indicated by the arrows. d) Comparison of simulated and measured electric field transmission coefficients of the MM on the undoped structure for both polarizations.

Fig. 3
Fig. 3

a) Simulated transmission coefficient for the meta-atoms on substrate (S), coupled to the QW using the Lorentz model (L), and using the Maxwell-Bloch model (MB) with 50V/cm incident field using linearly polarized light. b) Transmission coefficient of doped structure at 5K and RT obtained with the Fourier transform spectrometer using unpolarized light. The solid gray lines are fitted curves obtained from the coupled oscillator model. The inset shows the transmission coefficient of the undoped sample.

Equations (8)

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E ( t ) = E 0 cos ( ln 2 π ( t t 0 ) τ ) e 4 ln 2 ( t t 0 ) 2 τ 2 ,
η = d t 0 a d x 0 b d y E z 2 E z 2 + E x 2 ,
P z ( ω ) = f 12 n 0 e 2 / m eff ω 12 2 ω 2 + 2 i δ ω E z ( ω ) ,
u 1 t = 1 T 2 u 1 + ω 0 u 2 ,
u 2 t = ω 0 u 1 1 T 2 u 2 + 2 e μ 12 h ¯ E z u 3 ,
u 3 t = 2 e μ 12 h ¯ E z u 2 1 T 1 ( u 3 u 30 ) ,
d 2 d t 2 x c ( t ) + 2 δ c d d t x c ( t ) + ω c 2 x c ( t ) + Ω 2 x ( t ) = e m E x ( t ) ,
d 2 d t 2 x ( t ) + 2 δ 12 d d t x ( t ) + ω 12 2 x ( t ) + Ω 2 x c ( t ) = 0 ,

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