Abstract

In this paper, we propose a new and versatile mechanism for electrical tuning of planar metamaterials: strong coupling of metamaterial resonances to engineered intersubband transitions that can be tuned through the application of an electrical bias. We present the general formalism that allows calculating the permittivity tensor for intersubband transitions in generic semiconductor heterostructures and we study numerically the specific case of coupling and tuning metamaterials in the thermal infrared through coupling to biased GaAs semiconductor quantum wells. This tuning mechanism can be scaled from the visible to the far infrared by the proper choice of metamaterials and semiconductor heterostructures.

© 2012 OSA

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    [CrossRef]
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  33. E. R. Brown, S. J. Eglash, and K. A. McIntosh, “Observation of normal-incidence intersubband absorption in n-type Al0.09Ga0.91Sb quantum wells,” Phys. Rev. B Condens. Matter 46(11), 7244–7247 (1992).
    [CrossRef] [PubMed]
  34. Q. Du, J. Alperin, and W. I. Wang, “Infrared electroabsorption modulation in AlSb/InAs/AlGaSb/GaSb/AlSb stepped quantum-wells grown by molecular-beam epitaxy,” Appl. Phys. Lett. 67(15), 2218–2219 (1995).
    [CrossRef]
  35. L. A. Samoska, B. Brar, and H. Kroemer, “Strong far-infrared intersubband absorption under normal incidence in heavily n-type doped nonalloy GaSb-AlSb superlattices,” Appl. Phys. Lett. 62(20), 2539–2541 (1993).
    [CrossRef]
  36. Y. Zhang, N. Baruch, and W. I. Wang, “Normal incidence infrared photodetectors using intersubband transitions in GaSb l-valley quantum-wells,” Appl. Phys. Lett. 63(8), 1068–1070 (1993).
    [CrossRef]

2012 (1)

Y. Todorov and C. Sirtori, “Intersubband polaritons in the electrical dipole gauge,” Phys. Rev. B 85(4), 045304 (2012).
[CrossRef]

2011 (3)

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[CrossRef] [PubMed]

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

D. Dietze, A. Benz, G. Strasser, K. Unterrainer, and J. Darmo, “Terahertz meta-atoms coupled to a quantum well intersubband transition,” Opt. Express 19(14), 13700–13706 (2011).
[CrossRef] [PubMed]

2010 (2)

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

2009 (3)

2007 (1)

C. M. Soukoulis, T. Koschny, J. Zhou, M. Kafesaki, and E. N. Economou, “Magnetic response of split ring resonators at terahertz frequencies,” Phys. Status Solidi, B Basic Res. 244(4), 1181–1187 (2007).
[CrossRef]

2006 (1)

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

2004 (1)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

Q. Du, J. Alperin, and W. I. Wang, “Infrared electroabsorption modulation in AlSb/InAs/AlGaSb/GaSb/AlSb stepped quantum-wells grown by molecular-beam epitaxy,” Appl. Phys. Lett. 67(15), 2218–2219 (1995).
[CrossRef]

1994 (1)

V. Savona, Z. Hradil, A. Quattropani, and P. Schwendimann, “Quantum theory of quantum-well polaritons in semiconductor microcavities,” Phys. Rev. B Condens. Matter 49(13), 8774–8779 (1994).
[CrossRef] [PubMed]

1993 (4)

L. Wendler and E. Kandler, “Intrasubband and intersubband plasmon-polaritons in semiconductor quantum-wells,” Phys. Status Solidi, B Basic Res. 177(1), 9–67 (1993).
[CrossRef]

P. H. Tsao, “Derivation and implications of the symmetry property of the permittivity tensor,” Am. J. Phys. 61(9), 823–825 (1993).
[CrossRef]

L. A. Samoska, B. Brar, and H. Kroemer, “Strong far-infrared intersubband absorption under normal incidence in heavily n-type doped nonalloy GaSb-AlSb superlattices,” Appl. Phys. Lett. 62(20), 2539–2541 (1993).
[CrossRef]

Y. Zhang, N. Baruch, and W. I. Wang, “Normal incidence infrared photodetectors using intersubband transitions in GaSb l-valley quantum-wells,” Appl. Phys. Lett. 63(8), 1068–1070 (1993).
[CrossRef]

1992 (3)

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and Y. A. Cho, “Resonant Stark tuning of second-order susceptibility in coupled quantum wells,” Appl. Phys. Lett. 60(2), 151 (1992).
[CrossRef]

F. G. Pikus, “Excitons in quantum wells with a two dimensional electron gas,” Sov. Phys. Semicond. 26, 2633 (1992).

E. R. Brown, S. J. Eglash, and K. A. McIntosh, “Observation of normal-incidence intersubband absorption in n-type Al0.09Ga0.91Sb quantum wells,” Phys. Rev. B Condens. Matter 46(11), 7244–7247 (1992).
[CrossRef] [PubMed]

1991 (1)

E. Rosencher and P. Bois, “Model system for optical nonlinearities: asymmetric quantum wells,” Phys. Rev. B Condens. Matter 44(20), 11315–11327 (1991).
[CrossRef] [PubMed]

1990 (1)

E. R. Brown and S. J. Eglash, “Calculation of the intersubband absorption strength in ellipsoidal-valley quantum wells,” Phys. Rev. B Condens. Matter 41(11), 7559–7568 (1990).
[CrossRef] [PubMed]

1989 (1)

E. Rosencher, P. Bois, J. Nagle, and S. Delattre, “Second harmonic generation by intersubband transitions in compositionally asymmetrical MQWs,” Electron. Lett. 25(16), 1063 (1989).
[CrossRef]

1967 (1)

F. Stern and W. E. Howard, “Properties of semiconductor surface inversion layers in the electric quantum limit,” Phys. Rev. 163(3), 816–835 (1967).
[CrossRef]

Alperin, J.

Q. Du, J. Alperin, and W. I. Wang, “Infrared electroabsorption modulation in AlSb/InAs/AlGaSb/GaSb/AlSb stepped quantum-wells grown by molecular-beam epitaxy,” Appl. Phys. Lett. 67(15), 2218–2219 (1995).
[CrossRef]

Atwater, H. A.

Averitt, R. D.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[CrossRef]

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Aydin, K.

Azad, A. K.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[CrossRef]

Baruch, N.

Y. Zhang, N. Baruch, and W. I. Wang, “Normal incidence infrared photodetectors using intersubband transitions in GaSb l-valley quantum-wells,” Appl. Phys. Lett. 63(8), 1068–1070 (1993).
[CrossRef]

Benz, A.

Bois, P.

E. Rosencher and P. Bois, “Model system for optical nonlinearities: asymmetric quantum wells,” Phys. Rev. B Condens. Matter 44(20), 11315–11327 (1991).
[CrossRef] [PubMed]

E. Rosencher, P. Bois, J. Nagle, and S. Delattre, “Second harmonic generation by intersubband transitions in compositionally asymmetrical MQWs,” Electron. Lett. 25(16), 1063 (1989).
[CrossRef]

Boreman, G. D.

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[CrossRef] [PubMed]

Boyd, E. M.

Brar, B.

L. A. Samoska, B. Brar, and H. Kroemer, “Strong far-infrared intersubband absorption under normal incidence in heavily n-type doped nonalloy GaSb-AlSb superlattices,” Appl. Phys. Lett. 62(20), 2539–2541 (1993).
[CrossRef]

Brener, I.

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[CrossRef] [PubMed]

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Brown, E. R.

E. R. Brown, S. J. Eglash, and K. A. McIntosh, “Observation of normal-incidence intersubband absorption in n-type Al0.09Ga0.91Sb quantum wells,” Phys. Rev. B Condens. Matter 46(11), 7244–7247 (1992).
[CrossRef] [PubMed]

E. R. Brown and S. J. Eglash, “Calculation of the intersubband absorption strength in ellipsoidal-valley quantum wells,” Phys. Rev. B Condens. Matter 41(11), 7559–7568 (1990).
[CrossRef] [PubMed]

Capasso, F.

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and Y. A. Cho, “Resonant Stark tuning of second-order susceptibility in coupled quantum wells,” Appl. Phys. Lett. 60(2), 151 (1992).
[CrossRef]

Chen, H. T.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Chen, H.-T.

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[CrossRef]

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Cho, Y. A.

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and Y. A. Cho, “Resonant Stark tuning of second-order susceptibility in coupled quantum wells,” Appl. Phys. Lett. 60(2), 151 (1992).
[CrossRef]

Cich, M. J.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[CrossRef]

Coffey, K. R.

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[CrossRef] [PubMed]

Darmo, J.

Delattre, S.

E. Rosencher, P. Bois, J. Nagle, and S. Delattre, “Second harmonic generation by intersubband transitions in compositionally asymmetrical MQWs,” Electron. Lett. 25(16), 1063 (1989).
[CrossRef]

Dicken, M. J.

Dietze, D.

Du, Q.

Q. Du, J. Alperin, and W. I. Wang, “Infrared electroabsorption modulation in AlSb/InAs/AlGaSb/GaSb/AlSb stepped quantum-wells grown by molecular-beam epitaxy,” Appl. Phys. Lett. 67(15), 2218–2219 (1995).
[CrossRef]

Economou, E. N.

C. M. Soukoulis, T. Koschny, J. Zhou, M. Kafesaki, and E. N. Economou, “Magnetic response of split ring resonators at terahertz frequencies,” Phys. Status Solidi, B Basic Res. 244(4), 1181–1187 (2007).
[CrossRef]

Eglash, S. J.

E. R. Brown, S. J. Eglash, and K. A. McIntosh, “Observation of normal-incidence intersubband absorption in n-type Al0.09Ga0.91Sb quantum wells,” Phys. Rev. B Condens. Matter 46(11), 7244–7247 (1992).
[CrossRef] [PubMed]

E. R. Brown and S. J. Eglash, “Calculation of the intersubband absorption strength in ellipsoidal-valley quantum wells,” Phys. Rev. B Condens. Matter 41(11), 7559–7568 (1990).
[CrossRef] [PubMed]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Fedotov, V. A.

Gabbay, A.

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

Gin, A.

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

Ginn, J. C.

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[CrossRef] [PubMed]

Goodhue, W.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

Goodhue, W. D.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Gossard, A. C.

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Hoffman, A. J.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Howard, W. E.

F. Stern and W. E. Howard, “Properties of semiconductor surface inversion layers in the electric quantum limit,” Phys. Rev. 163(3), 816–835 (1967).
[CrossRef]

Hradil, Z.

V. Savona, Z. Hradil, A. Quattropani, and P. Schwendimann, “Quantum theory of quantum-well polaritons in semiconductor microcavities,” Phys. Rev. B Condens. Matter 49(13), 8774–8779 (1994).
[CrossRef] [PubMed]

Hutchinson, A. L.

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and Y. A. Cho, “Resonant Stark tuning of second-order susceptibility in coupled quantum wells,” Appl. Phys. Lett. 60(2), 151 (1992).
[CrossRef]

Ioffe, A. F.

Ivchenko, E. L.

Kafesaki, M.

C. M. Soukoulis, T. Koschny, J. Zhou, M. Kafesaki, and E. N. Economou, “Magnetic response of split ring resonators at terahertz frequencies,” Phys. Status Solidi, B Basic Res. 244(4), 1181–1187 (2007).
[CrossRef]

Kaliteevski, M. A.

Kandler, E.

L. Wendler and E. Kandler, “Intrasubband and intersubband plasmon-polaritons in semiconductor quantum-wells,” Phys. Status Solidi, B Basic Res. 177(1), 9–67 (1993).
[CrossRef]

Kavokin, A. V.

Koschny, T.

C. M. Soukoulis, T. Koschny, J. Zhou, M. Kafesaki, and E. N. Economou, “Magnetic response of split ring resonators at terahertz frequencies,” Phys. Status Solidi, B Basic Res. 244(4), 1181–1187 (2007).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Kroemer, H.

L. A. Samoska, B. Brar, and H. Kroemer, “Strong far-infrared intersubband absorption under normal incidence in heavily n-type doped nonalloy GaSb-AlSb superlattices,” Appl. Phys. Lett. 62(20), 2539–2541 (1993).
[CrossRef]

Kuo, P.

Langston, W.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

Li, J.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Ma, J.

McIntosh, K. A.

E. R. Brown, S. J. Eglash, and K. A. McIntosh, “Observation of normal-incidence intersubband absorption in n-type Al0.09Ga0.91Sb quantum wells,” Phys. Rev. B Condens. Matter 46(11), 7244–7247 (1992).
[CrossRef] [PubMed]

Miao, X.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

Nagle, J.

E. Rosencher, P. Bois, J. Nagle, and S. Delattre, “Second harmonic generation by intersubband transitions in compositionally asymmetrical MQWs,” Electron. Lett. 25(16), 1063 (1989).
[CrossRef]

Nesvizhskii, A. I.

O'hara, J. F.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Padilla, W. J.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[CrossRef]

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Passmore, B.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

Peralta, X. G.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Peters, D. W.

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[CrossRef] [PubMed]

Pikus, F. G.

F. G. Pikus, “Excitons in quantum wells with a two dimensional electron gas,” Sov. Phys. Semicond. 26, 2633 (1992).

Plum, E.

Pryce, I. M.

Quattropani, A.

V. Savona, Z. Hradil, A. Quattropani, and P. Schwendimann, “Quantum theory of quantum-well polaritons in semiconductor microcavities,” Phys. Rev. B Condens. Matter 49(13), 8774–8779 (1994).
[CrossRef] [PubMed]

Reno, J.

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Rosencher, E.

E. Rosencher and P. Bois, “Model system for optical nonlinearities: asymmetric quantum wells,” Phys. Rev. B Condens. Matter 44(20), 11315–11327 (1991).
[CrossRef] [PubMed]

E. Rosencher, P. Bois, J. Nagle, and S. Delattre, “Second harmonic generation by intersubband transitions in compositionally asymmetrical MQWs,” Electron. Lett. 25(16), 1063 (1989).
[CrossRef]

Samoska, L. A.

L. A. Samoska, B. Brar, and H. Kroemer, “Strong far-infrared intersubband absorption under normal incidence in heavily n-type doped nonalloy GaSb-AlSb superlattices,” Appl. Phys. Lett. 62(20), 2539–2541 (1993).
[CrossRef]

Savona, V.

V. Savona, Z. Hradil, A. Quattropani, and P. Schwendimann, “Quantum theory of quantum-well polaritons in semiconductor microcavities,” Phys. Rev. B Condens. Matter 49(13), 8774–8779 (1994).
[CrossRef] [PubMed]

Schwendimann, P.

V. Savona, Z. Hradil, A. Quattropani, and P. Schwendimann, “Quantum theory of quantum-well polaritons in semiconductor microcavities,” Phys. Rev. B Condens. Matter 49(13), 8774–8779 (1994).
[CrossRef] [PubMed]

Shaner, E.

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

Shelton, D. J.

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[CrossRef] [PubMed]

Sinclair, M. B.

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[CrossRef] [PubMed]

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

Sirtori, C.

Y. Todorov and C. Sirtori, “Intersubband polaritons in the electrical dipole gauge,” Phys. Rev. B 85(4), 045304 (2012).
[CrossRef]

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and Y. A. Cho, “Resonant Stark tuning of second-order susceptibility in coupled quantum wells,” Appl. Phys. Lett. 60(2), 151 (1992).
[CrossRef]

Sivco, D. L.

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and Y. A. Cho, “Resonant Stark tuning of second-order susceptibility in coupled quantum wells,” Appl. Phys. Lett. 60(2), 151 (1992).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, T. Koschny, J. Zhou, M. Kafesaki, and E. N. Economou, “Magnetic response of split ring resonators at terahertz frequencies,” Phys. Status Solidi, B Basic Res. 244(4), 1181–1187 (2007).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Stern, F.

F. Stern and W. E. Howard, “Properties of semiconductor surface inversion layers in the electric quantum limit,” Phys. Rev. 163(3), 816–835 (1967).
[CrossRef]

Strasser, G.

Sweatlock, L. A.

Taylor, A. J.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[CrossRef]

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Todorov, Y.

Y. Todorov and C. Sirtori, “Intersubband polaritons in the electrical dipole gauge,” Phys. Rev. B 85(4), 045304 (2012).
[CrossRef]

Tsai, D. P.

Tsao, P. H.

P. H. Tsao, “Derivation and implications of the symmetry property of the permittivity tensor,” Am. J. Phys. 61(9), 823–825 (1993).
[CrossRef]

Unterrainer, K.

Vangala, S.

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

Walavalkar, S.

Waldman, J.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Wang, W. I.

Q. Du, J. Alperin, and W. I. Wang, “Infrared electroabsorption modulation in AlSb/InAs/AlGaSb/GaSb/AlSb stepped quantum-wells grown by molecular-beam epitaxy,” Appl. Phys. Lett. 67(15), 2218–2219 (1995).
[CrossRef]

Y. Zhang, N. Baruch, and W. I. Wang, “Normal incidence infrared photodetectors using intersubband transitions in GaSb l-valley quantum-wells,” Appl. Phys. Lett. 63(8), 1068–1070 (1993).
[CrossRef]

Wanke, M. C.

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Wendler, L.

L. Wendler and E. Kandler, “Intrasubband and intersubband plasmon-polaritons in semiconductor quantum-wells,” Phys. Status Solidi, B Basic Res. 177(1), 9–67 (1993).
[CrossRef]

Wendt, J. R.

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

Wright, J. B.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Young, E. W.

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Zhang, Y.

Y. Zhang, N. Baruch, and W. I. Wang, “Normal incidence infrared photodetectors using intersubband transitions in GaSb l-valley quantum-wells,” Appl. Phys. Lett. 63(8), 1068–1070 (1993).
[CrossRef]

Zheludev, N. I.

Zhou, J.

C. M. Soukoulis, T. Koschny, J. Zhou, M. Kafesaki, and E. N. Economou, “Magnetic response of split ring resonators at terahertz frequencies,” Phys. Status Solidi, B Basic Res. 244(4), 1181–1187 (2007).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Zide, J. M.

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Am. J. Phys. (1)

P. H. Tsao, “Derivation and implications of the symmetry property of the permittivity tensor,” Am. J. Phys. 61(9), 823–825 (1993).
[CrossRef]

Appl. Phys. Lett. (6)

C. Sirtori, F. Capasso, D. L. Sivco, A. L. Hutchinson, and Y. A. Cho, “Resonant Stark tuning of second-order susceptibility in coupled quantum wells,” Appl. Phys. Lett. 60(2), 151 (1992).
[CrossRef]

X. Miao, B. Passmore, A. Gin, W. Langston, S. Vangala, W. Goodhue, E. Shaner, and I. Brener, “Doping tunable resonance: toward electrically tunable mid-infrared metamaterials,” Appl. Phys. Lett. 96(10), 101111 (2010).
[CrossRef]

Q. Du, J. Alperin, and W. I. Wang, “Infrared electroabsorption modulation in AlSb/InAs/AlGaSb/GaSb/AlSb stepped quantum-wells grown by molecular-beam epitaxy,” Appl. Phys. Lett. 67(15), 2218–2219 (1995).
[CrossRef]

L. A. Samoska, B. Brar, and H. Kroemer, “Strong far-infrared intersubband absorption under normal incidence in heavily n-type doped nonalloy GaSb-AlSb superlattices,” Appl. Phys. Lett. 62(20), 2539–2541 (1993).
[CrossRef]

Y. Zhang, N. Baruch, and W. I. Wang, “Normal incidence infrared photodetectors using intersubband transitions in GaSb l-valley quantum-wells,” Appl. Phys. Lett. 63(8), 1068–1070 (1993).
[CrossRef]

A. Gabbay, J. Reno, J. R. Wendt, A. Gin, M. C. Wanke, M. B. Sinclair, E. Shaner, and I. Brener, “Interaction between metamaterial resonators and intersubband transitions in semiconductor quantum wells,” Appl. Phys. Lett. 98(20), 203103 (2011).
[CrossRef]

Electron. Lett. (1)

E. Rosencher, P. Bois, J. Nagle, and S. Delattre, “Second harmonic generation by intersubband transitions in compositionally asymmetrical MQWs,” Electron. Lett. 25(16), 1063 (1989).
[CrossRef]

J. Opt. Soc. Am. B (1)

Metamaterials (Amst.) (1)

X. G. Peralta, I. Brener, W. J. Padilla, E. W. Young, A. J. Hoffman, M. J. Cich, R. D. Averitt, M. C. Wanke, J. B. Wright, H. T. Chen, J. F. O'hara, A. J. Taylor, J. Waldman, W. D. Goodhue, J. Li, and J. Reno, “External modulators for terahertz quantum cascade lasers based on electrically-driven active metamaterials,” Metamaterials (Amst.) 4(2-3), 83–88 (2010).
[CrossRef]

Nano Lett. (1)

D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. 11(5), 2104–2108 (2011).
[CrossRef] [PubMed]

Nat. Photonics (1)

H.-T. Chen, W. J. Padilla, M. J. Cich, A. K. Azad, R. D. Averitt, and A. J. Taylor, “A metamaterial solid-state terahertz phase modulator,” Nat. Photonics 3(3), 148–151 (2009).
[CrossRef]

Nature (1)

H.-T. Chen, W. J. Padilla, J. M. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Opt. Express (3)

Phys. Rev. (1)

F. Stern and W. E. Howard, “Properties of semiconductor surface inversion layers in the electric quantum limit,” Phys. Rev. 163(3), 816–835 (1967).
[CrossRef]

Phys. Rev. B (1)

Y. Todorov and C. Sirtori, “Intersubband polaritons in the electrical dipole gauge,” Phys. Rev. B 85(4), 045304 (2012).
[CrossRef]

Phys. Rev. B Condens. Matter (4)

E. R. Brown and S. J. Eglash, “Calculation of the intersubband absorption strength in ellipsoidal-valley quantum wells,” Phys. Rev. B Condens. Matter 41(11), 7559–7568 (1990).
[CrossRef] [PubMed]

E. Rosencher and P. Bois, “Model system for optical nonlinearities: asymmetric quantum wells,” Phys. Rev. B Condens. Matter 44(20), 11315–11327 (1991).
[CrossRef] [PubMed]

V. Savona, Z. Hradil, A. Quattropani, and P. Schwendimann, “Quantum theory of quantum-well polaritons in semiconductor microcavities,” Phys. Rev. B Condens. Matter 49(13), 8774–8779 (1994).
[CrossRef] [PubMed]

E. R. Brown, S. J. Eglash, and K. A. McIntosh, “Observation of normal-incidence intersubband absorption in n-type Al0.09Ga0.91Sb quantum wells,” Phys. Rev. B Condens. Matter 46(11), 7244–7247 (1992).
[CrossRef] [PubMed]

Phys. Status Solidi, B Basic Res. (2)

L. Wendler and E. Kandler, “Intrasubband and intersubband plasmon-polaritons in semiconductor quantum-wells,” Phys. Status Solidi, B Basic Res. 177(1), 9–67 (1993).
[CrossRef]

C. M. Soukoulis, T. Koschny, J. Zhou, M. Kafesaki, and E. N. Economou, “Magnetic response of split ring resonators at terahertz frequencies,” Phys. Status Solidi, B Basic Res. 244(4), 1181–1187 (2007).
[CrossRef]

Science (1)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Sov. Phys. Semicond. (1)

F. G. Pikus, “Excitons in quantum wells with a two dimensional electron gas,” Sov. Phys. Semicond. 26, 2633 (1992).

Other (10)

J. Faist and C. Sirtori, Intersubband Transitions in Quantum Wells: Physics and Device Applications I, Semiconductors and Semimetals (Academic Press, 2000), Vol. 62.

M. Helm, IntersubbandTransitions in Quantum Wells:Physics and Device Applications, Semiconductors and Semimetals (Academic Press, 2000), Vol. 62.

G. Bastard, Wave Mechanics Applied to Semiconductor Heterostructures, 1 ed. (Wiley-Interscience, 1991).

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. (World Scientific Publishing Company, 2004).

R. W. Boyd, Nonlinear Optics (Academic Press, 1992), chap. 3.

The issue of the symmetry of the permittivity tensor when dealing with transparent or passive media as been studied in numerous textbooks and publications (for example see [25]). For simplicity, we choose to display a non-symmetric tensor with the understanding that for computations we use only one diagonal half.

http://www.lumerical.com , “Fdtd solutions.”

C. Weisbuch and B. Vinter, Quantum Semiconductor Structures—Fundamentals and Applications (Academic Press, 1991).

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2009).

T. Cui, D. Smith, and R. Liu, Metamaterials: Theory, Design, and Applications (Springer, 2009).

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