Abstract

Our work describes a novel three dimensional meta-material resonator design for optoelectronic applications in the THz spectral range. In our resonant circuits, the capacitors are formed by double-metal regions cladding a dielectric core. Unlike conventional planar metamaterials, the electric field is perpendicular to the surface and totally confined in the dielectric core. Furthermore, the magnetic field, confined in the inductive part, is parallel to the electric field, ruling out coupling through propagation effects. Our geometry thus combines the benefit of double-metal structures that provide parallel plate capacitors, while maintaining the ability of meta-material resonators to adjust independently the capacitive and inductive parts. Furthermore, in our geometry, a constant bias can be applied across the dielectric, making these resonators very suitable for applications such as ultra-low dark current THz quantum detectors and amplifiers based on quantum cascade gain medium.

© 2015 Optical Society of America

Full Article  |  PDF Article

Corrections

19 October 2015: A correction was made to the author listing.


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References

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2015 (1)

A. Benz, S. Campione, J. F. Klem, M. B. Sinclair, and I. Brener, “Control of strong light-matter coupling using the capacitance of metamaterial nanocavities,” Nano Lett. 15(3), 1959–1966 (2015).
[Crossref] [PubMed]

2014 (8)

J. Madéo, Y. Todorov, and C. Sirtori, “Antenna-coupled microcavities for terahertz emission,” Appl. Phys. Lett. 104(3), 031108 (2014).
[Crossref]

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

S. Collin, “Nanostructure arrays in free-space: optical properties and applications,” Rep. Prog. Phys. 77(12), 126402 (2014).
[Crossref] [PubMed]

Y. N. Chen, Y. Todorov, B. Askenazi, A. Vasanelli, G. Biasiol, R. Colombelli, and C. Sirtori, “Antenna-coupled microcavities for enhanced infrared photo-detection,” Appl. Phys. Lett. 104(3), 031113 (2014).
[Crossref]

A. Bonakdar and H. Mohseni, “Impact of optical antennas on active optoelectronic devices,” Nanoscale 6(19), 10961–10974 (2014).
[Crossref] [PubMed]

Y. Todorov and C. Sirtori, “Few-electron ultrastrong light-matter coupling in a quantum LC circuit,” Phys. Rev. X 4, 041031 (2014).

S. Campione, A. Benz, J. F. Klem, M. B. Sinclair, I. Brener, and F. Capolino, “Electrodynamic modeling of strong coupling between a metasurface and intersubband transitions in quantum wells,” Phys. Rev. B 89(16), 165133 (2014).
[Crossref]

B. Paulillo, J. M. Manceau, A. Degiron, N. Zerounian, G. Beaudoin, I. Sagnes, and R. Colombelli, “Circuit-tunable sub-wavelength THz resonators: hybridizing optical cavities and loop antennas,” Opt. Express 22(18), 21302–21312 (2014).
[Crossref] [PubMed]

2013 (3)

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
[Crossref] [PubMed]

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
[Crossref] [PubMed]

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic sub-wavelength cavities operating at THz frequencies,” Phys. Rev. B 87(4), 041408 (2013).
[Crossref]

2012 (5)

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
[Crossref]

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
[Crossref] [PubMed]

M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
[Crossref] [PubMed]

C. Feuillet-Palma, Y. Todorov, R. Steed, A. Vasanelli, G. Biasiol, L. Sorba, and C. Sirtori, “Extremely sub-wavelength THz metal-dielectric wire microcavities,” Opt. Express 20(27), 29121–29130 (2012).
[PubMed]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (4)

Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the THz frequency range,” Opt. Express 18(13), 13886–13907 (2010).
[Crossref] [PubMed]

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(19), 191107 (2010).
[Crossref]

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
[Crossref] [PubMed]

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105(11), 117701 (2010).
[Crossref] [PubMed]

2009 (2)

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
[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]

2008 (1)

N. Laman and D. Grischowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93(5), 051105 (2008).
[Crossref]

2006 (2)

1965 (1)

C. Hoer and C. Love, “Exact inductance equations for rectangular conductors with application to more complicated geometries,” J. Res. NBS 69C, 127 (1965).

1927 (1)

H. B. Palmer, “Capacitance of a parallel-plate capacitor by the Schwartz-Christoffel transformation,” Trans. AIEE 56, 363 (1927).

Allerman, A.

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
[Crossref] [PubMed]

Al-Naib, I.

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Amanti, M. I.

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
[Crossref] [PubMed]

Andrews, A. M.

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
[Crossref]

Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the THz frequency range,” Opt. Express 18(13), 13886–13907 (2010).
[Crossref] [PubMed]

Askenazi, B.

Y. N. Chen, Y. Todorov, B. Askenazi, A. Vasanelli, G. Biasiol, R. Colombelli, and C. Sirtori, “Antenna-coupled microcavities for enhanced infrared photo-detection,” Appl. Phys. Lett. 104(3), 031113 (2014).
[Crossref]

Averitt, R. D.

H. Tao, E. A. Kadlec, A. C. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, E. A. Shaner, and X. Zhang, “Microwave and terahertz wave sensing with metamaterials,” Opt. Express 19(22), 21620–21626 (2011).
[Crossref] [PubMed]

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]

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]

Beaudoin, G.

B. Paulillo, J. M. Manceau, A. Degiron, N. Zerounian, G. Beaudoin, I. Sagnes, and R. Colombelli, “Circuit-tunable sub-wavelength THz resonators: hybridizing optical cavities and loop antennas,” Opt. Express 22(18), 21302–21312 (2014).
[Crossref] [PubMed]

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic sub-wavelength cavities operating at THz frequencies,” Phys. Rev. B 87(4), 041408 (2013).
[Crossref]

Beck, M.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
[Crossref] [PubMed]

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(19), 191107 (2010).
[Crossref]

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
[Crossref] [PubMed]

Beltram, F.

M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
[Crossref] [PubMed]

Benz, A.

A. Benz, S. Campione, J. F. Klem, M. B. Sinclair, and I. Brener, “Control of strong light-matter coupling using the capacitance of metamaterial nanocavities,” Nano Lett. 15(3), 1959–1966 (2015).
[Crossref] [PubMed]

S. Campione, A. Benz, J. F. Klem, M. B. Sinclair, I. Brener, and F. Capolino, “Electrodynamic modeling of strong coupling between a metasurface and intersubband transitions in quantum wells,” Phys. Rev. B 89(16), 165133 (2014).
[Crossref]

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
[Crossref] [PubMed]

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]

Biasiol, G.

Y. N. Chen, Y. Todorov, B. Askenazi, A. Vasanelli, G. Biasiol, R. Colombelli, and C. Sirtori, “Antenna-coupled microcavities for enhanced infrared photo-detection,” Appl. Phys. Lett. 104(3), 031113 (2014).
[Crossref]

C. Feuillet-Palma, Y. Todorov, R. Steed, A. Vasanelli, G. Biasiol, L. Sorba, and C. Sirtori, “Extremely sub-wavelength THz metal-dielectric wire microcavities,” Opt. Express 20(27), 29121–29130 (2012).
[PubMed]

Bonakdar, A.

A. Bonakdar and H. Mohseni, “Impact of optical antennas on active optoelectronic devices,” Nanoscale 6(19), 10961–10974 (2014).
[Crossref] [PubMed]

Brekenfeld, M.

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
[Crossref]

Brener, I.

A. Benz, S. Campione, J. F. Klem, M. B. Sinclair, and I. Brener, “Control of strong light-matter coupling using the capacitance of metamaterial nanocavities,” Nano Lett. 15(3), 1959–1966 (2015).
[Crossref] [PubMed]

S. Campione, A. Benz, J. F. Klem, M. B. Sinclair, I. Brener, and F. Capolino, “Electrodynamic modeling of strong coupling between a metasurface and intersubband transitions in quantum wells,” Phys. Rev. B 89(16), 165133 (2014).
[Crossref]

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
[Crossref] [PubMed]

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
[Crossref] [PubMed]

Campione, S.

A. Benz, S. Campione, J. F. Klem, M. B. Sinclair, and I. Brener, “Control of strong light-matter coupling using the capacitance of metamaterial nanocavities,” Nano Lett. 15(3), 1959–1966 (2015).
[Crossref] [PubMed]

S. Campione, A. Benz, J. F. Klem, M. B. Sinclair, I. Brener, and F. Capolino, “Electrodynamic modeling of strong coupling between a metasurface and intersubband transitions in quantum wells,” Phys. Rev. B 89(16), 165133 (2014).
[Crossref]

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
[Crossref] [PubMed]

Cao, W.

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S. Campione, A. Benz, J. F. Klem, M. B. Sinclair, I. Brener, and F. Capolino, “Electrodynamic modeling of strong coupling between a metasurface and intersubband transitions in quantum wells,” Phys. Rev. B 89(16), 165133 (2014).
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A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
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M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
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E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic sub-wavelength cavities operating at THz frequencies,” Phys. Rev. B 87(4), 041408 (2013).
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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).
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Y. N. Chen, Y. Todorov, B. Askenazi, A. Vasanelli, G. Biasiol, R. Colombelli, and C. Sirtori, “Antenna-coupled microcavities for enhanced infrared photo-detection,” Appl. Phys. Lett. 104(3), 031113 (2014).
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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).
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G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
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B. Paulillo, J. M. Manceau, A. Degiron, N. Zerounian, G. Beaudoin, I. Sagnes, and R. Colombelli, “Circuit-tunable sub-wavelength THz resonators: hybridizing optical cavities and loop antennas,” Opt. Express 22(18), 21302–21312 (2014).
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[Crossref]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
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Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the THz frequency range,” Opt. Express 18(13), 13886–13907 (2010).
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R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
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[Crossref]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
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E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic sub-wavelength cavities operating at THz frequencies,” Phys. Rev. B 87(4), 041408 (2013).
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M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
[Crossref] [PubMed]

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(19), 191107 (2010).
[Crossref]

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
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Feuillet-Palma, C.

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(19), 191107 (2010).
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Geiser, M.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
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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(19), 191107 (2010).
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Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
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N. Laman and D. Grischowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93(5), 051105 (2008).
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G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
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C. Hoer and C. Love, “Exact inductance equations for rectangular conductors with application to more complicated geometries,” J. Res. NBS 69C, 127 (1965).

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E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic sub-wavelength cavities operating at THz frequencies,” Phys. Rev. B 87(4), 041408 (2013).
[Crossref]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
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Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
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Kang, J. H.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
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Kim, D. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
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E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
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Klem, J. F.

A. Benz, S. Campione, J. F. Klem, M. B. Sinclair, and I. Brener, “Control of strong light-matter coupling using the capacitance of metamaterial nanocavities,” Nano Lett. 15(3), 1959–1966 (2015).
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S. Campione, A. Benz, J. F. Klem, M. B. Sinclair, I. Brener, and F. Capolino, “Electrodynamic modeling of strong coupling between a metasurface and intersubband transitions in quantum wells,” Phys. Rev. B 89(16), 165133 (2014).
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A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
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M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
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M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
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Laman, N.

N. Laman and D. Grischowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93(5), 051105 (2008).
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Laroche, M.

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105(11), 117701 (2010).
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Liu, S.

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
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C. Hoer and C. Love, “Exact inductance equations for rectangular conductors with application to more complicated geometries,” J. Res. NBS 69C, 127 (1965).

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J. Madéo, Y. Todorov, and C. Sirtori, “Antenna-coupled microcavities for terahertz emission,” Appl. Phys. Lett. 104(3), 031108 (2014).
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Maissen, C.

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
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Marquier, F.

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
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J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105(11), 117701 (2010).
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Nevou, L.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

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(19), 191107 (2010).
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H. Tao, E. A. Kadlec, A. C. Strikwerda, K. Fan, W. J. Padilla, R. D. Averitt, E. A. Shaner, and X. Zhang, “Microwave and terahertz wave sensing with metamaterials,” Opt. Express 19(22), 21620–21626 (2011).
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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).
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H. B. Palmer, “Capacitance of a parallel-plate capacitor by the Schwartz-Christoffel transformation,” Trans. AIEE 56, 363 (1927).

Park, D. J.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
[Crossref]

Park, G. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
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Park, H. R.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
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Park, N. K.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
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Park, Q. H.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
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Paulillo, B.

Pitanti, A.

M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
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Planken, P. C. M.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
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G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
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Reno, J.

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
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Ribaudo, T.

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
[Crossref] [PubMed]

Sagnes, I.

Scalari, G.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
[Crossref] [PubMed]

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(19), 191107 (2010).
[Crossref]

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
[Crossref] [PubMed]

Schuh, D.

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
[Crossref] [PubMed]

Seo, M. A.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
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Shaner, E.

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
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Shaner, E. A.

Sinclair, M.

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
[Crossref] [PubMed]

Sinclair, M. B.

A. Benz, S. Campione, J. F. Klem, M. B. Sinclair, and I. Brener, “Control of strong light-matter coupling using the capacitance of metamaterial nanocavities,” Nano Lett. 15(3), 1959–1966 (2015).
[Crossref] [PubMed]

S. Campione, A. Benz, J. F. Klem, M. B. Sinclair, I. Brener, and F. Capolino, “Electrodynamic modeling of strong coupling between a metasurface and intersubband transitions in quantum wells,” Phys. Rev. B 89(16), 165133 (2014).
[Crossref]

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
[Crossref] [PubMed]

Singh, R.

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Sirtori, C.

Y. N. Chen, Y. Todorov, B. Askenazi, A. Vasanelli, G. Biasiol, R. Colombelli, and C. Sirtori, “Antenna-coupled microcavities for enhanced infrared photo-detection,” Appl. Phys. Lett. 104(3), 031113 (2014).
[Crossref]

Y. Todorov and C. Sirtori, “Few-electron ultrastrong light-matter coupling in a quantum LC circuit,” Phys. Rev. X 4, 041031 (2014).

J. Madéo, Y. Todorov, and C. Sirtori, “Antenna-coupled microcavities for terahertz emission,” Appl. Phys. Lett. 104(3), 031108 (2014).
[Crossref]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
[Crossref]

C. Feuillet-Palma, Y. Todorov, R. Steed, A. Vasanelli, G. Biasiol, L. Sorba, and C. Sirtori, “Extremely sub-wavelength THz metal-dielectric wire microcavities,” Opt. Express 20(27), 29121–29130 (2012).
[PubMed]

Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the THz frequency range,” Opt. Express 18(13), 13886–13907 (2010).
[Crossref] [PubMed]

Sorba, L.

C. Feuillet-Palma, Y. Todorov, R. Steed, A. Vasanelli, G. Biasiol, L. Sorba, and C. Sirtori, “Extremely sub-wavelength THz metal-dielectric wire microcavities,” Opt. Express 20(27), 29121–29130 (2012).
[PubMed]

M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
[Crossref] [PubMed]

Soukoulis, C. M.

Steed, R.

Strasser, G.

Strikwerda, A. C.

Strupiechonski, E.

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic sub-wavelength cavities operating at THz frequencies,” Phys. Rev. B 87(4), 041408 (2013).
[Crossref]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
[Crossref]

Suwal, O. K.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
[Crossref]

Tao, H.

Taylor, A. J.

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]

Teissier, J.

Teppe, F.

M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
[Crossref] [PubMed]

Tignon, J.

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic sub-wavelength cavities operating at THz frequencies,” Phys. Rev. B 87(4), 041408 (2013).
[Crossref]

Todorov, Y.

J. Madéo, Y. Todorov, and C. Sirtori, “Antenna-coupled microcavities for terahertz emission,” Appl. Phys. Lett. 104(3), 031108 (2014).
[Crossref]

Y. Todorov and C. Sirtori, “Few-electron ultrastrong light-matter coupling in a quantum LC circuit,” Phys. Rev. X 4, 041031 (2014).

Y. N. Chen, Y. Todorov, B. Askenazi, A. Vasanelli, G. Biasiol, R. Colombelli, and C. Sirtori, “Antenna-coupled microcavities for enhanced infrared photo-detection,” Appl. Phys. Lett. 104(3), 031113 (2014).
[Crossref]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
[Crossref]

C. Feuillet-Palma, Y. Todorov, R. Steed, A. Vasanelli, G. Biasiol, L. Sorba, and C. Sirtori, “Extremely sub-wavelength THz metal-dielectric wire microcavities,” Opt. Express 20(27), 29121–29130 (2012).
[PubMed]

Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the THz frequency range,” Opt. Express 18(13), 13886–13907 (2010).
[Crossref] [PubMed]

Tosetto, L.

Tredicucci, A.

M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
[Crossref] [PubMed]

Turcinková, D.

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
[Crossref] [PubMed]

Unterrainer, K.

Vasanelli, A.

Y. N. Chen, Y. Todorov, B. Askenazi, A. Vasanelli, G. Biasiol, R. Colombelli, and C. Sirtori, “Antenna-coupled microcavities for enhanced infrared photo-detection,” Appl. Phys. Lett. 104(3), 031113 (2014).
[Crossref]

C. Feuillet-Palma, Y. Todorov, R. Steed, A. Vasanelli, G. Biasiol, L. Sorba, and C. Sirtori, “Extremely sub-wavelength THz metal-dielectric wire microcavities,” Opt. Express 20(27), 29121–29130 (2012).
[PubMed]

Vassant, S.

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
[Crossref] [PubMed]

Viti, L.

M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
[Crossref] [PubMed]

Vitiello, M. S.

M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
[Crossref] [PubMed]

Walther, C.

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
[Crossref] [PubMed]

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(19), 191107 (2010).
[Crossref]

Wegener, M.

Wegscheider, W.

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
[Crossref] [PubMed]

Wendt, J. R.

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
[Crossref] [PubMed]

Withayachumnankul, W.

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Xu, G.

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic sub-wavelength cavities operating at THz frequencies,” Phys. Rev. B 87(4), 041408 (2013).
[Crossref]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
[Crossref]

Zerounian, N.

Zhang, W.

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Zhang, X.

Appl. Phys. Lett. (6)

Y. N. Chen, Y. Todorov, B. Askenazi, A. Vasanelli, G. Biasiol, R. Colombelli, and C. Sirtori, “Antenna-coupled microcavities for enhanced infrared photo-detection,” Appl. Phys. Lett. 104(3), 031113 (2014).
[Crossref]

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

J. Madéo, Y. Todorov, and C. Sirtori, “Antenna-coupled microcavities for terahertz emission,” Appl. Phys. Lett. 104(3), 031108 (2014).
[Crossref]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Appl. Phys. Lett. 100(13), 131113 (2012).
[Crossref]

N. Laman and D. Grischowsky, “Terahertz conductivity of thin metal films,” Appl. Phys. Lett. 93(5), 051105 (2008).
[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(19), 191107 (2010).
[Crossref]

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C. Hoer and C. Love, “Exact inductance equations for rectangular conductors with application to more complicated geometries,” J. Res. NBS 69C, 127 (1965).

Nano Lett. (3)

Y. C. Jun, J. Reno, T. Ribaudo, E. Shaner, J.-J. Greffet, S. Vassant, F. Marquier, M. Sinclair, and I. Brener, “Epsilon-near-zero strong coupling in metamaterial-semiconductor hybrid structures,” Nano Lett. 13(11), 5391–5396 (2013).
[Crossref] [PubMed]

A. Benz, S. Campione, J. F. Klem, M. B. Sinclair, and I. Brener, “Control of strong light-matter coupling using the capacitance of metamaterial nanocavities,” Nano Lett. 15(3), 1959–1966 (2015).
[Crossref] [PubMed]

M. S. Vitiello, D. Coquillat, L. Viti, D. Ercolani, F. Teppe, A. Pitanti, F. Beltram, L. Sorba, W. Knap, and A. Tredicucci, “Room-temperature terahertz detectors based on semiconductor nanowire field-effect transistors,” Nano Lett. 12(1), 96–101 (2012).
[Crossref] [PubMed]

Nanoscale (1)

A. Bonakdar and H. Mohseni, “Impact of optical antennas on active optoelectronic devices,” Nanoscale 6(19), 10961–10974 (2014).
[Crossref] [PubMed]

Nat. Commun. (1)

A. Benz, S. Campione, S. Liu, I. Montaño, J. F. Klem, A. Allerman, J. R. Wendt, M. B. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nat. Commun. 4, 2882 (2013).
[Crossref] [PubMed]

Nat. Photonics (2)

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]

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano-slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. B (2)

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic sub-wavelength cavities operating at THz frequencies,” Phys. Rev. B 87(4), 041408 (2013).
[Crossref]

S. Campione, A. Benz, J. F. Klem, M. B. Sinclair, I. Brener, and F. Capolino, “Electrodynamic modeling of strong coupling between a metasurface and intersubband transitions in quantum wells,” Phys. Rev. B 89(16), 165133 (2014).
[Crossref]

Phys. Rev. Lett. (2)

J.-J. Greffet, M. Laroche, and F. Marquier, “Impedance of a nanoantenna and a single quantum emitter,” Phys. Rev. Lett. 105(11), 117701 (2010).
[Crossref] [PubMed]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108(10), 106402 (2012).
[Crossref] [PubMed]

Phys. Rev. X (1)

Y. Todorov and C. Sirtori, “Few-electron ultrastrong light-matter coupling in a quantum LC circuit,” Phys. Rev. X 4, 041031 (2014).

Rep. Prog. Phys. (1)

S. Collin, “Nanostructure arrays in free-space: optical properties and applications,” Rep. Prog. Phys. 77(12), 126402 (2014).
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Science (2)

G. Scalari, C. Maissen, D. Turcinková, D. Hagenmüller, S. De Liberato, C. Ciuti, C. Reichl, D. Schuh, W. Wegscheider, M. Beck, and J. Faist, “Ultrastrong coupling of the cyclotron transition of a 2D electron gas to a THz metamaterial,” Science 335(6074), 1323–1326 (2012).
[Crossref] [PubMed]

C. Walther, G. Scalari, M. I. Amanti, M. Beck, and J. Faist, “Microcavity laser oscillating in a circuit-based resonator,” Science 327(5972), 1495–1497 (2010).
[Crossref] [PubMed]

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H. B. Palmer, “Capacitance of a parallel-plate capacitor by the Schwartz-Christoffel transformation,” Trans. AIEE 56, 363 (1927).

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H. A. Haus and J. R. Melcher, Electromagnetic Fields and Energy. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed March 6, 2015). License: Creative Commons Attribution-NonCommercial-Share Alike.

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Figures (5)

Fig. 1
Fig. 1 (a) Perspective drawing of the resonator, indicating the subwavelength capacitor parts. (b,c) Microscope pictures of arrays realized by laser lithography on GaAs substrate and with SiO2 dielectric layer. The main geometrical parameters are indicated in (c). (d) Coordinate system and a set of planes chosen for the illustration of the electromagnetic field distribution. The surfaces A, B and C are contained by the dashed lines and the z-direction. (e) Upper panel: electric field component Ez in the (x,y)-plane from (d). Lower panel: electric energy density plotted in the planes A and B. (f) Upper panel: magnetic field component Hz in the (x,y)-plane. Lower panel: magnetic energy density in the planes (x,y) and C.
Fig. 2
Fig. 2 (a,b,c) Experimental reflectivity spectra of resonator arrays such as the one depicted in Fig. 1(c), with light polarized along the two capacitors, and under almost normal incidence on the array surface. The thickness is T = 2µm. The triplet of numbers indicates the parameters (W Lx Ly) defined in Fig. 1(c), for instance 264 indicates nominal values W = 2µm, Lx = 6µm and Ly = 4µm. (d) Spectra of the resonators 222 and 242 for two different thicknesses T = 2µm (dotted curves) and T = 1µm (continuous lines). The grey area corresponds to the phonon absorption of the GaAs substrate.
Fig. 3
Fig. 3 Left: plot of the resonator frequencies measured from the data in Fig. 3 as a function of the “scale parameter” p, that is roughly proportional to the square root of the inverse of the product of the capacitance and inductance of the structure, as explained in the main text. Right: pictures of the different family of resonators.
Fig. 4
Fig. 4 Circuit model of the structure. (a) Scheme of the equivalent circuit, with indication of the inductive and capacitive elements. (b) Total inductance as a function of the half-perimeter Lx + Ly of the magnetic loop (circles). The dotted line is a quadratic fit. (c) Total capacitance as a function of the parameter EW/T (diamonds). The dotted lines are extrapolation of the circuit model for decreasing capacitor surface EW, for a thickness T = 2µm, 1µm or 0.5µm of the dielectric layer. The red line is the parallel plate capacitor value C/2 = 0.5εε0WE/T. (d) Ratio fLC/fres between the modelled (fLC) and measured frequencies (fres) as a function fres. The full squares are the values obtained with the full circuit model from Fig. 4(a), while the open squares are the values of the simplified formula fLC = 1/2π[(C/2 + Cinter)L]1/2.
Fig. 5
Fig. 5 Ratio between the minimal photon optical path Lopt and the resonant wavelength λres = c/fres for different resonators reported in the literature (open dotted symbols) as comparison to our work (full symbols, with the same code as in Fig. 3). The case Loptres = 1 corresponds to the first standing wave mode in the structure. Higher order modes are provided by the condition Loptres = K, where K is positive integer. The case Lopt/ λres < 1 corresponds to resonators operating in the quasi-static regime. For simplicity, in this diagram we used the bulk refractive index of the dielectric filling the resonators; Lopt/ λres >1 signifies that the effective index of the guided mode is higher than the bulk refractive index.

Equations (1)

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C = ε ε 0 W E T { 1 + T π E ( 1 + ln [ 2 π E T ] ) } { 1 + T π W ( 1 + ln [ 2 π W T ] ) } .

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