Abstract

We demonstrate minimal volume wire THz metal-dielectric micro-cavities, in which all but one dimension have been reduced to highly sub-wavelength values. The smallest cavity features an effective volume of 0.4 µm3, which is ~5.10−7 times the volume defined by the resonant vacuum wavelength (λ = 94 µm) to the cube. When combined with a doped multi-quantum well structure, such micro-cavities enter the ultra-strong light matter coupling regime, even if the total number of electrons participating to the coupling is only in the order of 104, thus much less than in previous studies.

© 2012 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  22. E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  27. P. W. C. Hon, A. A. Tavallaee, Q.-S. Chen, B. S. Williams, and T. Itoh, “Radiation Model for Terahertz Transmission-Line Metamaterial Quantum-Cascade Lasers,” IEEE Trans. THz Sci. Technol.2(3), 323–332 (2012).

2012 (5)

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
[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]

S. Zanotto, R. Degl’Innocenti, L. Sorba, A. Tredicucci, and G. Biasiol, “Analysis of line shapes and strong coupling with intersubband transitions in one-dimensional metallodielectric photonic crystal slabs,” Phys. Rev. B85(3), 035307 (2012).
[CrossRef]

P. W. C. Hon, A. A. Tavallaee, Q.-S. Chen, B. S. Williams, and T. Itoh, “Radiation Model for Terahertz Transmission-Line Metamaterial Quantum-Cascade Lasers,” IEEE Trans. THz Sci. Technol.2(3), 323–332 (2012).

2011 (3)

C. Walther, G. Scalari, M. Beck, and J. Faist, “Purcell effect in the inductor-capacitor laser,” Opt. Lett.36(14), 2623–2625 (2011).
[CrossRef] [PubMed]

P. Jouy, Y. Todorov, A. Vasanelli, R. Colombelli, I. Sagnes, and C. Sirtori, “Coupling of a surface plasmon with localized subwavelength microcavity modes,” Appl. Phys. Lett.98(2), 021105 (2011).
[CrossRef]

P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett.98(23), 231114 (2011).
[CrossRef]

2010 (2)

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (2010).
[CrossRef] [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. Express18(13), 13886–13907 (2010).
[CrossRef] [PubMed]

2009 (1)

S. De Liberato and C. Ciuti, “Quantum theory of electron tunneling into intersubband cavity polariton states,” Phys. Rev. B79(7), 075317 (2009).
[CrossRef]

2007 (2)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007).
[CrossRef]

Y. Todorov, I. Sagnes, I. Abram, and C. Minot, “Purcell Enhancement of Spontaneous Emission from Quantum Cascades inside Mirror-Grating Metal Cavities at THz Frequencies,” Phys. Rev. Lett.99(22), 223603 (2007).
[CrossRef] [PubMed]

2006 (4)

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96(9), 097401 (2006).
[CrossRef] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett.31(9), 1259–1261 (2006).
[CrossRef] [PubMed]

S. A. Maier, “Plasmonic field enhancement and SERS in the effective mode volume picture,” Opt. Express14(5), 1957–1964 (2006).
[CrossRef] [PubMed]

C. Ciuti and I. Carusotto, “Input-output theory of cavities in the ultrastrong coupling regime: The case of time-independent cavity parameters,” Phys. Rev. A74(3), 033811 (2006).
[CrossRef]

2005 (2)

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B72(11), 115303 (2005).
[CrossRef]

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

2004 (3)

T. Atay, J.-H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole−dipole interaction to conductively coupled regime,” Nano Lett.4(9), 1627–1631 (2004).
[CrossRef]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing Millimeter Waves into Microns,” Phys. Rev. Lett.92(14), 143904 (2004).
[CrossRef] [PubMed]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors, and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

1946 (1)

E. M. Purcell, H. Torrey, and R. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev.69(1-2), 674 (1946).
[CrossRef]

Abram, I.

Y. Todorov, I. Sagnes, I. Abram, and C. Minot, “Purcell Enhancement of Spontaneous Emission from Quantum Cascades inside Mirror-Grating Metal Cavities at THz Frequencies,” Phys. Rev. Lett.99(22), 223603 (2007).
[CrossRef] [PubMed]

Andrews, A. M.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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. Express18(13), 13886–13907 (2010).
[CrossRef] [PubMed]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (2010).
[CrossRef] [PubMed]

Atay, T.

T. Atay, J.-H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole−dipole interaction to conductively coupled regime,” Nano Lett.4(9), 1627–1631 (2004).
[CrossRef]

Bastard, G.

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B72(11), 115303 (2005).
[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]

C. Walther, G. Scalari, M. Beck, and J. Faist, “Purcell effect in the inductor-capacitor laser,” Opt. Lett.36(14), 2623–2625 (2011).
[CrossRef] [PubMed]

Biagioni, P.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
[CrossRef] [PubMed]

Biasiol, G.

S. Zanotto, R. Degl’Innocenti, L. Sorba, A. Tredicucci, and G. Biasiol, “Analysis of line shapes and strong coupling with intersubband transitions in one-dimensional metallodielectric photonic crystal slabs,” Phys. Rev. B85(3), 035307 (2012).
[CrossRef]

P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett.98(23), 231114 (2011).
[CrossRef]

Bloch, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Brekenfeld, M.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

Brown, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing Millimeter Waves into Microns,” Phys. Rev. Lett.92(14), 143904 (2004).
[CrossRef] [PubMed]

Carusotto, I.

C. Ciuti and I. Carusotto, “Input-output theory of cavities in the ultrastrong coupling regime: The case of time-independent cavity parameters,” Phys. Rev. A74(3), 033811 (2006).
[CrossRef]

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B72(11), 115303 (2005).
[CrossRef]

Castellano, F.

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]

Chen, Q.-S.

P. W. C. Hon, A. A. Tavallaee, Q.-S. Chen, B. S. Williams, and T. Itoh, “Radiation Model for Terahertz Transmission-Line Metamaterial Quantum-Cascade Lasers,” IEEE Trans. THz Sci. Technol.2(3), 323–332 (2012).

Ciuti, C.

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (2010).
[CrossRef] [PubMed]

S. De Liberato and C. Ciuti, “Quantum theory of electron tunneling into intersubband cavity polariton states,” Phys. Rev. B79(7), 075317 (2009).
[CrossRef]

C. Ciuti and I. Carusotto, “Input-output theory of cavities in the ultrastrong coupling regime: The case of time-independent cavity parameters,” Phys. Rev. A74(3), 033811 (2006).
[CrossRef]

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B72(11), 115303 (2005).
[CrossRef]

Colombelli, R.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

P. Jouy, Y. Todorov, A. Vasanelli, R. Colombelli, I. Sagnes, and C. Sirtori, “Coupling of a surface plasmon with localized subwavelength microcavity modes,” Appl. Phys. Lett.98(2), 021105 (2011).
[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. Express18(13), 13886–13907 (2010).
[CrossRef] [PubMed]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (2010).
[CrossRef] [PubMed]

De Liberato, S.

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (2010).
[CrossRef] [PubMed]

S. De Liberato and C. Ciuti, “Quantum theory of electron tunneling into intersubband cavity polariton states,” Phys. Rev. B79(7), 075317 (2009).
[CrossRef]

Degiron, A.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

Degl’Innocenti, R.

S. Zanotto, R. Degl’Innocenti, L. Sorba, A. Tredicucci, and G. Biasiol, “Analysis of line shapes and strong coupling with intersubband transitions in one-dimensional metallodielectric photonic crystal slabs,” Phys. Rev. B85(3), 035307 (2012).
[CrossRef]

Delteil, A.

P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett.98(23), 231114 (2011).
[CrossRef]

Enkrich, C.

Faist, J.

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]

C. Walther, G. Scalari, M. Beck, and J. Faist, “Purcell effect in the inductor-capacitor laser,” Opt. Lett.36(14), 2623–2625 (2011).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Gérard, J. M.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Hecht, B.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
[CrossRef] [PubMed]

Hibbins, A. P.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing Millimeter Waves into Microns,” Phys. Rev. Lett.92(14), 143904 (2004).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors, and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

Hon, P. W. C.

P. W. C. Hon, A. A. Tavallaee, Q.-S. Chen, B. S. Williams, and T. Itoh, “Radiation Model for Terahertz Transmission-Line Metamaterial Quantum-Cascade Lasers,” IEEE Trans. THz Sci. Technol.2(3), 323–332 (2012).

Hours, J.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Huang, J.-S.

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
[CrossRef] [PubMed]

Isac, N.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

Itoh, T.

P. W. C. Hon, A. A. Tavallaee, Q.-S. Chen, B. S. Williams, and T. Itoh, “Radiation Model for Terahertz Transmission-Line Metamaterial Quantum-Cascade Lasers,” IEEE Trans. THz Sci. Technol.2(3), 323–332 (2012).

Jouy, P.

P. Jouy, Y. Todorov, A. Vasanelli, R. Colombelli, I. Sagnes, and C. Sirtori, “Coupling of a surface plasmon with localized subwavelength microcavity modes,” Appl. Phys. Lett.98(2), 021105 (2011).
[CrossRef]

P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett.98(23), 231114 (2011).
[CrossRef]

Klang, P.

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (2010).
[CrossRef] [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. Express18(13), 13886–13907 (2010).
[CrossRef] [PubMed]

Klein, M. W.

Kurokawa, Y.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96(9), 097401 (2006).
[CrossRef] [PubMed]

Lawrence, C. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing Millimeter Waves into Microns,” Phys. Rev. Lett.92(14), 143904 (2004).
[CrossRef] [PubMed]

Lemaître, A.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Linden, S.

Maier, S. A.

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Martrou, D.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Minot, C.

Y. Todorov, I. Sagnes, I. Abram, and C. Minot, “Purcell Enhancement of Spontaneous Emission from Quantum Cascades inside Mirror-Grating Metal Cavities at THz Frequencies,” Phys. Rev. Lett.99(22), 223603 (2007).
[CrossRef] [PubMed]

Miyazaki, H. T.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96(9), 097401 (2006).
[CrossRef] [PubMed]

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]

Nurmikko, A. V.

T. Atay, J.-H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole−dipole interaction to conductively coupled regime,” Nano Lett.4(9), 1627–1631 (2004).
[CrossRef]

Pendry, J. B.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors, and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

Peter, E.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Pound, R.

E. M. Purcell, H. Torrey, and R. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev.69(1-2), 674 (1946).
[CrossRef]

Purcell, E. M.

E. M. Purcell, H. Torrey, and R. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev.69(1-2), 674 (1946).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors, and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

Sagnes, I.

P. Jouy, Y. Todorov, A. Vasanelli, R. Colombelli, I. Sagnes, and C. Sirtori, “Coupling of a surface plasmon with localized subwavelength microcavity modes,” Appl. Phys. Lett.98(2), 021105 (2011).
[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. Express18(13), 13886–13907 (2010).
[CrossRef] [PubMed]

Y. Todorov, I. Sagnes, I. Abram, and C. Minot, “Purcell Enhancement of Spontaneous Emission from Quantum Cascades inside Mirror-Grating Metal Cavities at THz Frequencies,” Phys. Rev. Lett.99(22), 223603 (2007).
[CrossRef] [PubMed]

Sambles, J. R.

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing Millimeter Waves into Microns,” Phys. Rev. Lett.92(14), 143904 (2004).
[CrossRef] [PubMed]

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]

C. Walther, G. Scalari, M. Beck, and J. Faist, “Purcell effect in the inductor-capacitor laser,” Opt. Lett.36(14), 2623–2625 (2011).
[CrossRef] [PubMed]

Senellart, P.

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007).
[CrossRef]

Sirtori, C.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

P. Jouy, Y. Todorov, A. Vasanelli, R. Colombelli, I. Sagnes, and C. Sirtori, “Coupling of a surface plasmon with localized subwavelength microcavity modes,” Appl. Phys. Lett.98(2), 021105 (2011).
[CrossRef]

P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett.98(23), 231114 (2011).
[CrossRef]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (2010).
[CrossRef] [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. Express18(13), 13886–13907 (2010).
[CrossRef] [PubMed]

Song, J.-H.

T. Atay, J.-H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole−dipole interaction to conductively coupled regime,” Nano Lett.4(9), 1627–1631 (2004).
[CrossRef]

Sorba, L.

S. Zanotto, R. Degl’Innocenti, L. Sorba, A. Tredicucci, and G. Biasiol, “Analysis of line shapes and strong coupling with intersubband transitions in one-dimensional metallodielectric photonic crystal slabs,” Phys. Rev. B85(3), 035307 (2012).
[CrossRef]

P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett.98(23), 231114 (2011).
[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 Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

Strasser, G.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (2010).
[CrossRef] [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. Express18(13), 13886–13907 (2010).
[CrossRef] [PubMed]

Strupiechonski, E.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

Tavallaee, A. A.

P. W. C. Hon, A. A. Tavallaee, Q.-S. Chen, B. S. Williams, and T. Itoh, “Radiation Model for Terahertz Transmission-Line Metamaterial Quantum-Cascade Lasers,” IEEE Trans. THz Sci. Technol.2(3), 323–332 (2012).

Teissier, J.

Todorov, Y.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

P. Jouy, Y. Todorov, A. Vasanelli, R. Colombelli, I. Sagnes, and C. Sirtori, “Coupling of a surface plasmon with localized subwavelength microcavity modes,” Appl. Phys. Lett.98(2), 021105 (2011).
[CrossRef]

P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett.98(23), 231114 (2011).
[CrossRef]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (2010).
[CrossRef] [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. Express18(13), 13886–13907 (2010).
[CrossRef] [PubMed]

Y. Todorov, I. Sagnes, I. Abram, and C. Minot, “Purcell Enhancement of Spontaneous Emission from Quantum Cascades inside Mirror-Grating Metal Cavities at THz Frequencies,” Phys. Rev. Lett.99(22), 223603 (2007).
[CrossRef] [PubMed]

Torrey, H.

E. M. Purcell, H. Torrey, and R. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev.69(1-2), 674 (1946).
[CrossRef]

Tosetto, L.

Tredicucci, A.

S. Zanotto, R. Degl’Innocenti, L. Sorba, A. Tredicucci, and G. Biasiol, “Analysis of line shapes and strong coupling with intersubband transitions in one-dimensional metallodielectric photonic crystal slabs,” Phys. Rev. B85(3), 035307 (2012).
[CrossRef]

Vasanelli, A.

P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett.98(23), 231114 (2011).
[CrossRef]

P. Jouy, Y. Todorov, A. Vasanelli, R. Colombelli, I. Sagnes, and C. Sirtori, “Coupling of a surface plasmon with localized subwavelength microcavity modes,” Appl. Phys. Lett.98(2), 021105 (2011).
[CrossRef]

Walther, C.

Wegener, M.

Williams, B. S.

P. W. C. Hon, A. A. Tavallaee, Q.-S. Chen, B. S. Williams, and T. Itoh, “Radiation Model for Terahertz Transmission-Line Metamaterial Quantum-Cascade Lasers,” IEEE Trans. THz Sci. Technol.2(3), 323–332 (2012).

Xu, G.

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

Zanotto, S.

S. Zanotto, R. Degl’Innocenti, L. Sorba, A. Tredicucci, and G. Biasiol, “Analysis of line shapes and strong coupling with intersubband transitions in one-dimensional metallodielectric photonic crystal slabs,” Phys. Rev. B85(3), 035307 (2012).
[CrossRef]

Appl. Phys. Lett. (3)

E. Strupiechonski, G. Xu, N. Isac, M. Brekenfeld, Y. Todorov, A. M. Andrews, 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]

P. Jouy, Y. Todorov, A. Vasanelli, R. Colombelli, I. Sagnes, and C. Sirtori, “Coupling of a surface plasmon with localized subwavelength microcavity modes,” Appl. Phys. Lett.98(2), 021105 (2011).
[CrossRef]

P. Jouy, A. Vasanelli, Y. Todorov, A. Delteil, G. Biasiol, L. Sorba, and C. Sirtori, “Transition from strong to ultrastrong coupling regime in mid-infrared metal-dielectric-metal cavities,” Appl. Phys. Lett.98(23), 231114 (2011).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors, and Enhanced Non-Linear Phenomena,” IEEE Trans. Microw. Theory Tech.47(11), 2075–2084 (1999).
[CrossRef]

IEEE Trans. THz Sci. Technol. (1)

P. W. C. Hon, A. A. Tavallaee, Q.-S. Chen, B. S. Williams, and T. Itoh, “Radiation Model for Terahertz Transmission-Line Metamaterial Quantum-Cascade Lasers,” IEEE Trans. THz Sci. Technol.2(3), 323–332 (2012).

Nano Lett. (1)

T. Atay, J.-H. Song, and A. V. Nurmikko, “Strongly interacting plasmon nanoparticle pairs: from dipole−dipole interaction to conductively coupled regime,” Nano Lett.4(9), 1627–1631 (2004).
[CrossRef]

Nat. Photonics (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1(1), 41–48 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. (1)

E. M. Purcell, H. Torrey, and R. Pound, “Resonance Absorption by Nuclear Magnetic Moments in a Solid,” Phys. Rev.69(1-2), 674 (1946).
[CrossRef]

Phys. Rev. A (1)

C. Ciuti and I. Carusotto, “Input-output theory of cavities in the ultrastrong coupling regime: The case of time-independent cavity parameters,” Phys. Rev. A74(3), 033811 (2006).
[CrossRef]

Phys. Rev. B (3)

S. De Liberato and C. Ciuti, “Quantum theory of electron tunneling into intersubband cavity polariton states,” Phys. Rev. B79(7), 075317 (2009).
[CrossRef]

S. Zanotto, R. Degl’Innocenti, L. Sorba, A. Tredicucci, and G. Biasiol, “Analysis of line shapes and strong coupling with intersubband transitions in one-dimensional metallodielectric photonic crystal slabs,” Phys. Rev. B85(3), 035307 (2012).
[CrossRef]

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B72(11), 115303 (2005).
[CrossRef]

Phys. Rev. Lett. (6)

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong Light-Matter Coupling Regime with Polariton Dots,” Phys. Rev. Lett.105(19), 196402 (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]

E. Peter, P. Senellart, D. Martrou, A. Lemaître, J. Hours, J. M. Gérard, and J. Bloch, “Exciton-Photon Strong-Coupling Regime for a Single Quantum Dot Embedded in a Microcavity,” Phys. Rev. Lett.95(6), 067401 (2005).
[CrossRef] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96(9), 097401 (2006).
[CrossRef] [PubMed]

A. P. Hibbins, J. R. Sambles, C. R. Lawrence, and J. R. Brown, “Squeezing Millimeter Waves into Microns,” Phys. Rev. Lett.92(14), 143904 (2004).
[CrossRef] [PubMed]

Y. Todorov, I. Sagnes, I. Abram, and C. Minot, “Purcell Enhancement of Spontaneous Emission from Quantum Cascades inside Mirror-Grating Metal Cavities at THz Frequencies,” Phys. Rev. Lett.99(22), 223603 (2007).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

P. Biagioni, J.-S. Huang, and B. Hecht, “Nanoantennas for visible and infrared radiation,” Rep. Prog. Phys.75(2), 024402 (2012).
[CrossRef] [PubMed]

Science (1)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking Surface Plasmons with Structured Surfaces,” Science305(5685), 847–848 (2004).
[CrossRef] [PubMed]

Other (3)

M. J. Adams, An Introduction to Optical Waveguides, (John Wiley & Sons, Chichester, 1981).

U. Rössler, Solid State Theory, (Springer, 2009).

M. Helm, in Intersubband Transitions in Quantum Wells: Physics and Device Applications I, H. C. Liu, F. Capasso, eds. (Academic Press, 2000).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematics of a wire microcavity with the relevant geometrical dimensions. The structure consists of dielectric (typically GaAs) layer, bonded on a gold surface. A thin strip of gold is deposited on the top of the dielectric to complete the microcavity. (b) Scanning Electron Microscope (SEM) image of the top surface of an array of microcavities, with typical dimensions s = 12 µm, w = 1 µm and L = 1 µm. The relevant dimensions of the array are also indicated. (c), (d) Finite element simulations of the vertical electric field, for a microcavity with a thickness L = 1 µm. (e), (f), Vertical electric field for the fundamental resonance of a microcavity with a thickness L = 300 nm. In (c) and (e) we have indicated the corresponding computed eigenfrequencies for each structure.

Fig. 2
Fig. 2

Reflectivity spectra for cavities with s = 12 µm and various strip widths w, for core thicknesses L = 1 µm and L = 300 nm. a) w = 1 µm b) w = 100 nm. The insets in (a) and (b) show SEM pictures of the microcavity arrays employed in the experiments.

Fig. 3
Fig. 3

(a) Measured resonant frequencies of micro-resonators with s = 12 µm and w = 1 µm, as a function of the lateral wire-wire gap dy (logarithmic scale). The dashed lines are an exponential fit according to law ν= ν ( ν ν 0 )exp( d y / d 0 ) . Circles: L = 1 µm, triangles: L = 300 nm. (b) The corresponding effective index as deduced from Eq. (1). The dashed line corresponds to the bulk GaAs index, n = 3.55. (c) Vertical electric field Ez for the L = 1 µm resonator (identical to Fig. 1(d)) with a color map saturated below the maximum field amplitude, in order to render visible the spreading fields in the y-direction. (d) Logarithmic plots of Ez (normalized to its maximal value E0z) as a function of y along the two cuts A and B indicated in Fig. 3(c).

Fig. 4
Fig. 4

(a) Typical polariton resonances obtained in low temperature reflectivity measurements for nearly resonant square (dotted curve) and wire cavity (solid curve) arrays. (b) Polariton frequencies measured for both type of structures as a function of the microcavity resonance. (c) Polariton splitting as a function of the cavity frequency. The minimal polariton splitting corresponds to the vacuum Rabi splitting 2ΩR.

Fig. 5
Fig. 5

Squeezing factor (Eq. (4) and Eq. (5)) as a function of the wavelength. The continuous lines are theoretical projections for perfect wire resonators, the dots report the cavities studied in this work. The rightmost column indicates the geometrical parameters of the structures.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

v= c 2 n eff s
Ω R 2 = Ω 0 2 Ψ 2         with          Ω 0 2 = e 2 f 12 N 2D N QW 4m*ε ε 0 L
Ψ 2 = V E z 2 d 3 x V ( E x 2 + E y 2 + E z 2 ) d 3 x
R= (λ/2n) 3 V eff
R= n eff ψ 2 4wL n 3 λ 2

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