Abstract

We study the normal-mode splitting when an oscillator is placed in a two-dimensional photonic crystal microcavity embedded with an impedance-matched or an impedance-mismatched zero-index medium (ZIM). Because of the (nearly) uniform localized fields in the ZIM, the normal-mode splitting remains (almost) invariant no matter where the oscillator is. When a split ring resonator is coupled to a transmission-line- based effective ZIM at various locations, nearly position-independent mode splitting is observed.

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2011 (2)

H. T. Jiang, Z. L. Wang, Y. Sun, Y. H. Li, Y. W. Zhang, H. Q. Li, and H. Chen, “Enhancement of (nearly) homogeneous fields in a (effective) zero-index cavity,” J. Appl. Phys. 109(7), 073113 (2011).
[CrossRef]

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

2010 (4)

P. Holmström, L. Thylén, and A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107(6), 064307 (2010).
[CrossRef]

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[CrossRef] [PubMed]

J. M. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[CrossRef]

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010).
[CrossRef] [PubMed]

2008 (5)

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

K. Halterman and S. M. Feng, “Resonant transmission of electromagnetic fields through subwavelength zero-ε,” Phys. Rev. A 78(2), 021805 (2008).
[CrossRef]

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic crystal nanocavity,” Nat. Photonics 2(11), 688–692 (2008).
[CrossRef]

L. W. Zhang, Y. W. Zhang, Y. P. Yang, H. Q. Li, H. Chen, and S. Y. Zhu, “Experimental observation of Rabi splitting in effective near-zero-index media in the microwave regime,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 035601 (2008).
[CrossRef] [PubMed]

D. Y. Lu, H. Liu, T. Li, S. M. Wang, F. M. Wang, S. N. Zhu, and X. Zhang, “Creation of a magnetic plasmon polariton through strong coupling between an artificial magnetic atom and the defect state in a defective multilayer microcavity,” Phys. Rev. B 77(21), 214302 (2008).
[CrossRef]

2007 (4)

D. H. Werner, D. H. Kwon, I. C. Khoo, A. V. Kildishev, and V. M. Shalaev, “Liquid crystal clad near-infrared metamaterials with tunable negative-zero-positive refractive indices,” Opt. Express 15(6), 3342–3347 (2007).
[CrossRef] [PubMed]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (1)

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, “Investigation of magnetic resonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).
[CrossRef]

2004 (6)

M. Tokushima, H. Yamada, and Y. Arakawa, “1.5-μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab,” Appl. Phys. Lett. 84(21), 4298 (2004).
[CrossRef]

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[CrossRef] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69(6), 062320 (2004).
[CrossRef]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

2001 (1)

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73(3), 565–582 (2001).
[CrossRef]

1999 (1)

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71(5), 1591–1639 (1999).
[CrossRef]

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Alù, A.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Aoki, K.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic crystal nanocavity,” Nat. Photonics 2(11), 688–692 (2008).
[CrossRef]

Arakawa, Y.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic crystal nanocavity,” Nat. Photonics 2(11), 688–692 (2008).
[CrossRef]

M. Tokushima, H. Yamada, and Y. Arakawa, “1.5-μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab,” Appl. Phys. Lett. 84(21), 4298 (2004).
[CrossRef]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Aydin, K.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, “Investigation of magnetic resonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).
[CrossRef]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Blais, A.

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69(6), 062320 (2004).
[CrossRef]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

Bratkovsky, A.

P. Holmström, L. Thylén, and A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107(6), 064307 (2010).
[CrossRef]

Brune, M.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73(3), 565–582 (2001).
[CrossRef]

Bulu, I.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, “Investigation of magnetic resonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).
[CrossRef]

Chan, C. T.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Chen, H.

H. T. Jiang, Z. L. Wang, Y. Sun, Y. H. Li, Y. W. Zhang, H. Q. Li, and H. Chen, “Enhancement of (nearly) homogeneous fields in a (effective) zero-index cavity,” J. Appl. Phys. 109(7), 073113 (2011).
[CrossRef]

L. W. Zhang, Y. W. Zhang, Y. P. Yang, H. Q. Li, H. Chen, and S. Y. Zhu, “Experimental observation of Rabi splitting in effective near-zero-index media in the microwave regime,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 035601 (2008).
[CrossRef] [PubMed]

Chen, L.

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010).
[CrossRef] [PubMed]

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Diaz, A.

Edwards, B.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Engheta, N.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Feng, S. M.

K. Halterman and S. M. Feng, “Resonant transmission of electromagnetic fields through subwavelength zero-ε,” Phys. Rev. A 78(2), 021805 (2008).
[CrossRef]

Forchel, A.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Frunzio, L.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

Garcia, P. D.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[CrossRef] [PubMed]

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Gibbs, H. M.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71(5), 1591–1639 (1999).
[CrossRef]

Girvin, S. M.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69(6), 062320 (2004).
[CrossRef]

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Guimard, D.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic crystal nanocavity,” Nat. Photonics 2(11), 688–692 (2008).
[CrossRef]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Guven, K.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, “Investigation of magnetic resonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).
[CrossRef]

Halterman, K.

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010).
[CrossRef] [PubMed]

K. Halterman and S. M. Feng, “Resonant transmission of electromagnetic fields through subwavelength zero-ε,” Phys. Rev. A 78(2), 021805 (2008).
[CrossRef]

Hang, Z. H.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Hao, J. M.

J. M. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[CrossRef]

Haroche, S.

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73(3), 565–582 (2001).
[CrossRef]

Hendrickson, J.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Hofmann, C.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
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Holmström, P.

P. Holmström, L. Thylén, and A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107(6), 064307 (2010).
[CrossRef]

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Hu, E. L.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Huang, R. S.

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69(6), 062320 (2004).
[CrossRef]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

Huang, X. Q.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Imamoglu, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Iwamoto, S.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic crystal nanocavity,” Nat. Photonics 2(11), 688–692 (2008).
[CrossRef]

Jahnke, F.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71(5), 1591–1639 (1999).
[CrossRef]

Jiang, H. T.

H. T. Jiang, Z. L. Wang, Y. Sun, Y. H. Li, Y. W. Zhang, H. Q. Li, and H. Chen, “Enhancement of (nearly) homogeneous fields in a (effective) zero-index cavity,” J. Appl. Phys. 109(7), 073113 (2011).
[CrossRef]

Kafesaki, M.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, “Investigation of magnetic resonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).
[CrossRef]

Keldysh, L. V.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Khitrova, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71(5), 1591–1639 (1999).
[CrossRef]

Khoo, I. C.

Kildishev, A. V.

Kira, M.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71(5), 1591–1639 (1999).
[CrossRef]

Koch, S. W.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71(5), 1591–1639 (1999).
[CrossRef]

Kuhn, S.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Kulakovskii, V. D.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Kumar, S.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

Kwon, D. H.

Lai, Y.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
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Lakhtakia, A.

A. Lakhtakia, “Scattering by a nihility sphere,” Microw. Opt. Technol. Lett. 48(5), 895–896 (2006).
[CrossRef]

Li, H. Q.

H. T. Jiang, Z. L. Wang, Y. Sun, Y. H. Li, Y. W. Zhang, H. Q. Li, and H. Chen, “Enhancement of (nearly) homogeneous fields in a (effective) zero-index cavity,” J. Appl. Phys. 109(7), 073113 (2011).
[CrossRef]

L. W. Zhang, Y. W. Zhang, Y. P. Yang, H. Q. Li, H. Chen, and S. Y. Zhu, “Experimental observation of Rabi splitting in effective near-zero-index media in the microwave regime,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 035601 (2008).
[CrossRef] [PubMed]

Li, T.

D. Y. Lu, H. Liu, T. Li, S. M. Wang, F. M. Wang, S. N. Zhu, and X. Zhang, “Creation of a magnetic plasmon polariton through strong coupling between an artificial magnetic atom and the defect state in a defective multilayer microcavity,” Phys. Rev. B 77(21), 214302 (2008).
[CrossRef]

Li, Y. H.

H. T. Jiang, Z. L. Wang, Y. Sun, Y. H. Li, Y. W. Zhang, H. Q. Li, and H. Chen, “Enhancement of (nearly) homogeneous fields in a (effective) zero-index cavity,” J. Appl. Phys. 109(7), 073113 (2011).
[CrossRef]

Liang, X.

Liu, H.

D. Y. Lu, H. Liu, T. Li, S. M. Wang, F. M. Wang, S. N. Zhu, and X. Zhang, “Creation of a magnetic plasmon polariton through strong coupling between an artificial magnetic atom and the defect state in a defective multilayer microcavity,” Phys. Rev. B 77(21), 214302 (2008).
[CrossRef]

Lodahl, P.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[CrossRef] [PubMed]

Löffler, A.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Lu, D. Y.

D. Y. Lu, H. Liu, T. Li, S. M. Wang, F. M. Wang, S. N. Zhu, and X. Zhang, “Creation of a magnetic plasmon polariton through strong coupling between an artificial magnetic atom and the defect state in a defective multilayer microcavity,” Phys. Rev. B 77(21), 214302 (2008).
[CrossRef]

Majer, J.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

Narimanov, E. E.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
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Nguyen, V. C.

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105(23), 233908 (2010).
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Nishioka, M.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic crystal nanocavity,” Nat. Photonics 2(11), 688–692 (2008).
[CrossRef]

Nomura, M.

K. Aoki, D. Guimard, M. Nishioka, M. Nomura, S. Iwamoto, and Y. Arakawa, “Coupling of quantum-dot light emission with a three-dimensional photonic crystal nanocavity,” Nat. Photonics 2(11), 688–692 (2008).
[CrossRef]

Ozbay, E.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, “Investigation of magnetic resonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).
[CrossRef]

Podolskiy, V. A.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Qiu, M.

J. M. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[CrossRef]

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J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73(3), 565–582 (2001).
[CrossRef]

Reinecke, T. L.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Reithmaier, J. P.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Reitzenstein, S.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Rupper, G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Sapienza, L.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[CrossRef] [PubMed]

Scherer, A.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Schoelkopf, R. J.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69(6), 062320 (2004).
[CrossRef]

Schuster, D. I.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

Sek, G.

J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, “Strong coupling in a single quantum dot-semiconductor microcavity system,” Nature 432(7014), 197–200 (2004).
[CrossRef] [PubMed]

Shalaev, V. M.

Shchekin, O. B.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Silveirinha, M.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[CrossRef]

Sivco, D. L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Smolka, S.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[CrossRef] [PubMed]

Soukoulis, C. M.

K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, “Investigation of magnetic resonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).
[CrossRef]

Stobbe, S.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[CrossRef] [PubMed]

Sun, Y.

H. T. Jiang, Z. L. Wang, Y. Sun, Y. H. Li, Y. W. Zhang, H. Q. Li, and H. Chen, “Enhancement of (nearly) homogeneous fields in a (effective) zero-index cavity,” J. Appl. Phys. 109(7), 073113 (2011).
[CrossRef]

Thylén, L.

P. Holmström, L. Thylén, and A. Bratkovsky, “Dielectric function of quantum dots in the strong confinement regime,” J. Appl. Phys. 107(6), 064307 (2010).
[CrossRef]

Thyrrestrup, H.

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[CrossRef] [PubMed]

Tokushima, M.

M. Tokushima, H. Yamada, and Y. Arakawa, “1.5-μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab,” Appl. Phys. Lett. 84(21), 4298 (2004).
[CrossRef]

Wallraff, A.

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69(6), 062320 (2004).
[CrossRef]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431(7005), 162–167 (2004).
[CrossRef] [PubMed]

Wang, F. M.

D. Y. Lu, H. Liu, T. Li, S. M. Wang, F. M. Wang, S. N. Zhu, and X. Zhang, “Creation of a magnetic plasmon polariton through strong coupling between an artificial magnetic atom and the defect state in a defective multilayer microcavity,” Phys. Rev. B 77(21), 214302 (2008).
[CrossRef]

Wang, S. M.

D. Y. Lu, H. Liu, T. Li, S. M. Wang, F. M. Wang, S. N. Zhu, and X. Zhang, “Creation of a magnetic plasmon polariton through strong coupling between an artificial magnetic atom and the defect state in a defective multilayer microcavity,” Phys. Rev. B 77(21), 214302 (2008).
[CrossRef]

Wang, Z. L.

H. T. Jiang, Z. L. Wang, Y. Sun, Y. H. Li, Y. W. Zhang, H. Q. Li, and H. Chen, “Enhancement of (nearly) homogeneous fields in a (effective) zero-index cavity,” J. Appl. Phys. 109(7), 073113 (2011).
[CrossRef]

Wasserman, D.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[CrossRef] [PubMed]

Weiner, B.

Werner, D. H.

Winger, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Yamada, H.

M. Tokushima, H. Yamada, and Y. Arakawa, “1.5-μm-wavelength light guiding in waveguides in square-lattice-of-rod photonic crystal slab,” Appl. Phys. Lett. 84(21), 4298 (2004).
[CrossRef]

Yan, W.

J. M. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[CrossRef]

Yang, Y. P.

L. W. Zhang, Y. W. Zhang, Y. P. Yang, H. Q. Li, H. Chen, and S. Y. Zhu, “Experimental observation of Rabi splitting in effective near-zero-index media in the microwave regime,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 035601 (2008).
[CrossRef] [PubMed]

Yoshie, T.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[CrossRef] [PubMed]

Young, M. E.

B. Edwards, A. Alù, M. E. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. 100(3), 033903 (2008).
[CrossRef] [PubMed]

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L. W. Zhang, Y. W. Zhang, Y. P. Yang, H. Q. Li, H. Chen, and S. Y. Zhu, “Experimental observation of Rabi splitting in effective near-zero-index media in the microwave regime,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 035601 (2008).
[CrossRef] [PubMed]

Zhang, X.

D. Y. Lu, H. Liu, T. Li, S. M. Wang, F. M. Wang, S. N. Zhu, and X. Zhang, “Creation of a magnetic plasmon polariton through strong coupling between an artificial magnetic atom and the defect state in a defective multilayer microcavity,” Phys. Rev. B 77(21), 214302 (2008).
[CrossRef]

Zhang, Y. W.

H. T. Jiang, Z. L. Wang, Y. Sun, Y. H. Li, Y. W. Zhang, H. Q. Li, and H. Chen, “Enhancement of (nearly) homogeneous fields in a (effective) zero-index cavity,” J. Appl. Phys. 109(7), 073113 (2011).
[CrossRef]

L. W. Zhang, Y. W. Zhang, Y. P. Yang, H. Q. Li, H. Chen, and S. Y. Zhu, “Experimental observation of Rabi splitting in effective near-zero-index media in the microwave regime,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 035601 (2008).
[CrossRef] [PubMed]

Zheng, H. H.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[CrossRef] [PubMed]

Zhu, S. N.

D. Y. Lu, H. Liu, T. Li, S. M. Wang, F. M. Wang, S. N. Zhu, and X. Zhang, “Creation of a magnetic plasmon polariton through strong coupling between an artificial magnetic atom and the defect state in a defective multilayer microcavity,” Phys. Rev. B 77(21), 214302 (2008).
[CrossRef]

Zhu, S. Y.

L. W. Zhang, Y. W. Zhang, Y. P. Yang, H. Q. Li, H. Chen, and S. Y. Zhu, “Experimental observation of Rabi splitting in effective near-zero-index media in the microwave regime,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(3), 035601 (2008).
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R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
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Appl. Phys. Lett. (2)

J. M. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[CrossRef]

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Nat. Photonics (1)

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Figures (8)

Fig. 1
Fig. 1

Schematic of a 2D square-lattice PhC cavity in x-y plane. The radius and refractive index of the silicon rods in background polymer are 114.6 nm and 3.48, respectively. The refractive index of polymer is 1.45 and the lattice constant is 430 nm. The blue dotted circle with radius of 220 nm denotes a ZIM region and the red dotted ellipse denotes a zone for calculating intensities.

Fig. 2
Fig. 2

2D electric field pattern (a) and magnetic field pattern (b) at a cavity mode of 188.8 THz. The radius of the circle indicated by the dotted line is 220 nm.

Fig. 3
Fig. 3

2D electric field pattern (a) and magnetic field pattern (b) at a cavity mode of 175.4 THz. The circular zone denotes a ZIM within which the fields are largest and uniform.

Fig. 4
Fig. 4

2D and 3D electric field patterns at a cavity mode of 175.4 THz. The circular zone denotes an ENZ medium. The white, the black and the gray dots indicate an oscillator located at three different places.

Fig. 5
Fig. 5

Normal-mode splitting when an oscillator is put at three different places as indicated by the white, the black and the gray dots in the ENZ medium with varying degrees of loss, respectively.

Fig. 6
Fig. 6

Electric field patterns in x-z plane at y = 630 nm (a) and in y-z plane at x = 630 nm (b), respectively. The electric dipole source at frequency of 175.4 THz is put at the center of a cube filled with ENZ medium. Each side of the cube is 1300 nm.

Fig. 7
Fig. 7

Photograph of an effective ZIM coupled by a SRR at four different places, respectively. Inset of (a) is the layout of the SRR whose parameters are a = t = 0.4 mm, w = 5 mm, b = 0.3 mm, c = 0.27mm, d = 3 mm, L = 14 mm and h = 0.8 mm. The capacitance of the capacitor in the SRR is 0.77 pF.

Fig. 8
Fig. 8

Nearly position-independent mode splitting when a SRR is coupled to an effective ZIM at various locations.

Equations (4)

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χ res = G (ω ω 0 )+i γ 1 ,
q ¨ 1 (t)+ γ 1 q ˙ 1 (t)+ ω 0 2 q 1 (t)+κ( q 1 q 2 )=E( x 0 , y 0 ) e iωt ,
q ¨ 2 (t)+ γ 2 q ˙ 2 (t)+ ( ω 0 +δ) 2 q 2 (t)κ( q 1 q 2 )= E 0 e iωt ,
ε=μ=1 ω p 2 ω(ω+iΓ) ,

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