Position-independent normal-mode splitting in cavities filled with zero-index metamaterials

doi:10.1364/OE.20.006348

Position-independent normal-mode splitting in cavities filled with zero-index metamaterials

Hai-tao Jiang, Xiao-hu Xu, Zi-li Wang, Yun-hui Li, Yasha Yi, and Hong Chen »View Author Affiliations

Optics Express, Vol. 20, Issue 6, pp. 6348-6356 (2012)
http://dx.doi.org/10.1364/OE.20.006348

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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.

OCIS Codes
(270.5580) Quantum optics : Quantum electrodynamics
(160.3918) Materials : Metamaterials
(160.5298) Materials : Photonic crystals

ToC Category:
Metamaterials

History
Original Manuscript: December 1, 2011
Revised Manuscript: January 25, 2012
Manuscript Accepted: March 1, 2012
Published: March 5, 2012

Citation
Hai-tao Jiang, Xiao-hu Xu, Zi-li Wang, Yun-hui Li, Yasha Yi, and Hong Chen, "Position-independent normal-mode splitting in cavities filled with zero-index metamaterials," Opt. Express 20, 6348-6356 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-6-6348

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References

P. Berman, ed., Cavity Quantum Electrodynamics (Academic, 1994).
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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,” Nature431(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,” Nature432(7014), 197–200 (2004). [CrossRef] [PubMed]
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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,” Nature445(7130), 896–899 (2007). [CrossRef] [PubMed]
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. Photonics2(11), 688–692 (2008). [CrossRef]
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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). [CrossRef] [PubMed]
A. Lakhtakia, “Scattering by a nihility sphere,” Microw. Opt. Technol. Lett.48(5), 895–896 (2006). [CrossRef]
A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007). [CrossRef]
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. A78(2), 021805 (2008). [CrossRef]
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]
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]
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]
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]
Computer Simulation Technology (CST), User's Manual 5, in CST-Microwave Studio, 2003.
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]
I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett.31(17), 2592–2594 (2006). [CrossRef] [PubMed]
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. Express15(6), 3342–3347 (2007). [CrossRef] [PubMed]
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]
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]
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. B77(21), 214302 (2008). [CrossRef]

Alekseyev, L.
Alù, A.
Aoki, K.
Arakawa, Y.
Atatüre, M.
Aydin, K.
Badolato, A.
Blais, A.
Bratkovsky, A.
Brune, M.
Bulu, I.
Chan, C. T.
Chen, H.
Chen, L.
Deppe, D. G.
Diaz, A.
Edwards, B.
Ell, C.
Engheta, N.
Fält, S.
Feng, S. M.
Forchel, A.
Franz, K. J.
Frunzio, L.
Garcia, P. D.
Gerace, D.
Gibbs, H. M.
Girvin, S. M.
Gmachl, C.
Guimard, D.
Gulde, S.
Guven, K.
Halterman, K.
Hang, Z. H.
Hao, J. M.
Haroche, S.
Hendrickson, J.
Hennessy, K.
Hoffman, A. J.
Hofmann, C.
Holmström, P.
Howard, S. S.
Hu, E. L.
Huang, R. S.
Huang, X. Q.
Imamoglu, A.
Iwamoto, S.
Jahnke, F.
Jiang, H. T.
Kafesaki, M.
Keldysh, L. V.
Khitrova, G.
Khoo, I. C.
Kildishev, A. V.
Kira, M.
Koch, S. W.
Kuhn, S.
Kulakovskii, V. D.
Kumar, S.
Kwon, D. H.
Lai, Y.
Lakhtakia, A.
Li, H. Q.
Li, T.
Li, Y. H.
Liang, X.
Liu, H.
Lodahl, P.
Löffler, A.
Lu, D. Y.
Majer, J.
Narimanov, E. E.
Nguyen, V. C.
Nishioka, M.
Nomura, M.
Ozbay, E.
Podolskiy, V. A.
Qiu, M.
Raimond, J. M.
Reinecke, T. L.
Reithmaier, J. P.
Reitzenstein, S.
Rupper, G.
Salandrino, A.
Sapienza, L.
Scherer, A.
Schoelkopf, R. J.
Schuster, D. I.
Sek, G.
Shalaev, V. M.
Shchekin, O. B.
Silveirinha, M.
Silveirinha, M. G.
Sivco, D. L.
Smolka, S.
Soukoulis, C. M.
Stobbe, S.
Sun, Y.
Thylén, L.
Thyrrestrup, H.
Tokushima, M.
Wallraff, A.
Wang, F. M.
Wang, S. M.
Wang, Z. L.
Wasserman, D.
Weiner, B.
Werner, D. H.
Winger, M.
Yamada, H.
Yan, W.
Yang, Y. P.
Yoshie, T.
Young, M. E.
Zhang, L. W.
Zhang, X.
Zhang, Y. W.
Zheng, H. H.
Zhu, S. N.
Zhu, S. Y.
Ziolkowski, R. W.

Appl. Phys. Lett.

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]
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]

J. Appl. Phys.

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]
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]

Microw. Opt. Technol. Lett.

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

Nat. Mater.

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]
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]

Nat. Photonics

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. Photonics2(11), 688–692 (2008). [CrossRef]

Nature

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,” Nature431(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,” Nature432(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,” Nature432(7014), 200–203 (2004). [CrossRef] [PubMed]
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,” Nature445(7130), 896–899 (2007). [CrossRef] [PubMed]

New J. Phys.

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]

Opt. Express

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. Express15(6), 3342–3347 (2007). [CrossRef] [PubMed]

Opt. Lett.

I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett.31(17), 2592–2594 (2006). [CrossRef] [PubMed]

Phys. Rev. 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. A69(6), 062320 (2004). [CrossRef]
K. Halterman and S. M. Feng, “Resonant transmission of electromagnetic fields through subwavelength zero-ε,” Phys. Rev. A78(2), 021805 (2008). [CrossRef]

Phys. Rev. B

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007). [CrossRef]
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. B77(21), 214302 (2008). [CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

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]
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]

Phys. Rev. Lett.

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]
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]

Rev. Mod. Phys.

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]
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]

Science

L. Sapienza, H. Thyrrestrup, S. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science327(5971), 1352–1355 (2010). [CrossRef] [PubMed]

Other

P. Berman, ed., Cavity Quantum Electrodynamics (Academic, 1994).
Computer Simulation Technology (CST), User's Manual 5, in CST-Microwave Studio, 2003.

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