Abstract

We study quantum optical properties of a dipole emitter coupled to a rectangular nanoscale waveguide with dielectric core and silver cladding. We investigate enhanced spontaneous emission and the photonic Lamb shift for emitters whose resonant frequencies are near the waveguide frequency cutoff where the waveguide behaves as an ɛ-near-zero metamaterial. Via a dyadic Green’s function-based field quantization scheme, we calculate the photonic Lamb shift as well as the spontaneous emission enhancement and spectrum. Using realistic parameters for typical quantum emitters, we suggest experimentally realizable schemes to observe relatively large photonic Lamb shifts in waveguides.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2013

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett.110(1), 013902 (2013).
[CrossRef] [PubMed]

T. Hümmer, F. J. Garcia-Vidal, L. Martin-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B87(11), 115419 (2013).
[CrossRef]

R. Fleury and A. Alu, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B87, 201101(R) (2013).

2012

K. J. Russell, T. L. Liu, S. Y. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics6(7), 459–462 (2012).
[CrossRef]

2011

Y. M. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev.40(5), 2494–2507 (2011).
[CrossRef] [PubMed]

M. L. Andersen, S. Stobbe, A. S. Sorensen, and P. Lodahl, “Strongly modified plasmon-matter interaction with mesoscopic quantum emitters,” Nat. Phys.7(3), 215–218 (2011).
[CrossRef]

2010

A. Alu and N. Engheta, “Coaxial-to-waveguide matching with epsilon-near-zero ultranarrow channels and bends,” IEEE Trans. Antennas Propag.58(2), 328–339 (2010).
[CrossRef]

Q. Liu, H. W. Song, W. Wang, X. Bai, Y. Wang, B. A. Dong, L. Xu, and W. Han, “Observation of Lamb shift and modified spontaneous emission dynamics in the YBO3:Eu3+ inverse opal,” Opt. Lett.35(17), 2898–2900 (2010).
[CrossRef] [PubMed]

M. A. Swillam and A. S. Helmy, “Analysis and applications of 3D rectangular metallic waveguides,” Opt. Express18(19), 19831–19843 (2010).
[CrossRef] [PubMed]

Y. C. Jun, R. Pala, and M. L. Brongersma, “Strong modification of quantum dot spontaneous emission via gap plasmon coupling in metal nanoslits,” J. Phys. Chem. C114(16), 7269–7273 (2010).
[CrossRef]

2009

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B80(11), 115419 (2009).
[CrossRef]

A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett.103(4), 043902 (2009).
[CrossRef] [PubMed]

P. J. Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B80(19), 195106 (2009).
[CrossRef]

2008

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 and N. Engheta, “Dielectric sensing in epsilon-near-zero narrow waveguide channels,” Phys. Rev. B78(4), 045102 (2008).
[CrossRef]

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78(15), 153111 (2008).
[CrossRef]

T. T. Minh, K. Tanaka, and M. Tanaka, “Complex propagation constants of surface plasmon polariton rectangular waveguide by method of lines,” Opt. Express16(13), 9378–9390 (2008).
[CrossRef] [PubMed]

2007

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using epsilon near-zero metamaterials,” Phys. Rev. B76(24), 245109 (2007).
[CrossRef]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature450(7168), 397–401 (2007).
[CrossRef] [PubMed]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

2006

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys.2(2), 81–90 (2006).
[CrossRef]

2004

X. H. Wang, Y. S. Kivshar, and B. Y. Gu, “Giant lamb shift in photonic crystals,” Phys. Rev. Lett.93(7), 073901 (2004).
[CrossRef] [PubMed]

2003

X. H. Wang, B. Y. Gu, R. Z. Wang, and H. Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

2002

N. Vats, S. John, and K. Busch, “Theory of fluorescence in photonic crystals,” Phys. Rev. A65(4), 043808 (2002).
[CrossRef]

F. J. García de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B65(11), 115418 (2002).
[CrossRef]

Z. Ficek and R. Tanas, “Entangled states and collective nonclassical effects in two-atom systems,” Phys. Rep.372(5), 369–443 (2002).
[CrossRef]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1998

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett.80(23), 5180–5183 (1998).
[CrossRef]

H. T. Dung, L. Knoll, and D. G. Welsch, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A57(5), 3931–3942 (1998).
[CrossRef]

1997

T. Quang, M. Woldeyohannes, S. John, and G. S. Agarwal, “Coherent control of spontaneous emission near a photonic band edge: A single-atom optical memory device,” Phys. Rev. Lett.79(26), 5238–5241 (1997).
[CrossRef]

1985

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface. II,” Phys. Rev. A32(4), 2030–2043 (1985).
[CrossRef] [PubMed]

1954

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev.93(1), 99–110 (1954).
[CrossRef]

1947

W. E. Lamb and R. C. Retherford, “Fine structure of the hydrogen atom by a microwave method,” Phys. Rev.72(3), 241–243 (1947).
[CrossRef]

H. A. Bethe, “The electromagnetic shift of energy levels,” Phys. Rev.72(4), 339–341 (1947).
[CrossRef]

1946

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.69, 681 (1946).

Agarwal, G. S.

T. Quang, M. Woldeyohannes, S. John, and G. S. Agarwal, “Coherent control of spontaneous emission near a photonic band edge: A single-atom optical memory device,” Phys. Rev. Lett.79(26), 5238–5241 (1997).
[CrossRef]

Akimov, A. V.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

Alu, A.

R. Fleury and A. Alu, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B87, 201101(R) (2013).

A. Alu and N. Engheta, “Coaxial-to-waveguide matching with epsilon-near-zero ultranarrow channels and bends,” IEEE Trans. Antennas Propag.58(2), 328–339 (2010).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett.103(4), 043902 (2009).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Dielectric sensing in epsilon-near-zero narrow waveguide channels,” Phys. Rev. B78(4), 045102 (2008).
[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]

Andersen, M. L.

M. L. Andersen, S. Stobbe, A. S. Sorensen, and P. Lodahl, “Strongly modified plasmon-matter interaction with mesoscopic quantum emitters,” Nat. Phys.7(3), 215–218 (2011).
[CrossRef]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

Bai, X.

Bethe, H. A.

H. A. Bethe, “The electromagnetic shift of energy levels,” Phys. Rev.72(4), 339–341 (1947).
[CrossRef]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Bouhelier, A.

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B80(11), 115419 (2009).
[CrossRef]

Brongersma, M. L.

Y. C. Jun, R. Pala, and M. L. Brongersma, “Strong modification of quantum dot spontaneous emission via gap plasmon coupling in metal nanoslits,” J. Phys. Chem. C114(16), 7269–7273 (2010).
[CrossRef]

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78(15), 153111 (2008).
[CrossRef]

Busch, K.

N. Vats, S. John, and K. Busch, “Theory of fluorescence in photonic crystals,” Phys. Rev. A65(4), 043808 (2002).
[CrossRef]

Caglayan, H.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett.110(1), 013902 (2013).
[CrossRef] [PubMed]

Chang, D. E.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

Coenen, T.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett.110(1), 013902 (2013).
[CrossRef] [PubMed]

Colas des Francs, G.

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B80(11), 115419 (2009).
[CrossRef]

Cui, S. Y.

K. J. Russell, T. L. Liu, S. Y. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics6(7), 459–462 (2012).
[CrossRef]

Dereux, A.

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B80(11), 115419 (2009).
[CrossRef]

Dicke, R. H.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev.93(1), 99–110 (1954).
[CrossRef]

Dignam, M. M.

P. J. Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B80(19), 195106 (2009).
[CrossRef]

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

Dong, B. A.

Dung, H. T.

H. T. Dung, L. Knoll, and D. G. Welsch, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A57(5), 3931–3942 (1998).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

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]

Engheta, N.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett.110(1), 013902 (2013).
[CrossRef] [PubMed]

A. Alu and N. Engheta, “Coaxial-to-waveguide matching with epsilon-near-zero ultranarrow channels and bends,” IEEE Trans. Antennas Propag.58(2), 328–339 (2010).
[CrossRef]

A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett.103(4), 043902 (2009).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Dielectric sensing in epsilon-near-zero narrow waveguide channels,” Phys. Rev. B78(4), 045102 (2008).
[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]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using epsilon near-zero metamaterials,” Phys. Rev. B76(24), 245109 (2007).
[CrossRef]

Ficek, Z.

Z. Ficek and R. Tanas, “Entangled states and collective nonclassical effects in two-atom systems,” Phys. Rep.372(5), 369–443 (2002).
[CrossRef]

Fleury, R.

R. Fleury and A. Alu, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B87, 201101(R) (2013).

García de Abajo, F. J.

F. J. García de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B65(11), 115418 (2002).
[CrossRef]

F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett.80(23), 5180–5183 (1998).
[CrossRef]

Garcia-Vidal, F. J.

T. Hümmer, F. J. Garcia-Vidal, L. Martin-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B87(11), 115419 (2013).
[CrossRef]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys.2(2), 81–90 (2006).
[CrossRef]

Grandidier, J.

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B80(11), 115419 (2009).
[CrossRef]

Gu, B. Y.

X. H. Wang, Y. S. Kivshar, and B. Y. Gu, “Giant lamb shift in photonic crystals,” Phys. Rev. Lett.93(7), 073901 (2004).
[CrossRef] [PubMed]

X. H. Wang, B. Y. Gu, R. Z. Wang, and H. Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Han, W.

Helmy, A. S.

Hemmer, P. R.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Howie, A.

F. J. García de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B65(11), 115418 (2002).
[CrossRef]

F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett.80(23), 5180–5183 (1998).
[CrossRef]

Hu, E. L.

K. J. Russell, T. L. Liu, S. Y. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics6(7), 459–462 (2012).
[CrossRef]

Hughes, S.

P. J. Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B80(19), 195106 (2009).
[CrossRef]

Hümmer, T.

T. Hümmer, F. J. Garcia-Vidal, L. Martin-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B87(11), 115419 (2013).
[CrossRef]

John, S.

N. Vats, S. John, and K. Busch, “Theory of fluorescence in photonic crystals,” Phys. Rev. A65(4), 043808 (2002).
[CrossRef]

T. Quang, M. Woldeyohannes, S. John, and G. S. Agarwal, “Coherent control of spontaneous emission near a photonic band edge: A single-atom optical memory device,” Phys. Rev. Lett.79(26), 5238–5241 (1997).
[CrossRef]

Jun, Y. C.

Y. C. Jun, R. Pala, and M. L. Brongersma, “Strong modification of quantum dot spontaneous emission via gap plasmon coupling in metal nanoslits,” J. Phys. Chem. C114(16), 7269–7273 (2010).
[CrossRef]

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78(15), 153111 (2008).
[CrossRef]

Kekatpure, R. D.

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78(15), 153111 (2008).
[CrossRef]

Khitrova, G.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys.2(2), 81–90 (2006).
[CrossRef]

Kira, M.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys.2(2), 81–90 (2006).
[CrossRef]

Kivshar, Y. S.

X. H. Wang, Y. S. Kivshar, and B. Y. Gu, “Giant lamb shift in photonic crystals,” Phys. Rev. Lett.93(7), 073901 (2004).
[CrossRef] [PubMed]

Knoll, L.

H. T. Dung, L. Knoll, and D. G. Welsch, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A57(5), 3931–3942 (1998).
[CrossRef]

Koch, S. W.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys.2(2), 81–90 (2006).
[CrossRef]

Lamb, W. E.

W. E. Lamb and R. C. Retherford, “Fine structure of the hydrogen atom by a microwave method,” Phys. Rev.72(3), 241–243 (1947).
[CrossRef]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Liu, Q.

Liu, T. L.

K. J. Russell, T. L. Liu, S. Y. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics6(7), 459–462 (2012).
[CrossRef]

Liu, Y. M.

Y. M. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev.40(5), 2494–2507 (2011).
[CrossRef] [PubMed]

Lodahl, P.

M. L. Andersen, S. Stobbe, A. S. Sorensen, and P. Lodahl, “Strongly modified plasmon-matter interaction with mesoscopic quantum emitters,” Nat. Phys.7(3), 215–218 (2011).
[CrossRef]

Lukin, M. D.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

Martin-Moreno, L.

T. Hümmer, F. J. Garcia-Vidal, L. Martin-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B87(11), 115419 (2013).
[CrossRef]

Massenot, S.

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B80(11), 115419 (2009).
[CrossRef]

Minh, T. T.

Mukherjee, A.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

Pala, R.

Y. C. Jun, R. Pala, and M. L. Brongersma, “Strong modification of quantum dot spontaneous emission via gap plasmon coupling in metal nanoslits,” J. Phys. Chem. C114(16), 7269–7273 (2010).
[CrossRef]

Park, H.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

Patterson, M.

P. J. Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B80(19), 195106 (2009).
[CrossRef]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Polman, A.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett.110(1), 013902 (2013).
[CrossRef] [PubMed]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.69, 681 (1946).

Quang, T.

T. Quang, M. Woldeyohannes, S. John, and G. S. Agarwal, “Coherent control of spontaneous emission near a photonic band edge: A single-atom optical memory device,” Phys. Rev. Lett.79(26), 5238–5241 (1997).
[CrossRef]

Retherford, R. C.

W. E. Lamb and R. C. Retherford, “Fine structure of the hydrogen atom by a microwave method,” Phys. Rev.72(3), 241–243 (1947).
[CrossRef]

Reza, A.

P. J. Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B80(19), 195106 (2009).
[CrossRef]

Russell, K. J.

K. J. Russell, T. L. Liu, S. Y. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics6(7), 459–462 (2012).
[CrossRef]

Scherer, A.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys.2(2), 81–90 (2006).
[CrossRef]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[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.

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using epsilon near-zero metamaterials,” Phys. Rev. B76(24), 245109 (2007).
[CrossRef]

Sipe, J. E.

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface. II,” Phys. Rev. A32(4), 2030–2043 (1985).
[CrossRef] [PubMed]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Song, H. W.

Sorensen, A. S.

M. L. Andersen, S. Stobbe, A. S. Sorensen, and P. Lodahl, “Strongly modified plasmon-matter interaction with mesoscopic quantum emitters,” Nat. Phys.7(3), 215–218 (2011).
[CrossRef]

Stobbe, S.

M. L. Andersen, S. Stobbe, A. S. Sorensen, and P. Lodahl, “Strongly modified plasmon-matter interaction with mesoscopic quantum emitters,” Nat. Phys.7(3), 215–218 (2011).
[CrossRef]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

Swillam, M. A.

Tanaka, K.

Tanaka, M.

Tanas, R.

Z. Ficek and R. Tanas, “Entangled states and collective nonclassical effects in two-atom systems,” Phys. Rep.372(5), 369–443 (2002).
[CrossRef]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

Van Vlack, C.

P. J. Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B80(19), 195106 (2009).
[CrossRef]

Vats, N.

N. Vats, S. John, and K. Busch, “Theory of fluorescence in photonic crystals,” Phys. Rev. A65(4), 043808 (2002).
[CrossRef]

Vesseur, E. J. R.

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett.110(1), 013902 (2013).
[CrossRef] [PubMed]

Wang, R. Z.

X. H. Wang, B. Y. Gu, R. Z. Wang, and H. Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Wang, W.

Wang, X. H.

X. H. Wang, Y. S. Kivshar, and B. Y. Gu, “Giant lamb shift in photonic crystals,” Phys. Rev. Lett.93(7), 073901 (2004).
[CrossRef] [PubMed]

X. H. Wang, B. Y. Gu, R. Z. Wang, and H. Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Wang, Y.

Weeber, J.-C.

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B80(11), 115419 (2009).
[CrossRef]

Welsch, D. G.

H. T. Dung, L. Knoll, and D. G. Welsch, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A57(5), 3931–3942 (1998).
[CrossRef]

White, J. S.

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78(15), 153111 (2008).
[CrossRef]

Woldeyohannes, M.

T. Quang, M. Woldeyohannes, S. John, and G. S. Agarwal, “Coherent control of spontaneous emission near a photonic band edge: A single-atom optical memory device,” Phys. Rev. Lett.79(26), 5238–5241 (1997).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Wylie, J. M.

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface. II,” Phys. Rev. A32(4), 2030–2043 (1985).
[CrossRef] [PubMed]

Xu, H. Q.

X. H. Wang, B. Y. Gu, R. Z. Wang, and H. Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Xu, L.

Yao, P. J.

P. J. Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B80(19), 195106 (2009).
[CrossRef]

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]

Yu, C. L.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

Zhang, X.

Y. M. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev.40(5), 2494–2507 (2011).
[CrossRef] [PubMed]

Zibrov, A. S.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

Zueco, D.

T. Hümmer, F. J. Garcia-Vidal, L. Martin-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B87(11), 115419 (2013).
[CrossRef]

Chem. Soc. Rev.

Y. M. Liu and X. Zhang, “Metamaterials: a new frontier of science and technology,” Chem. Soc. Rev.40(5), 2494–2507 (2011).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag.

A. Alu and N. Engheta, “Coaxial-to-waveguide matching with epsilon-near-zero ultranarrow channels and bends,” IEEE Trans. Antennas Propag.58(2), 328–339 (2010).
[CrossRef]

J. Phys. Chem. C

Y. C. Jun, R. Pala, and M. L. Brongersma, “Strong modification of quantum dot spontaneous emission via gap plasmon coupling in metal nanoslits,” J. Phys. Chem. C114(16), 7269–7273 (2010).
[CrossRef]

Nat. Photonics

K. J. Russell, T. L. Liu, S. Y. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics6(7), 459–462 (2012).
[CrossRef]

Nat. Phys.

G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys.2(2), 81–90 (2006).
[CrossRef]

M. L. Andersen, S. Stobbe, A. S. Sorensen, and P. Lodahl, “Strongly modified plasmon-matter interaction with mesoscopic quantum emitters,” Nat. Phys.7(3), 215–218 (2011).
[CrossRef]

Nature

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef] [PubMed]

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, “Generation of single optical plasmons in metallic nanowires coupled to quantum dots,” Nature450(7168), 402–406 (2007).
[CrossRef] [PubMed]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature450(7168), 397–401 (2007).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature391(6668), 667–669 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rep.

Z. Ficek and R. Tanas, “Entangled states and collective nonclassical effects in two-atom systems,” Phys. Rep.372(5), 369–443 (2002).
[CrossRef]

Phys. Rev.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev.93(1), 99–110 (1954).
[CrossRef]

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev.69, 681 (1946).

W. E. Lamb and R. C. Retherford, “Fine structure of the hydrogen atom by a microwave method,” Phys. Rev.72(3), 241–243 (1947).
[CrossRef]

H. A. Bethe, “The electromagnetic shift of energy levels,” Phys. Rev.72(4), 339–341 (1947).
[CrossRef]

Phys. Rev. A

N. Vats, S. John, and K. Busch, “Theory of fluorescence in photonic crystals,” Phys. Rev. A65(4), 043808 (2002).
[CrossRef]

J. M. Wylie and J. E. Sipe, “Quantum electrodynamics near an interface. II,” Phys. Rev. A32(4), 2030–2043 (1985).
[CrossRef] [PubMed]

H. T. Dung, L. Knoll, and D. G. Welsch, “Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics,” Phys. Rev. A57(5), 3931–3942 (1998).
[CrossRef]

Phys. Rev. B

G. Colas des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B80(11), 115419 (2009).
[CrossRef]

P. J. Yao, C. Van Vlack, A. Reza, M. Patterson, M. M. Dignam, and S. Hughes, “Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides,” Phys. Rev. B80(19), 195106 (2009).
[CrossRef]

A. Alù and N. Engheta, “Dielectric sensing in epsilon-near-zero narrow waveguide channels,” Phys. Rev. B78(4), 045102 (2008).
[CrossRef]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using epsilon near-zero metamaterials,” Phys. Rev. B76(24), 245109 (2007).
[CrossRef]

Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B78(15), 153111 (2008).
[CrossRef]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B73(3), 035407 (2006).
[CrossRef]

T. Hümmer, F. J. Garcia-Vidal, L. Martin-Moreno, and D. Zueco, “Weak and strong coupling regimes in plasmonic QED,” Phys. Rev. B87(11), 115419 (2013).
[CrossRef]

R. Fleury and A. Alu, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B87, 201101(R) (2013).

F. J. García de Abajo and A. Howie, “Retarded field calculation of electron energy loss in inhomogeneous dielectrics,” Phys. Rev. B65(11), 115418 (2002).
[CrossRef]

Phys. Rev. Lett.

F. J. García de Abajo and A. Howie, “Relativistic electron energy loss and electron-induced photon emission in inhomogeneous dielectrics,” Phys. Rev. Lett.80(23), 5180–5183 (1998).
[CrossRef]

X. H. Wang, Y. S. Kivshar, and B. Y. Gu, “Giant lamb shift in photonic crystals,” Phys. Rev. Lett.93(7), 073901 (2004).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett.103(4), 043902 (2009).
[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]

E. J. R. Vesseur, T. Coenen, H. Caglayan, N. Engheta, and A. Polman, “Experimental verification of n = 0 structures for visible light,” Phys. Rev. Lett.110(1), 013902 (2013).
[CrossRef] [PubMed]

T. Quang, M. Woldeyohannes, S. John, and G. S. Agarwal, “Coherent control of spontaneous emission near a photonic band edge: A single-atom optical memory device,” Phys. Rev. Lett.79(26), 5238–5241 (1997).
[CrossRef]

X. H. Wang, B. Y. Gu, R. Z. Wang, and H. Q. Xu, “Decay kinetic properties of atoms in photonic crystals with absolute gaps,” Phys. Rev. Lett.91(11), 113904 (2003).
[CrossRef] [PubMed]

Science

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Other

P. Sheng, Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena, 2nd ed., Springer Series in Materials Science (Springer, 2006), 333 pp.

L. Novotny and B. Hecht, Principles of Nano-optics (Cambridge University, 2006), 539 pp.

R. Fitzpatrick, “Quantum mechanics,” pp. 192–193.

E. D. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

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Figures (4)

Fig. 1
Fig. 1

Rectangular waveguide with dielectric core and metal cladding.

Fig. 2
Fig. 2

The two-dimensional LDOS enhancement as a function of the field frequency (given in the eV units) and effective index. Figure 2(a) shows enhancement of the the total two-dimensional LDOS which is obtained by averaging over different emitter dipole orientations. The two vertical lines represent light lines in air (neff = 1) and in the dielectric core (neff = 1.49), correspondingly. In Figs. 2(b), 2(c), and 2(d) we plot x, y, and z projections of the two-dimensional LDOS, respectively, normalized to the total two-dimensional LDOS of the free space. The insets of Figs. 2(b)2(d) show field profiles of the waveguide modes, that is, the spatial distribution of the electric field intensity, supported in the different regions of the dispersion relation.

Fig. 3
Fig. 3

Figures 3(a) and 3(b) display the enhancement of the partial three-dimensional LDOS, ρy/ρ0y, in the center of the waveguide for an infinite waveguide with fixed height wy = 80 nm and different widths wx such that wx:wy = 1,2,34. Figures 3(c) and 3(d) plot the enhancement of the partial three-dimensional LDOS, ρy/ρ0y, in 80 × 240 nm waveguide as a function of frequency and (c) distance from the waveguide center in y direction, (d) distance from the waveguide center in x direction. For both plots the zero value on the abscess axis corresponds to the emitter in the center of the waveguide, while the upmost right value of the abscissa axis corresponds to the case when the emitter is 8nm away from the metal walls.

Fig. 4
Fig. 4

Figures 4(a) and 4(b) show photonic Lamb shifts for an emitter above the air-silver interface as a function of frequency. The dipole moment of the quantum emitter is perpendicular to the interface. (a) The emitter is 40 nm above the silver sheet. (b) The emitter is 10 nm above the silver sheet. Figures 4(c) and 4(d) display photonic Lamb shifts as a function of frequency for an emitter embedded in infinite rectangular waveguides, for different aspect ratios of the waveguides. The emitter is assumed y polarized (see Fig. 1). (c) The emitter is in the center of the wavegiude. (b) The emitter is 10 nm away from the top wall of the waveguide. Figures 4(c) and 4(d) use the same color code. Figures 4(e) and 4(f) display spontaneous emission power spectrum of the quantum emitter with resonant frequency around the cutoff frequency of the waveguide. Blue curve - the power spectrum of an emitter coupled to the waveguide, red curve - the emitter is embedded in the homogeneous dielectric (nd = 1.49). (e) The waveguide cross-section is 80 × 160 nm. (f) The waveguide cross-section is 40 × 160 nm.

Equations (2)

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ρ n i = 6ω π c 2 n i Im G ( r , r ) n i (i=x,y,z),
ρ n i 2D ( r , k z ,ω)= e i k z z ρ n i ( r ,ω) dz.

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