Abstract

Tunable surface plasmons on the interface of a multilevel atomic medium with a cross coupling of the electric and magnetic components of a plasmonic field are investigated. The strong chirality resulting from the quantum coherence leads to some exciting properties of the surface plasmons. Compared to the traditional chiral-metal interface, surface plasmonic mode can still be found at the interface between such atomic media and a dielectric even when both the permittivity and the permeability of the medium are positive. This is in contrast to the conventional plasmonic systems where the signs of the permittivities or permeabilities on the two sides of the interface are opposite. We call this phenomenon an electromagnetically induced plasmon. Additionally, as the chirality and effective refractive index of the atomic medium are dependent on the intensity and phase of the controlling field, we can conveniently manipulate the properties of the surface plasmons.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

A. J. Traverso, B. Hokr, Z. H. Yi, L. Yuan, S. Yamaguchi, M. O. Scully, and V. V. Yakovlev, “Two-photon infrared resonance can enhance coherent Raman scattering,” Phys. Rev. Lett. 120, 063602 (2018).
[Crossref] [PubMed]

Z. Wu, X. Chen, M. Wang, J. Dong, and Y. Zheng, “High-performance ultrathin active chiral metamaterials,” ACS Nano 12, 5030–5041 (2018).
[Crossref] [PubMed]

2017 (1)

X-D. Zeng, L. Fan, and M. S. Zubairy, “Deep-subwavelength lithography via graphene plasmons,” Phys. Rev. A 95, 053850 (2017).
[Crossref]

2016 (3)

X-D. Zeng, Z. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” EPL 115, 14002 (2016).
[Crossref]

I. Fernandez-Corbaton, M. Fruhnert, and C. Rockstuhl, “Objects of maximum electromagnetic chirality,” Phys. Rev. X 6, 031013 (2016).

A. P. Fang, W. Ge, M. Wang, F. L. Li, and M. S. Zubairy, “Negative refraction without absorption via quantum coherence,” Phys. Rev. A 93, 023822 (2016).
[Crossref]

2015 (1)

Y. Fang and M. Sun, “Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits,” Light: Science and applications 4, e294 (2015).

2014 (2)

S-W. Zeng, D. Baillargeat, H-P. Ho, and K-T. Yong, “Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications,” Chem. Soc. Rev. 43, 3426–3452 (2014).
[Crossref] [PubMed]

G. Mi and V. Van, “Characteristics of surface plasmon polaritons at a chiral/metal interface,” Opt. Lett. 39, 2028–2031 (2014).
[Crossref] [PubMed]

2013 (1)

P. P. Orth, R. Hennig, C. H Keitel, and J. Evers, “Negative refraction with tunable absorption in an active dense gas of atoms,” N. J. Phys. 15, 013027 (2013).
[Crossref]

2012 (2)

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

X-D. Zeng, G-X. Li, Y. Yang, and S. Zhu, “Enhancement of the vacuum Rabi oscillation via surface plasma modes in single-negative metamaterials,” Phys. Rev. A 86, 033819 (2012).
[Crossref]

2011 (2)

X-D. Zeng, J-P. Xu, and Y. Yang, “Spontaneous emission interference enhancement with a μ-negative metamaterial slab,” Phys. Rev. A 84, 033834 (2011).
[Crossref]

D. E. Sikes and D. D. Yavuz, “Negative refraction using Raman transitions and chirality,” Phys. Rev. A 84, 053836 (2011).
[Crossref]

2010 (3)

D. E. Sikes and D. D. Yavuz, “Negative refraction with low absorption using Raman transitions with magnetoelectric coupling,” Phys. Rev. A 82, 011806 (2010).
[Crossref]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature materials 9, 205–213 (2010).
[Crossref] [PubMed]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature photonics 4, 83–91 (2010).
[Crossref]

2009 (5)

G. X. Li, J. Evers, and C. H. Keitel, “Spontaneous emission interference in negative-refractive-index waveguides,” Phys. Rev. B 80, 045102 (2009).
[Crossref]

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Low-loss negative refraction by laser-induced magnetoelectric cross coupling,” Phys. Rev. A 79, 063818 (2009).
[Crossref]

R. Fleischhaker and J. Evers, “Phase-controlled pulse propagation in media with cross coupling of electric and magnetic probe field component,” Phys. Rev. A 80, 063816 (2009).
[Crossref]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

J. A. Polo and A. Lakhtakia, “On the surface plasmon polariton wave at the planar interface of a metal and a chiral sculptured thin film,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 465, 87–107 (2009).
[Crossref]

2007 (5)

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Tunable negative refraction without absorption via electromagnetically induced chirality,” Phys. Rev. Lett. 99, 073602 (2007).
[Crossref] [PubMed]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in Graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nature photonics 1, 641–648 (2007).
[Crossref]

2006 (2)

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006).
[Crossref] [PubMed]

2004 (2)

M. Ö. Oktel and Ö. E. Müstecaplıoğlu, “Electromagnetically induced left-handedness in a dense gas of three-level atoms,” Phys. Rev. A 96, 053806 (2004).
[Crossref]

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[Crossref] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

2002 (1)

E. Altewischer, “Plasmon-assisted transmission of entangled photons,” Nature 418, 304–306 (2002).
[Crossref] [PubMed]

1996 (1)

1991 (1)

1990 (1)

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Transactions on Antennas and Propagation 38, 90–98 (1990).
[Crossref]

1988 (1)

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Abdulrahman, A. N.

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Al-Amri, M.

X-D. Zeng, Z. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” EPL 115, 14002 (2016).
[Crossref]

Altewischer, E.

E. Altewischer, “Plasmon-assisted transmission of entangled photons,” Nature 418, 304–306 (2002).
[Crossref] [PubMed]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature materials 9, 205–213 (2010).
[Crossref] [PubMed]

Baillargeat, D.

S-W. Zeng, D. Baillargeat, H-P. Ho, and K-T. Yong, “Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications,” Chem. Soc. Rev. 43, 3426–3452 (2014).
[Crossref] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Bassiri, S.

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature photonics 4, 83–91 (2010).
[Crossref]

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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

Chen, X.

Z. Wu, X. Chen, M. Wang, J. Dong, and Y. Zheng, “High-performance ultrathin active chiral metamaterials,” ACS Nano 12, 5030–5041 (2018).
[Crossref] [PubMed]

Cook, D. M.

D. M. Cook, The Theory of the Electromagnetic Field, (Prentice-Hall, Inc., 1975).

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Dong, J.

Z. Wu, X. Chen, M. Wang, J. Dong, and Y. Zheng, “High-performance ultrathin active chiral metamaterials,” ACS Nano 12, 5030–5041 (2018).
[Crossref] [PubMed]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[Crossref] [PubMed]

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Engheta, N.

Evers, J.

P. P. Orth, R. Hennig, C. H Keitel, and J. Evers, “Negative refraction with tunable absorption in an active dense gas of atoms,” N. J. Phys. 15, 013027 (2013).
[Crossref]

R. Fleischhaker and J. Evers, “Phase-controlled pulse propagation in media with cross coupling of electric and magnetic probe field component,” Phys. Rev. A 80, 063816 (2009).
[Crossref]

G. X. Li, J. Evers, and C. H. Keitel, “Spontaneous emission interference in negative-refractive-index waveguides,” Phys. Rev. B 80, 045102 (2009).
[Crossref]

Fan, L.

X-D. Zeng, L. Fan, and M. S. Zubairy, “Deep-subwavelength lithography via graphene plasmons,” Phys. Rev. A 95, 053850 (2017).
[Crossref]

Fan, Z.

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

Fang, A. P.

A. P. Fang, W. Ge, M. Wang, F. L. Li, and M. S. Zubairy, “Negative refraction without absorption via quantum coherence,” Phys. Rev. A 93, 023822 (2016).
[Crossref]

Fang, Y.

Y. Fang and M. Sun, “Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits,” Light: Science and applications 4, e294 (2015).

Fedotov, V. A.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Fernandez-Corbaton, I.

I. Fernandez-Corbaton, M. Fruhnert, and C. Rockstuhl, “Objects of maximum electromagnetic chirality,” Phys. Rev. X 6, 031013 (2016).

Fleischhaker, R.

R. Fleischhaker and J. Evers, “Phase-controlled pulse propagation in media with cross coupling of electric and magnetic probe field component,” Phys. Rev. A 80, 063816 (2009).
[Crossref]

Fleischhauer, M.

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Low-loss negative refraction by laser-induced magnetoelectric cross coupling,” Phys. Rev. A 79, 063818 (2009).
[Crossref]

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Tunable negative refraction without absorption via electromagnetically induced chirality,” Phys. Rev. Lett. 99, 073602 (2007).
[Crossref] [PubMed]

Flood, K. M.

Fruhnert, M.

I. Fernandez-Corbaton, M. Fruhnert, and C. Rockstuhl, “Objects of maximum electromagnetic chirality,” Phys. Rev. X 6, 031013 (2016).

Gadegaard, N.

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

Ge, W.

A. P. Fang, W. Ge, M. Wang, F. L. Li, and M. S. Zubairy, “Negative refraction without absorption via quantum coherence,” Phys. Rev. A 93, 023822 (2016).
[Crossref]

Govorov, A. O.

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature photonics 4, 83–91 (2010).
[Crossref]

Halas, N. J.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nature photonics 1, 641–648 (2007).
[Crossref]

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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

Hendry, E.

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

Hennig, R.

P. P. Orth, R. Hennig, C. H Keitel, and J. Evers, “Negative refraction with tunable absorption in an active dense gas of atoms,” N. J. Phys. 15, 013027 (2013).
[Crossref]

Ho, H-P.

S-W. Zeng, D. Baillargeat, H-P. Ho, and K-T. Yong, “Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications,” Chem. Soc. Rev. 43, 3426–3452 (2014).
[Crossref] [PubMed]

Hokr, B.

A. J. Traverso, B. Hokr, Z. H. Yi, L. Yuan, S. Yamaguchi, M. O. Scully, and V. V. Yakovlev, “Two-photon infrared resonance can enhance coherent Raman scattering,” Phys. Rev. Lett. 120, 063602 (2018).
[Crossref] [PubMed]

Jaggard, D. L.

Kadodwala, M.

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

Kästel, J.

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Low-loss negative refraction by laser-induced magnetoelectric cross coupling,” Phys. Rev. A 79, 063818 (2009).
[Crossref]

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Tunable negative refraction without absorption via electromagnetically induced chirality,” Phys. Rev. Lett. 99, 073602 (2007).
[Crossref] [PubMed]

Keitel, C. H

P. P. Orth, R. Hennig, C. H Keitel, and J. Evers, “Negative refraction with tunable absorption in an active dense gas of atoms,” N. J. Phys. 15, 013027 (2013).
[Crossref]

Keitel, C. H.

G. X. Li, J. Evers, and C. H. Keitel, “Spontaneous emission interference in negative-refractive-index waveguides,” Phys. Rev. B 80, 045102 (2009).
[Crossref]

Kelly, S. M.

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

Koschny, T.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Lakhtakia, A.

J. A. Polo and A. Lakhtakia, “On the surface plasmon polariton wave at the planar interface of a metal and a chiral sculptured thin film,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 465, 87–107 (2009).
[Crossref]

Lal, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nature photonics 1, 641–648 (2007).
[Crossref]

Li, F. L.

A. P. Fang, W. Ge, M. Wang, F. L. Li, and M. S. Zubairy, “Negative refraction without absorption via quantum coherence,” Phys. Rev. A 93, 023822 (2016).
[Crossref]

Li, G. X.

G. X. Li, J. Evers, and C. H. Keitel, “Spontaneous emission interference in negative-refractive-index waveguides,” Phys. Rev. B 80, 045102 (2009).
[Crossref]

Li, G-X.

X-D. Zeng, G-X. Li, Y. Yang, and S. Zhu, “Enhancement of the vacuum Rabi oscillation via surface plasma modes in single-negative metamaterials,” Phys. Rev. A 86, 033819 (2012).
[Crossref]

Liao, Z.

X-D. Zeng, Z. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” EPL 115, 14002 (2016).
[Crossref]

Link, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nature photonics 1, 641–648 (2007).
[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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

Mandel, P.

Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006).
[Crossref] [PubMed]

Mi, G.

Mikhailov, S. A.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in Graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref] [PubMed]

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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Müstecaplioglu, Ö. E.

M. Ö. Oktel and Ö. E. Müstecaplıoğlu, “Electromagnetically induced left-handedness in a dense gas of three-level atoms,” Phys. Rev. A 96, 053806 (2004).
[Crossref]

Oktel, M. Ö.

M. Ö. Oktel and Ö. E. Müstecaplıoğlu, “Electromagnetically induced left-handedness in a dense gas of three-level atoms,” Phys. Rev. A 96, 053806 (2004).
[Crossref]

Orth, P. P.

P. P. Orth, R. Hennig, C. H Keitel, and J. Evers, “Negative refraction with tunable absorption in an active dense gas of atoms,” N. J. Phys. 15, 013027 (2013).
[Crossref]

Papas, C. H.

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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Pelet, P.

N. Engheta and P. Pelet, “Surface waves in chiral layers,” Opt. Lett. 16, 723–725 (1991).
[Crossref] [PubMed]

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Transactions on Antennas and Propagation 38, 90–98 (1990).
[Crossref]

Pendry, J. B.

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[Crossref] [PubMed]

Plum, E.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature materials 9, 205–213 (2010).
[Crossref] [PubMed]

Polo, J. A.

J. A. Polo and A. Lakhtakia, “On the surface plasmon polariton wave at the planar interface of a metal and a chiral sculptured thin film,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 465, 87–107 (2009).
[Crossref]

Rockstuhl, C.

I. Fernandez-Corbaton, M. Fruhnert, and C. Rockstuhl, “Objects of maximum electromagnetic chirality,” Phys. Rev. X 6, 031013 (2016).

Scully, M. O.

A. J. Traverso, B. Hokr, Z. H. Yi, L. Yuan, S. Yamaguchi, M. O. Scully, and V. V. Yakovlev, “Two-photon infrared resonance can enhance coherent Raman scattering,” Phys. Rev. Lett. 120, 063602 (2018).
[Crossref] [PubMed]

M. O. Scully and M. S. Zubairy, Quantum Optics, (Cambridge University, 1999).

Sikes, D. E.

D. E. Sikes and D. D. Yavuz, “Negative refraction using Raman transitions and chirality,” Phys. Rev. A 84, 053836 (2011).
[Crossref]

D. E. Sikes and D. D. Yavuz, “Negative refraction with low absorption using Raman transitions with magnetoelectric coupling,” Phys. Rev. A 82, 011806 (2010).
[Crossref]

Sørensen, A. S.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

Soukoulis, C. M.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Sun, M.

Y. Fang and M. Sun, “Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits,” Light: Science and applications 4, e294 (2015).

Thommen, Q.

Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006).
[Crossref] [PubMed]

Tonooka, T.

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

Traverso, A. J.

A. J. Traverso, B. Hokr, Z. H. Yi, L. Yuan, S. Yamaguchi, M. O. Scully, and V. V. Yakovlev, “Two-photon infrared resonance can enhance coherent Raman scattering,” Phys. Rev. Lett. 120, 063602 (2018).
[Crossref] [PubMed]

Van, V.

Walsworth, R. L.

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Low-loss negative refraction by laser-induced magnetoelectric cross coupling,” Phys. Rev. A 79, 063818 (2009).
[Crossref]

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Tunable negative refraction without absorption via electromagnetically induced chirality,” Phys. Rev. Lett. 99, 073602 (2007).
[Crossref] [PubMed]

Wang, M.

Z. Wu, X. Chen, M. Wang, J. Dong, and Y. Zheng, “High-performance ultrathin active chiral metamaterials,” ACS Nano 12, 5030–5041 (2018).
[Crossref] [PubMed]

A. P. Fang, W. Ge, M. Wang, F. L. Li, and M. S. Zubairy, “Negative refraction without absorption via quantum coherence,” Phys. Rev. A 93, 023822 (2016).
[Crossref]

Wu, Z.

Z. Wu, X. Chen, M. Wang, J. Dong, and Y. Zheng, “High-performance ultrathin active chiral metamaterials,” ACS Nano 12, 5030–5041 (2018).
[Crossref] [PubMed]

Xu, J-P.

X-D. Zeng, J-P. Xu, and Y. Yang, “Spontaneous emission interference enhancement with a μ-negative metamaterial slab,” Phys. Rev. A 84, 033834 (2011).
[Crossref]

Yakovlev, V. V.

A. J. Traverso, B. Hokr, Z. H. Yi, L. Yuan, S. Yamaguchi, M. O. Scully, and V. V. Yakovlev, “Two-photon infrared resonance can enhance coherent Raman scattering,” Phys. Rev. Lett. 120, 063602 (2018).
[Crossref] [PubMed]

Yamaguchi, S.

A. J. Traverso, B. Hokr, Z. H. Yi, L. Yuan, S. Yamaguchi, M. O. Scully, and V. V. Yakovlev, “Two-photon infrared resonance can enhance coherent Raman scattering,” Phys. Rev. Lett. 120, 063602 (2018).
[Crossref] [PubMed]

Yang, Y.

X-D. Zeng, G-X. Li, Y. Yang, and S. Zhu, “Enhancement of the vacuum Rabi oscillation via surface plasma modes in single-negative metamaterials,” Phys. Rev. A 86, 033819 (2012).
[Crossref]

X-D. Zeng, J-P. Xu, and Y. Yang, “Spontaneous emission interference enhancement with a μ-negative metamaterial slab,” Phys. Rev. A 84, 033834 (2011).
[Crossref]

Yavuz, D. D.

D. E. Sikes and D. D. Yavuz, “Negative refraction using Raman transitions and chirality,” Phys. Rev. A 84, 053836 (2011).
[Crossref]

D. E. Sikes and D. D. Yavuz, “Negative refraction with low absorption using Raman transitions with magnetoelectric coupling,” Phys. Rev. A 82, 011806 (2010).
[Crossref]

Yelin, S. F.

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Low-loss negative refraction by laser-induced magnetoelectric cross coupling,” Phys. Rev. A 79, 063818 (2009).
[Crossref]

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Tunable negative refraction without absorption via electromagnetically induced chirality,” Phys. Rev. Lett. 99, 073602 (2007).
[Crossref] [PubMed]

Yi, Z. H.

A. J. Traverso, B. Hokr, Z. H. Yi, L. Yuan, S. Yamaguchi, M. O. Scully, and V. V. Yakovlev, “Two-photon infrared resonance can enhance coherent Raman scattering,” Phys. Rev. Lett. 120, 063602 (2018).
[Crossref] [PubMed]

Yong, K-T.

S-W. Zeng, D. Baillargeat, H-P. Ho, and K-T. Yong, “Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications,” Chem. Soc. Rev. 43, 3426–3452 (2014).
[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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Yuan, L.

A. J. Traverso, B. Hokr, Z. H. Yi, L. Yuan, S. Yamaguchi, M. O. Scully, and V. V. Yakovlev, “Two-photon infrared resonance can enhance coherent Raman scattering,” Phys. Rev. Lett. 120, 063602 (2018).
[Crossref] [PubMed]

Zeng, S-W.

S-W. Zeng, D. Baillargeat, H-P. Ho, and K-T. Yong, “Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications,” Chem. Soc. Rev. 43, 3426–3452 (2014).
[Crossref] [PubMed]

Zeng, X-D.

X-D. Zeng, L. Fan, and M. S. Zubairy, “Deep-subwavelength lithography via graphene plasmons,” Phys. Rev. A 95, 053850 (2017).
[Crossref]

X-D. Zeng, Z. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” EPL 115, 14002 (2016).
[Crossref]

X-D. Zeng, G-X. Li, Y. Yang, and S. Zhu, “Enhancement of the vacuum Rabi oscillation via surface plasma modes in single-negative metamaterials,” Phys. Rev. A 86, 033819 (2012).
[Crossref]

X-D. Zeng, J-P. Xu, and Y. Yang, “Spontaneous emission interference enhancement with a μ-negative metamaterial slab,” Phys. Rev. A 84, 033834 (2011).
[Crossref]

Zheludev, N. I.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Zheng, Y.

Z. Wu, X. Chen, M. Wang, J. Dong, and Y. Zheng, “High-performance ultrathin active chiral metamaterials,” ACS Nano 12, 5030–5041 (2018).
[Crossref] [PubMed]

Zhou, J.

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

Zhu, S.

X-D. Zeng, G-X. Li, Y. Yang, and S. Zhu, “Enhancement of the vacuum Rabi oscillation via surface plasma modes in single-negative metamaterials,” Phys. Rev. A 86, 033819 (2012).
[Crossref]

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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Ziegler, K.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in Graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref] [PubMed]

Zubairy, M. S.

X-D. Zeng, L. Fan, and M. S. Zubairy, “Deep-subwavelength lithography via graphene plasmons,” Phys. Rev. A 95, 053850 (2017).
[Crossref]

X-D. Zeng, Z. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” EPL 115, 14002 (2016).
[Crossref]

A. P. Fang, W. Ge, M. Wang, F. L. Li, and M. S. Zubairy, “Negative refraction without absorption via quantum coherence,” Phys. Rev. A 93, 023822 (2016).
[Crossref]

M. O. Scully and M. S. Zubairy, Quantum Optics, (Cambridge University, 1999).

ACS Nano (1)

Z. Wu, X. Chen, M. Wang, J. Dong, and Y. Zheng, “High-performance ultrathin active chiral metamaterials,” ACS Nano 12, 5030–5041 (2018).
[Crossref] [PubMed]

Chem. Soc. Rev. (1)

S-W. Zeng, D. Baillargeat, H-P. Ho, and K-T. Yong, “Nanomaterials enhanced surface plasmon resonance for biological and chemical sensing applications,” Chem. Soc. Rev. 43, 3426–3452 (2014).
[Crossref] [PubMed]

EPL (1)

X-D. Zeng, Z. Liao, M. Al-Amri, and M. S. Zubairy, “Controllable waveguide via dielectric cylinder covered with graphene: Tunable entanglement,” EPL 115, 14002 (2016).
[Crossref]

IEEE Transactions on Antennas and Propagation (1)

P. Pelet and N. Engheta, “The theory of chirowaveguides,” IEEE Transactions on Antennas and Propagation 38, 90–98 (1990).
[Crossref]

J. Opt. Soc. Am. A (1)

Light: Science and applications (1)

Y. Fang and M. Sun, “Nanoplasmonic waveguides: towards applications in integrated nanophotonic circuits,” Light: Science and applications 4, e294 (2015).

N. J. Phys. (1)

P. P. Orth, R. Hennig, C. H Keitel, and J. Evers, “Negative refraction with tunable absorption in an active dense gas of atoms,” N. J. Phys. 15, 013027 (2013).
[Crossref]

Nano Lett. (1)

A. N. Abdulrahman, Z. Fan, T. Tonooka, S. M. Kelly, N. Gadegaard, E. Hendry, A. O. Govorov, and M. Kadodwala, “Induced chirality through electromagnetic coupling between chiral molecular layers and plasmonic nanostructures,” Nano Lett. 12, 977–983 (2012).
[Crossref] [PubMed]

Nature (3)

E. Altewischer, “Plasmon-assisted transmission of entangled photons,” Nature 418, 304–306 (2002).
[Crossref] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (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,” Nature 450, 402–406 (2007).
[Crossref] [PubMed]

Nature materials (1)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature materials 9, 205–213 (2010).
[Crossref] [PubMed]

Nature photonics (2)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nature photonics 4, 83–91 (2010).
[Crossref]

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nature photonics 1, 641–648 (2007).
[Crossref]

Opt. Lett. (3)

Phys. Rev. (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Phys. Rev. A (9)

X-D. Zeng, G-X. Li, Y. Yang, and S. Zhu, “Enhancement of the vacuum Rabi oscillation via surface plasma modes in single-negative metamaterials,” Phys. Rev. A 86, 033819 (2012).
[Crossref]

X-D. Zeng, J-P. Xu, and Y. Yang, “Spontaneous emission interference enhancement with a μ-negative metamaterial slab,” Phys. Rev. A 84, 033834 (2011).
[Crossref]

X-D. Zeng, L. Fan, and M. S. Zubairy, “Deep-subwavelength lithography via graphene plasmons,” Phys. Rev. A 95, 053850 (2017).
[Crossref]

A. P. Fang, W. Ge, M. Wang, F. L. Li, and M. S. Zubairy, “Negative refraction without absorption via quantum coherence,” Phys. Rev. A 93, 023822 (2016).
[Crossref]

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Low-loss negative refraction by laser-induced magnetoelectric cross coupling,” Phys. Rev. A 79, 063818 (2009).
[Crossref]

R. Fleischhaker and J. Evers, “Phase-controlled pulse propagation in media with cross coupling of electric and magnetic probe field component,” Phys. Rev. A 80, 063816 (2009).
[Crossref]

D. E. Sikes and D. D. Yavuz, “Negative refraction using Raman transitions and chirality,” Phys. Rev. A 84, 053836 (2011).
[Crossref]

D. E. Sikes and D. D. Yavuz, “Negative refraction with low absorption using Raman transitions with magnetoelectric coupling,” Phys. Rev. A 82, 011806 (2010).
[Crossref]

M. Ö. Oktel and Ö. E. Müstecaplıoğlu, “Electromagnetically induced left-handedness in a dense gas of three-level atoms,” Phys. Rev. A 96, 053806 (2004).
[Crossref]

Phys. Rev. B (3)

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

G. X. Li, J. Evers, and C. H. Keitel, “Spontaneous emission interference in negative-refractive-index waveguides,” Phys. Rev. B 80, 045102 (2009).
[Crossref]

Phys. Rev. Lett. (5)

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in Graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref] [PubMed]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. 97, 053002 (2006).
[Crossref] [PubMed]

J. Kästel, M. Fleischhauer, S. F. Yelin, and R. L. Walsworth, “Tunable negative refraction without absorption via electromagnetically induced chirality,” Phys. Rev. Lett. 99, 073602 (2007).
[Crossref] [PubMed]

A. J. Traverso, B. Hokr, Z. H. Yi, L. Yuan, S. Yamaguchi, M. O. Scully, and V. V. Yakovlev, “Two-photon infrared resonance can enhance coherent Raman scattering,” Phys. Rev. Lett. 120, 063602 (2018).
[Crossref] [PubMed]

Q. Thommen and P. Mandel, “Electromagnetically induced left handedness in optically excited four-level atomic media,” Phys. Rev. Lett. 96, 053601 (2006).
[Crossref] [PubMed]

Phys. Rev. X (1)

I. Fernandez-Corbaton, M. Fruhnert, and C. Rockstuhl, “Objects of maximum electromagnetic chirality,” Phys. Rev. X 6, 031013 (2016).

Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (1)

J. A. Polo and A. Lakhtakia, “On the surface plasmon polariton wave at the planar interface of a metal and a chiral sculptured thin film,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 465, 87–107 (2009).
[Crossref]

Science (1)

J. B. Pendry, “A chiral route to negative refraction,” Science 306, 1353–1355 (2004).
[Crossref] [PubMed]

Other (2)

M. O. Scully and M. S. Zubairy, Quantum Optics, (Cambridge University, 1999).

D. M. Cook, The Theory of the Electromagnetic Field, (Prentice-Hall, Inc., 1975).

Supplementary Material (2)

NameDescription
» Visualization 1       Time dependent visualization of the plasmonic field along x-axis.
» Visualization 2       Time dependent variations of the y-component of the plasmonic field.

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Figures (7)

Fig. 1
Fig. 1 Two infinite half media conjunct at x = 0 plane. A surface plasmon propagates along the z direction. The inset circle is the atomic energy structure of medium 1. Two strong external laser fields with Rabi frequencies Ω1 and Ω2 prepare a coherent superposition of states |1〉 and |4〉.
Fig. 2
Fig. 2 The permittivities, permeabilities, refractive indices and eigen surface plasmons versus the light frequency. Here, φ = π / 2 and in (a) Ω c = 60 γ p whereas in (b) Ω c = 6 γ p. γp represents the non-radiative dephasing rate and is taken to be 10 3 /s.
Fig. 3
Fig. 3 The permittivities, permeabilities, refractive indices and eigen surface plasmons versus the control field Rabi frequency. (a) φ = π / 4, Δ B = Δ E (b) φ = π / 2 and (c) φ = π / 4 but Δ B = 2 Δ E. The other parameters are the same as in Fig. 2.
Fig. 4
Fig. 4 The corresponding wave numbers perpendicular to the interface of the surface plasmons as shown in Figs. 3(a4)–(c4).
Fig. 5
Fig. 5 The permittivities, permeabilities, eigen surface plasmons, versus the quantum coherence ρ41. Here, Ωc=6.145γp and ρ 41 = | ρ 41 |.
Fig. 6
Fig. 6 The electric field distributions as a function of the distance to the interface. The electric fields decay as e I m ( k ) z along z direction. (a) is the field intensity. (b) and (c) are the real parts of the electric field at time 0 and π / 2 ω. Here | Ω c | = 5.93 γ p and φ = π / 4. Time dependent variations of the plasmonic field can be seen more clearly in the supplementary Visualization 1 and Visualization 2 .
Fig. 7
Fig. 7 The ratio between the energy densities of TE- and TM-polarized components of the surface plasmons. The parameters are the same as in Fig. 3.

Equations (40)

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H = i = 1 5 ω i A | i i | + [ 1 2 d 34 E e i ω t | 3 4 |   1 2 μ ˜ 21 B e i ω t | 2 1 | 2 Ω 1 e i ω 1 t | 5 1 |   2 Ω 2 e i ω 2 t | 5 4 | 2 Ω ˜ c e i ω c t | 3 2 | + H . c . ] .
( Ω 2 | 1 Ω 1 | 4 ) / Ω 1 2 + Ω 2 2 .
P = χ e ε 0 E + ξ E H c H ;
μ 0 M = ξ H E c E + χ m μ 0 H .
ε 1 = 1 + χ e = 1 + N L l o c [ α E E + N 3 ( α E B α B E α E E α B B ) ] ,
μ 1 = 1 + χ m = 1 + N L l o c [ α B B + N 3 ( α E B α B E α E E α B B ) ] ,
ξ E H = N L l o c α E B ,
ξ H E = N L l o c α B E ,
L l o c = 1 N α E E 3 N α B B 3   N 2 9 ( α E B α B E α E E α B B ) .
× E = B t ; × H = D t ;   D = 0 ; B = 0
× × E = 2 E = × ( B t )   = i ω μ 1 μ 0 × ( H + ξ H E c μ 1 μ 0 E )   = ω 2 μ 1 μ 0 ε 1 ε 0 E + ω 2 μ 1 μ 0 ξ E H c H ω 2 ξ H E c μ 1 μ 0 ( H + ξ H E c μ 1 μ 0 E )   = ω 2 [ μ 1 μ 0 ε 1 ε 0 ( ξ H E c ) 2 ] E + ω 2 μ 1 μ 0 ( ξ E H c ξ H E c ) H .
2 E + ω 2 [ ε 1 ε 0 μ 1 μ 0 ( ξ H E / c ) 2 ] E   + ω 2 μ 1 μ 0 ( ξ E H / c ξ H E / c ) H = 0 ,
k ± = n ± k 0   = k 0 2 [ 4 ε 1 μ 1 ( ξ E H + ξ H E ) 2 ± i ( ξ E H ξ H E ) ] ,
E 1 y = i ( a 1 b 1 ) ,
H 1 y = 1 c μ 1 μ 0 m a 1 + 1 c μ 1 μ 0 m + b 1 ,
m ± = 1 2 [ 4 ε 1 μ 1 ( ξ E H + ξ H E ) 2 ± i ( ξ E H + ξ H E ) ] .
E 1 z = β n k 0 a 1 β + n + k 0 b 1 ,
H 1 z = i β c μ 1 μ 0 n k 0 m a 1 i β + c μ 1 μ 0 n + k 0 m + b 1 .
E 2 y = a 2 , E 2 z = β 2 k b 2 .
H 2 y = ( β 2 2 ω μ 0 k + k ω μ 0 ) b 2 , H 2 z = β 2 ω μ 0 a 2 .
i ( a 1 b 1 ) = a 2 ; β n k 0 a 1 β + n + k 0 b 1 = β 2 k b 2 ; 1 c μ 1 μ 0 m a 1 + 1 c μ 1 μ 0 m + b 1 = ( β 2 2 ω μ 0 k + k ω μ 0 ) b 2 ; i β c μ 1 μ 0 n k 0 m a 1 i β + c μ 1 μ 0 n + k 0 m + b 1 = β 2 ω μ 0 a 2 .
( ε 2 β n + β 2 μ 1 m ) ( n + n β 2 + β + μ 1 m + n ) + ( ε 2 β + n + + β 2 μ 1 m + ) ( n + n β 2 + β μ 1 m n + ) = 0 .
S = | E y | 2 / ( | E x | 2 + | E z | 2 ) ,
P / ε 0 = N d 34 ρ 34 / ε 0 = N α E E E + N α E B c B ,
μ 0 M = N μ 0 μ ˜ 21 ρ 21 = N α B E E / c + N α B B B .
α E E = i 2 ε 0 d 34 2 ρ 44 [ γ 42 + i ( Δ E δ c ) ] [ γ 42 + i ( Δ E δ c ) ] ( γ 34 + i Δ E ) + | Ω c | 2 / 4 , α B B = i 2 ε 0 μ 21 2 ρ 11 [ γ 31 + i ( Δ B + δ c ) ] [ γ 31 + i ( Δ B + δ c ) ] ( γ 21 + i Δ B ) + | Ω c | 2 / 4 , α E B = 1 4 ε 0 d 34 μ 21 ρ 41 Ω c [ γ 42 + i ( Δ E δ c ) ] ( γ 34 + i Δ E ) + | Ω c | 2 / 4 , α B E = i 4 ε 0 d 34 μ 21 ρ 41 Ω c * [ γ 31 + i ( Δ B + δ c ) ] ( γ 21 + i Δ B ) + | Ω c | 2 / 4 . }
P / ε 0 = N α E E E l o c + N α E B c B l o c ,
μ 0 M = N α B E E l o c / c + N α B B B l o c .
E l o c = E + P / 3 ε 0 , H l o c = H + M / 3 .
P = N α E E ( ε 0 E + P / 3 ) + N ε 0 α E B c μ 0 ( H + M / 3 ) ,
M = N α B E ( E + P / 3 ε 0 ) / μ 0 c + N α B B ( H + M / 3 ) .
E = E 1 x e ^ x + E 1 y e ^ y .
H = [ ( k E 1 y ω ξ H E E 1 x c ) e ^ x + ( k E 1 x ω ξ H E E 1 y c ) e ^ y ] / μ 1 μ 0 .
k 2 E 1 x + ω 2 [ ε 1 ε 0 μ 1 μ 0 ( ξ H E c ) 2 ] E 1 x ω 2 ( ξ E H c ξ H E c ) ( ξ H E c E 1 x + k ω E 1 y ) = 0 ,
k 2 E 1 y + ω 2 [ ε 1 ε 0 μ 1 μ 0 ( ξ H E c ) 2 ] E 1 y ω 2 ( ξ E H c ξ H E c ) ( ξ H E c E 1 y k ω E 1 x ) = 0 .
Ξ = k 2 + ω 2 [ ε 1 ε 0 μ 1 μ 0 ( ξ H E c ) 2 ] ω 2 ( ξ E H c ξ H E c ) ξ H E c
Λ = k ω ( ξ E H c ξ H E c ) ,
Ξ Λ = E 1 y E 1 x = E 1 x E 1 y .
E 1 y = ± i E 1 x ,
k 2 + ω 2 [ ε 1 ε 0 μ 1 μ 0 ( ξ H E c ) 2 ] ω 2 ( ξ E H c ξ H E c ) ( ξ H E c i k ω ) = 0 .

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