Abstract

The properties of the phase shift of wave reflected from one-dimensional photonic crystals consisting of periodic layers of single-negative (permittivity- or permeability-negative) materials are demonstrated. As the incident angle increases, the reflection phase shift of TE wave decreases, while that of TM wave increases. The phase shifts of both polarized waves vary smoothly as the frequency changes across the photonic crystal stop band. Consequently, the difference between the phase shift of TE and that of TM wave could remain constant in a rather wide frequency range inside the stop band. These properties are useful to design wave plate or retarder which can be used in wide spectral band. In addition, a broadband photonic crystal quarter-wave plate is proposed.

© 2010 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
  35. N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
    [CrossRef] [PubMed]
  36. A. Alù and N. Engheta, “All optical metamaterial circuit board at the nanoscale,” Phys. Rev. Lett. 103(14), 143902 (2009).
    [CrossRef] [PubMed]

2010 (1)

J. M. Manceau, N. H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: Blueshift tunability and phase modulation,” Appl. Phys. Lett. 96(2), 021111 (2010).
[CrossRef]

2009 (5)

2008 (2)

O. Paul, C. Imhof, B. Reinhard, R. Zengerle, and R. Beigang, “Negative index bulk metamaterial at terahertz frequencies,” Opt. Express 16(9), 6736–6744 (2008).
[CrossRef] [PubMed]

Y. H. Chen, “Defect modes merging in one-dimensional photonic crystals with multiple single-negative material defects,” Appl. Phys. Lett. 92(1), 011925 (2008).
[CrossRef]

2007 (2)

R. P. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2 Pt 2), 026606 (2007).
[CrossRef] [PubMed]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

2006 (3)

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89(6), 061121 (2006).
[CrossRef]

L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(5 Pt 2), 056615 (2006).
[CrossRef]

2005 (3)

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86(15), 151112 (2005).
[CrossRef]

T. Fujishige, C. Caloz, and T. Itoh, “Experimental demonstration of transparency in the ENG-MNG pair in a CRLH transmission-line implementation,” Microw. Opt. Technol. Lett. 46(5), 476–481 (2005).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
[CrossRef] [PubMed]

2004 (2)

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1 Pt 2), 016601 (2004).
[CrossRef] [PubMed]

L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70(24), 245102 (2004).
[CrossRef]

2003 (7)

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
[CrossRef]

A. Lakhtakia and C. M. Krowne, “Restricted equivalence of paired epsilon-negative and mu-negative layers to a negative phase-velocity material (alias left-handed material),” Optik (Stuttg.) 114(7), 305–307 (2003).

A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. 51(10), 2558–2571 (2003).
[CrossRef]

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[CrossRef]

F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, “Large polarization change in two-dimensional metallic photonic crystals in subterahertz region,” Appl. Phys. Lett. 82(16), 2568–2570 (2003).
[CrossRef]

2002 (1)

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92(10), 5930–5935 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000 (1)

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1998 (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers, ” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

1997 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

1991 (1)

A. Z. Genack and N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66(16), 2064–2067 (1991).
[CrossRef] [PubMed]

1990 (1)

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[CrossRef] [PubMed]

1987 (2)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Ahmad, F. R.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

Alù, A.

A. Alù and N. Engheta, “All optical metamaterial circuit board at the nanoscale,” Phys. Rev. Lett. 103(14), 143902 (2009).
[CrossRef] [PubMed]

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. 51(10), 2558–2571 (2003).
[CrossRef]

Beigang, R.

Birks, T. A.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers, ” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers, ” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

Caloz, C.

T. Fujishige, C. Caloz, and T. Itoh, “Experimental demonstration of transparency in the ENG-MNG pair in a CRLH transmission-line implementation,” Microw. Opt. Technol. Lett. 46(5), 476–481 (2005).
[CrossRef]

Chen, H.

L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(5 Pt 2), 056615 (2006).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70(24), 245102 (2004).
[CrossRef]

Chen, Y. H.

Y. H. Chen, “Omnidirectional and independently tunable defect modes in fractal photonic crystals containing single-negative materials,” Appl. Phys. B 95(4), 757–761 (2009).
[CrossRef]

Y. H. Chen, “Defect modes merging in one-dimensional photonic crystals with multiple single-negative material defects,” Appl. Phys. Lett. 92(1), 011925 (2008).
[CrossRef]

Chiao, R. Y.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Cui, T. J.

R. P. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2 Pt 2), 026606 (2007).
[CrossRef] [PubMed]

Dai, Q. F.

Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89(6), 061121 (2006).
[CrossRef]

Dong, J. F.

Eleftheriades, G. V.

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92(10), 5930–5935 (2002).
[CrossRef]

Engheta, N.

A. Alù and N. Engheta, “All optical metamaterial circuit board at the nanoscale,” Phys. Rev. Lett. 103(14), 143902 (2009).
[CrossRef] [PubMed]

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. 51(10), 2558–2571 (2003).
[CrossRef]

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
[CrossRef]

Fujishige, T.

T. Fujishige, C. Caloz, and T. Itoh, “Experimental demonstration of transparency in the ENG-MNG pair in a CRLH transmission-line implementation,” Microw. Opt. Technol. Lett. 46(5), 476–481 (2005).
[CrossRef]

Gaeta, A. L.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

Gallagher, M. T.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

Garcia, N.

A. Z. Genack and N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66(16), 2064–2067 (1991).
[CrossRef] [PubMed]

Genack, A. Z.

A. Z. Genack and N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66(16), 2064–2067 (1991).
[CrossRef] [PubMed]

Grbic, A.

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92(10), 5930–5935 (2002).
[CrossRef]

Hangyo, M.

F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, “Large polarization change in two-dimensional metallic photonic crystals in subterahertz region,” Appl. Phys. Lett. 82(16), 2568–2570 (2003).
[CrossRef]

He, L.

L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(5 Pt 2), 056615 (2006).
[CrossRef]

Hickmann, J. M.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Huang, D.

R. P. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2 Pt 2), 026606 (2007).
[CrossRef] [PubMed]

Huang, W. P.

Imada, M.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Imhof, C.

Istrate, E.

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86(15), 151112 (2005).
[CrossRef]

Itoh, T.

T. Fujishige, C. Caloz, and T. Itoh, “Experimental demonstration of transparency in the ENG-MNG pair in a CRLH transmission-line implementation,” Microw. Opt. Technol. Lett. 46(5), 476–481 (2005).
[CrossRef]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

Kafesaki, M.

J. M. Manceau, N. H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: Blueshift tunability and phase modulation,” Appl. Phys. Lett. 96(2), 021111 (2010).
[CrossRef]

Kim, G. H.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

Kim, S. B.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

Knight, J. C.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers, ” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

Koch, K. W.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

Kondo, T.

F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, “Large polarization change in two-dimensional metallic photonic crystals in subterahertz region,” Appl. Phys. Lett. 82(16), 2568–2570 (2003).
[CrossRef]

Koschny, T.

J. F. Dong, J. F. Zhou, T. Koschny, and C. Soukoulis, “Bi-layer cross chiral structure with strong optical activity and negative refractive index,” Opt. Express 17(16), 14172–14179 (2009).
[CrossRef] [PubMed]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
[CrossRef]

Krowne, C. M.

A. Lakhtakia and C. M. Krowne, “Restricted equivalence of paired epsilon-negative and mu-negative layers to a negative phase-velocity material (alias left-handed material),” Optik (Stuttg.) 114(7), 305–307 (2003).

Kwon, S. H.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia and C. M. Krowne, “Restricted equivalence of paired epsilon-negative and mu-negative layers to a negative phase-velocity material (alias left-handed material),” Optik (Stuttg.) 114(7), 305–307 (2003).

Lee, Y. H.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

Leung, K. M.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[CrossRef] [PubMed]

Li, H. Q.

L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(5 Pt 2), 056615 (2006).
[CrossRef]

Li, Y. W.

Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89(6), 061121 (2006).
[CrossRef]

Li-Gang, W.

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1 Pt 2), 016601 (2004).
[CrossRef] [PubMed]

Liu, J. H.

Liu, R. P.

R. P. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2 Pt 2), 026606 (2007).
[CrossRef] [PubMed]

Liu, Y. F.

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[CrossRef] [PubMed]

Manceau, J. M.

J. M. Manceau, N. H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: Blueshift tunability and phase modulation,” Appl. Phys. Lett. 96(2), 021111 (2010).
[CrossRef]

Markos, P.

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
[CrossRef]

McCormick, C. F.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[CrossRef]

Miyamaru, F.

F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, “Large polarization change in two-dimensional metallic photonic crystals in subterahertz region,” Appl. Phys. Lett. 82(16), 2568–2570 (2003).
[CrossRef]

Mock, J. J.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

Müller, D.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

Nagashima, T.

F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, “Large polarization change in two-dimensional metallic photonic crystals in subterahertz region,” Appl. Phys. Lett. 82(16), 2568–2570 (2003).
[CrossRef]

Nian-Hua, L.

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1 Pt 2), 016601 (2004).
[CrossRef] [PubMed]

Noda, S.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Ouzounov, D. G.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

Paul, O.

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Qiang, L.

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1 Pt 2), 016601 (2004).
[CrossRef] [PubMed]

Reinhard, B.

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Russell, P. S. J.

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers, ” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

Ryu, H. Y.

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

Salandrino, A.

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
[CrossRef] [PubMed]

Sargent, E. H.

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86(15), 151112 (2005).
[CrossRef]

Schubert, E. F.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Shen, N. H.

J. M. Manceau, N. H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: Blueshift tunability and phase modulation,” Appl. Phys. Lett. 96(2), 021111 (2010).
[CrossRef]

Shi-Yao, Z.

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1 Pt 2), 016601 (2004).
[CrossRef] [PubMed]

Silcox, J.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

Smith, D. R.

R. P. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2 Pt 2), 026606 (2007).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Solli, D. R.

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[CrossRef]

Soukoulis, C.

Soukoulis, C. M.

J. M. Manceau, N. H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: Blueshift tunability and phase modulation,” Appl. Phys. Lett. 96(2), 021111 (2010).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Thomas, M. G.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

Tzortzakis, S.

J. M. Manceau, N. H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: Blueshift tunability and phase modulation,” Appl. Phys. Lett. 96(2), 021111 (2010).
[CrossRef]

Venkataraman, N.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
[CrossRef]

Wang, H. Z.

Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89(6), 061121 (2006).
[CrossRef]

Wang, L. G.

L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70(24), 245102 (2004).
[CrossRef]

Wu, C. J.

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Yeh, D. W.

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

Zengerle, R.

Zhang, L. W.

L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(5 Pt 2), 056615 (2006).
[CrossRef]

Zhang, W. F.

Zhang, Y. W.

L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(5 Pt 2), 056615 (2006).
[CrossRef]

Zhao, B.

R. P. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2 Pt 2), 026606 (2007).
[CrossRef] [PubMed]

Zhao, W.

Zhou, J. F.

Zhu, S. Y.

L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70(24), 245102 (2004).
[CrossRef]

Appl. Phys. B (1)

Y. H. Chen, “Omnidirectional and independently tunable defect modes in fractal photonic crystals containing single-negative materials,” Appl. Phys. B 95(4), 757–761 (2009).
[CrossRef]

Appl. Phys. Lett. (8)

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[CrossRef]

J. M. Manceau, N. H. Shen, M. Kafesaki, C. M. Soukoulis, and S. Tzortzakis, “Dynamic response of metamaterials in the terahertz regime: Blueshift tunability and phase modulation,” Appl. Phys. Lett. 96(2), 021111 (2010).
[CrossRef]

Y. H. Chen, “Defect modes merging in one-dimensional photonic crystals with multiple single-negative material defects,” Appl. Phys. Lett. 92(1), 011925 (2008).
[CrossRef]

S. H. Kwon, H. Y. Ryu, G. H. Kim, Y. H. Lee, and S. B. Kim, “Photonic bandedge lasers in two-dimensional square-lattice photonic crystal slabs,” Appl. Phys. Lett. 83(19), 3870–3872 (2003).
[CrossRef]

D. R. Solli, C. F. McCormick, R. Y. Chiao, and J. M. Hickmann, “Experimental demonstration of photonic crystal waveplates,” Appl. Phys. Lett. 82(7), 1036–1038 (2003).
[CrossRef]

F. Miyamaru, T. Kondo, T. Nagashima, and M. Hangyo, “Large polarization change in two-dimensional metallic photonic crystals in subterahertz region,” Appl. Phys. Lett. 82(16), 2568–2570 (2003).
[CrossRef]

E. Istrate and E. H. Sargent, “Measurement of the phase shift upon reflection from photonic crystals,” Appl. Phys. Lett. 86(15), 151112 (2005).
[CrossRef]

Q. F. Dai, Y. W. Li, and H. Z. Wang, “Broadband two-dimensional photonic crystal wave plate,” Appl. Phys. Lett. 89(6), 061121 (2006).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

A. Alù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. 51(10), 2558–2571 (2003).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. Appl. Phys. (1)

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92(10), 5930–5935 (2002).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

T. Fujishige, C. Caloz, and T. Itoh, “Experimental demonstration of transparency in the ENG-MNG pair in a CRLH transmission-line implementation,” Microw. Opt. Technol. Lett. 46(5), 476–481 (2005).
[CrossRef]

Nature (1)

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Optik (Stuttg.) (1)

A. Lakhtakia and C. M. Krowne, “Restricted equivalence of paired epsilon-negative and mu-negative layers to a negative phase-velocity material (alias left-handed material),” Optik (Stuttg.) 114(7), 305–307 (2003).

Phys. Rev. B (1)

L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70(24), 245102 (2004).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (4)

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 065602 (2003).
[CrossRef]

R. P. Liu, T. J. Cui, D. Huang, B. Zhao, and D. R. Smith, “Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2 Pt 2), 026606 (2007).
[CrossRef] [PubMed]

W. Li-Gang, L. Nian-Hua, L. Qiang, and Z. Shi-Yao, “Propagation of coherent and partially coherent pulses through one-dimensional photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1 Pt 2), 016601 (2004).
[CrossRef] [PubMed]

L. W. Zhang, Y. W. Zhang, L. He, H. Q. Li, and H. Chen, “Experimental study of photonic crystals consisting of E-negative and μ-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(5 Pt 2), 056615 (2006).
[CrossRef]

Phys. Rev. Lett. (8)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58(23), 2486–2489 (1987).
[CrossRef] [PubMed]

K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in face-centered-cubic dielectric media,” Phys. Rev. Lett. 65(21), 2646–2649 (1990).
[CrossRef] [PubMed]

A. Z. Genack and N. Garcia, “Observation of photon localization in a three-dimensional disordered system,” Phys. Rev. Lett. 66(16), 2064–2067 (1991).
[CrossRef] [PubMed]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High Extraction Efficiency of Spontaneous Emission from Slabs of Photonic Crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, “Circuit elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors,” Phys. Rev. Lett. 95(9), 095504 (2005).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76(25), 4773–4776 (1996).
[CrossRef] [PubMed]

A. Alù and N. Engheta, “All optical metamaterial circuit board at the nanoscale,” Phys. Rev. Lett. 103(14), 143902 (2009).
[CrossRef] [PubMed]

Science (4)

N. Engheta, “Circuits with light at nanoscales: optical nanocircuits inspired by metamaterials,” Science 317(5845), 1698–1702 (2007).
[CrossRef] [PubMed]

J. C. Knight, J. Broeng, T. A. Birks, and P. S. J. Russell, “Photonic band gap guidance in optical fibers, ” Science 282(5393), 1476–1478 (1998).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Schematic representation of the 1D PC constituted by SNG materials. The gray and white regions represent the ENG materials and MIMs, respectively.

Fig. 2
Fig. 2

Photonic band structure as a function of the incident angle for an infinite periodic structure (AB) s without considering the losses. The thicknesses are dA = 16 mm and dB = 8 mm.

Fig. 3
Fig. 3

(a) Reflectance spectrum at normal incidence in structure (AB)8 with dA = 16 mm and dB = 8. (b)-(e) The reflection phase shift Ф as a function of frequency at different angles of incidence. The dot line and dash line denote Ф for TE and TM wave, respectively. The dash-dot line denotes ΔФ = Ф TM TE.

Fig. 4
Fig. 4

(a) The reflectance spectra, the effective permittivity ε eff and the effective permeability μ eff for (b) TE and (c) TM wave of structure (AB)8 with dA = 16 mm and dB = 8 at angle of incidence θ = 60°. (d) The reflection phase of the effective medium slab with parameters the same as in (b) and (c).

Fig. 5
Fig. 5

Numerical simulation and effective medium theoretical calculation results of the reflection phase and the phase difference at ω = 5.00 GHz under different incident angles.

Fig. 6
Fig. 6

The reflection phase shift Ф as a function of frequency at angle of incidence θ = 60° in PC structure (AB)8 with dA = 16 mm and (a) dB = 10 mm, (b) dB = 8 mm, (c) dB = 6 mm, (d) dB = 4 mm.

Fig. 7
Fig. 7

(a) Reflectance and (b) the reflection phase shift as functions of frequency at angle of incidence θ = 65° in PC structure (AB)8 with dA = 16 mm and dB = 4 mm.

Fig. 8
Fig. 8

Photonic band structure for the infinite periodic structure (AB) s with parameters given by Eqs. (8) and (9) without considering the losses. The thicknesses are dA = 4 mm and dB = 20 mm.

Fig. 9
Fig. 9

Dependence of ФTE , ФTM , and ΔФ on the incident angle in periodic structure (AB)12 with parameters given by Eqs. (8) and (9).

Fig. 10
Fig. 10

(a) Reflectance and (b) the reflection phase shift as functions of frequency at angle of incidence θ = 55° in PC structure (AB)12 with parameters given by Eqs. (8) and (9).

Equations (9)

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

M l = ( cos ( k l z d l )     i 1 q l sin ( k l z d l ) i q l sin ( k l z d l )     cos ( k l z d l ) ) ,
r ( ω ) = cos θ ( x 11 x 22 ) ( cos 2 θ x 12 x 21 ) cos θ ( x 11 + x 22 ) ( cos 2 θ x 12 + x 21 ) ,
cos β z ( d A + d B ) = cos ( k A z d A ) cos ( k B z d B ) 1 2 ( k A z μ 1 μ 2 k B z + k B z μ 2 μ 1 k A z ) sin ( k A z d A ) sin ( k B z d B ) ,
ε 1 = ε a ω e p 2 ω 2 i ω γ e ,     μ 1 = μ a
ε 2 = ε b ,     μ 2 = μ b ω m p 2 ω 2 i ω γ m
μ e f f = d A d A + d B μ A + d B d A + d B μ B , ε e f f = d A d A + d B ε A + d B d A + d B ε B sin 2 θ ( d A d A + d B 1 μ A + d B d A + d B 1 μ B )     + sin 2 θ ( 1 d A d A + d B 1 μ A + d B d A + d B 1 μ B ) ,                          
ε e f f = d A d A + d B ε A + d B d A + d B ε B , μ e f f = d A d A + d B μ A + d B d A + d B μ B sin 2 θ ( d A d A + d B 1 ε A + d B d A + d B 1 ε B )     + sin 2 θ ( 1 d A d A + d B 1 ε A + d B d A + d B 1 ε B ) ,                            
ε 1 = 1 F 1 ω 2 ω 2 ω e r 2 + i ω γ e ,     μ 1 = 1 ,
ε 2 = 1 ,     μ 2 = 1 F 2 ω 2 ω 2 ω m r 2 + i ω γ m ,

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