Abstract

We study the nonreciprocal Tamm plasmon polaritons (TPPs) inside the light cone, which can be directly excited at the interface between the one-dimensional photonic crystal (1DPC) and magneto-optical (MO) metal film. Applying an external magnetic field on the MO metal, the broken time-reversal symmetry gives rise to such nonreciprocal electrons oscillation mediated plasmon mode. Separately exciting the forward and backward TPPs, light can be transmitted and reflected in one-way. An analytic dispersion relation based on admittance-matching approach is obtained. This design offers promising potential in realizing the optical diode.

© 2013 Optical Society of America

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  8. X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
    [CrossRef] [PubMed]
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  10. L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
    [CrossRef] [PubMed]
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  12. Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States,” Phys. Rev. Lett.106(9), 093903 (2011).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B79(8), 085416 (2009).
    [CrossRef]
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    [CrossRef]
  29. H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Opt. Lett.35(24), 4112–4114 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  34. A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,”Phys.- Usp.53(3), 243–256 (2010).
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    [CrossRef] [PubMed]

2013

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Phys. Rev. B87(4), 045406 (2013).
[CrossRef]

2011

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

C. He, M.-H. Lu, X. Heng, L. Feng, and Y.-F. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B83(7), 075117 (2011).
[CrossRef]

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Opt. Express19(19), 18393–18398 (2011).
[CrossRef] [PubMed]

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States,” Phys. Rev. Lett.106(9), 093903 (2011).
[CrossRef] [PubMed]

2010

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, “Robust one-way modes in gyromagnetic photonic crystal waveguides with different interfaces,” Appl. Phys. Lett.97(4), 041112 (2010).
[CrossRef]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys.6(3), 192–195 (2010).
[CrossRef]

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Opt. Lett.35(24), 4112–4114 (2010).
[CrossRef] [PubMed]

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,”Phys.- Usp.53(3), 243–256 (2010).
[CrossRef]

2009

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B79(8), 085416 (2009).
[CrossRef]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

B. Liang, B. Yuan, and J. C. Cheng, “Acoustic Diode: Rectification of Acoustic Energy Flux in One-Dimensional Systems,” Phys. Rev. Lett.103(10), 104301 (2009).
[CrossRef] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B80(15), 155117 (2009).
[CrossRef]

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Appl. Phys. Lett.95(1), 011101 (2009).
[CrossRef]

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B80(3), 033105 (2009).
[CrossRef]

2008

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-Way Electromagnetic Waveguide Formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008).
[CrossRef]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal,” Phys. Rev. Lett.100(1), 013905 (2008).
[CrossRef] [PubMed]

A. S. Ramírez-Duverger, J. Gaspar-Armenta, and R. García-Llamas, “Experimental determination of a surface wave at the one-dimensional photonic crystal-metal interface,” J. Opt. Soc. Am. B25(6), 1016–1024 (2008).
[CrossRef]

2007

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B76(16), 165415 (2007).
[CrossRef]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007).
[CrossRef] [PubMed]

2005

D. C. Skigin and R. A. Depine, “Transmission Resonances of Metallic Compound Gratings with Subwavelength Slits,” Phys. Rev. Lett.95(21), 217402 (2005).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

2003

J. A. Gaspar-Armenta and F. Villa, “Photonic surface-wave excitation: photonic crystal-metal interface,” J. Opt. Soc. Am. B20(11), 2349–2354 (2003).
[CrossRef]

F. Villa and J. A. Gaspar-Armenta, “Electromagnetic surface waves: photonic crystal-photonic crystal interface,” Opt. Commun.223(1-3), 109–115 (2003).
[CrossRef]

1996

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]

Abram, R. A.

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B79(8), 085416 (2009).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B76(16), 165415 (2007).
[CrossRef]

Ao, X.

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B80(3), 033105 (2009).
[CrossRef]

Ayache, M.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Baryshev, A. V.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Appl. Phys. Lett.95(1), 011101 (2009).
[CrossRef]

Brand, S.

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B79(8), 085416 (2009).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B76(16), 165415 (2007).
[CrossRef]

Chamberlain, J. M.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B76(16), 165415 (2007).
[CrossRef]

Chan, C. T.

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States,” Phys. Rev. Lett.106(9), 093903 (2011).
[CrossRef] [PubMed]

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B80(3), 033105 (2009).
[CrossRef]

Chen, X.-L.

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

Chen, Y.-F.

C. He, M.-H. Lu, X. Heng, L. Feng, and Y.-F. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B83(7), 075117 (2011).
[CrossRef]

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

Cheng, J. C.

B. Liang, B. Yuan, and J. C. Cheng, “Acoustic Diode: Rectification of Acoustic Energy Flux in One-Dimensional Systems,” Phys. Rev. Lett.103(10), 104301 (2009).
[CrossRef] [PubMed]

Chong, Y.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal,” Phys. Rev. Lett.100(1), 013905 (2008).
[CrossRef] [PubMed]

Christodoulides, D. N.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys.6(3), 192–195 (2010).
[CrossRef]

Cui, T. J.

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Phys. Rev. B87(4), 045406 (2013).
[CrossRef]

Depine, R. A.

D. C. Skigin and R. A. Depine, “Transmission Resonances of Metallic Compound Gratings with Subwavelength Slits,” Phys. Rev. Lett.95(21), 217402 (2005).
[CrossRef] [PubMed]

Dong, H. Y.

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Phys. Rev. B87(4), 045406 (2013).
[CrossRef]

Dorofeenko, A. V.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,”Phys.- Usp.53(3), 243–256 (2010).
[CrossRef]

Ebbesen, T. W.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007).
[CrossRef] [PubMed]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys.6(3), 192–195 (2010).
[CrossRef]

Fainman, Y.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Fan, S.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-Way Electromagnetic Waveguide Formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Feng, L.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

C. He, M.-H. Lu, X. Heng, L. Feng, and Y.-F. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B83(7), 075117 (2011).
[CrossRef]

Fu, J.-X.

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, “Robust one-way modes in gyromagnetic photonic crystal waveguides with different interfaces,” Appl. Phys. Lett.97(4), 041112 (2010).
[CrossRef]

García-Llamas, R.

Gaspar-Armenta, J.

Gaspar-Armenta, J. A.

F. Villa and J. A. Gaspar-Armenta, “Electromagnetic surface waves: photonic crystal-photonic crystal interface,” Opt. Commun.223(1-3), 109–115 (2003).
[CrossRef]

J. A. Gaspar-Armenta and F. Villa, “Photonic surface-wave excitation: photonic crystal-metal interface,” J. Opt. Soc. Am. B20(11), 2349–2354 (2003).
[CrossRef]

Genet, C.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Gong, Y.

Haldane, F. D. M.

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008).
[CrossRef]

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

He, C.

C. He, M.-H. Lu, X. Heng, L. Feng, and Y.-F. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B83(7), 075117 (2011).
[CrossRef]

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

Heng, X.

C. He, M.-H. Lu, X. Heng, L. Feng, and Y.-F. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B83(7), 075117 (2011).
[CrossRef]

Holden, A. J.

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, J.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Inoue, M.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Appl. Phys. Lett.95(1), 011101 (2009).
[CrossRef]

Iorsh, I.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B76(16), 165415 (2007).
[CrossRef]

Joannopoulos, J. D.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal,” Phys. Rev. Lett.100(1), 013905 (2008).
[CrossRef] [PubMed]

Kaliteevski, M.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B76(16), 165415 (2007).
[CrossRef]

Kaliteevski, M. A.

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B79(8), 085416 (2009).
[CrossRef]

Kavokin, A. V.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B76(16), 165415 (2007).
[CrossRef]

Khanikaev, A. B.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Appl. Phys. Lett.95(1), 011101 (2009).
[CrossRef]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys.6(3), 192–195 (2010).
[CrossRef]

Kivshar, Y. S.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Appl. Phys. Lett.95(1), 011101 (2009).
[CrossRef]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Li, X.-F.

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

Li, Z.-Y.

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, “Robust one-way modes in gyromagnetic photonic crystal waveguides with different interfaces,” Appl. Phys. Lett.97(4), 041112 (2010).
[CrossRef]

Liang, B.

B. Liang, B. Yuan, and J. C. Cheng, “Acoustic Diode: Rectification of Acoustic Energy Flux in One-Dimensional Systems,” Phys. Rev. Lett.103(10), 104301 (2009).
[CrossRef] [PubMed]

Lin, Z.

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States,” Phys. Rev. Lett.106(9), 093903 (2011).
[CrossRef] [PubMed]

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B80(3), 033105 (2009).
[CrossRef]

Lisyansky, A. A.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,”Phys.- Usp.53(3), 243–256 (2010).
[CrossRef]

Liu, R.-J.

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, “Robust one-way modes in gyromagnetic photonic crystal waveguides with different interfaces,” Appl. Phys. Lett.97(4), 041112 (2010).
[CrossRef]

Liu, X.

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

Long, H.

Lu, H.

Lu, M.-H.

C. He, M.-H. Lu, X. Heng, L. Feng, and Y.-F. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B83(7), 075117 (2011).
[CrossRef]

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

Lu, P.

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys.6(3), 192–195 (2010).
[CrossRef]

Merzlikin, A. M.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,”Phys.- Usp.53(3), 243–256 (2010).
[CrossRef]

Ming, N.-B.

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

Ni, X.

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Pendry, J. B.

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]

Poo, Y.

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States,” Phys. Rev. Lett.106(9), 093903 (2011).
[CrossRef] [PubMed]

Qian, X.-S.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

Raghu, S.

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008).
[CrossRef]

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

Ramírez-Duverger, A. S.

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys.6(3), 192–195 (2010).
[CrossRef]

Scherer, A.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys.6(3), 192–195 (2010).
[CrossRef]

Serebryannikov, A. E.

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B80(15), 155117 (2009).
[CrossRef]

Shelykh, I. A.

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B76(16), 165415 (2007).
[CrossRef]

Skigin, D. C.

D. C. Skigin and R. A. Depine, “Transmission Resonances of Metallic Compound Gratings with Subwavelength Slits,” Phys. Rev. Lett.95(21), 217402 (2005).
[CrossRef] [PubMed]

Soljacic, M.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal,” Phys. Rev. Lett.100(1), 013905 (2008).
[CrossRef] [PubMed]

Stewart, W. J.

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]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Tang, H.

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

Veronis, G.

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-Way Electromagnetic Waveguide Formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

Villa, F.

J. A. Gaspar-Armenta and F. Villa, “Photonic surface-wave excitation: photonic crystal-metal interface,” J. Opt. Soc. Am. B20(11), 2349–2354 (2003).
[CrossRef]

F. Villa and J. A. Gaspar-Armenta, “Electromagnetic surface waves: photonic crystal-photonic crystal interface,” Opt. Commun.223(1-3), 109–115 (2003).
[CrossRef]

Vinogradov, A. P.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,”Phys.- Usp.53(3), 243–256 (2010).
[CrossRef]

Wan, W.-W.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

Wang, G.

Wang, J.

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Phys. Rev. B87(4), 045406 (2013).
[CrossRef]

Wang, K.

Wang, L.

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-Way Electromagnetic Waveguide Formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal,” Phys. Rev. Lett.100(1), 013905 (2008).
[CrossRef] [PubMed]

Wu, R. X.

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States,” Phys. Rev. Lett.106(9), 093903 (2011).
[CrossRef] [PubMed]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

Xu, Y.-L.

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Yang, G.

Yang, Y.

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States,” Phys. Rev. Lett.106(9), 093903 (2011).
[CrossRef] [PubMed]

Yin, R.-C.

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

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]

Yu, Z.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-Way Electromagnetic Waveguide Formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

Yuan, B.

B. Liang, B. Yuan, and J. C. Cheng, “Acoustic Diode: Rectification of Acoustic Energy Flux in One-Dimensional Systems,” Phys. Rev. Lett.103(10), 104301 (2009).
[CrossRef] [PubMed]

Yuan, C.-S.

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Zhou, H.

Appl. Phys. Lett.

J.-X. Fu, R.-J. Liu, and Z.-Y. Li, “Robust one-way modes in gyromagnetic photonic crystal waveguides with different interfaces,” Appl. Phys. Lett.97(4), 041112 (2010).
[CrossRef]

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Appl. Phys. Lett.95(1), 011101 (2009).
[CrossRef]

C. He, X.-L. Chen, M.-H. Lu, X.-F. Li, W.-W. Wan, X.-S. Qian, R.-C. Yin, and Y.-F. Chen, “Tunable one-way cross-waveguide splitter based on gyromagnetic photonic crystal,” Appl. Phys. Lett.96(11), 111111 (2010).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Photonics

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics3(2), 91–94 (2009).
[CrossRef]

Nat. Phys.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys.6(3), 192–195 (2010).
[CrossRef]

Nature

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature461(7265), 772–775 (2009).
[CrossRef] [PubMed]

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature445(7123), 39–46 (2007).
[CrossRef] [PubMed]

Opt. Commun.

F. Villa and J. A. Gaspar-Armenta, “Electromagnetic surface waves: photonic crystal-photonic crystal interface,” Opt. Commun.223(1-3), 109–115 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A78(3), 033834 (2008).
[CrossRef]

Phys. Rev. B

A. E. Serebryannikov, “One-way diffraction effects in photonic crystal gratings made of isotropic materials,” Phys. Rev. B80(15), 155117 (2009).
[CrossRef]

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B80(3), 033105 (2009).
[CrossRef]

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Phys. Rev. B87(4), 045406 (2013).
[CrossRef]

M. Kaliteevski, I. Iorsh, S. Brand, R. A. Abram, J. M. Chamberlain, A. V. Kavokin, and I. A. Shelykh, “Tamm plasmon-polaritons: Possible electromagnetic states at the interface of a metal and a dielectric Bragg mirror,” Phys. Rev. B76(16), 165415 (2007).
[CrossRef]

S. Brand, M. A. Kaliteevski, and R. A. Abram, “Optical Tamm states above the bulk plasma frequency at a Bragg stack/metal interface,” Phys. Rev. B79(8), 085416 (2009).
[CrossRef]

C. He, M.-H. Lu, X. Heng, L. Feng, and Y.-F. Chen, “Parity-time electromagnetic diodes in a two-dimensional nonreciprocal photonic crystal,” Phys. Rev. B83(7), 075117 (2011).
[CrossRef]

Phys. Rev. Lett.

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]

D. C. Skigin and R. A. Depine, “Transmission Resonances of Metallic Compound Gratings with Subwavelength Slits,” Phys. Rev. Lett.95(21), 217402 (2005).
[CrossRef] [PubMed]

Y. Poo, R. X. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental Realization of Self-Guiding Unidirectional Electromagnetic Edge States,” Phys. Rev. Lett.106(9), 093903 (2011).
[CrossRef] [PubMed]

F. D. M. Haldane and S. Raghu, “Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry,” Phys. Rev. Lett.100(1), 013904 (2008).
[CrossRef] [PubMed]

Z. Yu, G. Veronis, Z. Wang, and S. Fan, “One-Way Electromagnetic Waveguide Formed at the Interface between a Plasmonic Metal under a Static Magnetic Field and a Photonic Crystal,” Phys. Rev. Lett.100(2), 023902 (2008).
[CrossRef] [PubMed]

X.-F. Li, X. Ni, L. Feng, M.-H. Lu, C. He, and Y.-F. Chen, “Tunable Unidirectional Sound Propagation through a Sonic-Crystal-Based Acoustic Diode,” Phys. Rev. Lett.106(8), 084301 (2011).
[CrossRef] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacić, “Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal,” Phys. Rev. Lett.100(1), 013905 (2008).
[CrossRef] [PubMed]

B. Liang, B. Yuan, and J. C. Cheng, “Acoustic Diode: Rectification of Acoustic Energy Flux in One-Dimensional Systems,” Phys. Rev. Lett.103(10), 104301 (2009).
[CrossRef] [PubMed]

Phys.- Usp.

A. P. Vinogradov, A. V. Dorofeenko, A. M. Merzlikin, and A. A. Lisyansky, “Surface states in photonic crystals,”Phys.- Usp.53(3), 243–256 (2010).
[CrossRef]

Physica B

C.-S. Yuan, H. Tang, C. He, X.-L. Chen, X. Ni, M.-H. Lu, Y.-F. Chen, and N.-B. Ming, “Resonant optical transmission through a one-dimensional photonic crystal adjacent to a thin metal film,” Physica B406(10), 1983–1988 (2011).
[CrossRef]

Science

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-Field Optical Hyperlens Magnifying Sub-Diffraction-Limited Objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, “Nonreciprocal Light Propagation in a Silicon Photonic Circuit,” Science333(6043), 729–733 (2011).
[CrossRef] [PubMed]

Other

H. Raether, Surface Plasmons (Springer, 1988).

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

H. A. Macleod, Thin Film Optical Filters (McGraw-Hill, 1989).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Modeling the Flow of Loght (Princeton University Press, 1995).

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Figures (6)

Fig. 1
Fig. 1

Schematic of 1DPC-MO metal model including 8 periodical TiO2/SiO2/TiO2 layers PC and MO metal film.

Fig. 2
Fig. 2

The imaginary part of optical admittances of the PC (black line) and MO metal (red and blue lines) with a pair of ± 30° incident waves (external magnetic field ωb = 0.1ωp). The dot-dashed line is the optical admittance of metal without external magnetic field.

Fig. 3
Fig. 3

The nonreciprocal TPPs at the interface of 1DPC-MO metal of the first band-gap (ωb = 0.1ωp). The shadow regions are the projected band of 1DPC along ky direction.

Fig. 4
Fig. 4

Zoom-in TPPs are calculated by various methods: the solid lines by analytic Eq. (4), the open circles by supercell method and the pluses by transmission spectra.

Fig. 5
Fig. 5

(a) The nonreciprocal transmission spectra of forward (blue lines) and backward (red lines) waves with incidence angles ± 15° (dashed lines), ± 30° (solid lines), and ± 45° (open circles), the external magnetic field ωb = 0.1ωp. (b) The transmission spectra of ± 30° incident waves, where dashed (ωb = 0.1ωp) and solid (ωb = 0.3ωp) lines represent lossless condition, open circles represent ωb = 0.1ωp and 1/τ = 0.01ωp.

Fig. 6
Fig. 6

Out-of-plane field magnetic distributions with ± 30° incident waves [open circles in Fig. 5(b)]. (a) Exciting the forward TPP at frequency 0.4175ωp. (b) Exciting the backward TPP at frequency 0.4293ωp. Red and blue color represents the positive and negative phase, respectively.

Equations (4)

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ε (ω)= I ω p 2 (ω+i/τ) 2 ω b 2 [ 1+i 1 τω i ω b ω 0 i ω b ω 1+i 1 τω 0 0 0 (ω+i/τ) 2 ω b 2 ω(ω+i/τ) ].
η m ± = η 0 n 2 ω ε d i ε f c k y ε d n 2 ω 2 c 2 k y 2 .
η PC = η p [sin(2 δ p )cos( δ q )+ ρ + cos(2 δ p )sin( δ q ) ρ sin( δ q )] sin{accos[cos(2 δ p )cos( δ q ) ρ + sin(2 δ p )sin( δ q )]} ,
η PC = η m .

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