Abstract

Nonreciprocal light phenomena, including one-way wave propagation along an interface and one-way optical tunneling, are presented at terahertz frequencies in a system of magnetically controlled multi-layered structure. By varying the surface termination and the surrounding medium, it is found that the nonreciprocal bound or radiative Tamm plasmon polartions can be supported, manipulated, and well excited. Two different types of contributions to the non-reciprocity are analyzed, including the direct effect of magnetization-dependent surface terminating layer as well as violation of the periodicity in truncated multi-layered systems. Calculations on the asymmetrical dispersion relation of surface modes, field distribution, and transmission spectra through the structure are employed to confirm the theoretical results, which may potentially impact the design of tunable and compact optical isolators.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  42. H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Physical Review B 87, 045406 (2013).
    [Crossref]
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    [Crossref]
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2018 (1)

B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
[Crossref]

2017 (1)

M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
[Crossref]

2016 (2)

F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

S. Lin, K. Bhattarai, J. Zhou, and D. Talbayev, “Thin InSb layers with metallic gratings: a novel platform for spectrally-selective THz plasmonic sensing,” Opt. Express 24, 19448–19457 (2016).
[Crossref] [PubMed]

2015 (5)

B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
[Crossref]

S. Chen, F. Fan, X. Wang, P. Wu, H. Zhang, and S. Chang, “Terahertz isolator based on nonreciprocal magneto-metasurface,” Opt. Express 23, 1015–1024 (2015).
[Crossref] [PubMed]

S. Longhi, “Nonreciprocal transmission in photonic lattices based on unidirectional coherent perfect absorption,” Optics Letters 40, 1278–1281 (2015).
[Crossref]

J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
[Crossref]

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

2014 (5)

R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
[Crossref]

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with a nonlinear Fano diode,” Physical Review B 89, 134306 (2014).
[Crossref]

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
[Crossref]

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

2013 (5)

F. Fan, S. Chen, X. Wang, and S. Chang, “Tunable nonreciprocal terahertz transmission and enhancement base on metal/magneto-optic plasmonic lens,” Opt. Express 21, 8614–8621 (2013).
[Crossref] [PubMed]

M. Mandehgar, Y. Yang, and D. Grischkowsky, “Atmosphere characterization for simulation of the two optimal wireless terahertz digital communication links,” Opt. Lett. 38, 3437–3440 (2013).
[Crossref] [PubMed]

H. Y. Dong, J. Wang, and T. J. Cui, “One-way Tamm plasmon polaritons at the interface between magnetophotonic crystals and conducting metal oxides,” Physical Review B 87, 045406 (2013).
[Crossref]

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
[Crossref]

2012 (6)

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
[Crossref] [PubMed]

H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
[Crossref] [PubMed]

L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

2011 (3)

K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
[Crossref]

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
[Crossref] [PubMed]

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

2010 (2)

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

W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010).
[Crossref]

2009 (3)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nature Photonics 3, 91–94 (2009).
[Crossref]

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
[Crossref]

2008 (4)

F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguide in photonic crystals with broken time-reversal symmetry,” Physical Review Letters 100, 013904 (2008).
[Crossref]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Physical Review A 78, 033834 (2008).
[Crossref]

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[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 crytal,” Physical Review Letters 100, 023902 (2008).
[Crossref]

2007 (3)

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,” Physical Review B 76, 165415 (2007).
[Crossref]

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

2005 (3)

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
[Crossref]

R. Li and M. Levy, “Bragg grating magnetic photonic crystal waveguides,” Applied Physics Letters 86, 251102 (2005).
[Crossref]

J. G. Rivas, C. Janke, P. H. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express 13, 847–859 (2005).
[Crossref]

2004 (1)

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717–754 (2004).
[Crossref]

2003 (1)

M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
[Crossref]

2001 (1)

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
[Crossref]

Abram, R. A.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[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,” Physical Review B 76, 165415 (2007).
[Crossref]

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

Alù, A.

M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
[Crossref]

F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
[Crossref]

Assanto, G.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
[Crossref]

Azzini, S.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

Badugu, R.

R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
[Crossref]

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

Baets, R.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Baryshev, A. V.

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
[Crossref]

Bellessa, J.

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

Bhattarai, K.

Bolivar, P. H.

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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,” Physical Review B 76, 165415 (2007).
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C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
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A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
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M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
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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,” Physical Review B 76, 165415 (2007).
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A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
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K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
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A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
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Lakowicz, J. R.

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Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
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R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
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B. H. Cheng, H. W. Chen, K. J. Chang, Y. Lan, and D. P. Tsai, “Magnetically controlled planar hyperbolic metamaterials for subwavelength resolutions,” Scientific Reports 5, 18172 (2015).
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K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
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G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
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O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
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C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
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J. Wang, H. Y. Dong, C. W. Ling, C. T. Chan, and K. H. Fung, “Nonreciprocal μ-near-zero mode in PT-symmetric magnetic domains,” Physical Review B 91, 235410 (2015).
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H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
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H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
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K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
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Liu, X.

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
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M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
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K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
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I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
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A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
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Marquardt, F.

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
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K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
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M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
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Ming, H.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
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Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
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M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
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F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

Miroshnichenko, A. E.

Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with a nonlinear Fano diode,” Physical Review B 89, 134306 (2014).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
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K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
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K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
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D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
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Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
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F. D. M. Haldane and S. Raghu, “Possible realization of directional optical waveguide in photonic crystals with broken time-reversal symmetry,” Physical Review Letters 100, 013904 (2008).
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D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
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M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
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F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
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G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
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M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
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G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
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O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
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C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
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A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
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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,” Physical Review B 76, 165415 (2007).
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I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
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Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
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M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
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N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
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G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
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O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
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C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
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Vasil’ev, A. P.

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
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Verhagen, E.

M. Miri, F. Ruesink, E. Verhagen, and A. Alù, “Optical nonreciprocity based on optomechanical coupling,” Physical Review Applied 7, 064014 (2017).
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F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
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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 crytal,” Physical Review Letters 100, 023902 (2008).
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Wang, G.

Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
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Wang, K.

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
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Y. Gong, X. Liu, H. Lu, L. Wang, and G. Wang, “Perfect absorber supported by optical Tamm states in plasmonic waveguide,” Optics Express 19, 18393–18398 (2011).
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Wang, P.

Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
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Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
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Wang, Q. J.

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
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Wang, R.

Wang, X.

Wang, Z.

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
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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 crytal,” Physical Review Letters 100, 023902 (2008).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
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K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
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Wu, R.

Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
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B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
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Y. Xu and A. E. Miroshnichenko, “Reconfigurable nonreciprocity with a nonlinear Fano diode,” Physical Review B 89, 134306 (2014).
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L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, “An all-silicon passive optical diode,” Science 335, 447–450 (2012).
[Crossref]

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H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
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B. He, L. Yang, X. Jiang, and M. Xiao, “Transmission nonreciprocity in a mutually coupled circulating structure,” Physical Review Letters 120, 203904 (2018).
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M. Mandehgar, Y. Yang, and D. Grischkowsky, “Atmosphere characterization for simulation of the two optimal wireless terahertz digital communication links,” Opt. Lett. 38, 3437–3440 (2013).
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Y. Poo, R. Wu, Z. Lin, Y. Yang, and C. T. Chan, “Experimental realization of self-guiding unidirectional electromagnetic edge states,” Physical Review Letters 106, 093903 (2011).
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Yao, P.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
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Yu, S.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
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Yu, S. F.

W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010).
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Yu, Z.

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
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H. Lira, Z. Yu, S. Fan, and M. Lipson, “Electrically driven nonreciprocity induced by interband photonic transition on a silicon chip,” Physical Review Letters 109, 033901 (2012).
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K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nature Photonics 3, 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 crytal,” Physical Review Letters 100, 023902 (2008).
[Crossref]

Zhang, D.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
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Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
[Crossref] [PubMed]

Zhang, H.

Zhang, W. L.

W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010).
[Crossref]

Zhang, Y.

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
[Crossref] [PubMed]

Zhou, H.

H. Zhou, G. Yang, K. Wang, H. Long, and P. Lu, “Multiple optical Tamm states at a metal-dielectric mirror interface,” Optics Letters 35, 4112–4114 (2010).
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Zhou, J.

Zhu, L.

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
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Y. Chen, D. Zhang, L. Zhu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Tamm plasmon- and surface plasmon-coupled emission from hybrid plasmonic-photonic structures,” Optica 1, 407–413 (2014).
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ACS Photonics (1)

G. Lheureux, S. Azzini, C. Symonds, P. Senellart, A. Lemaître, C. Sauvan, J. Hugonin, J. Greffet, and J. Bellessa, “Polarization-controlled confined Tamm plasmon laser,” ACS Photonics 2, 842–848 (2015).
[Crossref]

Analytical Biochemistry (1)

R. Badugu, E. Descrovi, and J. R. Lakowicz, “Radiative decay engineering 7: Tamm state-coupled emission using a hybrid plasmonic-photonic structure,” Analytical Biochemistry 445, 1–13 (2014).
[Crossref]

Applied Physics Letters (7)

O. Gazzano, S. M. de Vasconcellos, K. Gauthron, C. Symonds, P. Voisin, J. Bellessa, A. Lemaître, and P. Senellart, “Single photon source using confined Tamm plasmon modes,” Applied Physics Letters 100, 232111 (2012).
[Crossref]

A. Kavokin, I. Shelykh, and G. Malpuech, “Optical Tamm states for the fabrication of polariton lasers,” Applied Physics Letters 87, 261105 (2005).
[Crossref]

C. Symonds, A. Lemaître, P. Senellart, M. H. Jomaa, S. A. Guebrou, E. Homeyer, G. Brucoli, and J. Bellessa, “Lasing in a hybrid GaAs/silver Tamm structure,” Applied Physics Letters 100, 121122 (2012).
[Crossref]

M. E. Sasin, R. P. Seisyan, M. A. Kaliteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil’ev, V. S. Mikhrin, and A. V. Kavokin, “Tamm plasmon polaritons: slow and spatially compact light,” Applied Physics Letters 92, 251112 (2008).
[Crossref]

R. Li and M. Levy, “Bragg grating magnetic photonic crystal waveguides,” Applied Physics Letters 86, 251102 (2005).
[Crossref]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, “All-optical diode in a periodically poled lithium niobate waveguide,” Applied Physics Letters 79, 314–316 (2001).
[Crossref]

A. B. Khanikaev, A. V. Baryshev, M. Inoue, and Y. S. Kivshar, “One-way electromagnetic Tamm states in magnetophotonic structures,” Applied Physics Letters 95, 011101 (2009).
[Crossref]

Laser Photonics Reviews (1)

Y. Chen, D. Zhang, D. Qiu, L. Zhu, S. Yu, P. Yao, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Back focal plane imaging of Tamm plasmons and their coupled emission,” Laser Photonics Reviews 8, 933–940 (2014).
[Crossref]

Nat. Photonics (1)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

Nature (1)

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461, 772–775 (2009).
[Crossref] [PubMed]

Nature Communications (1)

F. Ruesink, M. Miri, A. Alù, and E. Verhagen, “Nonreciprocity and magnetic-free isolation based on optomechanical interactions,” Nature Communications 7, 13662 (2016).
[Crossref] [PubMed]

Nature Photonics (2)

D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, “What is and what is not an optical isolator,” Nature Photonics 7, 579–582 (2013).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nature Photonics 3, 91–94 (2009).
[Crossref]

Nature Physics (2)

N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, “Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops,” Nature Physics 10, 923–927 (2014).
[Crossref]

K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, “Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering,” Nature Physics 13, 465–471 (2012).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Optica (1)

Optics Communications (1)

W. L. Zhang and S. F. Yu, “Bistable switching using an optical Tamm cavity with a Kerr medium,” Optics Communications 283, 2622–2626 (2010).
[Crossref]

Optics Express (2)

K. J. Lee, J. W. Wu, and K. Kim, “Enhanced nonlinear optical effects due to the excitation of optical Tamm plasmon polaritons in one-dimensional photonic crytal structures,” Optics Express 21, 28817–28823 (2013).
[Crossref]

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

Optics Letters (5)

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

M. Soljačić, C. Luo, and J. D. Joannopoulos, “Nonlinear photonic crystal microdevices for optical integration,” Optics Letters 28, 637–639 (2003).
[Crossref]

S. Longhi, “Nonreciprocal transmission in photonic lattices based on unidirectional coherent perfect absorption,” Optics Letters 40, 1278–1281 (2015).
[Crossref]

K. Fang, Z. Yu, V. Liu, and S. Fan, “Ultracompact nonreciprocal optical isolator based on guided resonance in a magneto-optical photonic crystal slab,” Optics Letters 36, 4254–4256 (2011).
[Crossref]

B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Optics Letters 37, 1895–1897 (2012).
[Crossref] [PubMed]

Phys. Stat. Sol. (a) (1)

I. A. Shelykh, M. Kaliteevski, A. V. Kavokin, S. Brand, R. A. Abram, J. M. Chamberlain, and G. Malpuech, “Interface photonic states at the boundary between a metal and a dielectric Bragg mirror,” Phys. Stat. Sol. (a) 204, 522–525 (2007).
[Crossref]

Physical Review A (1)

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Physical Review A 78, 033834 (2008).
[Crossref]

Physical Review Applied (1)

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic diagram of the proposed MPC structure, formed by alternating magneto-optical active [permittivity ϵ 1 ¯ ] and isotropic dielectric layers [permittivity ϵ 2 ]. The semi-infinite MPC structure with a top magneto-active layer is embedded into a kind of homogeneous background dielectric material with its permittivity ϵ b . (b) Dispersion of bound TPPs at the surface of MPCs. Gray and red lines correspond to the TPPs solutions when the external magnetic field is absent [B = 0T] or present [ B = 0.1 T], respectively. f + and f denote respectively the cutoff frequencies where the forward- and backward-propagating modes vanish, then representing the one-way wave propagation by light blue region. Yellow and white regions correspond to pass-bands and stop-gaps of an infinite MPC. Light lines for the background material are also shown by dotted lines.
Fig. 2
Fig. 2 Steady-state field distribution Hz at a frequency f = 2.8 THz with the applied magnetic field (a) B = 0T; (b) B = 0.1 T, in the absence of the scatterer; (c) B = 0.1 T, when a large PEC obstacle [height 40 μ m and width 8 μ m ] is inserted. The line source at the interface is marked with " " in the figure.
Fig. 3
Fig. 3 Effect of (a) applied magnetic field B and (b) the permittivity ϵ b of the background material on the cutoff frequency f + and f , and the bandwidth Δ f = f + f of one-way wave propagation band. Note that ϵ b = 4 and B = 0.1 T are used in (a) and (b), respectively. Other parameters are the same as Fig. 1.
Fig. 4
Fig. 4 (a) Dispersion for bound (or radiative) TPPs lying outside (inside) the light cone for the background material by tuning the surface terminating layer from σ = 0.8 to σ = 0.1 . (b) Effect of surface terminating layer on the cutoff frequency f + and f , and the bandwidth Δ f = f + f of one-way wave propagation band. Note that ϵ b = 4 and B = 0.1 T are used in (b). Other parameters are the same as Fig. 1.
Fig. 5
Fig. 5 (a) The schematic diagram is the same as Fig. 1(a) except that the top layer of the MPC and the surrounding materials are replaced by the dielectric and metallic material, respectively. (b) Dispersion for TPPs [the red line] consists of radiativesolutions lying inside the light cone for the background material (with permittivity, ϵ e = 16 ). The applied magnetic field B = 0.3 T and the parameter γ for surface terminating layer is set to γ = 0.4 . All other parameters and settings are the same as in Fig. 1.
Fig. 6
Fig. 6 Steady-state field patterns Hz for the finite-size structure consisting of a unmagnetized InSb layer (with thickness a = 28 μ m ) on the surface of a 3-period MPC plus with a dielectric first layer under the back illumination (a) and front illumination (b), when the incident angle θ is chosen to be θ = 17.72 0 . The proposed finite-size structure is embedded into a uniform surrounding medium with permittivity ϵ e = ϵ 2 = 16 . Here f = 2.67 THz is used. Other parametersare identical with those in Fig. 5. In (a), the TPPs are well excited at the interface between non-magnetized InSb and MPCs, exhibiting strong enhancement on the magnetic field by the white color with its magnitude beyond the scope of the colorbar.
Fig. 7
Fig. 7 Nonreciprocal transmittance T through the finite-size structure in Fig. 6.
Fig. 8
Fig. 8 The calculated isolation spectra for positive and negative incident angles when the loss in ML is absent (a) α = 0 , and present (b) α = 0.1 THz.

Equations (10)

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ϵ ¯ 1 = ( ϵ 1 i Δ 1 0 i Δ 1 ϵ 1 0 0 0 ϵ 1 ) .
M ^ i j = ϵ j 2 Δ j 2 2 ϵ j k x j ( F j * + F i F j * F i * F j F i F j + F i * ) ,
T ^ ( a 0 b 0 ) = e i K Λ ( a 0 b 0 ) .
( a σ b σ ) = P ^ σ 1 ( a 0 b 0 ) .
q b = i k x 1 ϵ b ϵ 1 ϵ 1 2 Δ 1 2 T 12 e 2 i k x 1 σ d 1 + T 11 e i K Λ T 12 e 2 i k x 1 σ d 1 T 11 + e i K Λ k y ϵ b Δ 1 ϵ 1 2 Δ 1 2 , l m o d e s
q b = k y 2 ( ω c ) 2 ϵ b ,
q b = ϵ b ϵ 1 2 Δ 1 2 ( k y Δ 1 + k x 1 ϵ 1 )
f + = 1 2 π [ ω c 2 4 + ϵ ω p 2 ϵ b + ϵ + ω c 2 ] ,
f = 1 2 π [ ω c 2 4 + ϵ ω p 2 ϵ b + ϵ ω c 2 ] .
q b = i k x 2 ϵ b ϵ 2 T 12 e 2 i k x 2 γ d 2 + T 11 e i K Λ T 12 e 2 i k x 2 γ d 2 T 11 + e i K Λ ,

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