Abstract

Surface magnetoplasmon (SMP) supported at an interface between magnetized plasmonic and dielectric materials has been widely explored; however, it suffers with narrow bandwidth for one-way propagation. Here we propose a novel metal-semiconductor-dielectricmetal (MSDM) structure showing the large bandwidth for the complete one-way propagation (COWP). Because of the compression of the zone for two-way propagating modes in the semiconductor layer by reducing semiconductor thickness, the bandwidth is significantly increased by several times. More importantly, in such MSDM structure, the SMP dispersion can be engineered by controlling the semiconductor thickness, and based on this, slowing wave and trapping rainbow can be realized in a tapered system at terahertz frequencies.

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

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References

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  1. R. E. Prange and S. M. Girvin, The Quantum Hall Effect (Springer, 1987).
    [Crossref]
  2. 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]
  3. S. A. Skirlo, L. Lu, and M. Soljačić, “Multimode one-way waveguides of large Chern numbers,” Phys. Rev. Lett. 113(11), 113904 (2014).
    [Crossref] [PubMed]
  4. L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
    [Crossref]
  5. A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
    [Crossref]
  6. K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
    [Crossref] [PubMed]
  7. S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
    [Crossref]
  8. Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
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  9. X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80(3), 033105 (2009).
    [Crossref]
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  11. Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
    [Crossref] [PubMed]
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  14. B. Hu, Q. J. Wang, and Y. Zhang, “Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons,” Opt. Lett. 37(11), 1895–1897 (2012).
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    [Crossref] [PubMed]
  16. X. Deng, L. Hong, X. Zheng, and L. Shen, “One-way regular electromagnetic mode immune to backscattering,” Appl. Opt. 54(14), 4608–4612 (2015).
    [Crossref] [PubMed]
  17. J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
    [Crossref]
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    [Crossref]
  19. L. Shen, J. Xu, Y. You, K. Yuan, and X. Deng, “One-way electromagnetic mode guided by the mechanism of total internal reflection,” IEEE Photonics Technol. Lett. 30(2), 133–136 (2018).
    [Crossref]
  20. B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
    [Crossref]
  21. M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
    [Crossref] [PubMed]
  22. Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
    [Crossref] [PubMed]
  23. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
    [Crossref] [PubMed]
  24. K. Liu and S. He, “Truly trapped rainbow by utilizing nonreciprocal waveguides,” Sci. Rep. 6, 30206 (2016).
    [Crossref] [PubMed]
  25. A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).
  26. T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
    [Crossref]

2018 (1)

L. Shen, J. Xu, Y. You, K. Yuan, and X. Deng, “One-way electromagnetic mode guided by the mechanism of total internal reflection,” IEEE Photonics Technol. Lett. 30(2), 133–136 (2018).
[Crossref]

2017 (2)

A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
[Crossref]

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

2016 (1)

K. Liu and S. He, “Truly trapped rainbow by utilizing nonreciprocal waveguides,” Sci. Rep. 6, 30206 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (2)

S. A. Skirlo, L. Lu, and M. Soljačić, “Multimode one-way waveguides of large Chern numbers,” Phys. Rev. Lett. 113(11), 113904 (2014).
[Crossref] [PubMed]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

2012 (1)

2009 (3)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80(3), 033105 (2009).
[Crossref]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

2008 (5)

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]

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[Crossref]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (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]

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
[Crossref]

2007 (1)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

2005 (1)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

2004 (1)

M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[Crossref] [PubMed]

1974 (1)

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9(8), 3424–3437 (1974).
[Crossref]

1972 (1)

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Altug, H.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

Ao, X.

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80(3), 033105 (2009).
[Crossref]

Barnes, W. L.

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
[Crossref]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

Boyd, R. W.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

Brion, J. J.

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9(8), 3424–3437 (1974).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Burstein, E.

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9(8), 3424–3437 (1974).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Chan, C. T.

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80(3), 033105 (2009).
[Crossref]

Chong, Y. D.

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref] [PubMed]

Corcoran, B.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Deng, X.

L. Shen, J. Xu, Y. You, K. Yuan, and X. Deng, “One-way electromagnetic mode guided by the mechanism of total internal reflection,” IEEE Photonics Technol. Lett. 30(2), 133–136 (2018).
[Crossref]

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

L. Shen, Y. You, Z. Wang, and X. Deng, “Backscattering-immune one-way surface magnetoplasmons at terahertz frequencies,” Opt. Express 23(2), 950–962 (2015).
[Crossref] [PubMed]

X. Deng, L. Hong, X. Zheng, and L. Shen, “One-way regular electromagnetic mode immune to backscattering,” Appl. Opt. 54(14), 4608–4612 (2015).
[Crossref] [PubMed]

Eggleton, B. J.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Fan, S.

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]

Girvin, S. M.

R. E. Prange and S. M. Girvin, The Quantum Hall Effect (Springer, 1987).
[Crossref]

Grillet, C.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Haldane, F. D. M.

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. A 78(3), 033834 (2008).
[Crossref]

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Hartstein, A.

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9(8), 3424–3437 (1974).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

He, S.

K. Liu and S. He, “Truly trapped rainbow by utilizing nonreciprocal waveguides,” Sci. Rep. 6, 30206 (2016).
[Crossref] [PubMed]

Hendry, E.

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
[Crossref]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

Hong, L.

Hu, B.

Isaac, T. H.

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
[Crossref]

Joannopoulos, J. D.

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref] [PubMed]

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2 (Princeton University, 2008).

Khanikaev, A. B.

A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
[Crossref]

Krauss, T. F.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Lin, Z.

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80(3), 033105 (2009).
[Crossref]

Liu, K.

K. Liu and S. He, “Truly trapped rainbow by utilizing nonreciprocal waveguides,” Sci. Rep. 6, 30206 (2016).
[Crossref] [PubMed]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Lu, L.

S. A. Skirlo, L. Lu, and M. Soljačić, “Multimode one-way waveguides of large Chern numbers,” Phys. Rev. Lett. 113(11), 113904 (2014).
[Crossref] [PubMed]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Meade, R. D.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2 (Princeton University, 2008).

Monat, C.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Moss, D. J.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

O’Faolain, L.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Prange, R. E.

R. E. Prange and S. M. Girvin, The Quantum Hall Effect (Springer, 1987).
[Crossref]

Raether, H.

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

Raghu, S.

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. A 78(3), 033834 (2008).
[Crossref]

Schulz, S. A.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

Shen, L.

L. Shen, J. Xu, Y. You, K. Yuan, and X. Deng, “One-way electromagnetic mode guided by the mechanism of total internal reflection,” IEEE Photonics Technol. Lett. 30(2), 133–136 (2018).
[Crossref]

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

L. Shen, Y. You, Z. Wang, and X. Deng, “Backscattering-immune one-way surface magnetoplasmons at terahertz frequencies,” Opt. Express 23(2), 950–962 (2015).
[Crossref] [PubMed]

X. Deng, L. Hong, X. Zheng, and L. Shen, “One-way regular electromagnetic mode immune to backscattering,” Appl. Opt. 54(14), 4608–4612 (2015).
[Crossref] [PubMed]

Shvets, G.

A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
[Crossref]

Skirlo, S. A.

S. A. Skirlo, L. Lu, and M. Soljačić, “Multimode one-way waveguides of large Chern numbers,” Phys. Rev. Lett. 113(11), 113904 (2014).
[Crossref] [PubMed]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

Soljacic, M.

S. A. Skirlo, L. Lu, and M. Soljačić, “Multimode one-way waveguides of large Chern numbers,” Phys. Rev. Lett. 113(11), 113904 (2014).
[Crossref] [PubMed]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (2008).
[Crossref] [PubMed]

Stockman, M. I.

M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[Crossref] [PubMed]

Tsakmakidis, K. L.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

Upham, J.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

Vakakis, A. F.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

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]

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Wallis, R. F.

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9(8), 3424–3437 (1974).
[Crossref]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[Crossref]

Wang, Q. J.

Wang, Z.

L. Shen, Y. You, Z. Wang, and X. Deng, “Backscattering-immune one-way surface magnetoplasmons at terahertz frequencies,” Opt. Express 23(2), 950–962 (2015).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (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]

White, T. P.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Winn, J. N.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2 (Princeton University, 2008).

Xu, J.

L. Shen, J. Xu, Y. You, K. Yuan, and X. Deng, “One-way electromagnetic mode guided by the mechanism of total internal reflection,” IEEE Photonics Technol. Lett. 30(2), 133–136 (2018).
[Crossref]

You, Y.

L. Shen, J. Xu, Y. You, K. Yuan, and X. Deng, “One-way electromagnetic mode guided by the mechanism of total internal reflection,” IEEE Photonics Technol. Lett. 30(2), 133–136 (2018).
[Crossref]

L. Shen, Y. You, Z. Wang, and X. Deng, “Backscattering-immune one-way surface magnetoplasmons at terahertz frequencies,” Opt. Express 23(2), 950–962 (2015).
[Crossref] [PubMed]

Yu, Z.

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, K.

L. Shen, J. Xu, Y. You, K. Yuan, and X. Deng, “One-way electromagnetic mode guided by the mechanism of total internal reflection,” IEEE Photonics Technol. Lett. 30(2), 133–136 (2018).
[Crossref]

Zhang, Y.

Zheng, X.

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

X. Deng, L. Hong, X. Zheng, and L. Shen, “One-way regular electromagnetic mode immune to backscattering,” Appl. Opt. 54(14), 4608–4612 (2015).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. H. Isaac, W. L. Barnes, and E. Hendry, “Determining the terahertz optical properties of subwavelength films using semiconductor surface plasmons,” Appl. Phys. Lett. 93(24), 241115 (2008).
[Crossref]

IEEE Photonics Technol. Lett. (1)

L. Shen, J. Xu, Y. You, K. Yuan, and X. Deng, “One-way electromagnetic mode guided by the mechanism of total internal reflection,” IEEE Photonics Technol. Lett. 30(2), 133–136 (2018).
[Crossref]

Nat. Photonics (3)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
[Crossref]

Nature (3)

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
[Crossref] [PubMed]

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (1)

S. Raghu and F. D. M. Haldane, “Analogs of quantum-Hall-effect edge states in photonic crystals,” Phys. Rev. A 78(3), 033834 (2008).
[Crossref]

Phys. Rev. B (2)

X. Ao, Z. Lin, and C. T. Chan, “One-way edge mode in a magneto-optical honeycomb photonic crystal,” Phys. Rev. B 80(3), 033105 (2009).
[Crossref]

R. F. Wallis, J. J. Brion, E. Burstein, and A. Hartstein, “Theory of surface polaritons in anisotropic dielectric media with application to surface magnetoplasmons in semiconductors,” Phys. Rev. B 9(8), 3424–3437 (1974).
[Crossref]

Phys. Rev. Lett. (6)

M. I. Stockman, “Nanofocusing of Optical Energy in Tapered Plasmonic Waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[Crossref] [PubMed]

Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljačić, “Reflection-free one-way edge modes in a gyromagnetic photonic crystal,” Phys. Rev. Lett. 100(1), 013905 (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. A. Skirlo, L. Lu, and M. Soljačić, “Multimode one-way waveguides of large Chern numbers,” Phys. Rev. Lett. 113(11), 113904 (2014).
[Crossref] [PubMed]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28(22), 1455–1458 (1972).
[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]

Sci. Rep. (1)

K. Liu and S. He, “Truly trapped rainbow by utilizing nonreciprocal waveguides,” Sci. Rep. 6, 30206 (2016).
[Crossref] [PubMed]

Science (1)

K. L. Tsakmakidis, L. Shen, S. A. Schulz, X. Zheng, J. Upham, X. Deng, H. Altug, A. F. Vakakis, and R. W. Boyd, “Breaking lorentz reciprocity to overcome the time-bandwidth limit in physics and engineering,” Science 356(6344), 1260–1264 (2017).
[Crossref] [PubMed]

Other (4)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, 2 (Princeton University, 2008).

R. E. Prange and S. M. Girvin, The Quantum Hall Effect (Springer, 1987).
[Crossref]

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

A. W. Snyder and J. D. Love, Optical Waveguide Theory(Chapman and Hall, 1983).

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Figures (8)

Fig. 1
Fig. 1 Schematics of the metal-semiconductor-dielectric-metal (a) and related semiconductordielectric-metal (b) structures for sustaining one-way SMPs. An external dc magnetic field is applied along the −y direction in the two structures.
Fig. 2
Fig. 2 Dispersion relations of SMPs in the MSDM (a) and SDM (b) systems. Solid and dot-dashed lines correspond to SMPs supported by the dielectric-semiconductor and metal-semiconductor interfaces, respectively. Dotted lines in (a) represent the dispersion curves for normal modes with lowest order in the semiconductor layer, and shaded areas in (b) represent bulk-mode zones for the semiconductor itself. The shaded rectangle in (a) and (b) represents the COWP region and dashed lines the light line in air. The parameters of the two systems are as follows: εr = 1, d1=0.1λp; ωc =0.25ωp, d2=0.2λp.
Fig. 3
Fig. 3 (a) COWP bandwidth (Δωcowp) as a function of ωc in the MSDM system. The corresponding COWP bandwidth (dashed line) for the SDM system is included for comparison. (b) Dispersion relation of SMPs in the MSDM system when ωc =0.75ωp. Solid and dot-dashed lines correspond to SMPs supported by the dielectric-semiconductor and metal-semiconductor interfaces, respectively. Dotted line represents the dispersion curve for the normal mode with lowest order in the semiconductor layer, and shaded rectangle represents the COWP region. The other parameters are the same as in Fig. 2.
Fig. 4
Fig. 4 Dispersion curves for SMPs (solid) and lowest-order normal mode (dotted) in the MSDM system for different d2 values. (a) d2=0.2λp, (b) d2=0.1λp, (c) d2=0.05λp, (d) d2=0.03λp. The horizontal dashed line indicates the frequency ω =0.9ωp. ωc =0.5ωp, and the other parameters are the same as in Fig. 2.
Fig. 5
Fig. 5 (a) Upper (ωu) and lower (ωl) limit frequencies of the COWP band as functions of d2. (b) COWP bandwidth as a function of d2. ωc =0.5ωp, and other parameter are the same as in Fig. 2.
Fig. 6
Fig. 6 (a)-(c) Simulated magnetic field amplitudes in the MSDM systems with different d2 values. (a) d2=0.2λp, (b) d2=0.1λp, and (c) d2=0.03λp. (d) Simulated magnetic field amplitudes in the MSDM system of d2=0.1λp but with an obstacle. The obstacle consists of two square columns of air and semiconductor, which are respectively located below and above the semiconductor surface. The white dashed line in (a)-(d) indicates the semiconductor surface. (e) Magnetic field amplitudes along a horizontal line at the semiconductor surface in (b) (dashed line) and (d) (dotted line). For each case, the source with the frequency f =1.8 THz lies at d1/2 above the semiconductor surface. The semiconductor is lossy with ν =0.01ωp. ωc =0.5ωp, and the other parameters are the same as in Fig. 2.
Fig. 7
Fig. 7 SMP bands (with the symptotic frequency ω s p ( 2 )) for different d2 values. From top to bottom: d2=0.02λp,0.032λp, 0.045λp, 0.06λp, and 0.09λp. ωc = −0.5ωp, and the other parameters are the same as in Fig. 2.
Fig. 8
Fig. 8 (a)-(d) Simulated electric field amplitudes for different frequencies in a system consisting of a uniform and tapered MSDM structures. (a) 1.6 THz, (b) 1.7 THz, (c) 1.8 THz, and (d) 1.9 THz. In the system, the semiconductor thickness is d2=0.03λp in the uniform section of the length 200 µm, and in the tapered section, it linearly increases from 0.03λp to 0.09λp over the length 500 µm. (e) Electric field amplitudes along the semiconductor surface in (a)-(d). The source lies at d1/2 above the semiconductor surface in the uniform section. ωc = −0.5ωp, ν =0.01ωp, and the other parameters are the same as in Fig. 2.

Equations (14)

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ε = [ ε 1 0 i ε 2 0 ε 3 0 i ε 2 0 ε 1 ] ,
H y ( x , z ) = [ A 1 exp ( α d x ) + A 2 exp ( α d x ) ] exp ( i k z )
H y ( x , z ) = [ B 1 exp ( α s x ) + B 2 exp ( α s x ) ] exp ( i k z )
( k 2 ε 1 k 0 2 ) tanh ( α s d 2 ) + ε 1 ε r α d [ α s ε 2 ε 1 k tanh ( α s d 2 ) ] tanh ( α d d 1 ) = 0 ,
ω s p ( 1 ) = 1 2 ( ω c 2 + 4 ε ε + ε r ω p 2 + ω c ) .
ω s p ( 2 ) = 1 2 ( ω c 2 + 4 ε ε + ε r ω p 2 ω c ) ,
ω s p ( 3 ) = ω c ,
α + ε 2 ε 1 k + ε v ε r α d tanh ( α d d ) = 0 ,
ω c f , b = 1 2 ( ω c 2 + 4 ω p 2 ω c ) ,
( k z 2 ε 1 k 0 2 ) tan ( k x d 2 ) + ε 1 ε r α d [ k x ε 2 ε 1 k z tan ( k x d 2 ) ] tanh ( α d d 1 ) = 0 ,
ω c , 1 = ε r 2 ( ε r + 2 ε ) ( ε r + ε ) ω p ,
ω c , 2 = ε 2 ( ε + ε r ) ω p ,
ε 1 = ε { 1 ( ω + i ν ) ω p 2 ω [ ( ω + i ν ) 2 ω c 2 ] } , r
ε 2 = ε ω c ω p 2 ω [ ( ω + i ν ) 2 ω c 2 ] ,

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