Abstract

In topological photonics, there is a class of designing approaches that usually tunes topological phase from trivial to non-trivial in a magneto-optical photonic crystal by applying an external magnetic field to break time reversal symmetry. Here we theoretically realize topological phase transition by rotating square gyro-electric rods with broken time reversal symmetry. By calculating band structures and Chern numbers, in a simple square-lattice photonic crystal, we demonstrate the topological phase transition at a specific orientation angle of the rods. Based on the dependence of topological phase on the orientation angle, we propose several terahertz devices including an isolator, circulator and splitter in a 50x50 reconfigurable rod array by locally controlling topological phases of the rods. These results may have potential applications in producing reconfigurable terahertz topological devices.

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

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  1. L. Lu, J. D. Joannopoulos, and M. Soljačić, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
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  2. A. B. Khanikaev and G. Shvets, “Two-dimensional topological photonics,” Nat. Photonics 11(12), 763–773 (2017).
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  3. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics” arXiv:1802.04173 (2018).
  4. 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]
  5. 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]
  6. Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacić, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
    [Crossref] [PubMed]
  7. 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]
  8. K. Liu, L. Shen, and S. He, “One-way edge mode in a gyromagnetic photonic crystal slab,” Opt. Lett. 37(19), 4110–4112 (2012).
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  9. L. Zhang, D. X. Yang, K. Chen, T. Li, and S. Xia, “Design of nonreciprocal waveguide devices based on two-dimensional magneto-optical photonic crystals,” Opt. Laser Technol. 50(2), 195–201 (2013).
    [Crossref]
  10. 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]
  11. S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
    [Crossref] [PubMed]
  12. H. C. Chan and G. Y. Guo, “Tuning topological phase transitions in hexagonal photonic lattices made of triangular rods,” Phys. Rev. B 97(4), 045422 (2018).
    [Crossref]
  13. A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
    [Crossref] [PubMed]
  14. L. H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
    [Crossref] [PubMed]
  15. S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
    [Crossref]
  16. T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
    [Crossref]
  17. X. D. Chen, F. L. Zhao, M. Chen, and J. W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
    [Crossref]
  18. J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
    [Crossref] [PubMed]
  19. X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
    [Crossref] [PubMed]
  20. 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).
    [Crossref] [PubMed]
  21. F. Fan, S. Chen, X. H. Wang, and S. J. Chang, “Tunable nonreciprocal terahertz transmission and enhancement based on metal/magneto-optic plasmonic lens,” Opt. Express 21(7), 8614–8621 (2013).
    [Crossref] [PubMed]
  22. 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]
  23. L. Shen, Z. Wang, X. Deng, J. J. Wu, and T. J. Yang, “Complete trapping of electromagnetic radiation using surface magnetoplasmons,” Opt. Lett. 40(8), 1853–1856 (2015).
    [Crossref] [PubMed]
  24. F. Fan, C. Z. Xiong, J. R. Chen, and S. J. Chang, “Terahertz nonreciprocal isolator based on a magneto-optical microstructure at room temperature,” Opt. Lett. 43(4), 687–690 (2018).
    [Crossref] [PubMed]
  25. B. Bahari, R. Tellezlimon, and B. Kanté, “Topological terahertz circuits using semiconductors,” Appl. Phys. Lett. 109(14), 143501 (2016).
    [Crossref]
  26. L. He, Q. Shen, J. Xu, Y. You, T. Yu, L. Shen, and X. Deng, “One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies,” Sci. Rep. 8(1), 8165 (2018).
    [Crossref] [PubMed]
  27. J. Han, A. Lakhtakia, and C. W. Qiu, “Terahertz metamaterials with semiconductor split-ring resonators for magnetostatic tunability,” Opt. Express 16(19), 14390–14396 (2008).
    [Crossref] [PubMed]
  28. J. Gómez Rivas, C. Janke, P. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express 13(3), 847–859 (2005).
    [Crossref] [PubMed]
  29. D. Xiao, M. C. Chang, and Q. Niu, “Berry phase effects on electronic properties,” Rev. Mod. Phys. 82(3), 1959–2007 (2010).
    [Crossref]
  30. D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
    [Crossref] [PubMed]
  31. T. Fukui, Y. Hatsugai, and H. Suzuki, “Chern numbers in a discretized Brillouin zone: efficient method to compute (spin) Hall conductances,” J. Phys. Soc. Jpn. 74(6), 1674–1677 (2005).
    [Crossref]

2018 (3)

H. C. Chan and G. Y. Guo, “Tuning topological phase transitions in hexagonal photonic lattices made of triangular rods,” Phys. Rev. B 97(4), 045422 (2018).
[Crossref]

L. He, Q. Shen, J. Xu, Y. You, T. Yu, L. Shen, and X. Deng, “One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies,” Sci. Rep. 8(1), 8165 (2018).
[Crossref] [PubMed]

F. Fan, C. Z. Xiong, J. R. Chen, and S. J. Chang, “Terahertz nonreciprocal isolator based on a magneto-optical microstructure at room temperature,” Opt. Lett. 43(4), 687–690 (2018).
[Crossref] [PubMed]

2017 (5)

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

X. D. Chen, F. L. Zhao, M. Chen, and J. W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref] [PubMed]

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

2016 (3)

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

B. Bahari, R. Tellezlimon, and B. Kanté, “Topological terahertz circuits using semiconductors,” Appl. Phys. Lett. 109(14), 143501 (2016).
[Crossref]

2015 (4)

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]

L. Shen, Z. Wang, X. Deng, J. J. Wu, and T. J. Yang, “Complete trapping of electromagnetic radiation using surface magnetoplasmons,” Opt. Lett. 40(8), 1853–1856 (2015).
[Crossref] [PubMed]

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref] [PubMed]

L. H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[Crossref] [PubMed]

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]

2013 (3)

L. Zhang, D. X. Yang, K. Chen, T. Li, and S. Xia, “Design of nonreciprocal waveguide devices based on two-dimensional magneto-optical photonic crystals,” Opt. Laser Technol. 50(2), 195–201 (2013).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref] [PubMed]

F. Fan, S. Chen, X. H. Wang, and S. J. Chang, “Tunable nonreciprocal terahertz transmission and enhancement based on metal/magneto-optic plasmonic lens,” Opt. Express 21(7), 8614–8621 (2013).
[Crossref] [PubMed]

2012 (2)

2011 (1)

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 (1)

D. Xiao, M. C. Chang, and Q. Niu, “Berry phase effects on electronic properties,” Rev. Mod. Phys. 82(3), 1959–2007 (2010).
[Crossref]

2009 (1)

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

2008 (3)

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]

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]

J. Han, A. Lakhtakia, and C. W. Qiu, “Terahertz metamaterials with semiconductor split-ring resonators for magnetostatic tunability,” Opt. Express 16(19), 14390–14396 (2008).
[Crossref] [PubMed]

2005 (2)

T. Fukui, Y. Hatsugai, and H. Suzuki, “Chern numbers in a discretized Brillouin zone: efficient method to compute (spin) Hall conductances,” J. Phys. Soc. Jpn. 74(6), 1674–1677 (2005).
[Crossref]

J. Gómez Rivas, C. Janke, P. Bolivar, and H. Kurz, “Transmission of THz radiation through InSb gratings of subwavelength apertures,” Opt. Express 13(3), 847–859 (2005).
[Crossref] [PubMed]

Bahari, B.

B. Bahari, R. Tellezlimon, and B. Kanté, “Topological terahertz circuits using semiconductors,” Appl. Phys. Lett. 109(14), 143501 (2016).
[Crossref]

Barik, S.

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

Bolivar, P.

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]

Chan, H. C.

H. C. Chan and G. Y. Guo, “Tuning topological phase transitions in hexagonal photonic lattices made of triangular rods,” Phys. Rev. B 97(4), 045422 (2018).
[Crossref]

Chang, M. C.

D. Xiao, M. C. Chang, and Q. Niu, “Berry phase effects on electronic properties,” Rev. Mod. Phys. 82(3), 1959–2007 (2010).
[Crossref]

Chang, S. J.

Chen, J. R.

Chen, K.

L. Zhang, D. X. Yang, K. Chen, T. Li, and S. Xia, “Design of nonreciprocal waveguide devices based on two-dimensional magneto-optical photonic crystals,” Opt. Laser Technol. 50(2), 195–201 (2013).
[Crossref]

Chen, M.

X. D. Chen, F. L. Zhao, M. Chen, and J. W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

Chen, S.

Chen, X. D.

X. D. Chen, F. L. Zhao, M. Chen, and J. W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

Chong, Y.

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

Christensen, T.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

DeGottardi, W.

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

Deng, X.

Dong, J. W.

X. D. Chen, F. L. Zhao, M. Chen, and J. W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

Fan, F.

Fang, N. X.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

Fukui, T.

T. Fukui, Y. Hatsugai, and H. Suzuki, “Chern numbers in a discretized Brillouin zone: efficient method to compute (spin) Hall conductances,” J. Phys. Soc. Jpn. 74(6), 1674–1677 (2005).
[Crossref]

Gómez Rivas, J.

Guo, G. Y.

H. C. Chan and G. Y. Guo, “Tuning topological phase transitions in hexagonal photonic lattices made of triangular rods,” Phys. Rev. B 97(4), 045422 (2018).
[Crossref]

Hafezi, M.

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

Haldane, F. D. M.

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]

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]

Han, D.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref] [PubMed]

Han, J.

Hatsugai, Y.

T. Fukui, Y. Hatsugai, and H. Suzuki, “Chern numbers in a discretized Brillouin zone: efficient method to compute (spin) Hall conductances,” J. Phys. Soc. Jpn. 74(6), 1674–1677 (2005).
[Crossref]

He, L.

L. He, Q. Shen, J. Xu, Y. You, T. Yu, L. Shen, and X. Deng, “One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies,” Sci. Rep. 8(1), 8165 (2018).
[Crossref] [PubMed]

He, S.

Hu, B.

Hu, X.

L. H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[Crossref] [PubMed]

Huang, Y.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref] [PubMed]

Igarashi, Y.

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref] [PubMed]

Janke, C.

Jin, D.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

Joannopoulos, J.

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref] [PubMed]

Joannopoulos, J. D.

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

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

Kanté, B.

B. Bahari, R. Tellezlimon, and B. Kanté, “Topological terahertz circuits using semiconductors,” Appl. Phys. Lett. 109(14), 143501 (2016).
[Crossref]

Kargarian, M.

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref] [PubMed]

Khanikaev, A. B.

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

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref] [PubMed]

Kurz, H.

Lakhtakia, A.

Li, T.

L. Zhang, D. X. Yang, K. Chen, T. Li, and S. Xia, “Design of nonreciprocal waveguide devices based on two-dimensional magneto-optical photonic crystals,” Opt. Laser Technol. 50(2), 195–201 (2013).
[Crossref]

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]

Liu, K.

Lu, L.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[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]

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

Ma, T.

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

MacDonald, A. H.

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref] [PubMed]

Meng, Y.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref] [PubMed]

Miyake, H.

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

Mousavi, S. H.

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref] [PubMed]

Niu, Q.

D. Xiao, M. C. Chang, and Q. Niu, “Berry phase effects on electronic properties,” Rev. Mod. Phys. 82(3), 1959–2007 (2010).
[Crossref]

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]

Qiu, C. W.

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]

Shen, L.

Shen, Q.

L. He, Q. Shen, J. Xu, Y. You, T. Yu, L. Shen, and X. Deng, “One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies,” Sci. Rep. 8(1), 8165 (2018).
[Crossref] [PubMed]

Shvets, G.

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

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref] [PubMed]

Skirlo, S. A.

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[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]

Soljacic, M.

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[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]

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

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

Suzuki, H.

T. Fukui, Y. Hatsugai, and H. Suzuki, “Chern numbers in a discretized Brillouin zone: efficient method to compute (spin) Hall conductances,” J. Phys. Soc. Jpn. 74(6), 1674–1677 (2005).
[Crossref]

Tellezlimon, R.

B. Bahari, R. Tellezlimon, and B. Kanté, “Topological terahertz circuits using semiconductors,” Appl. Phys. Lett. 109(14), 143501 (2016).
[Crossref]

Tian, J.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref] [PubMed]

Tse, W. K.

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref] [PubMed]

Waks, E.

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

Wang, Q. J.

Wang, X. H.

Wang, Y.

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

Wang, Z.

Wen, W.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref] [PubMed]

Wu, J. J.

Wu, L. H.

L. H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[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]

Wu, X.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref] [PubMed]

Xia, S.

L. Zhang, D. X. Yang, K. Chen, T. Li, and S. Xia, “Design of nonreciprocal waveguide devices based on two-dimensional magneto-optical photonic crystals,” Opt. Laser Technol. 50(2), 195–201 (2013).
[Crossref]

Xiang, H.

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref] [PubMed]

Xiao, D.

D. Xiao, M. C. Chang, and Q. Niu, “Berry phase effects on electronic properties,” Rev. Mod. Phys. 82(3), 1959–2007 (2010).
[Crossref]

Xiong, C. Z.

Xu, J.

L. He, Q. Shen, J. Xu, Y. You, T. Yu, L. Shen, and X. Deng, “One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies,” Sci. Rep. 8(1), 8165 (2018).
[Crossref] [PubMed]

Yan, Q.

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[Crossref] [PubMed]

Yang, D. X.

L. Zhang, D. X. Yang, K. Chen, T. Li, and S. Xia, “Design of nonreciprocal waveguide devices based on two-dimensional magneto-optical photonic crystals,” Opt. Laser Technol. 50(2), 195–201 (2013).
[Crossref]

Yang, T. J.

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]

You, Y.

L. He, Q. Shen, J. Xu, Y. You, T. Yu, L. Shen, and X. Deng, “One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies,” Sci. Rep. 8(1), 8165 (2018).
[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]

Yu, T.

L. He, Q. Shen, J. Xu, Y. You, T. Yu, L. Shen, and X. Deng, “One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies,” Sci. Rep. 8(1), 8165 (2018).
[Crossref] [PubMed]

Zhang, L.

L. Zhang, D. X. Yang, K. Chen, T. Li, and S. Xia, “Design of nonreciprocal waveguide devices based on two-dimensional magneto-optical photonic crystals,” Opt. Laser Technol. 50(2), 195–201 (2013).
[Crossref]

Zhang, X.

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

Zhang, Y.

Zhao, F. L.

X. D. Chen, F. L. Zhao, M. Chen, and J. W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

Zhu, H.

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

B. Bahari, R. Tellezlimon, and B. Kanté, “Topological terahertz circuits using semiconductors,” Appl. Phys. Lett. 109(14), 143501 (2016).
[Crossref]

J. Phys. Soc. Jpn. (1)

T. Fukui, Y. Hatsugai, and H. Suzuki, “Chern numbers in a discretized Brillouin zone: efficient method to compute (spin) Hall conductances,” J. Phys. Soc. Jpn. 74(6), 1674–1677 (2005).
[Crossref]

Nat. Commun. (1)

X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, and W. Wen, “Direct observation of valley-polarized topological edge states in designer surface plasmon crystals,” Nat. Commun. 8(1), 1304 (2017).
[Crossref] [PubMed]

Nat. Mater. (2)

A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, “Photonic topological insulators,” Nat. Mater. 12(3), 233–239 (2013).
[Crossref] [PubMed]

J. W. Dong, X. D. Chen, H. Zhu, Y. Wang, and X. Zhang, “Valley photonic crystals for control of spin and topology,” Nat. Mater. 16(3), 298–302 (2017).
[Crossref] [PubMed]

Nat. Photonics (2)

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 (1)

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

New J. Phys. (2)

S. Barik, H. Miyake, W. DeGottardi, E. Waks, and M. Hafezi, “Two-dimensionally confined topological edge states in photonic crystals,” New J. Phys. 18(11), 113013 (2016).
[Crossref]

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
[Crossref]

Opt. Express (4)

Opt. Laser Technol. (1)

L. Zhang, D. X. Yang, K. Chen, T. Li, and S. Xia, “Design of nonreciprocal waveguide devices based on two-dimensional magneto-optical photonic crystals,” Opt. Laser Technol. 50(2), 195–201 (2013).
[Crossref]

Opt. Lett. (4)

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)

H. C. Chan and G. Y. Guo, “Tuning topological phase transitions in hexagonal photonic lattices made of triangular rods,” Phys. Rev. B 97(4), 045422 (2018).
[Crossref]

X. D. Chen, F. L. Zhao, M. Chen, and J. W. Dong, “Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation,” Phys. Rev. B 96(2), 020202 (2017).
[Crossref]

Phys. Rev. Lett. (6)

L. H. Wu and X. Hu, “Scheme for achieving a topological photonic crystal by using dielectric material,” Phys. Rev. Lett. 114(22), 223901 (2015).
[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]

S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, “Experimental observation of large Chern numbers in photonic crystals,” Phys. Rev. Lett. 115(25), 253901 (2015).
[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]

D. Jin, T. Christensen, M. Soljačić, N. X. Fang, L. Lu, and X. Zhang, “Infrared topological plasmons in graphene,” Phys. Rev. Lett. 118(24), 245301 (2017).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

D. Xiao, M. C. Chang, and Q. Niu, “Berry phase effects on electronic properties,” Rev. Mod. Phys. 82(3), 1959–2007 (2010).
[Crossref]

Sci. Rep. (1)

L. He, Q. Shen, J. Xu, Y. You, T. Yu, L. Shen, and X. Deng, “One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies,” Sci. Rep. 8(1), 8165 (2018).
[Crossref] [PubMed]

Other (1)

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics” arXiv:1802.04173 (2018).

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Figures (5)

Fig. 1
Fig. 1 Schematic of square semiconductor rod array arranged in a square lattice filled with air. In enlarged unit cell, a is the lattice constant, L is the side length of the square rod, θ is the rotated angle from + x to + x’ axis presenting the rod orientation. The first Brillouin zone is also square. The magnetic field B is applied along z-axis.

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Fig. 2
Fig. 2 Band structures of the rod arrays with different rod orientation showing phase transition process. The time reversal symmetry is broken by an external magnetic field B = 0.8 T. The composite Chern numbers are labeled by red integers in the black dash eclipse covering corresponding bands. (a) θ = 0°; The green gap is topologically non-trivial with its gap Chern number Cg = + 1. (b) θ = 33.2°, the phase transition angle. There is no gap between 2nd and 3rd bands but degenerate points instead as pointed out with purple circles. (c) θ = 45°; The cyan gap is topologically trivial with its gap Chern number Cg = 0.

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Fig. 3
Fig. 3 (a) Projected band diagram of the supercell in θ = 0° case with upper and lower edges ended by PEC. The blue lines represent bulk projected bands. The red and orange lines inside the gap represent upper and lower edge bands. (b) Enlarged region including the target band gap. A and B are the chosen points of the edge band at ω = 0.436 (2πc/a). (c) The structure of the supercell and the normalized electric field distribution at the chosen points. The field is confined on the upper edge at A point and on the lower edge at B point.

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Fig. 4
Fig. 4 Normalized electric field distribution of the edge wave propagation. The wave is excited by a point source. Blue areas denote the metal wall and the obstacle. (a) Distribution of edge wave between the array with θ = 0° and a metal wall at 3.5 THz. (b) Transmission spectrum without and with material loss involved when the wave propagates a length of 30a along the edge. (c) Distribution of edge wave between upper sub array with θ = 0° and lower sub array with θ = 45°. (d) Distribution of edge wave along the interface with two right-angled bends.

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Fig. 5
Fig. 5 Reconfigurable square array consists of 50x50 rotatable square rods allowing waves propagating along desired path such as going straight (isolation), going circularly (circulation) and going separately (wave splitting). Blue area is the sub array with θ = 0° and gray area is the sub array with θ = 45°. Four ports are fix as the uniform interfaces for wave input or output in four red frames. Wave are all input from Port 1 at the frequency of 3.5 THz as an example. Yellow lines in the field plots describe the constructed edges after desired rotating operations. (a-b) 2-port isolation and the waveguiding distribution. (c-d) 4-port circulation and the waveguiding distribution. (e-f) 3-port wave splitting and the waveguiding distribution.

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Equations (6)

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

ε= ε ∞ [ ε 1 i ε 2 0 −i ε 2 ε 1 0 0 0 ε 3 ],
ε 1 =1− ω p 2 (ω+iγ) ω[ (ω+iγ) 2 − ω c 2 ] , ε 2 = ω p 2 ω c ω[ (ω+iγ) 2 − ω c 2 ] , ε 3 =1− ω p 2 ω(ω+iγ)
∇×[ ε −1 (r)∇×H(r)]= ω 2 μ(r)H(r),
C n = (2π) −1 ∫ BZ F k (n) d S k ,
F k (n) = ∇ k × A k (n) = ∇ k ×〈 u nk | ∇ k | u nk 〉,
C n⊕n+1 = (2π) −1 ∫ BZ F k (n⊕n+1) d S k = (2π) −1 ∫ BZ Tr ∇ k × A k (n⊕n+1) d S k .

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