Abstract

An anti-phase boundary is formed by shifting a portion of photonic crystal lattice along the direction of periodicity. A spinning magnetic dipole is applied to excite edge modes on the anti-phase boundary. We show the unidirectional propagation of the edge modes which is also known as spin-momentum locking. Band inversion of the edge modes is discovered when we sweep the geometrical parameters, which leads to a change in the propagation direction. Also, an optimized source is applied to excite the unidirectional edge mode with high directivity.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. C. L. Kane and E. J. Mele, “Quantum spin hall effect in graphene,” Phys. Rev. Lett. 95(22), 226801 (2005).
    [Crossref]
  2. C. L. Kane and E. J. Mele, “Z 2 topological order and the quantum spin hall effect,” Phys. Rev. Lett. 95(14), 146802 (2005).
    [Crossref]
  3. D. Sheng, Z. Weng, L. Sheng, and F. Haldane, “Quantum spin-hall effect and topologically invariant chern numbers,” Phys. Rev. Lett. 97(3), 036808 (2006).
    [Crossref]
  4. M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
    [Crossref]
  5. F. Kuemmeth, S. Ilani, D. Ralph, and P. McEuen, “Coupling of spin and orbital motion of electrons in carbon nanotubes,” Nature 452(7186), 448–452 (2008).
    [Crossref]
  6. A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, “Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces,” Nature 539(7630), 509–517 (2016).
    [Crossref]
  7. 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]
  8. 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]
  9. T. Ma and G. Shvets, “Scattering-free edge states between heterogeneous photonic topological insulators,” Phys. Rev. B 95(16), 165102 (2017).
    [Crossref]
  10. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
    [Crossref]
  11. M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7(11), 907–912 (2011).
    [Crossref]
  12. I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
    [Crossref]
  13. R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
    [Crossref]
  14. A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
    [Crossref]
  15. T. Van Mechelen and Z. Jacob, “Universal spin-momentum locking of evanescent waves,” Optica 3(2), 118–126 (2016).
    [Crossref]
  16. F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
    [Crossref]
  17. D. Cohen and C. Carter, “Structure of the (110) antiphase boundary in gallium phosphide,” J. Microsc. 208(2), 84–99 (2002).
    [Crossref]
  18. K. Ahn, T. Lookman, A. Saxena, and A. Bishop, “Electronic properties of structural twin and antiphase boundaries in materials with strong electron-lattice couplings,” Phys. Rev. B 71(21), 212102 (2005).
    [Crossref]
  19. Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
    [Crossref]
  20. X.-K. Wei, A. K. Tagantsev, A. Kvasov, K. Roleder, C.-L. Jia, and N. Setter, “Ferroelectric translational antiphase boundaries in nonpolar materials,” Nat. Commun. 5(1), 3031 (2014).
    [Crossref]
  21. J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
    [Crossref]

2019 (1)

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

2018 (1)

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

2017 (1)

T. Ma and G. Shvets, “Scattering-free edge states between heterogeneous photonic topological insulators,” Phys. Rev. B 95(16), 165102 (2017).
[Crossref]

2016 (3)

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

T. Van Mechelen and Z. Jacob, “Universal spin-momentum locking of evanescent waves,” Optica 3(2), 118–126 (2016).
[Crossref]

A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, “Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces,” Nature 539(7630), 509–517 (2016).
[Crossref]

2015 (3)

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]

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

2014 (2)

X.-K. Wei, A. K. Tagantsev, A. Kvasov, K. Roleder, C.-L. Jia, and N. Setter, “Ferroelectric translational antiphase boundaries in nonpolar materials,” Nat. Commun. 5(1), 3031 (2014).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

2013 (2)

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (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]

2011 (1)

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7(11), 907–912 (2011).
[Crossref]

2008 (2)

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
[Crossref]

F. Kuemmeth, S. Ilani, D. Ralph, and P. McEuen, “Coupling of spin and orbital motion of electrons in carbon nanotubes,” Nature 452(7186), 448–452 (2008).
[Crossref]

2006 (1)

D. Sheng, Z. Weng, L. Sheng, and F. Haldane, “Quantum spin-hall effect and topologically invariant chern numbers,” Phys. Rev. Lett. 97(3), 036808 (2006).
[Crossref]

2005 (3)

C. L. Kane and E. J. Mele, “Quantum spin hall effect in graphene,” Phys. Rev. Lett. 95(22), 226801 (2005).
[Crossref]

C. L. Kane and E. J. Mele, “Z 2 topological order and the quantum spin hall effect,” Phys. Rev. Lett. 95(14), 146802 (2005).
[Crossref]

K. Ahn, T. Lookman, A. Saxena, and A. Bishop, “Electronic properties of structural twin and antiphase boundaries in materials with strong electron-lattice couplings,” Phys. Rev. B 71(21), 212102 (2005).
[Crossref]

2002 (1)

D. Cohen and C. Carter, “Structure of the (110) antiphase boundary in gallium phosphide,” J. Microsc. 208(2), 84–99 (2002).
[Crossref]

Ahn, K.

K. Ahn, T. Lookman, A. Saxena, and A. Bishop, “Electronic properties of structural twin and antiphase boundaries in materials with strong electron-lattice couplings,” Phys. Rev. B 71(21), 212102 (2005).
[Crossref]

Amo, A.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Androvitsaneas, P.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

Beggs, D. M.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

Bishop, A.

K. Ahn, T. Lookman, A. Saxena, and A. Bishop, “Electronic properties of structural twin and antiphase boundaries in materials with strong electron-lattice couplings,” Phys. Rev. B 71(21), 212102 (2005).
[Crossref]

Buhmann, H.

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
[Crossref]

Carter, C.

D. Cohen and C. Carter, “Structure of the (110) antiphase boundary in gallium phosphide,” J. Microsc. 208(2), 84–99 (2002).
[Crossref]

Carusotto, I.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Clarke, E.

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

Cohen, D.

D. Cohen and C. Carter, “Structure of the (110) antiphase boundary in gallium phosphide,” J. Microsc. 208(2), 84–99 (2002).
[Crossref]

Coles, R.

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

Demler, E. A.

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7(11), 907–912 (2011).
[Crossref]

Dixon, J.

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

El-Ella, H.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Fert, A.

A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, “Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces,” Nature 539(7630), 509–517 (2016).
[Crossref]

Fittipaldi, R.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Fox, A.

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

Ginzburg, P.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Goldman, N.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Guo, H.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Hafezi, M.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7(11), 907–912 (2011).
[Crossref]

Haldane, F.

D. Sheng, Z. Weng, L. Sheng, and F. Haldane, “Quantum spin-hall effect and topologically invariant chern numbers,” Phys. Rev. Lett. 97(3), 036808 (2006).
[Crossref]

Hansen, S. L.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

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]

Hughes, S.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

Hughes, T.

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
[Crossref]

Ilani, S.

F. Kuemmeth, S. Ilani, D. Ralph, and P. McEuen, “Coupling of spin and orbital motion of electrons in carbon nanotubes,” Nature 452(7186), 448–452 (2008).
[Crossref]

Jacob, Z.

Javadi, A.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Jia, C.-L.

X.-K. Wei, A. K. Tagantsev, A. Kvasov, K. Roleder, C.-L. Jia, and N. Setter, “Ferroelectric translational antiphase boundaries in nonpolar materials,” Nat. Commun. 5(1), 3031 (2014).
[Crossref]

Kane, C. L.

C. L. Kane and E. J. Mele, “Quantum spin hall effect in graphene,” Phys. Rev. Lett. 95(22), 226801 (2005).
[Crossref]

C. L. Kane and E. J. Mele, “Z 2 topological order and the quantum spin hall effect,” Phys. Rev. Lett. 95(14), 146802 (2005).
[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]

Khanikaev, A. B.

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]

Kiršanske, G.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Kok, P.

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

König, M.

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
[Crossref]

Kuemmeth, F.

F. Kuemmeth, S. Ilani, D. Ralph, and P. McEuen, “Coupling of spin and orbital motion of electrons in carbon nanotubes,” Nature 452(7186), 448–452 (2008).
[Crossref]

Kuipers, L.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

Kvasov, A.

X.-K. Wei, A. K. Tagantsev, A. Kvasov, K. Roleder, C.-L. Jia, and N. Setter, “Ferroelectric translational antiphase boundaries in nonpolar materials,” Nat. Commun. 5(1), 3031 (2014).
[Crossref]

Lee, E. H.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Li, J.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Liu, C.-X.

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
[Crossref]

Lodahl, P.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Lookman, T.

K. Ahn, T. Lookman, A. Saxena, and A. Bishop, “Electronic properties of structural twin and antiphase boundaries in materials with strong electron-lattice couplings,” Phys. Rev. B 71(21), 212102 (2005).
[Crossref]

Lu, L.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Lukin, M. D.

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7(11), 907–912 (2011).
[Crossref]

Ma, T.

T. Ma and G. Shvets, “Scattering-free edge states between heterogeneous photonic topological insulators,” Phys. Rev. B 95(16), 165102 (2017).
[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]

Mahmoodian, S.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Makhonin, M.

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

Marino, G.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Martínez, A.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

McEuen, P.

F. Kuemmeth, S. Ilani, D. Ralph, and P. McEuen, “Coupling of spin and orbital motion of electrons in carbon nanotubes,” Nature 452(7186), 448–452 (2008).
[Crossref]

Mele, E. J.

C. L. Kane and E. J. Mele, “Quantum spin hall effect in graphene,” Phys. Rev. Lett. 95(22), 226801 (2005).
[Crossref]

C. L. Kane and E. J. Mele, “Z 2 topological order and the quantum spin hall effect,” Phys. Rev. Lett. 95(14), 146802 (2005).
[Crossref]

Midolo, L.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Molenkamp, L. W.

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
[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]

O’Connor, D.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Oulton, R.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

Ozawa, T.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Panagopoulos, C.

A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, “Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces,” Nature 539(7630), 509–517 (2016).
[Crossref]

Petersen, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

Plummer, E. W.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Pregnolato, T.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Price, D.

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

Price, H. M.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Qi, X.-L.

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
[Crossref]

Ralph, D.

F. Kuemmeth, S. Ilani, D. Ralph, and P. McEuen, “Coupling of spin and orbital motion of electrons in carbon nanotubes,” Nature 452(7186), 448–452 (2008).
[Crossref]

Rarity, J. G.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

Rauschenbeutel, A.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

Rechtsman, M. C.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Reyren, N.

A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, “Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces,” Nature 539(7630), 509–517 (2016).
[Crossref]

Rodríguez-Fortuño, F. J.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Roleder, K.

X.-K. Wei, A. K. Tagantsev, A. Kvasov, K. Roleder, C.-L. Jia, and N. Setter, “Ferroelectric translational antiphase boundaries in nonpolar materials,” Nat. Commun. 5(1), 3031 (2014).
[Crossref]

Royall, B.

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

Saghayezhian, M.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Saxena, A.

K. Ahn, T. Lookman, A. Saxena, and A. Bishop, “Electronic properties of structural twin and antiphase boundaries in materials with strong electron-lattice couplings,” Phys. Rev. B 71(21), 212102 (2005).
[Crossref]

Schuster, D.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Setter, N.

X.-K. Wei, A. K. Tagantsev, A. Kvasov, K. Roleder, C.-L. Jia, and N. Setter, “Ferroelectric translational antiphase boundaries in nonpolar materials,” Nat. Commun. 5(1), 3031 (2014).
[Crossref]

Shao, S.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Sheng, D.

D. Sheng, Z. Weng, L. Sheng, and F. Haldane, “Quantum spin-hall effect and topologically invariant chern numbers,” Phys. Rev. Lett. 97(3), 036808 (2006).
[Crossref]

Sheng, L.

D. Sheng, Z. Weng, L. Sheng, and F. Haldane, “Quantum spin-hall effect and topologically invariant chern numbers,” Phys. Rev. Lett. 97(3), 036808 (2006).
[Crossref]

Shvets, G.

T. Ma and G. Shvets, “Scattering-free edge states between heterogeneous photonic topological insulators,” Phys. Rev. B 95(16), 165102 (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]

Simon, J.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Siwakoti, P.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Skolnick, M.

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

Söllner, I.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Song, J. D.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Soumyanarayanan, A.

A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, “Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces,” Nature 539(7630), 509–517 (2016).
[Crossref]

Stobbe, S.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Tagantsev, A. K.

X.-K. Wei, A. K. Tagantsev, A. Kvasov, K. Roleder, C.-L. Jia, and N. Setter, “Ferroelectric translational antiphase boundaries in nonpolar materials,” Nat. Commun. 5(1), 3031 (2014).
[Crossref]

Taylor, J. M.

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7(11), 907–912 (2011).
[Crossref]

Thijssen, A.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

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]

Van Mechelen, T.

Vecchione, A.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Volz, J.

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

Wang, Z.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Wei, X.-K.

X.-K. Wei, A. K. Tagantsev, A. Kvasov, K. Roleder, C.-L. Jia, and N. Setter, “Ferroelectric translational antiphase boundaries in nonpolar materials,” Nat. Commun. 5(1), 3031 (2014).
[Crossref]

Weng, Z.

D. Sheng, Z. Weng, L. Sheng, and F. Haldane, “Quantum spin-hall effect and topologically invariant chern numbers,” Phys. Rev. Lett. 97(3), 036808 (2006).
[Crossref]

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]

Wurtz, G. A.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Young, A. B.

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

Zayats, A. V.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

Zhang, J.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Zhang, S.-C.

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
[Crossref]

Zhu, Y.

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Zilberberg, O.

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

J. Microsc. (1)

D. Cohen and C. Carter, “Structure of the (110) antiphase boundary in gallium phosphide,” J. Microsc. 208(2), 84–99 (2002).
[Crossref]

J. Phys. Soc. Jpn. (1)

M. König, H. Buhmann, L. W. Molenkamp, T. Hughes, C.-X. Liu, X.-L. Qi, and S.-C. Zhang, “The quantum spin hall effect: theory and experiment,” J. Phys. Soc. Jpn. 77(3), 031007 (2008).
[Crossref]

Nat. Commun. (2)

R. Coles, D. Price, J. Dixon, B. Royall, E. Clarke, P. Kok, M. Skolnick, A. Fox, and M. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7(1), 11183 (2016).
[Crossref]

X.-K. Wei, A. K. Tagantsev, A. Kvasov, K. Roleder, C.-L. Jia, and N. Setter, “Ferroelectric translational antiphase boundaries in nonpolar materials,” Nat. Commun. 5(1), 3031 (2014).
[Crossref]

Nat. Mater. (1)

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]

Nat. Nanotechnol. (1)

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon–emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10(9), 775–778 (2015).
[Crossref]

Nat. Phys. (1)

M. Hafezi, E. A. Demler, M. D. Lukin, and J. M. Taylor, “Robust optical delay lines with topological protection,” Nat. Phys. 7(11), 907–912 (2011).
[Crossref]

Nature (2)

F. Kuemmeth, S. Ilani, D. Ralph, and P. McEuen, “Coupling of spin and orbital motion of electrons in carbon nanotubes,” Nature 452(7186), 448–452 (2008).
[Crossref]

A. Soumyanarayanan, N. Reyren, A. Fert, and C. Panagopoulos, “Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces,” Nature 539(7630), 509–517 (2016).
[Crossref]

Optica (1)

Phys. Rev. B (2)

K. Ahn, T. Lookman, A. Saxena, and A. Bishop, “Electronic properties of structural twin and antiphase boundaries in materials with strong electron-lattice couplings,” Phys. Rev. B 71(21), 212102 (2005).
[Crossref]

T. Ma and G. Shvets, “Scattering-free edge states between heterogeneous photonic topological insulators,” Phys. Rev. B 95(16), 165102 (2017).
[Crossref]

Phys. Rev. Lett. (5)

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]

C. L. Kane and E. J. Mele, “Quantum spin hall effect in graphene,” Phys. Rev. Lett. 95(22), 226801 (2005).
[Crossref]

C. L. Kane and E. J. Mele, “Z 2 topological order and the quantum spin hall effect,” Phys. Rev. Lett. 95(14), 146802 (2005).
[Crossref]

D. Sheng, Z. Weng, L. Sheng, and F. Haldane, “Quantum spin-hall effect and topologically invariant chern numbers,” Phys. Rev. Lett. 97(3), 036808 (2006).
[Crossref]

A. B. Young, A. Thijssen, D. M. Beggs, P. Androvitsaneas, L. Kuipers, J. G. Rarity, S. Hughes, and R. Oulton, “Polarization engineering in photonic crystal waveguides for spin-photon entanglers,” Phys. Rev. Lett. 115(15), 153901 (2015).
[Crossref]

Proc. Natl. Acad. Sci. (1)

Z. Wang, H. Guo, S. Shao, M. Saghayezhian, J. Li, R. Fittipaldi, A. Vecchione, P. Siwakoti, Y. Zhu, J. Zhang, and E. W. Plummer, “Designing antiphase boundaries by atomic control of heterointerfaces,” Proc. Natl. Acad. Sci. 115(38), 9485–9490 (2018).
[Crossref]

Rev. Mod. Phys. (1)

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys. 91(1), 015006 (2019).
[Crossref]

Science (2)

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340(6130), 328–330 (2013).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346(6205), 67–71 (2014).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. (a) Unit cell of photonic crystal with $d$ the diameter of cylinders, $a_0$ the length of diamond edge, and $R$ the distance between the center of the diamond and the center of the cylinders. $\varepsilon _d$ and $\varepsilon _A$ are the relative permittivities of the cylinders and surrounding environment respectively. (b) Anti-phase boundary (red dashed line) formed by shifting the photonic crystal along $ \overrightarrow {a}_2$ by one-half period $t=-a_0/2$ where $ \overrightarrow {a}_1$ and $ \overrightarrow {a}_2$ are lattice vectors of the crystal. The angle between $ \overrightarrow {a}_1$ and $ \overrightarrow {a}_2$ is $\pi /3$ .
Fig. 2.
Fig. 2. The red hexagons are unit cells of the crystal for $R=a_0/3$ while $ \overrightarrow {a}_1^{'}$ and $ \overrightarrow {a}_2^{'}$ are lattice vectors.
Fig. 3.
Fig. 3. (a) Dispersion relation of the super-cell which is periodic in $ \overrightarrow {a}_2$ direction and of 8 unit cells on each side of anti-phase boundary in $ \overrightarrow {a}_1$ direction. Label $k_2$ means the projection of k vector onto $ \overrightarrow {a}_2/| \overrightarrow {a}_2|$ . The green-shaded region is the projected band diagram of the bulk modes. Red and blue lines represent the odd modes and even modes respectively. The diameter of cylinder and distance between cylinder center and diamond center are $d=0.24a_0$ and $R=0.345a_0$ . The relative permittivities are $\varepsilon _d=11.7$ and $\varepsilon _A=1$ . (b) Real part of $E_z$ distributions at points $P_1$ , $P_2$ and $P_3$ as shown in (a). The black arrows indicate the time-averaged Poynting vectors over a period. (c) Real part distributions of $E_z$ of magnetic dipoles $(\hat {x}-i\hat {y})/\sqrt {2}$ (left) and $(\hat {x}+i\hat {y})/\sqrt {2}$ (right) are plotted. The red arrows represent the time-averaged Poynting vectors. (d) $|E_z|$ are plotted for the driven modes excited by magnetic dipoles $(\hat {x}-i\hat {y})/\sqrt {2}$ (left) and $(\hat {x}+i\hat {y})/\sqrt {2}$ (right) respectively. The yellow arrow indicates the location of the source, which is at the center of the unit cell. The normalized frequency of the source is chosen to be $f_0a_0/c=0.46$ .
Fig. 4.
Fig. 4. (a) Dispersion relation of the super-cell when $R=0.3a_0$ . Red and blue lines represent the odd modes and even modes respectively. (b) Real part of $E_z$ distributions at points $P_1$ , $P_2$ and $P_3$ as shown in (a). (c) $|E_z|$ are plotted for the driven modes excited by magnetic dipoles $(\hat {x}-i\hat {y})/\sqrt {2}$ (left) and $(\hat {x}+i\hat {y})/\sqrt {2}$ (right) respectively. The normalized frequency of the source is chosen to be $f_0a_0/c=0.473$ .
Fig. 5.
Fig. 5. Dispersion relations of the super-cells with (a) $R=0.345a_0$ and (b) $R=0.3a_0$ when tuning the offset $t$ in units of $a_0$ . $|E_z|$ distributions are plotted for the edge modes with $R=0.345a_0$ when (c) $k_2a_0/2\pi =0$ and (d) $k_2a_0/2\pi =0.1$ .
Fig. 6.
Fig. 6. (a) Comparison between radical and gradual shift super-cell. A shift of $t=0.05a_0$ is set between adjacent unit cells on the two sides of the boundary marked by red dashed line. The far left with $t=-0.25a_0$ has the same pattern as the far right. (b) Dispersion relation of the gradual shift super-cell when $R=0.345a_0$ . (c) $|E_z|$ distributions at points $P_1$ , $P_2$ and $P_3$ as shown in (b). (d) $|E_z|$ are plotted for the driven modes excited by magnetic dipoles $(\hat {x}-i\hat {y})/\sqrt {2}$ (left) and $(\hat {x}+i\hat {y})/\sqrt {2}$ (right) respectively. The normalized frequency of the source is chosen to be $f_0a_0/c=0.462$ . The source is located at the center of the unit cell with $t=0$ .
Fig. 7.
Fig. 7. Directionality $D$ defined in Eq. (2) is plotted as a function of $\theta$ and $\phi$ for (a) $R=0.345a_0, f_0a_0/c=0.46$ and (b) $R=0.30a_0, f_0a_0/c=0.473$ . The white dots indicate the locations of the sources $(\hat {x}-i\hat {y})/\sqrt {2}$ (upper) and $(\hat {x}+i\hat {y})/\sqrt {2}$ (lower).

Equations (2)

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m = cos θ x ^ + sin θ exp ( i ϕ ) y ^
D = c + c c + + c

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