Abstract

Photonic analogs of electronic systems with topologically non-trivial behavior such as unidirectional scatter-free propagation has tremendous potential for transforming photonic systems. Like in electronics topological behavior can be observed in photonics for systems either preserving time-reversal (TR) symmetry or explicitly breaking it. TR symmetry breaking requires magneto-optic photonics crystals (PC) or generation of synthetic gauge fields. For on-chip photonics that operate at optical frequencies both are quite challenging because of poor magneto-optic response of materials or substantial nanofabrication challenges in generating synthetic gauge fields. A recent work by Ma, et al. [Phys. Rev. Lett. 114, 223901 (2015)] based on preserving pseudo TR symmetry offers a promising design scheme for observing unidirectional edge states in a modified honeycomb photonic crystal (PC) lattice of circular rods that offers encouraging alternatives. Here we propose through bandstructure calculations the inverse system of modified honeycomb PC of circular holes in a dielectric membrane which is more attractive from fabrication standpoint for on-chip applications. We observe trivial and non-trivial bandgaps as well as unidirectional edge states of opposite helicity propagating in opposite directions at the interface of a trivial and non-trivial PC structures. Around 1550nm operating wavelength ~55nm of bandwidth is possible for practicable values of design parameters (lattice constant, hole radii, membrane thickness, scaling factor etc.) and robust to reasonable variations in those parameters.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2017 (1)

S. Kruk, A. Slobozhanyuk, D. Denkova, A. Poddubny, I. Kravchenko, A. Miroshnichenko, D. Neshev, and Y. Kivshar, “Edge states and topological phase transitions in chains of dielectric nanoparticles,” Small 13, 1603190 (2017).

2016 (4)

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat. Photonics 11(2), 130–136 (2016).
[Crossref]

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]

L. Lu, C. Fang, L. Fu, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Symmetry-protected topological photonic crystal in three dimensions,” Nat. Phys. 12(4), 337–340 (2016).
[Crossref]

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

2015 (6)

T. Ma, A. B. Khanikaev, S. H. Mousavi, and G. Shvets, “Guiding electromagnetic waves around sharp corners: topologically protected photonic transport in metawaveguides,” Phys. Rev. Lett. 114(12), 127401 (2015).
[Crossref] [PubMed]

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (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]

P. Titum, N. H. Lindner, M. C. Rechtsman, and G. Refael, “Disorder-induced floquet topological insulators,” Phys. Rev. Lett. 114(5), 056801 (2015).
[Crossref] [PubMed]

S. Longhi, D. Gatti, and G. D. Valle, “Robust light transport in non-Hermitian photonic lattices,” Sci. Rep. 5(1), 13376 (2015).
[Crossref] [PubMed]

A. Shaltout, A. Kildishev, and V. Shalaev, “Time-varying metasurfaces and Lorentz non-reciprocity,” Opt. Mater. Express 5(11), 2459–2467 (2015).
[Crossref]

2014 (4)

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

V. Yannopapas, “Dirac points, topological edge modes and nonreciprocal transmission in one-dimensional metamaterial-based coupled-cavity arrays,” Int. J. Mod. Phys. B 28(02), 1441006 (2014).
[Crossref]

W.-J. Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

2013 (2)

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[Crossref]

K. Fang and S. Fan, “Effective magnetic field for photons based on the magneto-optical effect,” Phys. Rev. A 88(4), 043847 (2013).
[Crossref]

2012 (4)

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Phys. Rev. Lett. 108(24), 243901 (2012).
[Crossref] [PubMed]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6(11), 782–787 (2012).
[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 (2012).
[Crossref] [PubMed]

M. C. Rechtsman, J. M. Zeuner, A. Tunnermann, S. Nolte, M. Segev, and A. Szameit, “Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures,” Nat. Photonics 7(2), 153–158 (2012).
[Crossref]

2011 (1)

2010 (1)

M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[Crossref]

2009 (2)

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

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
[Crossref]

2008 (2)

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]

2007 (1)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

2005 (2)

2004 (1)

2003 (1)

G. Subramania, S. Y. Lin, J. R. Wendt, and J. M. Rivera, “Tuning the microcavity resonant wavelength in a two-dimensional photonic crystal by modifying the cavity geometry,” Appl. Phys. Lett. 83(22), 4491–4493 (2003).
[Crossref]

2002 (2)

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10(15), 670–684 (2002).
[Crossref] [PubMed]

J. Vucković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(1 Pt 2), 016608 (2002).
[PubMed]

2000 (1)

1997 (2)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
[Crossref]

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Top. Quantum Electron. 3(3), 808–830 (1997).
[Crossref]

1980 (1)

K. Klitzing, G. Dorda, and M. Pepper, “New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance,” Phys. Rev. Lett. 45(6), 494–497 (1980).
[Crossref]

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

Baba, T.

T. Baba, “Photonic crystals and microdisk cavities based on GaInAsP-InP system,” IEEE J. Sel. Top. Quantum Electron. 3(3), 808–830 (1997).
[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]

Béri, B.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Brinker, J. C.

Chan, C. T.

W.-J. Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Chen, W.-J.

W.-J. Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Chen, X.-D.

W.-J. Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Chong, Y.

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

Chow, E.

Chow, W. W.

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]

Denkova, D.

S. Kruk, A. Slobozhanyuk, D. Denkova, A. Poddubny, I. Kravchenko, A. Miroshnichenko, D. Neshev, and Y. Kivshar, “Edge states and topological phase transitions in chains of dielectric nanoparticles,” Small 13, 1603190 (2017).

Dong, J.-W.

W.-J. Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Dorda, G.

K. Klitzing, G. Dorda, and M. Pepper, “New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance,” Phys. Rev. Lett. 45(6), 494–497 (1980).
[Crossref]

Englund, D.

Fan, J.

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[Crossref]

Fan, S.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

K. Fang and S. Fan, “Effective magnetic field for photons based on the magneto-optical effect,” Phys. Rev. A 88(4), 043847 (2013).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6(11), 782–787 (2012).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
[Crossref]

Fang, C.

L. Lu, C. Fang, L. Fu, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Symmetry-protected topological photonic crystal in three dimensions,” Nat. Phys. 12(4), 337–340 (2016).
[Crossref]

Fang, F.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Fang, K.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
[Crossref]

K. Fang and S. Fan, “Effective magnetic field for photons based on the magneto-optical effect,” Phys. Rev. A 88(4), 043847 (2013).
[Crossref]

K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6(11), 782–787 (2012).
[Crossref]

Fischer, A. J.

Fu, L.

L. Lu, C. Fang, L. Fu, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Symmetry-protected topological photonic crystal in three dimensions,” Nat. Phys. 12(4), 337–340 (2016).
[Crossref]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
[Crossref]

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
[Crossref]

Fushman, I.

Gao, W.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
[Crossref] [PubMed]

Gatti, D.

S. Longhi, D. Gatti, and G. D. Valle, “Robust light transport in non-Hermitian photonic lattices,” Sci. Rep. 5(1), 13376 (2015).
[Crossref] [PubMed]

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]

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
[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]

Hasan, M. Z.

M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[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] [PubMed]

Jiang, S.-J.

W.-J. Chen, S.-J. Jiang, X.-D. Chen, B. Zhu, L. Zhou, J.-W. Dong, and C. T. Chan, “Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide,” Nat. Commun. 5, 5782 (2014).
[Crossref] [PubMed]

Joannopoulos, J. D.

L. Lu, C. Fang, L. Fu, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Symmetry-protected topological photonic crystal in three dimensions,” Nat. Phys. 12(4), 337–340 (2016).
[Crossref]

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

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Phys. Rev. Lett. 108(24), 243901 (2012).
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Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
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S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-µm wavelength,” Opt. Lett. 25(17), 1297–1299 (2000).
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S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
[Crossref]

Johnson, S. G.

L. Lu, C. Fang, L. Fu, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Symmetry-protected topological photonic crystal in three dimensions,” Nat. Phys. 12(4), 337–340 (2016).
[Crossref]

S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-µm wavelength,” Opt. Lett. 25(17), 1297–1299 (2000).
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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 (2012).
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Khanikaev, A. B.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat. Photonics 11(2), 130–136 (2016).
[Crossref]

T. Ma, A. B. Khanikaev, S. H. Mousavi, and G. Shvets, “Guiding electromagnetic waves around sharp corners: topologically protected photonic transport in metawaveguides,” Phys. Rev. Lett. 114(12), 127401 (2015).
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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 (2012).
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Kivshar, Y.

S. Kruk, A. Slobozhanyuk, D. Denkova, A. Poddubny, I. Kravchenko, A. Miroshnichenko, D. Neshev, and Y. Kivshar, “Edge states and topological phase transitions in chains of dielectric nanoparticles,” Small 13, 1603190 (2017).

Kivshar, Y. S.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat. Photonics 11(2), 130–136 (2016).
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K. Klitzing, G. Dorda, and M. Pepper, “New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance,” Phys. Rev. Lett. 45(6), 494–497 (1980).
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S. Kruk, A. Slobozhanyuk, D. Denkova, A. Poddubny, I. Kravchenko, A. Miroshnichenko, D. Neshev, and Y. Kivshar, “Edge states and topological phase transitions in chains of dielectric nanoparticles,” Small 13, 1603190 (2017).

Kruk, S.

S. Kruk, A. Slobozhanyuk, D. Denkova, A. Poddubny, I. Kravchenko, A. Miroshnichenko, D. Neshev, and Y. Kivshar, “Edge states and topological phase transitions in chains of dielectric nanoparticles,” Small 13, 1603190 (2017).

Kuramochi, E.

Lawrence, M.

W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
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W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
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G. Subramania, S. Y. Lin, J. R. Wendt, and J. M. Rivera, “Tuning the microcavity resonant wavelength in a two-dimensional photonic crystal by modifying the cavity geometry,” Appl. Phys. Lett. 83(22), 4491–4493 (2003).
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S. Y. Lin, E. Chow, S. G. Johnson, and J. D. Joannopoulos, “Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-µm wavelength,” Opt. Lett. 25(17), 1297–1299 (2000).
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P. Titum, N. H. Lindner, M. C. Rechtsman, and G. Refael, “Disorder-induced floquet topological insulators,” Phys. Rev. Lett. 114(5), 056801 (2015).
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Lipson, M.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
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W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
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J. Vucković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(1 Pt 2), 016608 (2002).
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S. Longhi, D. Gatti, and G. D. Valle, “Robust light transport in non-Hermitian photonic lattices,” Sci. Rep. 5(1), 13376 (2015).
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B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68(5), 1129–1179 (2005).
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L. Lu, C. Fang, L. Fu, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Symmetry-protected topological photonic crystal in three dimensions,” Nat. Phys. 12(4), 337–340 (2016).
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L. Lu, J. D. Joannopoulos, and M. Soljacic, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Phys. Rev. Lett. 108(24), 243901 (2012).
[Crossref] [PubMed]

Luk, T. S.

Ma, T.

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

T. Ma, A. B. Khanikaev, S. H. Mousavi, and G. Shvets, “Guiding electromagnetic waves around sharp corners: topologically protected photonic transport in metawaveguides,” Phys. Rev. Lett. 114(12), 127401 (2015).
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Mabuchi, H.

J. Vucković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(1 Pt 2), 016608 (2002).
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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 (2012).
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Miao, X.

Migdall, A.

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
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S. Kruk, A. Slobozhanyuk, D. Denkova, A. Poddubny, I. Kravchenko, A. Miroshnichenko, D. Neshev, and Y. Kivshar, “Edge states and topological phase transitions in chains of dielectric nanoparticles,” Small 13, 1603190 (2017).

Mitsugi, S.

Mittal, S.

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
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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).
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A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat. Photonics 11(2), 130–136 (2016).
[Crossref]

T. Ma, A. B. Khanikaev, S. H. Mousavi, and G. Shvets, “Guiding electromagnetic waves around sharp corners: topologically protected photonic transport in metawaveguides,” Phys. Rev. Lett. 114(12), 127401 (2015).
[Crossref] [PubMed]

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 (2012).
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S. Kruk, A. Slobozhanyuk, D. Denkova, A. Poddubny, I. Kravchenko, A. Miroshnichenko, D. Neshev, and Y. Kivshar, “Edge states and topological phase transitions in chains of dielectric nanoparticles,” Small 13, 1603190 (2017).

Ni, X.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat. Photonics 11(2), 130–136 (2016).
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S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
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M. C. Rechtsman, J. M. Zeuner, A. Tunnermann, S. Nolte, M. Segev, and A. Szameit, “Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures,” Nat. Photonics 7(2), 153–158 (2012).
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Nussenzveig, P.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
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J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
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B. Lounis and M. Orrit, “Single-photon sources,” Rep. Prog. Phys. 68(5), 1129–1179 (2005).
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Pepper, M.

K. Klitzing, G. Dorda, and M. Pepper, “New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance,” Phys. Rev. Lett. 45(6), 494–497 (1980).
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S. Kruk, A. Slobozhanyuk, D. Denkova, A. Poddubny, I. Kravchenko, A. Miroshnichenko, D. Neshev, and Y. Kivshar, “Edge states and topological phase transitions in chains of dielectric nanoparticles,” Small 13, 1603190 (2017).

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P. Titum, N. H. Lindner, M. C. Rechtsman, and G. Refael, “Disorder-induced floquet topological insulators,” Phys. Rev. Lett. 114(5), 056801 (2015).
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M. C. Rechtsman, J. M. Zeuner, A. Tunnermann, S. Nolte, M. Segev, and A. Szameit, “Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures,” Nat. Photonics 7(2), 153–158 (2012).
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P. Titum, N. H. Lindner, M. C. Rechtsman, and G. Refael, “Disorder-induced floquet topological insulators,” Phys. Rev. Lett. 114(5), 056801 (2015).
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Resnick, P. J.

Rivera, J. M.

G. Subramania, S. Y. Lin, J. R. Wendt, and J. M. Rivera, “Tuning the microcavity resonant wavelength in a two-dimensional photonic crystal by modifying the cavity geometry,” Appl. Phys. Lett. 83(22), 4491–4493 (2003).
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Scherer, A.

J. Vucković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(1 Pt 2), 016608 (2002).
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S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
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M. C. Rechtsman, J. M. Zeuner, A. Tunnermann, S. Nolte, M. Segev, and A. Szameit, “Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures,” Nat. Photonics 7(2), 153–158 (2012).
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Shaltout, A.

Shinya, A.

Shvets, G.

T. Ma and G. Shvets, “All-Si valley-Hall photonic topological insulator,” New J. Phys. 18(2), 025012 (2016).
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T. Ma, A. B. Khanikaev, S. H. Mousavi, and G. Shvets, “Guiding electromagnetic waves around sharp corners: topologically protected photonic transport in metawaveguides,” Phys. Rev. Lett. 114(12), 127401 (2015).
[Crossref] [PubMed]

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 (2012).
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Slobozhanyuk, A.

S. Kruk, A. Slobozhanyuk, D. Denkova, A. Poddubny, I. Kravchenko, A. Miroshnichenko, D. Neshev, and Y. Kivshar, “Edge states and topological phase transitions in chains of dielectric nanoparticles,” Small 13, 1603190 (2017).

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat. Photonics 11(2), 130–136 (2016).
[Crossref]

Smirnova, D.

A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat. Photonics 11(2), 130–136 (2016).
[Crossref]

Soljacic, M.

L. Lu, C. Fang, L. Fu, S. G. Johnson, J. D. Joannopoulos, and M. Soljacic, “Symmetry-protected topological photonic crystal in three dimensions,” Nat. Phys. 12(4), 337–340 (2016).
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L. Lu, J. D. Joannopoulos, and M. Soljacic, “Topological photonics,” Nat. Photonics 8(11), 821–829 (2014).
[Crossref]

L. Lu, J. D. Joannopoulos, and M. Soljačić, “Waveguiding at the edge of a three-dimensional photonic crystal,” Phys. Rev. Lett. 108(24), 243901 (2012).
[Crossref] [PubMed]

Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
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Subramania, G.

T. S. Luk, S. Xiong, W. W. Chow, X. Miao, G. Subramania, P. J. Resnick, A. J. Fischer, and J. C. Brinker, “Anomalous enhanced emission from PbS quantum dots on a photonic-crystal microcavity,” J. Opt. Soc. Am. B 28(6), 1365–1373 (2011).
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M. C. Rechtsman, J. M. Zeuner, A. Tunnermann, S. Nolte, M. Segev, and A. Szameit, “Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures,” Nat. Photonics 7(2), 153–158 (2012).
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Taylor, J. M.

M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
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P. Titum, N. H. Lindner, M. C. Rechtsman, and G. Refael, “Disorder-induced floquet topological insulators,” Phys. Rev. Lett. 114(5), 056801 (2015).
[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 (2012).
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Tunnermann, A.

M. C. Rechtsman, J. M. Zeuner, A. Tunnermann, S. Nolte, M. Segev, and A. Szameit, “Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures,” Nat. Photonics 7(2), 153–158 (2012).
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Tzuang, L. D.

L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, “Non-reciprocal phase shift induced by an effective magnetic flux for light,” Nat. Photonics 8(9), 701–705 (2014).
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S. Longhi, D. Gatti, and G. D. Valle, “Robust light transport in non-Hermitian photonic lattices,” Sci. Rep. 5(1), 13376 (2015).
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S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett. 78(17), 3294–3297 (1997).
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J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
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J. Vucković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(1 Pt 2), 016608 (2002).
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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).
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Z. Wang, Y. Chong, J. D. Joannopoulos, and M. Soljacic, “Observation of unidirectional backscattering-immune topological electromagnetic states,” Nature 461(7265), 772–775 (2009).
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G. Subramania, S. Y. Lin, J. R. Wendt, and J. M. Rivera, “Tuning the microcavity resonant wavelength in a two-dimensional photonic crystal by modifying the cavity geometry,” Appl. Phys. Lett. 83(22), 4491–4493 (2003).
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W. Gao, M. Lawrence, B. Yang, F. Liu, F. Fang, B. Béri, J. Li, and S. Zhang, “Topological photonic phase in chiral hyperbolic metamaterials,” Phys. Rev. Lett. 114(3), 037402 (2015).
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G. Subramania, S. Y. Lin, J. R. Wendt, and J. M. Rivera, “Tuning the microcavity resonant wavelength in a two-dimensional photonic crystal by modifying the cavity geometry,” Appl. Phys. Lett. 83(22), 4491–4493 (2003).
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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 (2012).
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Nat. Photonics (8)

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3(12), 687–695 (2009).
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S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007).
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M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, “Imaging topological edge states in silicon photonics,” Nat. Photonics 7(12), 1001–1005 (2013).
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A. Slobozhanyuk, S. H. Mousavi, X. Ni, D. Smirnova, Y. S. Kivshar, and A. B. Khanikaev, “Three-dimensional all-dielectric photonic topological insulator,” Nat. Photonics 11(2), 130–136 (2016).
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M. C. Rechtsman, J. M. Zeuner, A. Tunnermann, S. Nolte, M. Segev, and A. Szameit, “Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures,” Nat. Photonics 7(2), 153–158 (2012).
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K. Fang, Z. Yu, and S. Fan, “Realizing effective magnetic field for photons by controlling the phase of dynamic modulation,” Nat. Photonics 6(11), 782–787 (2012).
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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of a honeycomb photonic crystal (PC) of hole arrays in high dielectric membrane. The dotted black diamond indicates a two ‘atom’ unit cell and the ‘6-atom’ unit cell shown as dotted hexagon. The structure can also be regarded as a triangular lattice with lattice constant ‘a’ with a unit cell of six holes of radii ‘r’ located at the corners of the hexagon or radius ‘R’ (inset). The lower image shows a titled view of the structure indicating the height of the membrane ‘h’ along the vertical (z) direction. The dotted line indicates the ‘z = 0’ plane for which the field distributions are plotted. (b) Bandstructure plot for the regular honeycomb PC for the triangular lattice (a/R = 3.0; r = 0.13a) of six hole unit cell showing the doubly degenerate Dirac points at Γ point.

Fig. 2
Fig. 2

(a) Schematic of a compressed honeycomb photonic crystal(PC) of hole arrays in high dielectric membrane showing a topologically trivial PC where hole centers are brought closer to the center of the hexagon (indicated by inward pointing arrows) with a/R = 3.1. ‘Δ’ and ‘δ’ show the gaps between in the holes within the unit cells and across the unit cells. (b) Bandstructure with the shaded area indicating the bandgap. (c) Re (Hz (x,y)) field distribution at the lower band edge (green, px) and the upper (red, dxy) at the Γ point. The yellow dotted rectangles encompassing a single lattice point are guides to the eye to help visualize the two and four-fold nature of the px and dxy symmetries. (d) Schematic of expanded honeycomb photonic crystal (PC) of hole arrays in high dielectric membrane showing a topologically non-trivial PC where hole centers are moved away from the center of the hexagon (indicated by outward pointing arrows) with a/R = 3.1. (e) Bandstructure with the shaded area indicating the bandgap. (f) Re (Hz (x,y)) field distribution at the lower (red, dxy) and upper (green, px) band edge at the Γ point which is now inverted relative to the compressed (trivial) PC.

Fig. 3
Fig. 3

(a) Plot of midgap frequency for varying hole radii ‘r’ for the 4 different cases of a/R ratios. (b) Gap size in reduced frequencies (a/λ) for varying hole radii for the 4 different a/R ratios. (c) Gap/midgap ratios for varying hole radii. (d) Midgap frequency for varying membrane thicknesses (h) for the 4 different a/R ratios. (e) Gap size for varying membrane thicknesses. (f) Gap/midgap ratios for varying membrane thicknesses.

Fig. 4
Fig. 4

(a) Schematic of the zig-zag interface between topological and trivial lattice for a/R 2.9, 3.1 respectively. (b) Plot of the projected band structure along the interface ‘y’ direction showing two unidirectional gap states. (c) Average power flow at the interface corresponding ky = −0.051(2π/a) (indicated by red up arrow in (b)) in the upward or positive ‘y’ direction. (d) Average power flow at the interface corresponding ky = 0.051(2π/a) (indicated by blue down arrow in (b)) in the downward or negative ‘y’direction.

Fig. 5
Fig. 5

(a) Schematic of the armchair interface between topological and trivial lattice for a/R 2.9, 3.1 respectively. (b) Plot of the projected band structure along the interface ‘y’ direction showing two gap unidirectional gap states. (c) Average power flow at the interface corresponding to ky = −0.06(2π/a) (indicated by red up arrow in (b)) in the upward or positive ‘y’ direction. (d) Average power flow at the interface corresponding ky = 0.06(2π/a) (indicated by blue down arrow in (b)) in the downward or negative ‘y’direction.

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