Abstract

We introduce the concept of a quasi-triply-degenerate state (QTDS) and demonstrate its relation to an effective zero refractive index (ZRI) in a two-dimensional (2D) square lattice photonic crystal (PC) of all dielectric pillars. A QTDS is characterized by a triple band structure (TBS), wherein two of the bands manifest a linear dispersion around the Γ-point, i.e. a Dirac-like cone, while the third is a flat zero refractive index (ZRI) band with a frequency that is degenerate with one of the other bands. Significantly, we find that while triple degeneracy of the bands is not observed, the three bands approach one another so close that the observable properties of PCs adapted to the QTDS frequency perform as expected of a ZRI material. We closely examine the ZRI band at the Γ-point and show that by varying the PC material and structure parameters, the ZRI band behavior extends over a wide range of dielectric refractive indices enabling materials made with polymeric constituents. Moreover, the ZRI characteristics are robust and tolerant over a range of frequencies. Furthermore, the computational screening we employ to identify QTDS parameters enables the rational design of low-loss 2D ZRI materials for a broad range of photonic applications, including distributing a common reference phase, cloaking and focusing light.

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

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  4. Y. Y. Fu, L. Xu, Z. H. Hang, and H. Y. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
    [Crossref]
  5. J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
    [Crossref]
  6. Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
    [Crossref]
  7. S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
    [Crossref]
  8. P. Moitra, Y. M. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
    [Crossref]
  9. M. Kandpal, C. Sharan, P. Poddar, K. Prashanthi, P. R. Apte, and V. R. Rao, “Photopatternable nano-composite (su-8/zno) thin films for piezo-electric applications,” Appl. Phys. Lett. 101(10), 104102 (2012).
    [Crossref]
  10. J. Y. Kim, C. Martin-Olmos, N. S. Baek, and J. Brugger, “Simple and easily controllable parabolic-shaped microlenses printed on polymeric mesas,” J. Mater. Chem. C 1(11), 2152–2157 (2013).
    [Crossref]
  11. J. Mei, Y. Wu, C. T. Chan, and Z. Q. Zhang, “First-principles study of dirac and dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
    [Crossref]
  12. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
    [Crossref]
  13. K. Sakoda, “Dirac cone in two- and three-dimensional metamaterials,” Opt. Express 20(4), 3898–3917 (2012).
    [Crossref]
  14. Y. Li, Y. Wu, X. Chen, and J. Mei, “Selection rule for dirac-like points in two-dimensional dielectric photonic crystals,” Opt. Express 21(6), 7699–7711 (2013).
    [Crossref]
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    [Crossref]
  16. C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. OptoElectron. 2012, 1–11 (2012).
    [Crossref]
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    [Crossref]
  18. K. Sakoda, “Proof of the universality of mode symmetries in creating photonic dirac cones,” Opt. Express 20(22), 25181–25194 (2012).
    [Crossref]
  19. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
    [Crossref]
  20. F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, and A. Tunnermann, “Avoided crossings in photonic crystal fibers,” Opt. Express 19(14), 13578–13589 (2011).
    [Crossref]
  21. M. Olschlager, G. Wirth, T. Kock, and A. Hemmerich, “Topologically induced avoided band crossing in an optical checkerboard lattice,” Phys. Rev. Lett. 108(7), 075302 (2012).
    [Crossref]
  22. N. R. Bernier, E. G. D. Torre, and E. Demler, “Unstable avoided crossing in coupled spinor condensates,” Phys. Rev. Lett. 113(6), 065303 (2014).
    [Crossref]
  23. J. R. Duke and N. Ananth, “Simulating excited state dynamics in systems with multiple avoided crossings using mapping variable ring polymer molecular dynamics,” J. Phys. Chem. Lett. 6(21), 4219–4223 (2015).
    [Crossref]
  24. S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
    [Crossref]
  25. J. Jin, The Finite Element Method in Electromagnetics (Wiley, 2015).

2016 (1)

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
[Crossref]

2015 (5)

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

P. Zhang, C. Fietz, P. Tassin, T. Koschny, and C. M. Soukoulis, “Numerical investigation of the flat band bloch modes in a 2d photonic crystal with dirac cones,” Opt. Express 23(8), 10444–10452 (2015).
[Crossref]

X. Wang, H. T. Jiang, Y. Li, C. Yan, F. S. Deng, Y. Sun, Y. H. Li, Y. L. Shi, and H. Chen, “Transport properties of disordered photonic crystals around a dirac-like point,” Opt. Express 23(4), 5126–5133 (2015).
[Crossref]

J. R. Duke and N. Ananth, “Simulating excited state dynamics in systems with multiple avoided crossings using mapping variable ring polymer molecular dynamics,” J. Phys. Chem. Lett. 6(21), 4219–4223 (2015).
[Crossref]

2014 (3)

N. R. Bernier, E. G. D. Torre, and E. Demler, “Unstable avoided crossing in coupled spinor condensates,” Phys. Rev. Lett. 113(6), 065303 (2014).
[Crossref]

Y. Li, Y. Wu, and J. Mei, “Double dirac cones in phononic crystals,” Appl. Phys. Lett. 105(1), 014107 (2014).
[Crossref]

Y. Y. Fu, L. Xu, Z. H. Hang, and H. Y. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
[Crossref]

2013 (4)

H. Guo, H. G. Liu, X. Zhang, H. J. Chen, W. X. Liu, S. K. Wang, and Y. P. Cui, “Dirac point and cloaking based on honeycomb lattice photonic crystal,” Appl. Phys. Express 6(4), 042003 (2013).
[Crossref]

P. Moitra, Y. M. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

J. Y. Kim, C. Martin-Olmos, N. S. Baek, and J. Brugger, “Simple and easily controllable parabolic-shaped microlenses printed on polymeric mesas,” J. Mater. Chem. C 1(11), 2152–2157 (2013).
[Crossref]

Y. Li, Y. Wu, X. Chen, and J. Mei, “Selection rule for dirac-like points in two-dimensional dielectric photonic crystals,” Opt. Express 21(6), 7699–7711 (2013).
[Crossref]

2012 (6)

K. Sakoda, “Dirac cone in two- and three-dimensional metamaterials,” Opt. Express 20(4), 3898–3917 (2012).
[Crossref]

J. Mei, Y. Wu, C. T. Chan, and Z. Q. Zhang, “First-principles study of dirac and dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. OptoElectron. 2012, 1–11 (2012).
[Crossref]

K. Sakoda, “Proof of the universality of mode symmetries in creating photonic dirac cones,” Opt. Express 20(22), 25181–25194 (2012).
[Crossref]

M. Kandpal, C. Sharan, P. Poddar, K. Prashanthi, P. R. Apte, and V. R. Rao, “Photopatternable nano-composite (su-8/zno) thin films for piezo-electric applications,” Appl. Phys. Lett. 101(10), 104102 (2012).
[Crossref]

M. Olschlager, G. Wirth, T. Kock, and A. Hemmerich, “Topologically induced avoided band crossing in an optical checkerboard lattice,” Phys. Rev. Lett. 108(7), 075302 (2012).
[Crossref]

2011 (2)

F. Jansen, F. Stutzki, C. Jauregui, J. Limpert, and A. Tunnermann, “Avoided crossings in photonic crystal fibers,” Opt. Express 19(14), 13578–13589 (2011).
[Crossref]

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

2003 (1)

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[Crossref]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref]

Ananth, N.

J. R. Duke and N. Ananth, “Simulating excited state dynamics in systems with multiple avoided crossings using mapping variable ring polymer molecular dynamics,” J. Phys. Chem. Lett. 6(21), 4219–4223 (2015).
[Crossref]

Anderson, Z.

P. Moitra, Y. M. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Apte, P. R.

M. Kandpal, C. Sharan, P. Poddar, K. Prashanthi, P. R. Apte, and V. R. Rao, “Photopatternable nano-composite (su-8/zno) thin films for piezo-electric applications,” Appl. Phys. Lett. 101(10), 104102 (2012).
[Crossref]

Baek, N. S.

J. Y. Kim, C. Martin-Olmos, N. S. Baek, and J. Brugger, “Simple and easily controllable parabolic-shaped microlenses printed on polymeric mesas,” J. Mater. Chem. C 1(11), 2152–2157 (2013).
[Crossref]

Bernier, N. R.

N. R. Bernier, E. G. D. Torre, and E. Demler, “Unstable avoided crossing in coupled spinor condensates,” Phys. Rev. Lett. 113(6), 065303 (2014).
[Crossref]

Briggs, D. P.

P. Moitra, Y. M. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Brugger, J.

J. Y. Kim, C. Martin-Olmos, N. S. Baek, and J. Brugger, “Simple and easily controllable parabolic-shaped microlenses printed on polymeric mesas,” J. Mater. Chem. C 1(11), 2152–2157 (2013).
[Crossref]

Chan, C. T.

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

J. Mei, Y. Wu, C. T. Chan, and Z. Q. Zhang, “First-principles study of dirac and dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. OptoElectron. 2012, 1–11 (2012).
[Crossref]

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref]

Chang, M. L.

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

Chen, H.

Chen, H. J.

H. Guo, H. G. Liu, X. Zhang, H. J. Chen, W. X. Liu, S. K. Wang, and Y. P. Cui, “Dirac point and cloaking based on honeycomb lattice photonic crystal,” Appl. Phys. Express 6(4), 042003 (2013).
[Crossref]

Chen, H. Y.

Y. Y. Fu, L. Xu, Z. H. Hang, and H. Y. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
[Crossref]

Chen, W. J.

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

Chen, X.

Cui, Y. P.

H. Guo, H. G. Liu, X. Zhang, H. J. Chen, W. X. Liu, S. K. Wang, and Y. P. Cui, “Dirac point and cloaking based on honeycomb lattice photonic crystal,” Appl. Phys. Express 6(4), 042003 (2013).
[Crossref]

Demler, E.

N. R. Bernier, E. G. D. Torre, and E. Demler, “Unstable avoided crossing in coupled spinor condensates,” Phys. Rev. Lett. 113(6), 065303 (2014).
[Crossref]

Deng, F. S.

Dong, J. W.

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Duke, J. R.

J. R. Duke and N. Ananth, “Simulating excited state dynamics in systems with multiple avoided crossings using mapping variable ring polymer molecular dynamics,” J. Phys. Chem. Lett. 6(21), 4219–4223 (2015).
[Crossref]

Fietz, C.

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Foteinopoulou, S.

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[Crossref]

Fu, Y. Y.

Y. Y. Fu, L. Xu, Z. H. Hang, and H. Y. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
[Crossref]

Geim, A. K.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Guo, H.

H. Guo, H. G. Liu, X. Zhang, H. J. Chen, W. X. Liu, S. K. Wang, and Y. P. Cui, “Dirac point and cloaking based on honeycomb lattice photonic crystal,” Appl. Phys. Express 6(4), 042003 (2013).
[Crossref]

Hang, Z. H.

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

Y. Y. Fu, L. Xu, Z. H. Hang, and H. Y. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
[Crossref]

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. OptoElectron. 2012, 1–11 (2012).
[Crossref]

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref]

Hemmerich, A.

M. Olschlager, G. Wirth, T. Kock, and A. Hemmerich, “Topologically induced avoided band crossing in an optical checkerboard lattice,” Phys. Rev. Lett. 108(7), 075302 (2012).
[Crossref]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref]

Huang, X.

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. OptoElectron. 2012, 1–11 (2012).
[Crossref]

Huang, X. Q.

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref]

Huang, Z. Y.

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

Jacob, Z.

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
[Crossref]

Jahani, S.

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
[Crossref]

Jansen, F.

Jauregui, C.

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Jiang, H. T.

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (Wiley, 2015).

Kandpal, M.

M. Kandpal, C. Sharan, P. Poddar, K. Prashanthi, P. R. Apte, and V. R. Rao, “Photopatternable nano-composite (su-8/zno) thin films for piezo-electric applications,” Appl. Phys. Lett. 101(10), 104102 (2012).
[Crossref]

Kim, J. Y.

J. Y. Kim, C. Martin-Olmos, N. S. Baek, and J. Brugger, “Simple and easily controllable parabolic-shaped microlenses printed on polymeric mesas,” J. Mater. Chem. C 1(11), 2152–2157 (2013).
[Crossref]

Kita, S.

Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Kock, T.

M. Olschlager, G. Wirth, T. Kock, and A. Hemmerich, “Topologically induced avoided band crossing in an optical checkerboard lattice,” Phys. Rev. Lett. 108(7), 075302 (2012).
[Crossref]

Koschny, T.

Kravchenko, I. I.

P. Moitra, Y. M. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Lai, Y.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref]

Li, Y.

Li, Y. H.

Limpert, J.

Liu, H. G.

H. Guo, H. G. Liu, X. Zhang, H. J. Chen, W. X. Liu, S. K. Wang, and Y. P. Cui, “Dirac point and cloaking based on honeycomb lattice photonic crystal,” Appl. Phys. Express 6(4), 042003 (2013).
[Crossref]

Liu, W. X.

H. Guo, H. G. Liu, X. Zhang, H. J. Chen, W. X. Liu, S. K. Wang, and Y. P. Cui, “Dirac point and cloaking based on honeycomb lattice photonic crystal,” Appl. Phys. Express 6(4), 042003 (2013).
[Crossref]

Loncar, M.

Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Martin-Olmos, C.

J. Y. Kim, C. Martin-Olmos, N. S. Baek, and J. Brugger, “Simple and easily controllable parabolic-shaped microlenses printed on polymeric mesas,” J. Mater. Chem. C 1(11), 2152–2157 (2013).
[Crossref]

Mazur, E.

Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Mei, J.

Y. Li, Y. Wu, and J. Mei, “Double dirac cones in phononic crystals,” Appl. Phys. Lett. 105(1), 014107 (2014).
[Crossref]

Y. Li, Y. Wu, X. Chen, and J. Mei, “Selection rule for dirac-like points in two-dimensional dielectric photonic crystals,” Opt. Express 21(6), 7699–7711 (2013).
[Crossref]

J. Mei, Y. Wu, C. T. Chan, and Z. Q. Zhang, “First-principles study of dirac and dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

Moitra, P.

P. Moitra, Y. M. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Munoz, P.

Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Novoselov, K. S.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Olschlager, M.

M. Olschlager, G. Wirth, T. Kock, and A. Hemmerich, “Topologically induced avoided band crossing in an optical checkerboard lattice,” Phys. Rev. Lett. 108(7), 075302 (2012).
[Crossref]

Poddar, P.

M. Kandpal, C. Sharan, P. Poddar, K. Prashanthi, P. R. Apte, and V. R. Rao, “Photopatternable nano-composite (su-8/zno) thin films for piezo-electric applications,” Appl. Phys. Lett. 101(10), 104102 (2012).
[Crossref]

Prashanthi, K.

M. Kandpal, C. Sharan, P. Poddar, K. Prashanthi, P. R. Apte, and V. R. Rao, “Photopatternable nano-composite (su-8/zno) thin films for piezo-electric applications,” Appl. Phys. Lett. 101(10), 104102 (2012).
[Crossref]

Rao, V. R.

M. Kandpal, C. Sharan, P. Poddar, K. Prashanthi, P. R. Apte, and V. R. Rao, “Photopatternable nano-composite (su-8/zno) thin films for piezo-electric applications,” Appl. Phys. Lett. 101(10), 104102 (2012).
[Crossref]

Reshef, O.

Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Sakoda, K.

Sharan, C.

M. Kandpal, C. Sharan, P. Poddar, K. Prashanthi, P. R. Apte, and V. R. Rao, “Photopatternable nano-composite (su-8/zno) thin films for piezo-electric applications,” Appl. Phys. Lett. 101(10), 104102 (2012).
[Crossref]

Shi, Y. L.

Soukoulis, C. M.

P. Zhang, C. Fietz, P. Tassin, T. Koschny, and C. M. Soukoulis, “Numerical investigation of the flat band bloch modes in a 2d photonic crystal with dirac cones,” Opt. Express 23(8), 10444–10452 (2015).
[Crossref]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[Crossref]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref]

Stutzki, F.

Sun, Y.

Tassin, P.

Torre, E. G. D.

N. R. Bernier, E. G. D. Torre, and E. Demler, “Unstable avoided crossing in coupled spinor condensates,” Phys. Rev. Lett. 113(6), 065303 (2014).
[Crossref]

Tunnermann, A.

Valentine, J.

P. Moitra, Y. M. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Vulis, D. I.

Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Wang, S. K.

H. Guo, H. G. Liu, X. Zhang, H. J. Chen, W. X. Liu, S. K. Wang, and Y. P. Cui, “Dirac point and cloaking based on honeycomb lattice photonic crystal,” Appl. Phys. Express 6(4), 042003 (2013).
[Crossref]

Wang, X.

Wirth, G.

M. Olschlager, G. Wirth, T. Kock, and A. Hemmerich, “Topologically induced avoided band crossing in an optical checkerboard lattice,” Phys. Rev. Lett. 108(7), 075302 (2012).
[Crossref]

Wu, Y.

Y. Li, Y. Wu, and J. Mei, “Double dirac cones in phononic crystals,” Appl. Phys. Lett. 105(1), 014107 (2014).
[Crossref]

Y. Li, Y. Wu, X. Chen, and J. Mei, “Selection rule for dirac-like points in two-dimensional dielectric photonic crystals,” Opt. Express 21(6), 7699–7711 (2013).
[Crossref]

J. Mei, Y. Wu, C. T. Chan, and Z. Q. Zhang, “First-principles study of dirac and dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

Xu, L.

Y. Y. Fu, L. Xu, Z. H. Hang, and H. Y. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
[Crossref]

Yan, C.

Yang, Y. M.

P. Moitra, Y. M. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Yin, M.

Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Zhang, P.

Zhang, X.

H. Guo, H. G. Liu, X. Zhang, H. J. Chen, W. X. Liu, S. K. Wang, and Y. P. Cui, “Dirac point and cloaking based on honeycomb lattice photonic crystal,” Appl. Phys. Express 6(4), 042003 (2013).
[Crossref]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Zhang, Z. Q.

J. Mei, Y. Wu, C. T. Chan, and Z. Q. Zhang, “First-principles study of dirac and dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

Zheng, H. H.

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref]

Zhong, Z. C.

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

Adv. OptoElectron. (1)

C. T. Chan, Z. H. Hang, and X. Huang, “Dirac dispersion in two-dimensional photonic crystals,” Adv. OptoElectron. 2012, 1–11 (2012).
[Crossref]

Appl. Phys. Express (1)

H. Guo, H. G. Liu, X. Zhang, H. J. Chen, W. X. Liu, S. K. Wang, and Y. P. Cui, “Dirac point and cloaking based on honeycomb lattice photonic crystal,” Appl. Phys. Express 6(4), 042003 (2013).
[Crossref]

Appl. Phys. Lett. (3)

Y. Y. Fu, L. Xu, Z. H. Hang, and H. Y. Chen, “Unidirectional transmission using array of zero-refractive-index metamaterials,” Appl. Phys. Lett. 104(19), 193509 (2014).
[Crossref]

M. Kandpal, C. Sharan, P. Poddar, K. Prashanthi, P. R. Apte, and V. R. Rao, “Photopatternable nano-composite (su-8/zno) thin films for piezo-electric applications,” Appl. Phys. Lett. 101(10), 104102 (2012).
[Crossref]

Y. Li, Y. Wu, and J. Mei, “Double dirac cones in phononic crystals,” Appl. Phys. Lett. 105(1), 014107 (2014).
[Crossref]

J. Mater. Chem. C (1)

J. Y. Kim, C. Martin-Olmos, N. S. Baek, and J. Brugger, “Simple and easily controllable parabolic-shaped microlenses printed on polymeric mesas,” J. Mater. Chem. C 1(11), 2152–2157 (2013).
[Crossref]

J. Phys. Chem. Lett. (1)

J. R. Duke and N. Ananth, “Simulating excited state dynamics in systems with multiple avoided crossings using mapping variable ring polymer molecular dynamics,” J. Phys. Chem. Lett. 6(21), 4219–4223 (2015).
[Crossref]

Nat. Mater. (1)

X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. 10(8), 582–586 (2011).
[Crossref]

Nat. Nanotechnol. (1)

S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11(1), 23–36 (2016).
[Crossref]

Nat. Photonics (2)

P. Moitra, Y. M. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nat. Photonics 7(10), 791–795 (2013).
[Crossref]

Y. Li, S. Kita, P. Munoz, O. Reshef, D. I. Vulis, M. Yin, M. Loncar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Opt. Express (6)

Phys. Rev. B (2)

J. Mei, Y. Wu, C. T. Chan, and Z. Q. Zhang, “First-principles study of dirac and dirac-like cones in phononic and photonic crystals,” Phys. Rev. B 86(3), 035141 (2012).
[Crossref]

S. Foteinopoulou and C. M. Soukoulis, “Negative refraction and left-handed behavior in two-dimensional photonic crystals,” Phys. Rev. B 67(23), 235107 (2003).
[Crossref]

Phys. Rev. Lett. (4)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures,” Phys. Rev. Lett. 65(25), 3152–3155 (1990).
[Crossref]

M. Olschlager, G. Wirth, T. Kock, and A. Hemmerich, “Topologically induced avoided band crossing in an optical checkerboard lattice,” Phys. Rev. Lett. 108(7), 075302 (2012).
[Crossref]

N. R. Bernier, E. G. D. Torre, and E. Demler, “Unstable avoided crossing in coupled spinor condensates,” Phys. Rev. Lett. 113(6), 065303 (2014).
[Crossref]

J. W. Dong, M. L. Chang, X. Q. Huang, Z. H. Hang, Z. C. Zhong, W. J. Chen, Z. Y. Huang, and C. T. Chan, “Conical dispersion and effective zero refractive index in photonic quasicrystals,” Phys. Rev. Lett. 114(16), 163901 (2015).
[Crossref]

Science (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref]

Other (1)

J. Jin, The Finite Element Method in Electromagnetics (Wiley, 2015).

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Figures (5)

Fig. 1.
Fig. 1. PWE analysis of the TM modes of the square lattice 2D PC, $n^2$ = 12.5, $r = 0.2a$, $\mu _r$ = 1 [1]. The modes for Bands 1 to 3 are pictured on the right
Fig. 2.
Fig. 2. PWE analysis of bands 1, 2, 3 at the Dirac-like $\Gamma$-point as a function of the index $n$ and the radius $r$ of the pillars: (a) $r = 0.2a$ fixed, n $\epsilon$ [1,6]; (b) an expanded view of the QTDS in (a); (c) $n=3.53616$ fixed, r $\epsilon$ $[0, 0.5a$]; (d) An expanded view of the QTDS in (c); (e) the line follows the ZRI region for values of the cylinder radius in the range r $\epsilon$ $[0.15a, 0.35a$]
Fig. 3.
Fig. 3. Three bands for the 2D square lattice PC. Vertical: four values of the scaled rod radius r. Horizontal: EFCs for three bands, axes are $(kx, ky)$ coordinates in the Brillouin zone; BFs with axes $(x, y)$ in the unit cell; and 3D PBSs, axes are $(kx, ky)$ coordinates in the Brillouin zone.
Fig. 4.
Fig. 4. FEM analysis of ZRI behavior in a polygon prism metamaterial based on 2D SLAD PC: (a) Prism geometry with $n^2$ = 12.5, $r=0.2a$, $f=0.53383$; (b) PC lens design using the same physical parameters. In all cases $\mu _r=1$
Fig. 5.
Fig. 5. FEM analysis of PC ZRI behavior: (a) $n^2$ = 12.5, $r=0.2a$, $f=0.54065$; (b) same physical parameters as in (a) cloaking by removing three pillars and filling the space with gold.

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