Abstract

Zero-index metamaterials (ZIMs) offer unprecedented ways to manipulate the flow of light, and are of interest for wide range of applications including optical cloaking, super-coupling, and unconventional phase-matching properties in nonlinear optics. Impedance-matched ZIMs can be obtained through a photonic Dirac-cone (PDC) dispersion induced by an accidental degeneracy of an electric monopole and a transverse magnetic dipole mode at the center of the Brillouin zone. Therefore, PDC is very sensitive to fabrication imperfections. In this work, we propose and demonstrate fabrication-tolerant all-dielectric ZIM in telecom regime that supports near PDC dispersion over much wider parameter space than conventional designs. The prism device integrated with Si photonics is fabricated and measured for the verification.

© 2017 Optical Society of America

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References

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  1. X. Huang, Y. Lai, Z. H. Hang, 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] [PubMed]
  2. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
    [Crossref]
  3. J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
    [Crossref]
  4. M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B 76(24), 245109 (2007).
    [Crossref]
  5. N. Engheta, “Materials science. Pursuing near-zero response,” Science 340(6130), 286–287 (2013).
    [Crossref] [PubMed]
  6. D. I. Vulis, O. Reshef, P. Muñoz, S. Kita, Y. Li, M. Lončar, and E. Mazur, “Integrated super-couplers based on zero index metamaterials,” in The 6th International Conference on Metamaterials, Photonic Crystals and Plasmonics (New York, NY, 2015), pp. 832–833.
  7. H. Hajian, E. Ozbay, and H. Caglayan, “Enhanced transmission and beaming via a zero-index photonic crystal,” Appl. Phys. Lett. 109(3), 031105 (2016).
    [Crossref]
  8. H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
    [Crossref] [PubMed]
  9. D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
    [Crossref]
  10. M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
    [Crossref] [PubMed]
  11. O. Reshef, Y. Li, M. Yin, L. Christakis, D. I. Vulis, P. Muñoz, S. Kita, M. Lončar, and E. Mazur, “Phase-Matching in Dirac-Cone-Based Zero-Index Metamaterials,” in Conference on Laser and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2016), paper jTu5A.53.
    [Crossref]
  12. J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Enabling single-mode behavior over large areas with photonic Dirac cones,” Proc. Natl. Acad. Sci. U.S.A. 109(25), 9761–9765 (2012).
    [Crossref] [PubMed]
  13. S. L. Chua, L. Lu, J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point,” Opt. Lett. 39(7), 2072–2075 (2014).
    [Crossref] [PubMed]
  14. P. Moitra, Y. 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]
  15. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A Metamaterial for Directive Emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
    [Crossref] [PubMed]
  16. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
    [Crossref] [PubMed]
  17. A. M. Mahmoud and N. Engheta, “Wave-matter interactions in epsilon-and-mu-near-zero structures,” Nat. Commun. 5, 5638 (2014).
    [Crossref] [PubMed]
  18. R. Fleury and A. Alù, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B 87(20), 201101 (2013).
    [Crossref]
  19. X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
    [Crossref]
  20. V. Pacheco-Peña, V. Torres, M. Beruete, M. Navarro-Cía, and N. Engheta, “ε-near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves,” J. Opt. 16(9), 094009 (2014).
    [Crossref]
  21. J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009).
    [Crossref] [PubMed]
  22. Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero index materials,” Nat. Photonics 9(11), 738–742 (2015).
    [Crossref]
  23. B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
    [Crossref] [PubMed]
  24. T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
    [Crossref]
  25. S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066608 (2002).
    [Crossref] [PubMed]
  26. A. Oskooi, A. Mutapcic, S. Noda, J. D. Joannopoulos, S. P. Boyd, and S. G. Johnson, “Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides,” Opt. Express 20(19), 21558–21575 (2012).
    [Crossref] [PubMed]
  27. F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

2017 (1)

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

2016 (3)

H. Hajian, E. Ozbay, and H. Caglayan, “Enhanced transmission and beaming via a zero-index photonic crystal,” Appl. Phys. Lett. 109(3), 031105 (2016).
[Crossref]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

2015 (2)

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

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

2014 (3)

S. L. Chua, L. Lu, J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point,” Opt. Lett. 39(7), 2072–2075 (2014).
[Crossref] [PubMed]

A. M. Mahmoud and N. Engheta, “Wave-matter interactions in epsilon-and-mu-near-zero structures,” Nat. Commun. 5, 5638 (2014).
[Crossref] [PubMed]

V. Pacheco-Peña, V. Torres, M. Beruete, M. Navarro-Cía, and N. Engheta, “ε-near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves,” J. Opt. 16(9), 094009 (2014).
[Crossref]

2013 (5)

R. Fleury and A. Alù, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B 87(20), 201101 (2013).
[Crossref]

P. Moitra, Y. 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]

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[Crossref] [PubMed]

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

N. Engheta, “Materials science. Pursuing near-zero response,” Science 340(6130), 286–287 (2013).
[Crossref] [PubMed]

2012 (2)

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Enabling single-mode behavior over large areas with photonic Dirac cones,” Proc. Natl. Acad. Sci. U.S.A. 109(25), 9761–9765 (2012).
[Crossref] [PubMed]

A. Oskooi, A. Mutapcic, S. Noda, J. D. Joannopoulos, S. P. Boyd, and S. G. Johnson, “Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides,” Opt. Express 20(19), 21558–21575 (2012).
[Crossref] [PubMed]

2011 (1)

X. Huang, Y. Lai, Z. H. Hang, 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] [PubMed]

2010 (1)

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[Crossref]

2009 (2)

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
[Crossref]

J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009).
[Crossref] [PubMed]

2008 (1)

F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

2007 (1)

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B 76(24), 245109 (2007).
[Crossref]

2004 (1)

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

2002 (2)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066608 (2002).
[Crossref] [PubMed]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A Metamaterial for Directive Emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[Crossref] [PubMed]

Alam, M. Z.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

Alù, A.

R. Fleury and A. Alù, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B 87(20), 201101 (2013).
[Crossref]

Anderson, Z.

P. Moitra, Y. 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]

Beruete, M.

V. Pacheco-Peña, V. Torres, M. Beruete, M. Navarro-Cía, and N. Engheta, “ε-near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves,” J. Opt. 16(9), 094009 (2014).
[Crossref]

Biagioni, P.

J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009).
[Crossref] [PubMed]

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066608 (2002).
[Crossref] [PubMed]

Boyd, R. W.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

Boyd, S. P.

Bravo-Abad, J.

S. L. Chua, L. Lu, J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point,” Opt. Lett. 39(7), 2072–2075 (2014).
[Crossref] [PubMed]

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Enabling single-mode behavior over large areas with photonic Dirac cones,” Proc. Natl. Acad. Sci. U.S.A. 109(25), 9761–9765 (2012).
[Crossref] [PubMed]

Briggs, D. P.

P. Moitra, Y. 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]

Caglayan, H.

H. Hajian, E. Ozbay, and H. Caglayan, “Enhanced transmission and beaming via a zero-index photonic crystal,” Appl. Phys. Lett. 109(3), 031105 (2016).
[Crossref]

Campione, S.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

Capolino, F.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

Carbonell, J.

F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

Chan, C. T.

X. Huang, Y. Lai, Z. H. Hang, 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] [PubMed]

Chang, M. L.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Chua, S. L.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

S. L. Chua, L. Lu, J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point,” Opt. Lett. 39(7), 2072–2075 (2014).
[Crossref] [PubMed]

de Ceglia, D.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

De Leon, I.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

Deng, S. Z.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Dong, J. W.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Engheta, N.

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

V. Pacheco-Peña, V. Torres, M. Beruete, M. Navarro-Cía, and N. Engheta, “ε-near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves,” J. Opt. 16(9), 094009 (2014).
[Crossref]

A. M. Mahmoud and N. Engheta, “Wave-matter interactions in epsilon-and-mu-near-zero structures,” Nat. Commun. 5, 5638 (2014).
[Crossref] [PubMed]

N. Engheta, “Materials science. Pursuing near-zero response,” Science 340(6130), 286–287 (2013).
[Crossref] [PubMed]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B 76(24), 245109 (2007).
[Crossref]

Enoch, S.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A Metamaterial for Directive Emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[Crossref] [PubMed]

Feichtner, T.

J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009).
[Crossref] [PubMed]

Fleury, R.

R. Fleury and A. Alù, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B 87(20), 201101 (2013).
[Crossref]

Guérin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A Metamaterial for Directive Emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[Crossref] [PubMed]

Hajian, H.

H. Hajian, E. Ozbay, and H. Caglayan, “Enhanced transmission and beaming via a zero-index photonic crystal,” Appl. Phys. Lett. 109(3), 031105 (2016).
[Crossref]

Hang, Z. H.

X. Huang, Y. Lai, Z. H. Hang, 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] [PubMed]

Hao, J.

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[Crossref]

He, X. T.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Hecht, B.

J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009).
[Crossref] [PubMed]

Hsu, C. W.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

Huang, J. S.

J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009).
[Crossref] [PubMed]

Huang, X.

X. Huang, Y. Lai, Z. H. Hang, 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] [PubMed]

Huang, Z. Z.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Ibanescu, M.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066608 (2002).
[Crossref] [PubMed]

Igarashi, Y.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

Joannopoulos, J. D.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

S. L. Chua, L. Lu, J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point,” Opt. Lett. 39(7), 2072–2075 (2014).
[Crossref] [PubMed]

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Enabling single-mode behavior over large areas with photonic Dirac cones,” Proc. Natl. Acad. Sci. U.S.A. 109(25), 9761–9765 (2012).
[Crossref] [PubMed]

A. Oskooi, A. Mutapcic, S. Noda, J. D. Joannopoulos, S. P. Boyd, and S. G. Johnson, “Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides,” Opt. Express 20(19), 21558–21575 (2012).
[Crossref] [PubMed]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066608 (2002).
[Crossref] [PubMed]

Johnson, S. G.

A. Oskooi, A. Mutapcic, S. Noda, J. D. Joannopoulos, S. P. Boyd, and S. G. Johnson, “Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides,” Opt. Express 20(19), 21558–21575 (2012).
[Crossref] [PubMed]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066608 (2002).
[Crossref] [PubMed]

Kaminer, I.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

Kita, S.

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

Kravchenko, I. I.

P. Moitra, Y. 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. Huang, Y. Lai, Z. H. Hang, 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] [PubMed]

Lheurette, E.

F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

Li, Y.

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

Liberal, I.

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

Lidorikis, E.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066608 (2002).
[Crossref] [PubMed]

Lippens, D.

F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

Loncar, M.

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

Lu, L.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

S. L. Chua, L. Lu, J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point,” Opt. Lett. 39(7), 2072–2075 (2014).
[Crossref] [PubMed]

Mahmoud, A. M.

A. M. Mahmoud and N. Engheta, “Wave-matter interactions in epsilon-and-mu-near-zero structures,” Nat. Commun. 5, 5638 (2014).
[Crossref] [PubMed]

Mazur, E.

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

Moitra, P.

P. Moitra, Y. 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]

Muñoz, P.

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

Mutapcic, A.

Navarro-Cía, M.

V. Pacheco-Peña, V. Torres, M. Beruete, M. Navarro-Cía, and N. Engheta, “ε-near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves,” J. Opt. 16(9), 094009 (2014).
[Crossref]

Noda, S.

O’Brien, K.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[Crossref] [PubMed]

Ochiai, T.

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
[Crossref]

Onoda, M.

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
[Crossref]

Oskooi, A.

Ozbay, E.

H. Hajian, E. Ozbay, and H. Caglayan, “Enhanced transmission and beaming via a zero-index photonic crystal,” Appl. Phys. Lett. 109(3), 031105 (2016).
[Crossref]

Pacheco-Peña, V.

V. Pacheco-Peña, V. Torres, M. Beruete, M. Navarro-Cía, and N. Engheta, “ε-near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves,” J. Opt. 16(9), 094009 (2014).
[Crossref]

Pick, A.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

Potet, S.

F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

Qiu, M.

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[Crossref]

Reshef, O.

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

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A Metamaterial for Directive Emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[Crossref] [PubMed]

Salandrino, A.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[Crossref] [PubMed]

Scalora, M.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

She, J. C.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Silveirinha, M. G.

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B 76(24), 245109 (2007).
[Crossref]

Skorobogatiy, M. A.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066608 (2002).
[Crossref] [PubMed]

Soljacic, M.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

S. L. Chua, L. Lu, J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Larger-area single-mode photonic crystal surface-emitting lasers enabled by an accidental Dirac point,” Opt. Lett. 39(7), 2072–2075 (2014).
[Crossref] [PubMed]

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Enabling single-mode behavior over large areas with photonic Dirac cones,” Proc. Natl. Acad. Sci. U.S.A. 109(25), 9761–9765 (2012).
[Crossref] [PubMed]

Suchowski, H.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[Crossref] [PubMed]

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A Metamaterial for Directive Emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[Crossref] [PubMed]

Torres, V.

V. Pacheco-Peña, V. Torres, M. Beruete, M. Navarro-Cía, and N. Engheta, “ε-near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves,” J. Opt. 16(9), 094009 (2014).
[Crossref]

Valentine, J.

P. Moitra, Y. 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]

Vanbésien, O.

F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A Metamaterial for Directive Emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[Crossref] [PubMed]

Vincenti, M. A.

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

Vulis, D. I.

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

Wong, Z. J.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[Crossref] [PubMed]

Xu, S. Z.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Yan, W.

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[Crossref]

Yang, Y.

P. Moitra, Y. 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. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero index materials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Yin, X.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[Crossref] [PubMed]

Zhang, F.

F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

Zhang, X.

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[Crossref] [PubMed]

Zhao, F. L.

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Zhao, X.

F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

Zhen, B.

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

Zheng, H.

X. Huang, Y. Lai, Z. H. Hang, 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] [PubMed]

Ziolkowski, R. W.

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

ACS Photonics (1)

X. T. He, Z. Z. Huang, M. L. Chang, S. Z. Xu, F. L. Zhao, S. Z. Deng, J. C. She, and J. W. Dong, “Realization of Zero-Refractive-Index Lens with Ultralow Spherical Aberration,” ACS Photonics 3(12), 2262–2267 (2016).
[Crossref]

Appl. Phys. Lett. (2)

J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96(10), 101109 (2010).
[Crossref]

H. Hajian, E. Ozbay, and H. Caglayan, “Enhanced transmission and beaming via a zero-index photonic crystal,” Appl. Phys. Lett. 109(3), 031105 (2016).
[Crossref]

IEEE T. Microw. Theory (1)

F. Zhang, S. Potet, J. Carbonell, E. Lheurette, O. Vanbésien, X. Zhao, and D. Lippens, “Negative-Zero-Positive Refractive Index in a Prism-Like Omega-Type Metamaterial,” IEEE T. Microw. Theory 56(11), 2566–2573 (2008).

J. Opt. (1)

V. Pacheco-Peña, V. Torres, M. Beruete, M. Navarro-Cía, and N. Engheta, “ε-near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves,” J. Opt. 16(9), 094009 (2014).
[Crossref]

Nano Lett. (1)

J. S. Huang, T. Feichtner, P. Biagioni, and B. Hecht, “Impedance matching and emission properties of nanoantennas in an optical nanocircuit,” Nano Lett. 9(5), 1897–1902 (2009).
[Crossref] [PubMed]

Nat. Commun. (1)

A. M. Mahmoud and N. Engheta, “Wave-matter interactions in epsilon-and-mu-near-zero structures,” Nat. Commun. 5, 5638 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

X. Huang, Y. Lai, Z. H. Hang, 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] [PubMed]

Nat. Photonics (3)

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

P. Moitra, Y. 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. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero index materials,” Nat. Photonics 9(11), 738–742 (2015).
[Crossref]

Nature (1)

B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S. L. Chua, J. D. Joannopoulos, and M. Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525(7569), 354–358 (2015).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (4)

D. de Ceglia, S. Campione, M. A. Vincenti, F. Capolino, and M. Scalora, “Low-damping epsilon-near-zero slabs: Nonlinear and nonlocal optical properties,” Phys. Rev. B 87(15), 155140 (2013).
[Crossref]

R. Fleury and A. Alù, “Enhanced superradiance in epsilon-near-zero plasmonic channels,” Phys. Rev. B 87(20), 201101 (2013).
[Crossref]

M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B 76(24), 245109 (2007).
[Crossref]

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80(15), 155103 (2009).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 066608 (2002).
[Crossref] [PubMed]

R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(4), 046608 (2004).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A Metamaterial for Directive Emission,” Phys. Rev. Lett. 89(21), 213902 (2002).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. Bravo-Abad, J. D. Joannopoulos, and M. Soljačić, “Enabling single-mode behavior over large areas with photonic Dirac cones,” Proc. Natl. Acad. Sci. U.S.A. 109(25), 9761–9765 (2012).
[Crossref] [PubMed]

Science (3)

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

N. Engheta, “Materials science. Pursuing near-zero response,” Science 340(6130), 286–287 (2013).
[Crossref] [PubMed]

H. Suchowski, K. O’Brien, Z. J. Wong, A. Salandrino, X. Yin, and X. Zhang, “Phase Mismatch-Free Nonlinear Propagation in Optical Zero-Index Materials,” Science 342(6163), 1223–1226 (2013).
[Crossref] [PubMed]

Other (2)

D. I. Vulis, O. Reshef, P. Muñoz, S. Kita, Y. Li, M. Lončar, and E. Mazur, “Integrated super-couplers based on zero index metamaterials,” in The 6th International Conference on Metamaterials, Photonic Crystals and Plasmonics (New York, NY, 2015), pp. 832–833.

O. Reshef, Y. Li, M. Yin, L. Christakis, D. I. Vulis, P. Muñoz, S. Kita, M. Lončar, and E. Mazur, “Phase-Matching in Dirac-Cone-Based Zero-Index Metamaterials,” in Conference on Laser and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2016), paper jTu5A.53.
[Crossref]

Supplementary Material (1)

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Figures (6)

Fig. 1
Fig. 1

On-chip fabrication-tolerant AD-ZIM in the telecom regime. (a) Schematic. The inset shows the unit cell sandwiched by perfectly matched layers (PMLs). (b) Representative Ez (color) and H (black arrows) distribution at the middle of the Si pillar in a single unit cell for electric monopole (left) and magnetic dipole mode (right) at the Γ point for wavelength of 1596.7 nm. a = 918 nm, hSi = 860 nm, 2r = 528 nm were used. (c) Representative 3D dispersion surface of two modes with the k vector (kx, ky) around Γ point (a = 918 nm, hSi = 860 nm, 2r = 512 nm). Here, we omit the “dark” longitudinal magnetic dipole mode [1] for clarity.). The quality factors of monopole and dipole modes are Q > 105 and Q ~50, respectively. Different Qs result in different imaginary parts of modes’ eigenfrequencies, even when there is degeneracy in the real parts, giving rise to the quadratic dispersion around Γ point. This is confirmed by a 2D model of our structure (not shown), with infinitely long pillars: lack of out-of-plane losses results in infinitely large Qs for both modes and consequently the linear dispersion around Γ point is recovered. We note that the effect of finite and different Qs is analogous to parity-time symmetry without gain [23].

Fig. 2
Fig. 2

(a) neq for monopole (red dots) and dipole (blue dots) modes as a function of hSi (a = 879 nm, 2r = 512 nm). The modes have identical neq when hSi = 885 nm (circled point). (b) Wavelengths of two eigenmodes at Γ point as a function of 2r for hSi = 885 nm. In this case, Δλ/Δ2r of two modes are nearly identical for wide range of 2r, as indicated by nearly parallel curves.

Fig. 3
Fig. 3

Scaling laws for fabrication tolerance in AD-ZIM. (a) λ as a function of 2r with a and hSi of monopole (red dots) and dipole (blue dots) modes obtained by solving Eq. (1). The orange area indicates the near-degeneracy regime (Δλ < 1 nm). (b) λ as a function of 2r with all parameters scaled-down to 88%, 90%, and 92% of their values used in (a).

Fig. 4
Fig. 4

Fabrication-tolerant PDC, insensitive to variations in 2r. (a) Γ-point wavelengths for monopole (red dots) and dipole (blue dots) modes (top) and their difference Δλ (bottom) with different pillar diameter2r. (b) Photonic band diagrams with five different 2r showing PDCs at different wavelengths. Black dots indicate “dark” longitudinal magnetic dipole mode [1].

Fig. 5
Fig. 5

Experimental demonstration of an on-chip fabrication-tolerant AD-ZIM prism integrated with Si photonics. (a) Scanning electron microscope image of the fabricated device. The inset shows the magnified picture of the prism. (b) Representative NIR image showing light scattered from the prism (λ = 1.56 μm). The refracted beam with α ~0° is visible at the top. The white dashed line shows the outline of the SU-8 slab waveguide.

Fig. 6
Fig. 6

Demonstration of fabrication-tolerant AD-ZIM (a = 918 nm, hSi = 860 nm). (a) Observed angular intensity distribution of the scattered light along the edge of the SU-8 slab waveguide as a function of input wavelength for samples with different 2r (for the animation showing smaller 2r variations, please see Visualization 1). (b) Estimated effective index neff for (a). Blue dots with error bars and red curves indicate the experimental and theoretical results, respectively. The theoretical results are simulated using 3D finite difference time domain (FDTD) with the same geometries of the fabricated devices. Error bars depict uncertainties in the measurement.

Equations (4)

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n eq  ~   η Si n Si + η SiO2 n SiO2 + η air n air ,
{ λ i  ~  A i h Si  +  B i a +  C i n eq_i  ~  D i h Si  +  E i a +  F i ,
sin45° λ eff_prism + sin α m λ eff_SU8 = m 2 a ,
α m ~si n t1 ( m λ eff_SU8 2 a ).

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