Abstract

Zero-index materials exhibit exotic optical properties that can be utilized for integrated-optics applications. However, practical implementation requires compatibility with complementary metallic-oxide-semiconductor (CMOS) technologies. We demonstrate a CMOS-compatible zero-index metamaterial consisting of a square array of air holes in a 220-nm-thick silicon-on-insulator (SOI) wafer. This design supports zero-index modes with Dirac-cone dispersion. The metamaterial is entirely composed of silicon and offers compatibility through low-aspect-ratio structures that can be simply fabricated in a standard device layer. This platform enables mass adoption and exploration of zero-index-based photonic devices at low cost and high fidelity.

© 2017 Optical Society of America

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References

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2017 (4)

I. Liberal and N. Engheta, “Zero-index structures as an alternative platform for quantum optics,” Proc. Natl. Acad. Sci. U. S. A. 114, 822–827 (2017).
[Crossref] [PubMed]

S. Kita, Y. Li, P. Camayd-Muñoz, O. Reshef, D. I. Vulis, R. W. Day, E. Mazur, and M. Lončar, “On-chip all-dielectric fabrication-tolerant zero-index metamaterials,” Opt. Expres. 25, 8326–8334 (2017).
[Crossref]

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

A. M. Mahmoud, I. Liberal, and N. Engheta, “Dipole-dipole interactions mediated by epsilon-and-mu-near-zero waveguide supercoupling [invited],” Opt. Mater. Express, OME 7, 415–424 (2017).
[Crossref]

2016 (9)

C. W. Hsu, B. Zhen, A. Douglas Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nature Reviews Materials 1, 16048 (2016).
[Crossref]

I. Liberal and N. Engheta, “Zero-index platforms: Where light defies geometry,” Optics & Photonics News 27, 26–33 (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,” Scienc. 352, 795–797 (2016).
[Crossref]

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced nonlinear refractive index in -Near-Zero materials,” Phys. Rev. Lett. 116, 233901 (2016).
[Crossref]

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 Photonic. 3, 2262–2267 (2016).
[Crossref]

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

S. Nagai and A. Sanada, “Γ-point group velocity of lossy dirac cone composite right/left-handed metamaterials,” IEICE Electronics Expres. 13, 0281 (2016).
[Crossref]

M. Faryad and M. W. Ashraf, “On the mapping of dirac-like cone dispersion in dielectric photonic crystals to an effective zero-index medium,” J. Opt. Soc. Am. B 33, 1008–1013 (2016).
[Crossref]

Y. Zhou, X.-T. He, F.-L. Zhao, and J.-W. Dong, “Proposal for achieving in-plane magnetic mirrors by silicon photonic crystals,” Opt. Lett. 41, 2209–2212 (2016).
[Crossref] [PubMed]

2015 (3)

Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonic. 9, 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,” Natur. 525, 354–358 (2015).
[Crossref]

M. Memarian and G. V. Eleftheriades, “Dirac leaky-wave antennas for continuous beam scanning from photonic crystals,” Nat. Commun. 6, 5855 (2015).
[Crossref] [PubMed]

2014 (1)

C. Argyropoulos, G. DâǍŹAguanno, and A. Alù, “Giant second-harmonic generation efficiency and ideal phase matching with a double ϵ-near-zero cross-slit metamaterial,” Phys. Rev. B Condens. Matter 89, 235401 (2014).
[Crossref]

2013 (6)

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 Condens. Matter 87, 155140 (2013).
[Crossref]

R. Sokhoyan and H. A. Atwater, “Quantum optical properties of a dipole emitter coupled to an epsilon-near-zero nanoscale waveguide,” Opt. Expres. 21, 32279–32290 (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,” Scienc. 342, 1223–1226 (2013).
[Crossref]

N. Engheta, “Pursuing near-zero response,” Scienc. 340, 286–287 (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. Photonic. 7, 791–795 (2013).
[Crossref]

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonic. 7, 907–912 (2013).
[Crossref]

2012 (2)

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

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

2011 (5)

J. Schilling, “Fundamental optical physics: The quest for zero refractive index,” Nat. Photonic. 5, 449–451 (2011).
[Crossref]

A. Alù, A. D. Yaghjian, R. A. Shore, and M. G. Silveirinha, “Causality relations in the homogenization of metamaterials,” Phys. Rev. B Condens. Matter 84, 054305 (2011).
[Crossref]

A. Boltasseva and H. A. Atwater, “Low-loss plasmonic metamaterials,” Scienc. 331, 290–291 (2011).
[Crossref]

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonic. 5, 499–505 (2011).
[Crossref]

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, 582–586 (2011).
[Crossref] [PubMed]

2010 (2)

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

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105, 233908 (2010).
[Crossref]

2009 (2)

A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett. 103, 043902 (2009).
[Crossref] [PubMed]

D. A. B. Miller, “Device requirements for optical interconnects to silicon chips,” Proc. IEE. 97, 1166–1185 (2009).
[Crossref]

2008 (1)

2007 (3)

R. A. Shore and A. D. Yaghjian, “Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers,” Radio Sci. 42, RS6S21 (2007).
[Crossref]

C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B Condens. Matter 75, 195111 (2007).
[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 Condens. Matter 76, 1–17 (2007).
[Crossref]

2006 (3)

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref] [PubMed]

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[Crossref]

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24, 4600–4615 (2006).
[Crossref]

2005 (2)

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23, 4222–4238 (2005).
[Crossref]

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. 71, 1–11 (2005).

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,” Scienc. 352, 795–797 (2016).
[Crossref]

Alù, A.

C. Argyropoulos, G. DâǍŹAguanno, and A. Alù, “Giant second-harmonic generation efficiency and ideal phase matching with a double ϵ-near-zero cross-slit metamaterial,” Phys. Rev. B Condens. Matter 89, 235401 (2014).
[Crossref]

A. Alù, A. D. Yaghjian, R. A. Shore, and M. G. Silveirinha, “Causality relations in the homogenization of metamaterials,” Phys. Rev. B Condens. Matter 84, 054305 (2011).
[Crossref]

A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett. 103, 043902 (2009).
[Crossref] [PubMed]

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. Photonic. 7, 791–795 (2013).
[Crossref]

Aras, M. S.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonic. 5, 499–505 (2011).
[Crossref]

Argyropoulos, C.

C. Argyropoulos, G. DâǍŹAguanno, and A. Alù, “Giant second-harmonic generation efficiency and ideal phase matching with a double ϵ-near-zero cross-slit metamaterial,” Phys. Rev. B Condens. Matter 89, 235401 (2014).
[Crossref]

Ashraf, M. W.

Atwater, H. A.

R. Sokhoyan and H. A. Atwater, “Quantum optical properties of a dipole emitter coupled to an epsilon-near-zero nanoscale waveguide,” Opt. Expres. 21, 32279–32290 (2013).
[Crossref]

A. Boltasseva and H. A. Atwater, “Low-loss plasmonic metamaterials,” Scienc. 331, 290–291 (2011).
[Crossref]

Biris, C. G.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonic. 5, 499–505 (2011).
[Crossref]

Boltasseva, A.

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced nonlinear refractive index in -Near-Zero materials,” Phys. Rev. Lett. 116, 233901 (2016).
[Crossref]

A. Boltasseva and H. A. Atwater, “Low-loss plasmonic metamaterials,” Scienc. 331, 290–291 (2011).
[Crossref]

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,” Scienc. 352, 795–797 (2016).
[Crossref]

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. Photonic. 7, 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, 031105 (2016).
[Crossref]

Camayd-Muñoz, P.

S. Kita, Y. Li, P. Camayd-Muñoz, O. Reshef, D. I. Vulis, R. W. Day, E. Mazur, and M. Lončar, “On-chip all-dielectric fabrication-tolerant zero-index metamaterials,” Opt. Expres. 25, 8326–8334 (2017).
[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 Condens. Matter 87, 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 Condens. Matter 87, 155140 (2013).
[Crossref]

Caspani, L.

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced nonlinear refractive index in -Near-Zero materials,” Phys. Rev. Lett. 116, 233901 (2016).
[Crossref]

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, 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 Photonic. 3, 2262–2267 (2016).
[Crossref]

Chen, L.

V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105, 233908 (2010).
[Crossref]

Christakis, L.

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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,” Scienc. 342, 1223–1226 (2013).
[Crossref]

Sanada, A.

S. Nagai and A. Sanada, “Γ-point group velocity of lossy dirac cone composite right/left-handed metamaterials,” IEICE Electronics Expres. 13, 0281 (2016).
[Crossref]

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 Condens. Matter 87, 155140 (2013).
[Crossref]

Schilling, J.

J. Schilling, “Fundamental optical physics: The quest for zero refractive index,” Nat. Photonic. 5, 449–451 (2011).
[Crossref]

Shalaev, V. M.

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced nonlinear refractive index in -Near-Zero materials,” Phys. Rev. Lett. 116, 233901 (2016).
[Crossref]

N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33, 2350–2352 (2008).
[Crossref] [PubMed]

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 Photonic. 3, 2262–2267 (2016).
[Crossref]

Shore, R. A.

A. Alù, A. D. Yaghjian, R. A. Shore, and M. G. Silveirinha, “Causality relations in the homogenization of metamaterials,” Phys. Rev. B Condens. Matter 84, 054305 (2011).
[Crossref]

R. A. Shore and A. D. Yaghjian, “Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers,” Radio Sci. 42, RS6S21 (2007).
[Crossref]

Silveirinha, M.

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref] [PubMed]

Silveirinha, M. G.

A. Alù, A. D. Yaghjian, R. A. Shore, and M. G. Silveirinha, “Causality relations in the homogenization of metamaterials,” Phys. Rev. B Condens. Matter 84, 054305 (2011).
[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 Condens. Matter 76, 1–17 (2007).
[Crossref]

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C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B Condens. Matter 75, 195111 (2007).
[Crossref]

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D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. 71, 1–11 (2005).

Sokhoyan, R.

R. Sokhoyan and H. A. Atwater, “Quantum optical properties of a dipole emitter coupled to an epsilon-near-zero nanoscale waveguide,” Opt. Expres. 21, 32279–32290 (2013).
[Crossref]

Soljacic, M.

C. W. Hsu, B. Zhen, A. Douglas Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nature Reviews Materials 1, 16048 (2016).
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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,” Natur. 525, 354–358 (2015).
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R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
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D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. 71, 1–11 (2005).

Stein, A.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonic. 5, 499–505 (2011).
[Crossref]

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,” Scienc. 342, 1223–1226 (2013).
[Crossref]

Tretyakov, S. A.

C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B Condens. Matter 75, 195111 (2007).
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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. Photonic. 7, 791–795 (2013).
[Crossref]

Vier, D. C.

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. 71, 1–11 (2005).

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 Condens. Matter 87, 155140 (2013).
[Crossref]

Vulis, D. I.

S. Kita, Y. Li, P. Camayd-Muñoz, O. Reshef, D. I. Vulis, R. W. Day, E. Mazur, and M. Lončar, “On-chip all-dielectric fabrication-tolerant zero-index metamaterials,” Opt. Expres. 25, 8326–8334 (2017).
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Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonic. 9, 738–742 (2015).
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P. Muñoz, S. Kita, O. Mello, O. Reshef, D. I. Vulis, Y. Li, M. Loncar, and E. Mazur, “Lossless integrated dirac-cone metamaterials,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2016), paper JW2A.24.

O. Reshef, Y. Li, M. Yin, L. Christakis, D. I. Vulis, P. Muñoz, S. Kita, M. Loncar, and E. Mazur, “Phase-matching in dirac-cone-based zero-index metamaterials,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2016), paper JTu5A.53.

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2011).

Wong, C. W.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonic. 5, 499–505 (2011).
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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,” Scienc. 342, 1223–1226 (2013).
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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 Photonic. 3, 2262–2267 (2016).
[Crossref]

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A. Alù, A. D. Yaghjian, R. A. Shore, and M. G. Silveirinha, “Causality relations in the homogenization of metamaterials,” Phys. Rev. B Condens. Matter 84, 054305 (2011).
[Crossref]

R. A. Shore and A. D. Yaghjian, “Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers,” Radio Sci. 42, RS6S21 (2007).
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J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. 96, 101109 (2010).
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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. Photonic. 7, 791–795 (2013).
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A. Yariv, Optical Electronics in Modern Communications (Oxford University Press, 1997).

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Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, and E. Mazur, “On-chip zero-index metamaterials,” Nat. Photonic. 9, 738–742 (2015).
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O. Reshef, Y. Li, M. Yin, L. Christakis, D. I. Vulis, P. Muñoz, S. Kita, M. Loncar, and E. Mazur, “Phase-matching in dirac-cone-based zero-index metamaterials,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2016), paper JTu5A.53.

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,” Scienc. 342, 1223–1226 (2013).
[Crossref]

Yu, M. B.

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonic. 5, 499–505 (2011).
[Crossref]

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,” Scienc. 342, 1223–1226 (2013).
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Y. Zhou, X.-T. He, F.-L. Zhao, and J.-W. Dong, “Proposal for achieving in-plane magnetic mirrors by silicon photonic crystals,” Opt. Lett. 41, 2209–2212 (2016).
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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 Photonic. 3, 2262–2267 (2016).
[Crossref]

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C. W. Hsu, B. Zhen, A. Douglas Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nature Reviews Materials 1, 16048 (2016).
[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,” Natur. 525, 354–358 (2015).
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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, 582–586 (2011).
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ACS Photonic. (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 Photonic. 3, 2262–2267 (2016).
[Crossref]

Appl. Phys. Lett. (2)

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

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

IEEE J. Sel. Top. Quantum Electron. (1)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[Crossref]

IEICE Electronics Expres. (1)

S. Nagai and A. Sanada, “Γ-point group velocity of lossy dirac cone composite right/left-handed metamaterials,” IEICE Electronics Expres. 13, 0281 (2016).
[Crossref]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Nat. Commun. (1)

M. Memarian and G. V. Eleftheriades, “Dirac leaky-wave antennas for continuous beam scanning from photonic crystals,” Nat. Commun. 6, 5855 (2015).
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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, 582–586 (2011).
[Crossref] [PubMed]

Nat. Photonic. (6)

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. Photonic. 7, 791–795 (2013).
[Crossref]

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nat. Photonic. 7, 907–912 (2013).
[Crossref]

S. Kocaman, M. S. Aras, P. Hsieh, J. F. McMillan, C. G. Biris, N. C. Panoiu, M. B. Yu, D. L. Kwong, A. Stein, and C. W. Wong, “Zero phase delay in negative-refractive-index photonic crystal superlattices,” Nat. Photonic. 5, 499–505 (2011).
[Crossref]

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

J. Schilling, “Fundamental optical physics: The quest for zero refractive index,” Nat. Photonic. 5, 449–451 (2011).
[Crossref]

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

Natur. (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,” Natur. 525, 354–358 (2015).
[Crossref]

Nature Reviews Materials (1)

C. W. Hsu, B. Zhen, A. Douglas Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nature Reviews Materials 1, 16048 (2016).
[Crossref]

Opt. Expres. (4)

S. Kita, Y. Li, P. Camayd-Muñoz, O. Reshef, D. I. Vulis, R. W. Day, E. Mazur, and M. Lončar, “On-chip all-dielectric fabrication-tolerant zero-index metamaterials,” Opt. Expres. 25, 8326–8334 (2017).
[Crossref]

R. Sokhoyan and H. A. Atwater, “Quantum optical properties of a dipole emitter coupled to an epsilon-near-zero nanoscale waveguide,” Opt. Expres. 21, 32279–32290 (2013).
[Crossref]

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

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

Opt. Lett. (2)

Opt. Mater. Express, OME (1)

A. M. Mahmoud, I. Liberal, and N. Engheta, “Dipole-dipole interactions mediated by epsilon-and-mu-near-zero waveguide supercoupling [invited],” Opt. Mater. Express, OME 7, 415–424 (2017).
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Optics & Photonics News (1)

I. Liberal and N. Engheta, “Zero-index platforms: Where light defies geometry,” Optics & Photonics News 27, 26–33 (2016).
[Crossref]

Phys. Rev. (1)

D. R. Smith, D. C. Vier, T. Koschny, and C. M. Soukoulis, “Electromagnetic parameter retrieval from inhomogeneous metamaterials,” Phys. Rev. 71, 1–11 (2005).

Phys. Rev. B Condens. Matter (5)

A. Alù, A. D. Yaghjian, R. A. Shore, and M. G. Silveirinha, “Causality relations in the homogenization of metamaterials,” Phys. Rev. B Condens. Matter 84, 054305 (2011).
[Crossref]

C. R. Simovski and S. A. Tretyakov, “Local constitutive parameters of metamaterials from an effective-medium perspective,” Phys. Rev. B Condens. Matter 75, 195111 (2007).
[Crossref]

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 Condens. Matter 87, 155140 (2013).
[Crossref]

C. Argyropoulos, G. DâǍŹAguanno, and A. Alù, “Giant second-harmonic generation efficiency and ideal phase matching with a double ϵ-near-zero cross-slit metamaterial,” Phys. Rev. B Condens. Matter 89, 235401 (2014).
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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 Condens. Matter 76, 1–17 (2007).
[Crossref]

Phys. Rev. Lett. (4)

M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials,” Phys. Rev. Lett. 97, 157403 (2006).
[Crossref] [PubMed]

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced nonlinear refractive index in -Near-Zero materials,” Phys. Rev. Lett. 116, 233901 (2016).
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A. Alù and N. Engheta, “Boosting molecular fluorescence with a plasmonic nanolauncher,” Phys. Rev. Lett. 103, 043902 (2009).
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V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. 105, 233908 (2010).
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Proc. IEE. (1)

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

I. Liberal and N. Engheta, “Zero-index structures as an alternative platform for quantum optics,” Proc. Natl. Acad. Sci. U. S. A. 114, 822–827 (2017).
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Radio Sci. (1)

R. A. Shore and A. D. Yaghjian, “Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers,” Radio Sci. 42, RS6S21 (2007).
[Crossref]

Scienc. (4)

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,” Scienc. 342, 1223–1226 (2013).
[Crossref]

A. Boltasseva and H. A. Atwater, “Low-loss plasmonic metamaterials,” Scienc. 331, 290–291 (2011).
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N. Engheta, “Pursuing near-zero response,” Scienc. 340, 286–287 (2013).
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M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Scienc. 352, 795–797 (2016).
[Crossref]

Other (4)

P. Muñoz, S. Kita, O. Mello, O. Reshef, D. I. Vulis, Y. Li, M. Loncar, and E. Mazur, “Lossless integrated dirac-cone metamaterials,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2016), paper JW2A.24.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 2011).

A. Yariv, Optical Electronics in Modern Communications (Oxford University Press, 1997).

O. Reshef, Y. Li, M. Yin, L. Christakis, D. I. Vulis, P. Muñoz, S. Kita, M. Loncar, and E. Mazur, “Phase-matching in dirac-cone-based zero-index metamaterials,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2016), paper JTu5A.53.

Supplementary Material (18)

NameDescription
» Visualization 1: AVI (782 KB)      Propagation in the GX direction for positive index frequency
» Visualization 2: AVI (780 KB)      Propagation in the GX direction for negative index frequency
» Visualization 3: AVI (780 KB)      Propagation in the GX direction showing longitudinal dipole mode
» Visualization 4: AVI (840 KB)      Propagation in the GM direction for positive index frequency
» Visualization 5: AVI (835 KB)      Propagation in the GM direction for negativeindex frequency
» Visualization 6: AVI (816 KB)      Propagation in the GM direction showing longitudinal dipole mode
» Visualization 7: AVI (419 KB)      Mode at point 1 of Fig. 11, Ey
» Visualization 8: AVI (357 KB)      Mode at point 1 of Fig. 11, Hz
» Visualization 9: AVI (325 KB)      Mode at point 2 of Fig. 11, Ey
» Visualization 10: AVI (315 KB)      Mode at point 2 of Fig S7, Hz
» Visualization 11: AVI (388 KB)      Mode at point 3 of Fig. 11, Ey
» Visualization 12: AVI (381 KB)      Mode at point 3 of Fig. 11, Hz
» Visualization 13: AVI (352 KB)      Mode at point 4 of Fig. 11, Ey
» Visualization 14: AVI (371 KB)      Mode at point 4 of Fig. 11, Hz
» Visualization 15: AVI (350 KB)      Mode at point 5 of Fig. 11, Ey
» Visualization 16: AVI (368 KB)      Mode at point 5 of Fig. 11, Hz
» Visualization 17: MPG (4333 KB)      Power flow in metamaterial
» Visualization 18: AVI (186 KB)      Power flow in metamaterial showing Poynting Vector

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Figures (12)

Fig. 1
Fig. 1

Illustration of the fabrication stages of a sample photonic circuit that incorporates a zero-index metamaterial as a single, monolithic procedure. A substrate consisting of 220-nm-thick SOI is (a) patterned via electron beam lithography, then (b) structured through a reactive ion etch procedure, and finally (c) the resist is removed revealing the completed circuit. Inset: Close-up view of a metamaterial air-hole array with design parameters radius (r) and pitch (a) indicated.

Fig. 2
Fig. 2

Design of the zero-index metamaterial. (a) Photonic band structure of the zero-index metamaterial for TE modes. Two linear dispersion bands intersect at the Γ point at λ = 1550 nm. TE fraction is superimposed on the band structure. The grey lines are added to clarify the bands. (b) Three-dimensional dispersion surfaces. The linear bands (blue and red) form a Dirac-like cone. We show only the two modes that form the cone to clarify the dispersion. (c) Electric fields at the Γ point over a unit-cell cross section in the plane of the array, corresponding to an electric dipole mode and a magnetic quadrupole mode. (d) Effective index (blue line) and normalized impedance (red dashed line) of the metamaterial. The index crosses zero linearly at a wavelength of 1550 nm. Impedance is shown to have a finite value of 0.8 at the design wavelength. (e) Isowavelength contours of the zero-index metamaterial for wavelengths below (left) and above (right) the design wavelength. Lighter shades indicate wavelengths farther from the design wavelength. The nearly circular contours indicate that this metamaterial is almost isotropic near the Γ point.

Fig. 3
Fig. 3

Fabricated metamaterial and experimental setup. (a) Scanning electron microscopy image of the fabricated device. A silicon waveguide carries the incident beam towards the zero-index metamaterial prism as outlined in black, where the beam is refracted into the SU-8 slab waveguide. A silicon lip at the outside edge of the slab waveguide is used to scatter the output beam for optimal imaging. The angle of refraction α is determined by measuring the position of the refracted beam at the curved output edge of polymer slab waveguide as indicated by the yellow scattering point. An additional polymer waveguide around the outside edge of the slab waveguide includes defects that are used to align the infrared images during experimental data processing. (b) Fabricated zero-index metamaterial prism showing the incident and refracted beams

Fig. 4
Fig. 4

Experimental refractive index measurement. (a) Measured near-field pattern and (b) corresponding simulated far-field pattern. The white dashed lines show that the refracted beam crosses 0° at a wavelength of 1625 nm. The image is normalized to the maximum intensity at each wavelength. (c) Near-infrared microscope image of the prism [Fig. 3] at 1625 nm, showing the refracted beam, which propagates normal to the interface between the prism and the SU-8 slab waveguide. The black dotted lines indicate the position of the prism and input waveguide. The white dashed lines delineate the portion of the image that is used to produce the measured near-field pattern [Fig. 4(a)]. (d) Effective index of the metamaterial extracted from the measured (blue dots) and simulated (red line) angles of refraction, α.

Fig. 5
Fig. 5

The extracted transmission into the fundamental TE mode of the output slab as a function of propagation length within the ZIM. We fit to this transmission to a line and obtain a propagation loss of 1.12 dB/μm.

Fig. 6
Fig. 6

(a) The average eigenfrequency as a function of the lattice parameters. The white dashed line indicates the range of values where the average eigenfrequency of the modes occur at the operation wavelength (λ= 1550 nm). The red circles indicate points where sample band structures are calculated (as shown in I, II, III, and IV). The red star indicates the point with the ideal pitch and radius [Fig. 2(a)] to achieve degeneracy of the modes at the operation wavelength. (b) The absolute difference between the modal eigenfrequencies as a function of lattice parameters. The dashed white line indicates the range of values where the average eigenfrequency of the modes is equal to the operation wavelength [from Fig. S2(a)]. The dark blue region corresponds to a degeneracy of the two modes (0 nm difference between the two eigenfrequencies). The red circle indicates the single parameter configuration that corresponds to the degeneracy of the two modes at the given operation wavelength.

Fig. 7
Fig. 7

Comparison of band structures of the presented metamaterial [Fig. 1(d)] computed by determining the angular frequencies as a function of wave vector for all the Bloch modes (color map), and by K = n r eff ω / c with the retrieved effective index n r eff (red line).

Fig. 8
Fig. 8

Dirac-cone metamaterial with oblique incidence. (a) Top-down view of the Dirac-cone metamaterial. (b) Angle-dependent transmission of the Dirac-cone metamaterial. (c) Angle-dependent transmission at the design wavelength of 1550 nm

Fig. 9
Fig. 9

(a) Real and (b) imaginary parts of the effective relative permittivity and permeability of the metamaterial retrieved from numerically calculated reflection and transmission coefficients.

Fig. 10
Fig. 10

(a) The range of super-circle order as a function of frequencies, where n = 2 corresponds to a perfect circle. The highlighted region (f ≈ 192 – 195 THz) exhibits approximately circular isofrequency contours. (b) The extracted supercircle radii showing that the radii decrease and then increase linearly as a function of frequency.

Fig. 11
Fig. 11

Photonic band structure of the zero-index metamaterial for TE modes with marker size corresponding to confinement (larger circles correspond to higher confinement and smaller circles correspond to lower confinement) and TE fraction superimposed.

Fig. 12
Fig. 12

Finite-difference time-domain simulation of the metamaterial with a pulse source. (a) Top: top-down view of the simulation region. The metamaterial includes 10 unit cells. The vertical dashed lines indicate the boundaries of the metamaterial. Bottom: cross-section view of the simulation region, in which the horizontal dashed line indicates the position of the monitor planes. (b) Electric field intensity at different positions in the simulation region over the duration of the simulation.

Equations (1)

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n SU 8 / n r eff = sin 45 ° / sin α ,

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