
1.School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
2.Brown Theoretical Physics Center and Department of Physics, Brown University, Providence, RI, 02912, USA
Eric Mazur (mazur@seas.harvard.edu)
Published:30 September 2021,
Published Online:29 July 2021,
Received:26 March 2021,
Revised:29 June 2021,
Accepted:13 July 2021
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Tang, H. N. et al. Modeling the optical properties of twisted bilayer photonic crystals. Light: Science & Applications, 10, 1672-1679 (2021).
Tang, H. N. et al. Modeling the optical properties of twisted bilayer photonic crystals. Light: Science & Applications, 10, 1672-1679 (2021). DOI: 10.1038/s41377-021-00601-x.
We demonstrate a photonic analog of twisted bilayer graphene that has ultra-flat photonic bands and exhibits extreme slow-light behavior. Our twisted bilayer photonic device
which has an operating wavelength in the C-band of the telecom window
uses two crystalline silicon photonic crystal slabs separated by a methyl methacrylate tunneling layer. We numerically determine the magic angle using a finite-element method and the corresponding photonic band structure
which exhibits a flat band over the entire Brillouin zone. This flat band causes the group velocity to approach zero and introduces light localization
which enhances the electromagnetic field at the expense of bandwidth. Using our original plane-wave continuum model
we find that the photonic system has a larger band asymmetry. The band structure can easily be engineered by adjusting the device geometry
giving significant freedom in the design of devices. Our work provides a fundamental understanding of the photonic properties of twisted bilayer photonic crystals and opens the door to the nanoscale-based enhancement of nonlinear effects.
Bistritzer, R.&MacDonald, A. H. Moire bands in twisted double-layer graphene.Proc. Natl Acad. Sci. USA108, 12233–12237 (2011)..
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices.Nature556, 80–84 (2018)..
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices.Nature556, 43–50 (2018)..
Carr, S., Fang, S. A.&Kaxiras, E. Electronic-structure methods for twisted moiré layers.Nat. Rev. Mater.5, 748–763 (2020)..
Carr, S. et al. Twistronics: Manipulating the electronic properties of two-dimensional layered structures through their twist angle.Phys. Rev. B95, 075420 (2017)..
Sunku, S. S. et al. Photonic crystals for nano-light in moiré graphene superlattices.Science362, 1153–1156 (2018)..
Hu, G. W. et al. Topological polaritons and photonic magic angles in twisted α-MoO3bilayers.Nature582, 209–213 (2020)..
Duan, J. H. et al. Twisted nano-optics: manipulating light at the nanoscale with twisted phonon polaritonic slabs.Nano Lett.20, 5323–5329 (2020)..
Zheng, Z. B. et al. Phonon polaritons in twisted double-layers of hyperbolic van der waals crystals.Nano Lett.20, 5301–5308 (2020)..
Nguyen, D. X. et al. Magic configurations in Moiré superlattice of bilayer photonic crystal: almost-perfect flatbands and unconventional localization. Preprint athttps://arxiv.org/pdf/2104.12774.pdfhttps://arxiv.org/pdf/2104.12774.pdf(2021).
Khurgin, J. B. Light slowing down in Moir\'e fiber gratings and its implications for nonlinear optics.Phys. Rev. A62, 013821 (2000)..
Wang, P. et al. Localization and delocalization of light in photonic moire lattices.Nature577, 42–46 (2020)..
Lou, B. C. et al. Theory for twisted bilayer photonic crystal slabs.Phys. Rev. Lett.126, 136101 (2021)..
Lu, J. Y. et al. Valley topological phases in bilayer sonic crystals.Phys. Rev. Lett.120, 116802 (2018)..
Lu, L., Joannopoulos, J. D.&Soljačić, M. Topological photonics.Nat. Photonics8, 821–829 (2014)..
Lu, L., Joannopoulos, J. D.&Soljačić, M. Topological states in photonic systems.Nat. Phys.12, 626–629 (2016)..
Hafezi, M. et al. Imaging topological edge states in silicon photonics.Nat. Photonics7, 1001–1005 (2013)..
Fang, K. J.&Wang, Y. K. Anomalous quantum hall effect of light in bloch-wave modulated photonic crystals.Phys. Rev. Lett.122, 233904 (2019)..
Hafezi, M., Lukin, M. D.&Taylor, J. M. Non-equilibrium fractional quantum Hall state of light.N. J. Phys.15, 063001 (2013)..
Xie, B. Y. et al. Higher-order quantum spin Hall effect in a photonic crystal.Nat. Commun.11, 3768 (2020)..
Bliokh, K. Y., Smirnova, D.&Nori, F. Quantum spin Hall effect of light.Science348, 1448–1451 (2015)..
Jin, J. C. et al. Topologically enabled ultrahigh-Qguided resonances robust to out-of-plane scattering.Nature574, 501–504 (2019)..
Ochiai, T. Broken symmetry and topology in photonic analog of graphene.Int. J. Mod. Phys. B28, 1441004 (2014)..
Ochiai, T.&Onoda, M. Photonic analog of graphene model and its extension: dirac cone, symmetry, and edge states.Phys. Rev. B80, 155103 (2009)..
Wu, L. H.&Hu, X. Scheme for achieving a topological photonic crystal by using dielectric material.Phys. Rev. Lett.114, 223901 (2015)..
Parappurath, N. et al. Direct observation of topological edge states in silicon photonic crystals: spin, dispersion, and chiral routing.Sci. Adv.6, eaaw4137 (2020)..
Song, D. H. et al. Unveiling pseudospin and angular momentum in photonic graphene.Nat. Commun.6, 6272 (2015)..
Barik, S. et al. Two-dimensionally confined topological edge states in photonic crystals.N. J. Phys.18, 113013 (2016)..
Ozawa, T. et al. Topological photonics.Rev. Mod. Phys.91, 015006 (2019)..
Gardezi, S. M. et al. Acoustic twisted bilayer graphene. Preprint athttps://arxiv.org/abs/2010.10037https://arxiv.org/abs/2010.10037(2020).
Oudich, M. et al. Bilayer photonic graphene. Preprint athttps://arxiv.org/phys/2103.03686https://arxiv.org/phys/2103.03686(2021).
Wu, Z. L.&Zheng, Y. B. Moiré metamaterials and metasurfaces.Adv. Opt. Mater.6, 1701057 (2018)..
Wu, Z.&Zheng, Y. Moiré chiral metamaterials.Adv. Opt. Mater.5, 1700034 (2017)..
Chen, K. et al. Moiré nanosphere lithography.ACS Nano9, 6031–6040 (2015)..
Jin, C. et al. Preferential alignment of incommensurate block copolymer dot arrays forming Moiré superstructures.ACS Nano11, 3237–3246 (2017)..
Wang, Y. et al. Observation of magic angle and wall state in twisted bilayer photonic graphene. Preprint athttps://arxiv.org/cond-mat/1911.09174https://arxiv.org/cond-mat/1911.09174(2019).
Segev, M., Silberberg, Y.&Christodoulides, D. N. Anderson localization of light.Nat. Photonics7, 197–204 (2013)..
Li, J. et al. Systematic design of flat bandslow light in photonic crystal waveguides.Opt. Express16, 6227–6232 (2008)..
Tang, L. Q. et al. Photonic flat-band lattices and unconventional light localization.Nanophotonics9, 1161–1176 (2020)..
Leykam, D.&Flach, S. Perspective: photonic flatbands.APL Photonics3, 070901 (2018)..
Baba, T. Slow light in photonic crystals.Nat. Photonics2, 465–473 (2008)..
Shallcross, S. et al. Electronic structure of turbostratic graphene.Phys. Rev. B81, 165105 (2010)..
Koshino, M. et al. Maximally localized wannier orbitals and theextended hubbard model for twisted bilayer graphene.Phys. Rev. X8, 031087 (2018)..
Tarnopolsky, G., Kruchkov, A. J.&Vishwanath, A. Origin of magic angles in twisted bilayer graphene.Phys. Rev. Lett.122, 106405 (2019)..
Larson, D. T. et al. Effects of lithium intercalation in twisted bilayer graphene.Phys. Rev. B101, 075407 (2020)..
Fang, S. A.&Kaxiras, E. Electronic structure theory of weakly interacting bilayers.Phys. Rev. B93, 235153 (2016)..
Guinea, F.&Walet, N. R. Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters.Phys. Rev. B99, 205134 (2019)..
Carr, S. et al. Exact continuum model for low-energy electronic states of twisted bilayer graphene.Phys. Rev. Res.1, 013001 (2019)..
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