Photonic topological insulators

Journal name:
Nature Materials
Volume:
12,
Pages:
233–239
Year published:
DOI:
doi:10.1038/nmat3520
Received
Accepted
Published online

Abstract

Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal-invariant topological insulators. A remarkable and useful property of these materials is that they support unidirectional spin-polarized propagation at their surfaces. Unfortunately topological insulators are rare among solid-state materials. Using suitably designed electromagnetic media (metamaterials) we theoretically demonstrate a photonic analogue of a topological insulator. We show that metacrystals—superlattices of metamaterials with judiciously designed properties—provide a platform for designing topologically non-trivial photonic states, similar to those that have been identified for condensed-matter topological insulators. The interfaces of the metacrystals support helical edge states that exhibit spin-polarized one-way propagation of photons, robust against disorder. Our results demonstrate the possibility of attaining one-way photon transport without application of external magnetic fields or breaking of time-reversal symmetry. Such spin-polarized one-way transport enables exotic spin-cloaked photon sources that do not obscure each other.

At a glance

Figures

  1. Wave propagation in a 2D PTI.
    Figure 1: Wave propagation in a 2D PTI.

    a, Photonic analogue of Kramers partners in a spin-degenerate metamaterial. b, Band structure of a metacrystal comprising a hexagonal lattice of spin-degenerate metamaterials with (dashed lines, χ  =  0.5) and without (solid lines, χ  =  0) optical activity (right inset). The metacrystal becomes a PTI through the opening of the second (topological) bandgap near the K and K′ points of the Brillouin zone for finite optical activity. The left inset shows the Brillouin zone with the K and K′ valleys indicated by blue and red triangles, respectively. c, Eigen-frequency surfaces illustrating degeneracy removal at the K (K′) point for χ≠0. d, The hexagonal lattice of the metacrystals and two possible microscopic structures of its metamaterial constituent rods with desirable bi-anisotropic response. PTI parameters: circular rods of radius r0  =  0.34a0 arranged in a hexagonal lattice with period a0; each rod filled with spin-degenerate metamaterial with , εzz  =  μzz  =  1, and .

  2. One-way spin-polarized transport of photonic edge states.
    Figure 2: One-way spin-polarized transport of photonic edge states.

    a, Dispersion of the spin-up (green) and spin-down (red) helical edge states supported by a bi-anisotropic domain wall. Opaque and transparent bands correspond to two interfaces, with χxy < 0 to χxy > 0 and with χxy > 0 to χxy < 0 transitions, respectively. The blue lines illustrate the super-cell’s bulk photonic states corresponding to different wavenumbers in the direction perpendicular to the interface. b, The absolute value of |ψe±| for right/left-propagating edge states of a bi-anisotropic (χxy < 0 to χxy > 0) domain wall. The enlarged regions show the difference in the temporal evolution between the spin-up ψe+ and spin-down ψemodes. Although the field profiles Re(ψ+) and Re(ψ) are identical, the modes propagate in opposite directions and the power flux (black arrows) inside the rods rotates in opposite directions. Field dynamics can be found in the animations of the ψ± wavefunctions given in the Supplementary Information.

  3. Excitation of surface waves by a point dipole source at the interface between topologically trivial and non-trivial photonic insulators.
    Figure 3: Excitation of surface waves by a point dipole source at the interface between topologically trivial and non-trivial photonic insulators.

    a, Selective excitation of spin-up and spin-down photonic one-way edge states along a straight interface. Bottom metacrystal parameters: the same as in Fig. 1. Top metacrystal: the same as bottom, but all sizes are scaled by the factor η  =  0.76 to ensure the coincidence of photonic bandgaps in both metacrystals. bd, Robustness of the edge modes against different types of defect: sharp bending of the interface (b), a cavity obstacle (c) and a strongly disordered domain in both of the adjacent crystals (d). Colour scale in ad: local field intensity .

  4. Non-obstructing large photon antennas due to spin-cloaking.
    Figure 4: Non-obstructing large photon antennas due to spin-cloaking.

    Spin-cloaked electric-dipole antenna (indicated by the rectangular region) embedded into the cavity between topologically trivial and non-trivial metacrystals. a,b, The spin-polarized one-way transport of the spin-up and spin-down edge modes avoiding a silent dipole antenna placed in the cavity. c,d, Selective directional excitation of these modes by the electric-dipole antenna.

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Author information

  1. These authors contributed equally to this work

    • Alexander B. Khanikaev &
    • S. Hossein Mousavi

Affiliations

  1. Department of Physics, The University of Texas at Austin, One University Station, C1500, Austin, Texas 78712, USA

    • Alexander B. Khanikaev,
    • S. Hossein Mousavi,
    • Wang-Kong Tse,
    • Mehdi Kargarian,
    • Allan H. MacDonald &
    • Gennady Shvets

Contributions

All authors contributed extensively to the work presented in this paper.

Competing financial interests

The authors declare no competing financial interests.

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