Broadband Topological Slow Light through Brillouin Zone Winding

Sander A. Mann and Andrea Alù

Phys. Rev. Lett. 127, 123601 – Published 13 September 2021

Abstract

Topological photonic insulators have attracted significant attention for their robust transport of light, impervious to scattering and disorder. This feature is ideally suited for slow light applications, which are typically limited by disorder-induced attenuation. However, no practical approach to broadband topologically protected slow light has been demonstrated yet. In this work, we achieve slow light in topologically unidirectional waveguides based on periodically loading an edge termination with suitably tailored resonances. The resulting edge state dispersion can wind around the Brillouin zone multiple times sustaining broadband, topologically robust slow light, opening exciting opportunities in various photonic scenarios.

Received 20 January 2021
Accepted 5 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.123601

Physics Subject Headings (PhySH)

Metamaterials Photonic crystals

Topological materials

Atomic, Molecular & OpticalGeneral Physics

Authors & Affiliations

Sander A. Mann¹ and Andrea Alù ^1,2,3,*

¹Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, USA
²Department of Electrical Engineering, City College of The City University of New York, New York, New York 10031, USA
³Physics Program, Graduate Center, City University of New York, New York, New York 10016, USA

^*aalu@gc.cuny.edu

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Vol. 127, Iss. 12 — 17 September 2021

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Images

Figure 1
(a) Dispersion of a bare reciprocal waveguide (gray dashed lines), and a reciprocal waveguide side-coupled to a periodic array of resonances (blue, see inset for schematic). Near the center frequency a band gap opens, and on both sides of the gap narrowband and dispersive regions supporting slow light arise. (b) If the bare waveguide instead is nonreciprocal and unidirectional, so that only a forward mode is supported (gray dashed line), no band gap opens when the waveguide is coupled to the same periodic cavity array (see inset). A region of slow light arises at the resonance center frequency. Dispersion calculated with Eqs. (1),(2).
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Figure 2
(a) Schematic of a unidirectional waveguide (due to, e.g., a static magnetic induction bias $B$ ) side coupled to a periodic array of resonant cavities. (b) Dispersion of the bare waveguide (gray dashed line), and loaded with one (gray) and two (black) cavities per unit period. The waveguide is designed to support slow light in the gray shaded region. (c) Same as in (b), but now with three (orange) and four (blue) loading cavities. For each additional resonance, the dispersion wraps around the Brillouin zone once more. (d) Impact on the group velocity of adding resonances. The curves are normalized by a factor $λ_{0} / Λ$ : a small period decreases the net group velocity. All results in this figure are calculated using the coupled-mode theory framework.
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Figure 3
(a) Dispersion of the YIG photonic crystal, with Chern numbers shown on the left. The red lines are topologically protected nonreciprocal edge states. (b) Schematic of the edge terminations considered here: configurations containing up to three rectangular cavities, with supercell denoted by dashed lines. (c) Dispersion of the edge state with one (gray), two (black), and three (orange) cavities, showing increasing band folding. (d) Group velocity of the edge state across the nontrivial band gap with one (gray), two (black), or three (orange) cavities. The gray dashed line shows the group velocity of the bare edge state. All results in this figure are calculated using COMSOL Multiphysics.
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Figure 4
(a) Propagation of a Gaussian pulse through a nonreciprocal unidirectional waveguide side coupled to three cavities per unit cell. In the ideal case, there is no difference between the reciprocal and nonreciprocal systems. (b) Propagation of the same pulse through the unidirectional system with a 1% relative standard deviation in each parameter. (c) The same as (b), but now in a reciprocal system. The clockwise and anticlockwise modes are assumed to be coupled by $1 / 25$ th of the largest intercavity coupling rate [43]. (d) The output pulses for the three scenarios shown. While there is some distortion in the unidirectional system with disorder, as expected, it vastly outperforms the reciprocal system. All results in this figure are calculated based on the coupled-mode theory framework.
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