• Photonics Research
  • Vol. 10, Issue 12, 2901 (2022)
Ze-Sheng Xu1, Jun Gao1,2,*, Govind Krishna1, Stephan Steinhauer1..., Val Zwiller1 and Ali W. Elshaari1,3,*|Show fewer author(s)
Author Affiliations
  • 1Department of Applied Physics, Royal Institute of Technology, Albanova University Centre, 106 91 Stockholm, Sweden
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    DOI: 10.1364/PRJ.474165 Cite this Article Set citation alerts
    Ze-Sheng Xu, Jun Gao, Govind Krishna, Stephan Steinhauer, Val Zwiller, Ali W. Elshaari, "Direct measurement of topological invariants in photonic superlattices," Photonics Res. 10, 2901 (2022) Copy Citation Text show less

    Abstract

    Since the discovery of topological insulators, topological phases have generated considerable attention across the physics community. The superlattices in particular offer a rich system with several degrees of freedom to explore a variety of topological characteristics and control the localization of states. Albeit their importance, characterizing topological invariants in superlattices consisting of a multi-band structure is challenging beyond the basic case of two-bands as in the Su–Schreifer–Heeger model. Here, we experimentally demonstrate the direct measurement of the topological character of chiral superlattices with broken inversion symmetry. Using a CMOS-compatible nanophotonic chip, we probe the state evolving in the system along the propagation direction using novel nanoscattering structures. We employ a two-waveguide bulk excitation scheme to the superlattice, enabling the identification of topological zero-energy modes through measuring the beam displacement. Our measurements reveal quantized beam displacement corresponding to 0.088 and -0.245, in the cases of trivial and nontrivial photonic superlattices, respectively, showing good agreement with the theoretical values of 0 and -0.25. Our results provide direct identification of the quantized topological numbers in superlattices using a single-shot approach, paving the way for direct measurements of topological invariants in complex photonic structures using tailored excitations with Wannier functions.
    H^=nl=13(tla^n,la^n,l+1+τa^n,Ma^n+1,1+H.c.).

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    Nn=i=1nγi.

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    D(z)=(1/z)0zdξn=nan(ξ)|an(ξ).

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    D={0,forτ<τ00.25,forτ>τ0.

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    C(x)=C0eax,(A1)

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    Ze-Sheng Xu, Jun Gao, Govind Krishna, Stephan Steinhauer, Val Zwiller, Ali W. Elshaari, "Direct measurement of topological invariants in photonic superlattices," Photonics Res. 10, 2901 (2022)
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