• 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、*
Author Affiliations
  • 1Department of Applied Physics, Royal Institute of Technology, Albanova University Centre, 106 91 Stockholm, Sweden
  • 2e-mail:
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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[J]. Photonics Research, 2022, 10(12): 2901 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[J]. Photonics Research, 2022, 10(12): 2901
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