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Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing

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Science Advances  06 Mar 2020:
Vol. 6, no. 10, eaaw4137
DOI: 10.1126/sciadv.aaw4137
  • Fig. 1 Spectroscopy of topological edge states.

    (A) Spin-orbit coupling in topological photonic crystals: Chirality of the radiation field is connected to propagation direction of topological photonic crystal edge states. (B) A scanning electron micrograph of the fabricated sample. The yellow line represents the arm-chair edge between two pseudocolored regions of differing topology. Red and blue hexagons highlight the respective unit cells. (C) Schematic diagram of the experimental setup. In the Fourier-space spectroscopy mode (orange path), the back-focal plane (BFP) is imaged onto the spectrometer slit. A spatial filter (SF) chooses the area from which light is collected. Quarter-wave plates (QWPs) and polarizers define input polarization (PO1) and allow polarimetry of reflected light (PO2). In the real-space imaging mode (green path), the sample plane is imaged onto the camera without SF. See Materials and Methods for details and abbreviations. (D) Measured (top) and calculated (bottom) dispersion of shrunken (left) and expanded (right) lattices for diagonally polarized incidence. The measured reflection intensity is normalized to the maximum pixel value among the images. Linewidths of the calculated modes, scaled up five times, are shown as shaded regions in the bottom panels. (E and F). Measured and calculated dispersion of the edge states. Calculated linewidths are shown as a shaded region in (F).

  • Fig. 2 Polarimetry results.

    (A and B) Total reflected intensity of the polarized field (IP) as a function of frequency and wave vector ky when the edge is excited with right (A) and left (B) CP light. Images are normalized with respect to corresponding maximum pixel values. (C) Measured circular polarization intensity (normalized Stokes parameter S3) when the edge is excited with light that is linearly polarized along y. A center block is placed at the real-space plane to spatially filter background reflections (see Materials and Methods). (D) Normalized S3 for the edge states as predicted by the tight-binding model.

  • Fig. 3 Quantifying spin-spin scattering in the system.

    (A) Measured reflectance (left panel) showing dispersion of edge states as a function of wave vector ky and measured intensity (right panel) along the cross-cut indicated by the white line in the left panel (orange data). The black line shows a fit with a set of complex Lorentzians (see Materials and Methods). Red lines and shaded areas correspond to the extracted resonance frequencies and linewidths. (B) Splitting (red shaded region) of armchair (top) and zigzag (bottom) edge states obtained from finite element simulations.

  • Fig. 4 Real-space images of edge state propagation.

    (A) A schematic diagram showing the edge between expanded (E) and shrunken (S) lattices where a focused single wavelength laser excites the sample. (B to D) Real-space camera images when the incident light is left circularly, linearly, and right CP, respectively. Images are normalized to the maximum pixel value among the three. Scale bar, 10 μm. (E) Transverse dependence of excitation, showing that selectivity is independent of excitation position. The plotted value ΔI shows the difference between integrated intensities in two areas U and D as defined in each panel of (F), when a right (red) and a left CP (blue) excitation spot is moved across an armchair edge. The excitation position at 0 μm corresponds to an approximate center of the waveguide. (F) Images recorded for the excitation position 0 μm. The dashed rectangles correspond to the areas under which the intensity is integrated in (E).

  • Fig. 5 Routing of light around a topologically protected chiral junction.

    (A) A schematic diagram showing a junction formed by four topological edges. Inset shows a zoomed-in image of the chiral junction. Real-space images (B to D) show light propagation when the sample is excited by a left CP monochromatic laser at positions 1, 2, and 3 marked in (A). All three images (B to D) are normalized to the maximum pixel value among the three. Scale bar, 10 μm.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/10/eaaw4137/DC1

    Fig. S1. Fabry-Pérot background reflection.

    Fig. S2. Dispersion of bulk modes for orthogonally polarized incidences.

    Fig. S3. Comparison of band structure calculations for bulk lattices: FEM versus tight-binding model.

    Fig. S4. Polarization tomography of the edge states.

    Fig. S5. A cartoon depicting modification of the spatial filter placed in a real-space image plane in the detection path to isolate contribution from the edge modes for S3 measurement.

    Fig. S6. Design parameters for shrunken and expanded lattices.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Fabry-Pérot background reflection.
    • Fig. S2. Dispersion of bulk modes for orthogonally polarized incidences.
    • Fig. S3. Comparison of band structure calculations for bulk lattices: FEM versus tight-binding model.
    • Fig. S4. Polarization tomography of the edge states.
    • Fig. S5. A cartoon depicting modification of the spatial filter placed in a real-space image plane in the detection path to isolate contribution from the edge modes for S3 measurement.
    • Fig. S6. Design parameters for shrunken and expanded lattices.

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