Fig. 1. (a) Schematic of the TVHWs with A|Bx|C heterostructure composed of three photonic crystals domains, A, B, and C. The right panel demonstrates the three basic unit cells, which consist of a triangular air-hole honeycomb lattice on a 220 nm SOI platform with the same lattice constant a and different air-hole side lengths. (b) Corresponding band structures of the unit cells in (a). (c) Left panel: projected band diagrams for A|B10|C. The dashed line indicates the topological bandgap of A|C, and the red curve shows the topological waveguide transmission mode of A|B10|C. The 0th and1st bands are gapped modes supported by the waveguide, and the shadow area indicates the single-mode region of the A|B10|C. Right panel: magnetic field (Hz) and phase distribution (ΦHz) of the topological waveguide mode at K-valley. (d) Variation of the intermediate single-mode region (shadow area) with the number of x. The x is the number of layers used to quantify the width of domain B. The black dots and red (blue) lines depict the lower (upper) boundaries of the 0th, 1st, and 2nd bands.

Fig. 2. (a) Left panel: schematic diagram of the TVHW A|Bx|C with x=2, 6, and 10. Right panel: corresponding electric field strength distribution at 1520 nm. (b) Total transmission energies at different wavelengths for the three different structures in (a). (c) Fourier spectrum at 1520 nm, obtained by Fourier transformation of the electric field distribution in the blue dashed box in (a).

Fig. 3. (a) Schematic distribution of the electric field strength at 1520 nm for three heterostructure waveguides with different structural defects, including indentation, bulging, and disorder. (b) Transmission spectra of the three waveguides in (a).

Fig. 4. (a) Schematic illustration of the three different structures and the corresponding electric field distribution at 1520 nm, where Structures 1 and 3 have structural mutation from A|B10|C to A|B0|C. The dashed lines a, b, c, and d are electric field integration lines. (b) Transmission spectra of the three structures in (a), using ports for excitation and collection. (c) Distribution of the normalized electric field strength along the integration lines a and b in (a). (d) Distribution of the normalized electric field strength along the integration lines c and d in (a).

Fig. 5. (a) Optical microscope images of eight heterostructure waveguides with different structures. (b) Normalized transmission spectra of Structures 1–8 in (a). (c) Nonlinear imaging pictures of THG with different structures using 1520 nm picosecond pulsed light pumping.