Fig. 1. PhC with the honeycomb lattice on an SOI substrate. (a) 3D schematic of the Si-based PhC with a lattice constant of 408 nm on the 2  μm thick SiO2 layer. (b) Cross-sectional view of the PhC with the integration of heat electrodes. (c) Calculated band diagram for the unstrained PhC. The inset shows the FBZ of the PhC. (d) Top and side views of the electric field distributions in the unit cell of the lattice corresponded to the Dirac point.

Fig. 2. Calculated band structures for the uniaxially strained PhC ribbons. (a) Sketch of the uniaxially strained PhC with a linear parabolic deformation along the y axis. The inset shows the honeycomb lattices composed of the photonic atoms. (b) Band diagrams for the uniaxially strained PhC ribbons with u0 setting to be 0, 0.02, 0.04, 0.06, 0.1, and 0.2, respectively.

Fig. 3. Optical transports in the uniaxially strained PhC. (a) Left: Electrical measurement setup for the 2D materials. Right: Optical measurement setup for the Si-based PhC with the integration of Si waveguides and gratings. (b) SEM images of the pristine photonic lattices and the uniaxially strained photonic lattices with u0=0.04. (c) From left to right: SEM images, simulated band diagrams, calculated photonic DOS, and measured transmission spectra for the pristine and the uniaxially strained PhCs, respectively.

Fig. 4. Inspiration of helical snake states. (a) Electric field distributions of the bulk mode and the snake state mode in the uniaxially strained PhC. (b) Left: Illustration of the counterpropagating lightwaves (SK and SK′) with the snake orbits along the undeformed lattices of the uniaxially strained PhC based on the excitations of circularly polarized light sources. Right: FDTD simulations of the unidirectional coupling by introducing the LCP dipole source at λ=1550  nm and 1620 nm, respectively. (c) SEM images of the sample coupled with a microdisk at its left end. The input Si waveguide is directionally coupled to such microdisk, and the air gap is nearly 100 nm. (d) Simulated and measured transmission spectra for the sample under the excitation of circularly polarized light.

Fig. 5. Electrical manipulation of lightwaves in the uniaxially strained PhC. (a) Optoelectronic measurement setup for the sample. (b) Microscope images of the sample with the integration of heat electrodes. (c) Calculated photonic DOS and measured transmission spectra for the uniaxially strained PhC with different heating powers of 0, 8, 32, 72, and 128 mW, respectively. (d) Frequency shifts of the photonic DOS peak and the measured transmission dip at around 194.3 THz as a function of the applied electrical power.