Fig. 1. Schematic diagram of the dynamic beam shifting. (a) Beam shifts under small refractive index variations. The position vector r (x, y) describes the beam shift between the input (blue, LCP) and output (red, RCP) beams. Δr (Δx, Δx) is the amount of change in the beam offset during the refractive index change (Δn). θ represents the beam shift direction. (b) Phase-change material switch between the amorphous phase and the crystalline phase to switch the excited optical mode, therefore realizing a significant change in beam direction (Δθ) and beam displacement (Δr). (c) A unit cell of two-layer PhC. a is the lattice constant, d is the air hole diameter, h is the thickness of the phase-change material layer, and t is the thickness of the dielectric material.

Fig. 2. Beam shifts induced by cross-polarized phase and PB phase gradients of four BIC modes. (a), (e) Photonic band structures of four modes. The bands containing BIC modes with a +1 topological charge (modes 1 and 4) are marked with red lines, while those with a −1 topological charge (modes 2 and 3) are marked with black lines. (b), (f) The SOPs around four BICs in the far field. The angle of SOPs is represented by colors on the color map. (c), (g) Beam shifts of mode 1 (λ = 1620 nm), mode 2 (λ = 1408 nm), mode 3 (λ = 1790 nm), and mode 4 (λ = 1718 nm) of the RCP light with an LCP incidence in X and Y directions, which are caused by cross-polarized phase and PB phase gradients, respectively. (d), (h) Simulation shows the intensity distributions of modes 1, 2, 3, and 4 appearing in quadrants II, IV, III, and I, respectively.

Fig. 3. Dynamic beam shifts with slight changes in refractive index. (a) The beam shifts (X: red bar, Y: blue bar) as the refractive index varies on the order of 10⁻² at an incident wavelength of 1725 nm. (b) The trend of the cross-polarized phase gradient distribution. The gradient changes are caused by the radiation loss (γ) and the wave vector (k₀) of resonant modes changing with the system refractive index. (c) With the change of refractive index (0.01 every step), the variations of the angle of shift direction (θ) and the total displacement (|r|) are Δθ and |Δr|, respectively. When the refractive index varies by only 0.06, the change in shift direction Δθ can be up to 53.54°. (d), (e) The intensity distributions of the output RCP beams at the refractive indices of 3.28 (d) and 3.33 (e) showing a clear change in shift direction Δθ. (f) The beam shift as the refractive index varies on the order of 10⁻³, which is the order of magnitude of the change in refractive index when the Pockels effect occurs in lithium niobate.

Fig. 4. Dynamic beam shifts during switching between different states of the phase-change material (Sb₂Se₃). The band structure (a), the far field SOPs [(b) upper], the induced PB phase gradient [(b) lower], and normalized intensity distribution (c) of the device when Sb₂Se₃ is in the amorphous phase (a-Sb₂Se₃). From the reflection spectrum, it can be seen that the incident wave with a wavelength of 1438 nm interacts with the energy bands of mode 1, causing the outgoing wave to move towards the second quadrant (II). The band structure (d), the far-field SOPs [(e) upper], the induced PB phase gradient [(e) lower], and the normalized intensity distribution (f) of the device when Sb₂Se₃ is in the crystalline phase (c-Sb₂Se₃), in which case mode 2 is excited under the same incident conditions, leading to a dynamic beam shift to the third quadrant (III).