Spin Hall Effect of Light via Momentum-Space Topological Vortices around Bound States in the Continuum

Optical bound states in the continuum (BICs) are exotic topological defects in photonic crystal slabs, carrying polarization topological vortices in momentum space. The topological vortex configurations not only topologically protect the infinite radiation lifetime of BICs, but also intrinsically contain many unexploited degrees of freedom for light manipulation originating from BICs. Here, we theoretically propose and experimentally demonstrate the spin Hall effect of light in photonic crystal slabs via momentum-space topological vortices around BICs. The strong spin-orbit interactions of light are induced by using the topological vortices around BICs, introducing both wave-vector-dependent Pancharatnam-Berry phase gradients and cross-polarized resonant phase gradients to the spinning light beam, which lead to spin-dependent in-plane-oblique lateral light beam shifts. Our work reveals intriguing spin-related topological effects around BICs, opening an avenue toward applications of BICs in integrated spin-optical devices and information processing.

Figure 1

Lower panel: topological vortex around the BIC in momentum space. Middle panel: cross-polarized phase distribution in momentum space under circularly polarized incidence. Green line shows the cross-polarized resonant phase along the $k_x$ direction; cyan line shows the PB phase along the $k_y$ direction. Upper panel: schematic view of the spin Hall effect of light.

Figure 2

(a) Upper panel: diagram of the PhC slab. Lower panel: calculated band structure along the $\mathrm{\Gamma }\text{−}X$ direction. (b) Momentum-space polarization map of the ${\mathrm{TE}}_5$ band and the induced PB phase (from the RCP to LCP). (c) Momentum-space cross-polarized resonant phase distribution at a single wavelength. (d) PB phase gradients in the $k_y$ direction at different $k_x$ ($k_y=0$), which leads to the $Y$ shift. The PB phase gradient from the RCP to LCP (marked as blue color) is opposite to that from the LCP to RCP (marked as red color). (e) Cross-polarized resonant phase gradients in the $k_x$ direction at different $k_x$ ($k_y=0$) from Fig. 2, which leads to the $X$ shift. (f) Top view of the realized spin Hall effect of light by simulation.

Figure 3

(a) Angle-resolved $s$-polarized reflectance spectra of the ${\mathrm{TE}}_5$ band along the $\mathrm{\Gamma }\text{−}X$ direction. (b) Image of the spin-dependent lateral shifts via the topological vortex in the ${\mathrm{TE}}_5$ band. (c) Angle-resolved $s$-polarized reflectance spectra of the ${\mathrm{TE}}_2$ band along the $\mathrm{\Gamma }\text{−}X$ direction. (d) Image of the spin-dependent lateral shifts via the topological vortex in the ${\mathrm{TE}}_2$ band.

Figure 4

Spin Hall effect of light at different wavelengths. (a) Lateral shifts via the topological vortex in the ${\mathrm{TE}}_5$ band. (b) Lateral shifts via the topological vortex in the ${\mathrm{TE}}_2$ band.