Photonic crystal slabs are two dimensional periodic dielectric structures that exhibit band gaps for in-plane propagation while confine light in the third dimension. Inside the light cone, the modes guided in the photonic crystal slabs will interact with the modes of free space and become guided resonance modes. In this talk I will introduce some interesting functionalities of such guided resonance modes. I will show that, by carefully engineering the dispersion of the guided resonance modes, we are able to generate space-time light bullet, perform image differentiation, and realize topological protected polarization manipulating. Meanwhile, as quasi-eigenstates, the resonance modes can also exhibitmeronspin texture and merging BIC at an arbitrary position in the reciprocal space.
Refs.  C.Guo, M. Xiao, M.Minkov, Y. Shi & S. Fan,Optica5 251 (2018);  C.Guo, M. Xiao, et. al., Light 10 160 (2021);  Y.Guo, M. Xiao & S. Fan, PRL 119, 167401 (2017);  C.Guo, M. Xiao, Y.Guo, L. Yuan & S. Fan, PRL 124, 106103 (2020);  M. Kang, S. Zhang, M. Xiao, H. Xu, PRL 126, 117402 (2021).