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Topological manipulation of waves is at the heart of the cutting-edge metamaterial researches. Quadrupole topological insulators were recently discovered in twodimensional (2D) flux-threading lattices which exhibit higher-order topological wave trapping at both the edges and corners. Photonic crystals (PhCs), lying at the boundary between continuous media and discrete lattices, however, are incompatible with the present quadrupole topological theory. Here, we unveil quadrupole topological PhCs triggered by a twisting degree-of-freedom. Using a topologically trivial PhC as the motherboard, we show that twisting induces quadrupole topological PhCs without fluxthreading. The twisting-induced crystalline symmetry enriches the Wannier polarizations and lead to the anomalous quadrupole topology. Versatile edge and corner phenomena are observed by controlling the twisting angles in a lateral heterostructure of 2D PhCs. Our study paves the way toward topological twist-photonics as well as the quadrupole topology in the quasi-continuum regime for phonons and polaritons.

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Nodal chain (NC) semi-metals have the degeneracy of interlacing rings in their band structure in momentum space. With the projection of degenerate rings towards crystal boundaries, there is a special type of surface dispersion appearing at surface Brillouin zone and termed drumhead surface state (DSS). Previously, experimental investigations on photonic NC and DSS have been done on metallic photonic crystals at microwave frequencies. However, far-field detection of DSS and its coupling to radiative modes in free space have not been studied. In the work, we analyze the photonic DSS in a metallic lattice by angle-resolved far-field reflection measurement and numerical simulation at terahertz (THz) frequencies, and reveal its flatness and boundness in band structure, even in the radiation continuum. Particularly, the DSS band can be tuned being from negatively dispersive via flat to positively dispersive by a single surface parameter, and the DSS at Γ point in surface Brillouin zone is in fact a symmetry-protected bound state in the continuum. Our results might have some potential applications towards THz photonics.

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The recent advancements in higher-order topology have provided unprecedented opportunities in optical device designs and applications. Here, we propose a new, to the best of our knowledge, method to realize rainbow trapping based on higher-order topological corner modes (HOTCMs), which are constructed by two configurations of breathing kagome photonic crystals with distinct topological phases. Interestingly, the HOTCMs localized at corners with different geometric configurations are found to be frequency dispersive and thus initiate the possible application in realizing rainbow trapping. By designing a polygon structure containing several configurations of corners, we demonstrate that the HOTCMs can be excited with the frequency sequence locked to the corner order (clockwise/anticlockwise direction) in the polygon. The reported HOTCMs provide a new mechanism to realize multiple-frequency trapping, which may find potential applications in future integrated photonics.

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