Abstract
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.
Highlights
Nodal chain (NC) semi-metals have the degeneracy of interlacing rings in their band structure in momentum space
Being parallel to electronic systems and de Broglie wave in solids, photonic crystals (PhCs) and metamaterials provide an arena of extending the band theory to electromagnetic (EM) wave, including band gap and nodal degeneracy[4,5,6,7,8,9,10,11,12,13]
Such degeneracy is challenging to be observed in electronic systems, but can be readily engineered and measured in an ordinary photonic structure, which is a three-dimensional (3D) metal-wire mesh with simple cubic lattice and exhibits the nodal chain (NC) degeneracy in the band structure at microwave frequencies[21]
Summary
Our design is a 3D metallic PhC with sub-millimeter feature size, which is fabricated through 3D printing of polymer framework and subsequent chemical plating metallization. The dispersion of the photonic DSS can be tuned significantly by a simple surface characteristic, as depicted in Fig. 3d1, that is the extruding length, h, of the sectioned metallic rod on the surface Another feature of the DSS in simulated and measured results is its vanishing behavior as approaching to Γ point.
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