Abstract

The realization of topological band degeneracies in the photonic system is reported in this thesis. The topological band degeneracies have recently attracted considerable attention because they usually carry topological charges in the momentum space, which induces several interesting phenomena, such as helicoid surface state, chiral anomaly, and Imbert– Fedorov shift. Therefore, the realization of these band degeneracies in a photonic system, especially through a sufficiently simple structure to facilitate attainable experiments, is an important topic.

Weyl point, as a zero-dimensional point degeneracy in the momentum space, is the most common topological nodal point. A simple chiral woodpile photonic crystal is designed, and Weyl points with topological charges 1 and 2 are found. The topological charge distribution can be changed by modifying the material parameter, while the symmetry of the system is maintained. A tight-binding model is established to understand the physics and show these Weyl points in the real structure with full-wave simulation. The gapless surface states are shown in a ribbon of the woodpile photonic crystal. The unidirectional transport, which is immune to backscattering, is also demonstrated. Realizing the Weyl points in the simple fabricated woodpile structure provides a platform for exploring the Weyl physics toward infrared and optical frequency.

Meanwhile, the topological band degeneracies can also exhibit as a two-dimensional plane on the surface of the Brillouin zone, forming a topological charge nodal surface. A metacrystal with a topologically nontrivial nodal surface operating at microwave frequency is designed, fabricated, and characterized. Compared with the nodal surface in acoustic wave designed by the tight-binding model, the nodal surface in the proposed system is protected by a combination of two-fold screw rotation and time-reversal symmetry. The surface-state arcs connecting the nodal surface and charge-2 Weyl point in the system are experimentally observed to demonstrate the existence of the nodal surface and its topological properties. These surface-state arcs are derived from the helicoid sheet surface states. The band structure of the surface state is also measured. This system can facilitate the realization of the new class of topological degeneracy in electromagnetic waves.

We also show that a metacrystal with connected-spirals structure can exhibit highorder Weyl point as a gapless system that carries topological quadruple. We demonstrate the existence of topological quadruple index is protected by combining two-fold rotation symmetry and time-reversal symmetry. In this system, both gapless surface states induced by topologcal charge and gapped surface states induced by topological quadruple can coexist. The hinge state as the distinct feature of the topological high-order mode can be found on the hinge of a finite sample. We believe this work can offer a proposal to realize high-order Weyl point experimentally in an EM wave system.

The current work on Weyl point, topological nodal surface and high order Weyl point in photonic systems can help realize these topological degeneracies with a simple design and experimentally explore their novel physics properties.

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