Structural chirality is a special property of certain materials which affects the way in which electromagnetic waves propagating in them. This thesis is devoted to the study of two structurally chiral electromagnetic systems.

The first system is the cholesteric liquid crystal which can be regarded as a one-dimensional chiral photonic crystal. By using the 4 x 4 transfer matrix method, the polarization-selected gaps in the band structure and the corresponding transmission and reflection property of the system are revealed and various defect/interface states are identified. To understand these results and make connection with modern topological band theory, a general parallel transport procedure is adopted and applied to a closely related non-symmorphic layered system with glide...[ Read more ]

Structural chirality is a special property of certain materials which affects the way in which electromagnetic waves propagating in them. This thesis is devoted to the study of two structurally chiral electromagnetic systems.

The first system is the cholesteric liquid crystal which can be regarded as a one-dimensional chiral photonic crystal. By using the 4 x 4 transfer matrix method, the polarization-selected gaps in the band structure and the corresponding transmission and reflection property of the system are revealed and various defect/interface states are identified. To understand these results and make connection with modern topological band theory, a general parallel transport procedure is adopted and applied to a closely related non-symmorphic layered system with glide symmetry. The calculated non-Abelian geometric phases for a group of composite bands corresponding to Wannier charge centers may indicate possible locations within the unit-cell for photonic energy concentration. And the sum of them as a label for the group of bands as a whole gives some hint of the existence of the interface states in full gap regions.

In the second chiral system, metallic nanoparticles are arranged in the twisted bilayer honeycomb lattice which can be viewed as a plasmonic analogue of twisted bilayer graphene. To study the dispersion of the system, the coupled-dipole theory is adopted for the lattice-with-a-basis system where a unified and efficient framework based on Ewald’s method is developed for the calculation of lattice sums of dyadic Green’s function. The plasmonic band structures in the quasi-static regime show folded structures in a compressed energy range which are analyzed by mode coupling and Moiré pattern evolution. It is expected that flat band can also be achieved in the plasmonic analogue of twisted bilayer graphene exhibiting Moiré pattern like their electronic counterpart.