The research on classical wave systems has spawned many fantastic phenomena, such as topological photonics, but they limited to Hermitian systems in the past. Therefore, as the first part, we investigate the multi-state non-Hermitian system in both acoustics and photonic crystals. We found that multiple exceptional points (EPs) can emerge and as the system parameters vary, these EPs can collide and merge, leading to higher order singularities and topological characteristics much richer in physics than those seen in two-state systems. We demonstrate that chirality of EPs plays the central role during the coalescence of order-2 EPs. For photonic crystals, we study the complex band structures of photonic crystals by setting up a model Hamiltonian, and two types of phase diagram are found. Furthermore, by using angle-resolved thermal emission spectroscopy, we experimentally observe these EPs and associated topological features of such systems.
Another widely used technique in classical waves is macroscopic quantities, such as permittivity and permeability, which derived from linear response theory. This indicates that it ignores quantum nature of both particles and fields. We thus set up two different algorithms to investigate their roles in the nanostructures. By treating electrons and photons in the same footing, we first demonstrate that the microscopic optical force density of nanoplasmonic systems can be defined and calculated using the microscopic fields, which is a challenging task not only because macroscopic parameters become ill-defined, but also due to the debate of stress tensors inside media. Secondly, we investigate the plasmonic mode contribution to vacuum fluctuation induced phenomena in nanostructures. Due to the bosonic nature, the asymmetric splitting of plasmonic modes decrease the zero-point energy and Casimir energy of plasmonic nanostructures under corrugations.
