Nanostructured materials and topological materials have many unique and fascinating electronic and optical properties. In this dissertation, we explore the optics in those new materials from three aspects: 1. Optical properties of Weyl semimetals, a novel topological material recently observed in experiments, in a strong magnetic field. Our results show that the magneto-polaritons in Weyl semimetals have peculiar properties, such as hyperbolic dispersion, photonic stop bands, coupling-induced transparency, and broadband polarization conversion. 2. Superfluorescence in quasi one-dimensional structures, carbon nanotubes. We show that due to the enhanced density of states and confinement of electrons in nanotubes, superfluorescence could be achieved with high enough pumping. This result indicates potential application of carbon nanotubes as effective radiative emitter. 3. Purcell enhancement in subwavelength quasi two-dimensional materials. We use Heisenberg-Langevin approach which includes dissipation and fluctuation in both the fermionic ensemble and the electromagnetic field. We develop a general formalism and derive analytical expression for spontaneous emission and parametric down-conversion in such systems.
