Photonic crystals, metamaterials, and quantum metamaterials

In an optical medium possessing a spatial distribution of refractive index with periodicity on the order of wavelength, there exists a photonic band gap similar to the band gap in semiconductors. We call these optical medium the photonic crystals. By varying the incident light intensity or by use of external electric field, the band gap of photonic crystal can be controlled, which enables a realization of various photonic switching. Artificial optical media possessing the spatial distribution of refractive index smaller than wavelength are called metamaterials. When the spatial distribution is on the order of micrometer, THz metamaterials can be obtained, while the optical metamaterials can be realized in the nano-structured artificial optical medium. In these metamaterials, the optical property not existing in nature can be observed and a variety of new symmetric structures can be designed. By manipulating the boundaries of graphenes, the propagation of De Broglies wave can be tailored, which is called quantum metamaterial. In quatum metamaterials, phenomena can observed those appearing in optical metamaterials such as negative refraction and collimation.