Anomalous Dispersion And Guide Modes In The Photonic Crystals

The properties of light propagating in photonic crystals are investigated in this thesis. The contents include the following sections: (1) The guide modes in photonic crystal heterostructures; (2) The ultra-narrow optical filters consisting of photonic crystals composed of anomalous dispersion material; (3) Ultra-narrow optical mirrors consisting of photonic crystals composed of anomalous dispersion material.The heterostructures are assembled of two semi-infinite two-dimensional dielectric (or magnetic) photonic crystals they are different in the shapes of the rods and the lattice. The guide modes in heterostructures are investigated by using the plane wave expansion method combined with the supercell technique. We found that the dielectric photonic crystals heterostructures can produce local modes in absolute photonic band gap without any relative longitudinal gliding or transverse displacement. This feature is only found in the magnetic photonic crystal heterostructures in the past.A new theory about the ultra-narrow optical filters (mirrors) is proposed in this thesis. The ultra-narrow optical filters (mirrors) are composed of photonic crystals in which the scatterers are filled with the vapor anomalous dispersion atoms, which are abbreviated to PCADOF (PCADOM). Here the cesium vapor is chosen as theanomalous dispersion materials and its hyperfine structure transition of 6P3/2 ← 6S1/2(λ = 852.1nm) is calculated. And then the one-dimensional (1D) and two-dimensional (2D) PCADOF are investigated by using transfer-matrix method. The transmission spectra of PCADOF near λ = 852.1nm are calculated. The results show that the bandwidth of PCADOF may reach a very narrow frequency range, which is about 0.05-0.33GHz. The field-of-view and the response of transmission spectrum to the external magnetic field are also investigated. The feasibility of PCADOF consisting of other anomalous dispersion materials is discussed. The theory provided a new way to fabricate ultra-narrow optical filters.The optical properties of 1D and 2D PCADOM are investigated by using transfer-matrix method. For instance, we choose cesium atom vapor as the anomalousdispersion materials (λ = 852. 1nm is the transition wave-length of 6P3/2 ← 6S1/2hyperfine structure). The reflectivity spectrum of the PCADOM near X = 852.1nm is calculated. The reflectivity of the designed optical mirrors is very high in an ultra-narrow frequency range of a few GHz. This work may provide a new way to fabricate ultra-narrow optical mirrors.