Plane-Wave Expansion Method for Calculating Slow light Effefct of Photonic Crystals Waveguide

In the thesis, a plane-wave expansion method for alculating the band structure of the photonic crystal is presented. As we known, photonic crystal structures provide a promising tool to control of the flow electromagnetic(EM) waves in the integrated optical devices. Therefore, there is a growing interest in developing photonic crystal-based waveguide components which can guide EM waves either along a line defect (a row of missing rods) or through coupled cavities. In the latter case, which we called coupled-cavity waveguides (CCW), the EM waves were tightly confined at each defect site, and photons can propagate by hopping, due to interactions between the neighboring evanescent cavity modes. It is observed that photon lifetime increases drastically and group velocity of photons tends towards zero at the waveguiding band edges of the periodic coupled cavities. In the photonic crystal CCW, low group velocity of light can result from localized modes in the defect. An analogy between Schrodinger's equation and Maxwell's equations allows us to use tight-binding (TB) approximation which was originally developed for electronic systems.