Anomalous behavior of group velocity and index of refraction in a defect photonic band gap structure

In the present paper, we have made an analysis to observe the effect of introduction of defect on dispersion relation, group velocity, and effective group index in a conventional photonic band gap (PBG) structure. The study shows that inside the PBG materials group velocity and effective group index becomes negative in both types (conventional as well as defect PBG structure) of structure at a certain range of frequencies. Also, near the edges of the bands it attains very high values of index of refraction. A defect PBG structure gives a very unique feature that group velocity becomes exactly zero at a particular value of frequency and also becomes several hundred times greater than the velocity of light which is not attainable with the conventional PBG structure. Defect PBG structures with such peculiar characteristics are seen in lasing without inversion, in construction of perfect lens, in trapping of photon and other optical devices.