Frequency comparison of light transmission in a defected quasi-one-dimensional photonic crystal slab

In a new theoretical investigation, we study light transmission through a photonic crystal (PC) slab with limited boundaries at width. By using a tight binding model, photon dispersion relation and photon Green function for a perfect system are obtained. Then, based on the Lippmann-Schwinger formalism, we calculate the effects of disordering on light transmission in the PC channel. We found that the ratio of the electric field for a defected system with respect to a perfect system at a peculiar frequency is maximized for the wave vector corresponding to the first Brillouin zone (BZ) edge showing photon localization. The electric field difference of the first and second neighboring sites with respect to the defect site on the first BZ edges are depicted in several plots indicating frequency dependence which can be applicable in frequency filtering or resonating cavity studies.