Photonic band gaps and defects in two dimensions: Studies of the transmission coefficient

Using the transfer-matrix technique for the propagation of electromagnetic waves in dielectric structures, we calculate the transmission coefficient versus the frequency of the incident wave for different polarizations in two-dimensional periodic and/or random arrangements of dielectric cylinders. This technique has been applied to cases where the plane-wave method fails or becomes too time consuming, such as when the dielectric constant is frequency dependent or has a nonzero imaginary part, and when defects are present in an otherwise periodic system. For all the cases studied, the results compared well with experiment.