Characterization of defect modes in one-dimensional photonic crystals: An analytic approach

We introduce an analytical model to investigate the localized defect modes associated with a defect cell inserted in a one-dimensional photonic crystal for both transverse electric (TE) and transverse magnetic (TM) polarizations, at an arbitrary angle of incidence. The defect cell, which is made of two dielectric constituents, leads to the appearance of several localized defect modes within the photonic band gaps. We develop an analytical approach based on the both transfer matrix and Green's function methods to determine the number and frequency of the defect modes that can be controlled easily by varying the parameter values of the constituent layers of the photonic crystal. The method demonstrates that the electric field amplitude depends on the defect cell position in the photonic crystal while the defect mode frequency is independent of it. This method is useful for photonic band gap engineering and designing the photonic-based devices.