The defect modes in one-dimensional photonic crystal with multiple defects

A one-dimensional photonic crystal containing multilayered half-wave defects is designed and the transmission spectrum is studied by using transfer matrix theory. Under the first-order approximation of Taylor expansion, the analytic expression for the defect mode frequency is derived, from which the coupling factor is deduced. Our results are fitted with the experimental results or numerical simulation, and can be used to describe the characteristics of the defect modes. The result is helpful for designing a multiple channel filter.