The transfer matrix of multilayer and its application in photonic crystal

Leading into the four-dimensional wave vector,the transfer matrix and the reflection and transmission coefficients of a multilayer are derived.Using there xepressions, the longitudinal wave and transversal wave transmission coefficient of the one-dimensional doping phononic crystal is calculated.When a longitudinal wave is normally incident,there is a forbidden band of the longitudinal wave in the transmission wave,and there is a defect mode in forbidden band center.When a transversal wave is normally incident,the same results are oftaines.