The transmission and reflection of acoustic and optic phonons from a solid-solid interface treated in a linear chain model

A one-dimensional lattice model of a solid-solid interface is presented within which it is possible to calculate the transmission and reflection amplitudes of lattice vibrations at the interface. The model is applied for acoustic and optic phonons with arbitrary wavelength from the Brillouin zone. General expressions for the coefficients of power transmission and power reflection are evaluated. The reciprocity theorem is proved and applications of numerical results are discussed.