In this paper, we derive exact relations between the density of states and the reflection and transmission phase times of a scalar mode in a finite lamellar composite system sandwiched between two different homogeneous semi-infinite media. We illustrate the results of this analysis by analytical and numerical solutions for a substrate-buffer layer-finite superlattice-air system. We give the density of states and phase times as a function of the frequency $\omega$ and the wave vector $k_{\Vert }$ parallel to the interfaces. Specific applications of our results are given for electromagnetic modes of a ${\mathrm{SiO}}_2$ buffer layer/finite GaAs-AlAs superlattice sandwiched between a GaAs substrate and air.

• Received 18 July 2000

DOI:https://doi.org/10.1103/PhysRevB.63.035312