Theoretical analysis of the density of states and phase times: Application to resonant electromagnetic modes in finite superlattices

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(parallel to) parallel to the interfaces. Specific applications of our results are given for electromagnetic modes of a SiO2 buffer layer/finite GaAs-AlAs superlattice sandwiched between a GaAs substrate and air.