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The interaction Frohlich-like Hamiltonian between an electron and interface optical phonons in a four-layer heterostructure (FLHS) is obtained by means of the orthonormal eigenmodes of interface optical phonons given recently. The electron-phonon coupling functions and their plots for a FLHS and its special cases, an asymmetric trilayer heterostructure (asymmetric single quantum well) and a step quantum well, are given and discussed. We find that the three branches of higher-frequencies are more important for the electron-phonon interaction than the other three in the six branches of interface modes in a FLHS. Moreover, we also find that the situation in an asymmetric trilayer heterostructure is similar to that of a FLHS.

The equations of motion for the p-polarization field in a C/B/A/B/C-type five-layer heterostructure of polar crystals are solved exactly for the interface optical-phonon modes. The eigenvectors are obtained explicitly. The dispersion relation is derived and discussed in detail for some limiting cases. This work can be regarded as a generalization of the formalism of that of Shi and Pan [Phys. Rev. B46, 4268(1992)].

By using antitrace map method, we investigate the light transmission for a generalized Fibonacci multilayers. Analytical results are obtained for transmission coefficients in some special cases. We find that the transmission coefficients possess two-cycle property or six-cycle property. The cycle properties of the trace and antitrace are also obtained., 8 pages, no figures