Radiative phonon polaritons in semiconductor double heterostructures: A continuum approach

A recently reported continuum approach, based on the laws of macroscopic ph ysics, is applied to a calculation of the virtual oscillatory modes of radi ative phonon polaritons in the case of a semiconductor double heterostructu re of nanometric scale. The obtained results are in the form of TE and TM w aves propagating along the structure. We take advantage of the general form ulation already presented in a previous paper [Phys. Rev. B 56, 4115 (1997) ] in order to display the analytical expressions for the phonon mechanical displacement field (u)over arrow and the associated electromagnetic fields (E)over arrow and (B)over arrow, as well as the different dispersion relati ons of the modes. In this treatment a full account is taken of the electrom echanical character of the oscillations, and the matching problem is consis tently applied. We also calculate the optical coefficients (reflection, abs orption, and transmission) for the incident ir radiation field. A detailed discussion of the results is made, including comparisons with earlier works on the same subject.