Radiative phonon polaritons in semiconductor double heterostructures: A continuum approach

Abstract

A recently reported continuum approach, based on the laws of macroscopic physics, is applied to a calculation of the virtual oscillatory modes of radiative phonon polaritons in the case of a semiconductor double heterostructure of nanometric scale. The obtained results are in the form of TE and TM waves propagating along the structure. We take advantage of the general formulation 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 $\stackrel{\ensuremath{\rightarrow}}{u}$ and the associated electromagnetic fields $\stackrel{\ensuremath{\rightarrow}}{E}$ and $\stackrel{\ensuremath{\rightarrow}}{B},$ as well as the different dispersion relations of the modes. In this treatment a full account is taken of the electromechanical character of the oscillations, and the matching problem is consistently applied. We also calculate the optical coefficients (reflection, absorption, 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.