Optical modes in GaAs-based quantum wells

This paper describes some results obtained by using a theoretical formulation of a long-wave phenomenological model for polar optical phonons in heterostructures which takes full account of (i) the coupling between the mechanical vibration u and the electrostatic potential cphi, (ii) the fact that u in general has longitudinal and transverse parts, and (iii) the simultaneous satisfaction of all mechanical and electrostatic matching boundary conditions. The system of simultaneous differential equations thus established is explicitly solved without approximations. Two distinct classes of solutions are obtained. One consists of shear horizontal purely mechanical vibrations. The modes of the other class have mixed character and describe coupled electrical and mechanical vibrations. The results compare very well with experimental evidence and have the correct symmetry pattern.