Interlevel optical transitions in quantum wells

A general expression for optical matrix elements describing interlevel absorption in size-quantized systems in the presence of electric and magnetic fields is derived. For rectangular and triangular confining potentials, this approach does not require detailed knowledge of the electron wave function and considerably simplifies the problem. As a result, selection rules and analytical expressions for the matrix elements are obtained for many cases where the standard procedure is much more complicated. As examples, optical matrix elements and selection rules are calculated for some particular shapes of quantum wells: triangular, single, and double asymmetric rectangular. The problem is generalized to the case of heterostructures with effective-mass mismatch. A similar approach to quantum wires and dots is also considered. Interlevel absorption spectra for quantum wells in a parallel magnetic field are calculated.