  We explore similarities between the quantum wells and quantum dots used as
optical gain media in semiconductor lasers. We formulate a mapping procedure
which allows a simpler, often analytical, description of quantum well lasers to
study more complex lasers based on quantum dots. The key observation in
relating the two classes of laser is that the influence of a finite capture
time on the operation of quantum dot lasers can be approximated well by a
suitable choice of the gain compression factor in quantum well lasers. Our
findings are applied to the rate equations for both conventional
(spin-unpolarized) and spin lasers in which spin-polarized carriers are
injected optically or electrically. We distinguish two types of mapping that
pertain to the steady-state and dynamical operation respectively and elucidate
their limitations.
