Self-consistently determining mean field used in rate equations of semiconductor lasers

An analytical expression for the mean field has been derived from the traveling wave rate equations in terms of the geometric mean of the counter-propagating fields inside the cavity, and an implicit solution has been obtained for the geometric mean inside the laser. These lead to the establishment of the analytical relation between the mean field inside the cavity and the output field from the diode laser. It is hoped that this relation may provide a common reference for the evaluation of the injection coefficient when studies are made on the injected semiconductor lasers, whose nonlinear dynamic characteristics are critically dependent on the injection coefficient, with rate equations simplified by adopting the mean field approximation.