Solving traveling-wave rate equations of semiconductor lasers including gain compression factor

An implicit analytical solution for the geometric mean of the photon density of the counter-propagating fields inside the diode laser (LD) cavity has been derived from the steady-state traveling-wave rate equations including the gain suppression factor. Together with the expression of the position-dependent photon density and carrier density in terms of the geometric mean, the implicit analytical solution for the rate equations has been obtained. With the aid of the solutions, the effects of the gain suppression on static characteristics of LDs have been quantified.