We use the semi-classical random laser model, which is described by the Maxwell equations and the rate equations, and utilize the finite-difference time-domain method (FDTD) to investigate the differential characteristic of one-dimensional random laser. The results of the calculation indicate that emitting frequency changes continuously with the slight modification of the thickness of film. Thereby, the random laser is a stable system, not a chaotic system. Those thin films in the center of localized regime have stronger effect on the emitting frequency than those beyond the position of localized regime. The thin films in the center of localized regime form a resonant cavity actually and those thin films beyond the position of localization form reflecting mirrors of cavity. Modifying the thickness of the thin films in the center of the localized regime mean modification of the length of cavity, consequently the emitting frequency is changed. Modification of thickness of the thin films out of localized regime mean change of the reflectivity of the reflecting mirrors of cavity. So it has no effect on the emitting frequency, but it affects the emitting energy of laser. If the modification of the thickness is very great, it maybe changes the position of the localized regime and the emitting frequency of mode.
The characteristic of polarization of random laser is investigated by numerical method. We use the random laser model coupling semi-classical laser theory with Maxwell's equations. The model couples electronic number equations at different levels with field equations. The equations are solved by finite-difference time-domain method. We calculate the evolvement of transverse electric wave and transverse magnetic wave in a two-dimensional laser system, respectively. We draw conclusions as follows. Polarization influences the frequency and the position of mode in a random laser system. The threshold is affected by polarization as well.