Terabit pulse generation can be realized with a mode locked semiconductor laser resonator.The combination of high gain values and large gain bandwidth make semiconductor materials an ideal ultrahigh speed medium. Unfortunately, standard frequency domain techniques ingore transient solutions and become numerically intensive with large bandwidth calculations. Therefore, it is necessary to directly model the response of an electromagnetic field within such media in the time domain. Futhermore, the understanding of resonant structures is critical not only for modeling semiconductor lasers but for periodic resonant structures and photonic bandgap devices as well.
As a first step, we examine electromagnetic modes in a semiconductor medium inside a standing wave resonator. Because of the large bandwidth of the field and gain medium, a direct time-domain solution to the wave equation is desireable. Also, since the laser output power is proportional to pump current, conduction properties of the gain medium are emphasized. For this problem an exact solution to the time domain wave equation is obtained for a medium containing bound charges and free-carriers. Specific examples, which illustrate the transient and steady state nature of the fields, are given for doped GaAs.