Multimode interference (MMI) laser diode devices have been developed for a large number of optoelectronic applications. Frequency domain methods have been widely used to simulate the behavior of this class of device at fixed operating wavelengths. However time domain models are becoming more popular in photonic simulations as they are able to more accurately model the nonlinear optical gain media such as that present in the saturable absorber section used in the MMI laser diode. A detailed understanding of the electrodynamic behavior of this kind of device is most easily accessed using a time domain method. Therefore we have developed a time domain simulator: employing a full band (FB) time-domain beam propagation method (TD-BPM) for modeling laser devices. By making physically consistent approximations, the proposed method can obtain accurate results for the broadband electromagnetic response with a much larger time step size than those required by other conventional numerical techniques. In order to approximate saturable gain media used in laser device, we have extended the FB-TDBPM algorithm to include frequency-dependent saturable gain by using a Z transform technique. In this paper we will present this approach and its application to the time domain modeling of laser devices.