Simple form of multimode laser diode rate equations incorporating the band filling effect

To derive a simple form of the multimode laser diode rate equations incorporating the band filling effect, the laser diode gain in the direct bandgap model is introduced into the conventional multimode laser diode rate equations. By numerically examining each modal gain under the gain-switching condition, it is found that both the differential gain coefficient and the carrier density at transparency show an approximately linear dependency on the oscillation frequency. As a result, it is possible to derive a simple form of the multimode laser diode rate equations with linearized gain, which can be used to simulate the behaviors of a gain-switched laser diode characterized by the band filling effect, in both the multimode and single-mode oscillation cases.