This paper shows an improved rate equation by which the phase relation of the carriers and inhomogeneous property are taken into account for injection lasers. The direct modulation characteristics were analyzed as an application of this improved rate equation. A more general discussion was obtained for the resonance-like phenomenon and its suppression effect. For the undoped AlGaAs DH laser with index guiding structure, it is found that the resonance-like phenomenon is mainly suppressed by effect of spatial diffusion of injected carriers, reduction of the thresh-old level and lateral singlemode-operation. We also found that other mechanisms, such as mixing effect of the spontaneous emission, variation of longitudinal mode number and the intra-band relaxation, hardly affect to suppress the resonance-like phenomenon.

Injection lasers tend to show multi-longitudinal mode operation when the infection current is directly modulated, even if the laser shows single-longitudinal mode operation (SMO for short) at continuous wave operation. This paper gives a theoretical analysis for longitudinal mode behavior and conditions to get the SMO at direct modulation in a conventional AlGaAs laser. The strong-gain-suppression effect among the longitudinal modes, which has been introduced as a nonlinear solution of the density matrix equation, is taken into account. The SMO is mostly distorted in high (1 GHz) and low (300 MHz) modulation frequency regions. The high frequency regions is due to the resonance-like phenomena, and the SMO can be maintained with reduction of this phenomena by the carrier diffusion effect or electrical band stop filter. The low frequency region is due to the thermal instability of the device, and the SMO is maintained with reduction of the thermal resistance. Other conditions to keep the SMO during direct modulation are the same as during continuous wave operation.