Wavelength tunable laser diodes are critical components in a wide variety of WDM and packet switching architectures. And also wavelength-tuned short pulses generated from the semiconductor laser diodes are of great importance for the developments of ultrahigh speed and WDM optical communication systems. Over the past several years, both continuously and discontinuously tunable lasers incorporating periodically sampled and chirped grating have been studied theoretically and experimentally. These laser diodes show the wide tuning range of above 60 nm, stable lasing condition, and large side-mode suppression ratio. Directly modulated semiconductor laser diodes, even those with a single mode, exhibit a dynamic frequency chirp during the on/off modulation. The dynamic linewidth broadening caused by such a large frequency chirp can result in a significant penalty in the performance of high-speed long-haul optical communication systems. The CW laser diodes integrated with an external EA modulator are an breakthrough to realize the high-speed optical systems with low chirp. And also the short pulse generation using the external modulator has been realized experimentally, whose principle of the pulse generation is the optical gating of the electroabsorption modulator. In this paper, widely tunable laser diodes incorporating periodically sampled and chirped gratings and an external modulator are analyzed using an improved time-domain dynamic model. First, it is demonstrated that the improved model is very powerful in simulating the complex laser diodes with active and passive sections. And, the dynamic properties of the sampled grating DBR and chirped grating DBR laser diodes are investigated. Second, the modulation characteristics of the laser diode integrated with the external electroabsorption modulator are studied. It is shown that the external modulation are superior to the direct modulation in the aspect of the lower frequency chirp. And the pulse generation by the optical gating of the external modulator is observed theoretically.