A theoretical model for the mode-locked hybrid soliton pulse source HSPS is developed by using a time domain solution of coupled- mode equations and rate equations. Numerical simulations show that grating must be both linearly chirped and apodized to be used in HSPS systems with a wide mode-locking frequency range 2.1 to 3 GHz and transform-limited output pulses. © 2007 Society of Photo-Optical Instrumentation tively. HSPS utilizing a uniform grating Bragg reflector inte- grated into a fiber external cavity has been shown to oper- ate close to the required frequency with transform-limited pulses and very high output powers. 1 However, this device worked well only under specific operating conditions and showed spectral instabilities when operating parameters were changed. Utilizing the device with a linearly chirped grating has overcome the spectral instability problem of the earlier device. An interesting feature of these devices is the extremely wide operating repetition frequency range, which can be enhanced by using chirped gratings, as reported in Refs. 2 and 3. In Ref. 3, measured results showed that transform-limited pulses are generated over a repetition fre- quency range of 850 MHz using a linearly chirped Gauss- ian apodized fiber Bragg grating FBG. However, in this paper, the theoretical model of the mode-locked HSPS with linearly chirped Gaussian apodized FBG is described. Ob- tained results indicate that transform-limited pulses are generated over a wide tuning range of 900 MHz for linearly chirped Gaussian apodized FBG, and this grating is a good candidate to be used in soliton pulse propagation systems. All results have been found to fit well compared with the experimental results in the literature. 3 2 Model of the HSPS The structure of the HSPS utilizing linearly chirped FBG considered in our analysis is shown in Fig. 1. The geometry is the same as the one reported in Refs. 3-7. The HSPS system is made up of a multiquantum well MQW semi- conductor laser, a fiber, and a FBG. One facet of the diode is high reflectivity HR-coated, and the other is antireflec- tion AR-coated. The light from the AR-coated facet is coupled to the FBG reflector. The field in this system trav- els between the HR-coated laser end and the effective cav- ity length of the grating. The output power is taken through the grating. The mode-locked HSPS model is based on a time- domain solution of the coupled-mode equations. Assume that the longitudinal, effective-refractive index variation of the Bragg grating is given as