A theoretical model for the mode-locked hybrid soliton pulse source ͑HSPS͒ is developed by using a time domain solution of coupledmode 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 GHz͒ and transform-limited output pulses.

The small signal intensity modulation (IM) of a hybrid soliton pulse source (HSPS) utilizing Gaussian apodized fiber Bragg grating (FBG) is described using electric field approach. The HSPS is modeled by a time-domain solution of the coupled-mode equations. It is shown that type of external cavity is important effect on resonance peak spectral splitting (RPSS) in IM response as well as effect of laser and FBG parameters. It is also shown that the RPSS can be suppressed by using linearly chirped Gaussian apodized FBG as an external cavity insted of Gaussian apodized FBG.

The noise and mode-locking phenomena of a hybrid soliton pulse source (HSPS) utilizing Gaussian apodized fiber Bragg grating is described. The HSPS is modeled by a time-domain solution of the coupled-mode equations including spontaneous emission noise, and relative intensity noise (MN) is calculated using numerical solutions of these equations. It is found that transform limited pulses are not generated with Gaussian apodized grating even if system is properly mode-locked at the fundamental frequency. If transform limited pulses are not obtained, a noise peak in the RIN spectrum does not occur at the fundamental frequency.

The noise and mode-locking phenomena of a hybrid soliton pulse source (HSPS) utilizing Gaussian apodized fiber Bragg grating is described. The HSPS is modeled by a time-domain solution of the coupled-mode equations including spontaneous emission noise. Relative intensity noise (kilN) is calculated using numerical solutions of these equations. It is found that with and without noise near transform limited pulses are only generated over a limited frequency range even if system is properly mode-locked over a wide frequency range around the fundamental mode-locking frequency. If transform limited pulses are not obtained at the fundamental frequency, there is no noise peak in the PIN spectrum at this frequency.

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