We derived a theoretical model of a wavelength-locked Fabry-Perot laser diode (F-P LD) to a sliced spectrum of externally injected amplified spontaneous emission (ASE) from wave equations. The model explains the dynamics of the wavelength-locked F-P LD. Using this model, we investigated the noise characteristics of a wavelength-locked F-P LD with respect to the various parameters, such as, the injected ASE power, the bias current of F-P LD, and the wavelength detuning. We also investigated intensity noise increment by spectral filtering in optical access networks based on wavelength-locked F-P LDs.