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We derived analytic expression for the relative intensity noise (RIN) of a wavelength-locked Fabry-Perot laser diode (FP LD) in a single mode region. The RIN of the wavelength-locked output is a function of the photon density and the photon life time. It also depends on the wavelength detuning and the injected amplified spontaneous emission (ASE) power. We investigated the modulation transfer function of the wavelength-locked FP LD and its dependence on wavelength detuning. The analytic result has good agreement with the simulation result.