  In this article, we study the non-linear coupling between the stationary
(i.e. the beating modulation signal) and transient (i.e. the laser quantum
noise) dynamics of a laser subjected to frequency shifted optical feedback. We
show how the noise power spectrum and more specifically the relaxation
oscillation frequency of the laser are modified under different optical
feedback condition. Specifically we study the influence of (i) the amount of
light returning to the laser cavity and (ii) the initial detuning between the
frequency shift and intrinsic relaxation frequency. The present work shows how
the relaxation frequency is related to the strength of the beating signal and
the shape of the noise power spectrum gives an image of the Transfer Modulation
Function (i.e. of the amplification gain) of the nonlinear-laser dynamics.The
theoretical predictions, confirmed by numerical resolutions, are in good
agreements with the experimental data.
