We present a theoretical analysis of the modulation response of a semicondu
ctor laser amplifier. We find a resonance behavior similar to the well-know
n relaxation oscillation resonance found in semiconductor lasers, but of a
different physical origin. The role of the waveguide (scattering) loss is i
nvestigated in detail and is shown to influence the qualitative behavior of
the response, In particular, it is found that a certain amount of waveguid
e loss may be beneficial in some cases. Finally, the role of the microwave
propagation of the modulation signals is investigated and different feeding
schemes are analyzed. The nonlinear transparent waveguide, i.e., an amplif
ier saturated to the point where the stimulated emission balances the inter
nal losses, is shown to be analytically solvable and is a convenient vehicl
e for gaining qualitative understanding of the dynamics of modulated semico
nductor optical amplifiers.