Relaxation oscillations have been studied both theoretically and exper
imentally in a multimode YAG laser in the presence of a derivative fee
dback. In addition to the standard relaxation oscillations, discrete l
ow frequency components are present in the noise spectrum of each indi
vidual mode but they compensate almost exactly in the total intensity.
The influence of a combined derivative feedback involving both the to
tal intensity and that of one selected mode on the behavior of the rel
axation oscillations and nonlinear dynamics of the laser is investigat
ed. It is shown that the compensation nature of the low frequency rela
xation oscillations of the multimode class B lasers can be disturbed i
n this case and, as a consequence, the selected relaxation oscillation
s appear in the noise spectrum of the total intensity, A higher feedba
ck level can induce a destabilization of the laser and eventually chao
s. An excellent qualitative agreement between experiments and theory h
as been obtained.