We study a Nd-doped microchip glass laser that emits in two polarizations a
nd in many longitudinal modes. Saturation of the inversion by standing wave
s causes spatial inhomogeneity of both the longitudinal and azimuthal distr
ibutions of the laser gain. These nonlinear inhomogeneities couple the mode
s and result in low-frequency oscillations (10-500 kHz) of the light flux i
n the individual laser modes. These oscillations are steadily driven by qua
ntum noise and appear as 15% fluctuations of the power in each mode. In-pha
se fluctuations in the laser modes appear at the frequency of the main rela
xation oscillation of the total laser power. Antiphase fluctuations appear
at other frequencies in individual longitudinal and polarization laser mode
s only. The dominant frequency of these fluctuations is determined by the l
ight power in the mode. Numerical simulations of rate equations, including
Langevin forces, satisfactorily reproduce the experimental results. These p
henomena must be taken into account when lasers are applied as stable coher
ent optical light sources, and also with sensitive absorption measurements
in the laser cavity.