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We have linearized the equations for propagation of the beam of light in a semiconductor optical amplifier about an operating point and have derived the rate of growth of small sinusoidal perturbations of the phase and modulus of the complex field amplitude. The perturbations grow if the spatial frequency is below a critical value that depends on the intensity of the field at the operating point. For spatial frequencies above the critical value, the perturbations die out. The critical spatial frequency decreases as the intensity increases above a certain value. In other words, the tendency to filament becomes weaker as the intensity increases above a certain value. Computer‐generated solutions of the propagation and gain equations are included to illustrate the growth of filaments as the plane‐wave intensity changes in an amplifier.