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Spontaneous emission alters the phase and amplitude of the laser field. The amplitude changes induce relaxation oscillations, which cause additional phase changes while restoring the field amplitude to the steady state value. It was previously shown that the additional phase changes greatly enhance the linewidth. We show here that the additional phase changes also give rise to line shape structure in the form of additional peaks separated from the main peak by multiples of the relaxation oscillation frequency. The calculated mean square phase change and power spectrum are in good agreement with published observations.