Gain effects on laser mode formation

The theory of mode formation in unstable resonators is extended to include effects associated with the spatial and the temporal distribution of spontaneous emissions that contribute to the mode. The spatial distribution smears the far-field pattern and requires additional round-trip propagation of about 2/ln(M) to give a well-formed mode. The temporal effect depends on the rise time of the small-signal gain. The combined effect is a significant fraction of the previous theoretical value obtained by Anan'ev (1975).