Laser linewidth: Amplification of vacuum fluctuations and effects of spatial hole burning

The theory of the fundamental laser linewidth as expressed by the Schawlow-Townes formula is extended to include the amplification of vacuum field fluctuations as well as spatial hole burning. We give a physical interpretation of the Petermann K factor and a simple derivation that does not invoke nonorthogonality of cavity modes. Spatial hole burning introduces directional gain and reduces the output intensity, leading to an increase in the laser linewidth and a modified K factor for asymmetric cavities.