Compound-cavity laser modes for arbitrary interface reflectivity

Calculations of the longitudinal mode functions for the electric field of a compound-cavity laser show that the loss and gain coefficients are given by the Airy formula, as a function of the mode frequencies. Further, when the external cavity is longer than the gain-medium cavity, the frequency dependence of the gain is stronger than that of the loss, even when the intracavity surfaces are antireflection coated. These results provide a generalization of the oft used dielectric-bump model, in which the intracavity reflectivity has a lower bound fixed by the index mismatch at the interface between the gain medium and the external cavity.