Abstract
The linewidth of an unstable laser exceeds the quantum minimum by the Petermann factor K, which depends on the overlap between left and right eigenvectors of the (non-unitary) round-trip wave operator. When K is plotted as a function of the Fresnel number N, strong resonances occur, which are associated with degeneracies N c lying close to the real axis in the complex N plane. For certain values of the magnification, degeneracies can lie on the real axis, and K is infinite. The Horwitz-Southwell asymptotic theory of the spectrum, presented here in a very accurate form and with a streamlined derivation, is used to show that the peaks occur near N = s - 1/8 (s integer), and to give reliable formulae for the resonance widths Im N c and other features of the degeneracies. Low-lying resonances have discontinuous profiles associated with mode switching where the absolute values of the eigenvalues cross (these are not degeneracies).