We calculate excess noise factors (Petermann K-factors) for a circular
confocal unstable resonator. Typical mode profiles, and the dependenc
e of their eigenvalues and K-factors on cavity geometry, are presented
. The calculations are based upon the 'virtual source' method as well
as on a self-consistent solution of the Huygens-Fresnel integral equat
ion. It is known that in a one-dimensional strip resonator, K-factors
similar to 10(4) are possible; although simple arguments suggest that
the K-factors in two dimensions should vary roughly as the square of t
heir one-dimensional counterparts, this turns out to occur only in rec
tangular symmetry and not in the circular case.