We demonstrate that the quantum-limited linewidth of an unstable-cavit
y laser depends on the transverse symmetry of the resonator. This is d
ue to the occurrence of excess noise associated with the nonorthogonal
ity of the eigenmodes of an unstable-cavity laser. We show that square
symmetry leads to considerably larger excess noise than circular symm
etry, confirming recent predictions. Further we present measurements o
f the excess noise in lasers with 3, 4, 6 and 8-fold symmetry.