Eigenmodes of optical resonators with mirrors having Gaussian reflectivity profiles.

A general procedure for calculating all the eigenmodes of optical resonators with mirrors having Gaussian reflectivity profiles is described. The eigenmodes are expanded in terms of the freely propagating Her-mite-Gaussian beams. The expansion enables one to apply well known matrix techniques to this kind of systems. The eigenvalues found determine the eigenfrequencies and the mode discrimination properties of such resonators.