The modes and beam characteristics of a Gaussian gain laser resonator are analyzed. Such a gain is typically associated with an end pumped solid state laser. The beam propagation method is used to find the eigenmodes. The eigenmodes are non Gaussian in appearance and differ greatly from the modes of the same cavity with a quadratic gain. It is found that the cavity geometry strongly influences mode formation around degenerate cavity geometries throughout a broad range of operational parameters. The beam propagation method is used to evolve the field through the resonator, resulting in computation of the nonorthogonal eigenmodes. This permits evaluation of the excess noise dependence on geometric cavity parameters such as length and focal length. It is shown that the beam quality M² and Petermann K factor are related and are anticorrelated at degeneracies. An explanation is given based on the self Fourier transforming properties of degenerate cavity locations. It is shown how the empty cavity properties of transverse mode degeneracies are not revealed with a quadratic gain, but are strikingly present with a Gaussian gain. A confocal cavity is studied in detail and found to have the property that forces K to unity even in the presence of strong gains and narrow pump widths. The interplay between the diffraction effects of a geometrically stable cavity and the Gaussian gain will be studied to reveal the nature and implications of the non-normal modes encountered.
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