A new theory is formulated which describes the electromagnetic field inside of a laser resonator through an expansion of the field into an angular spectrum of plane waves. The resonator is composed of two identical, circular reflectors of arbitrary size, focal length, and axial separation. This theory is not limited by the usual paraxial approximations, and provides integral expressions for the spatial distribution of the field over the interior of the resonator in three dimensions. The integral expression for the transverse electric component of the field is evaluated numerically for several of the lower loss modes in confocal, spherical, and unstable resonators with linear dimensions the order of ten wavelengths. These results indicate that some of the modes in confocal and spherical resonators behave in some respects like modes that are unstable if the resonator has dimensions the order of a few wavelengths. The effect on the spatial distribution of the resonator field due to saturation of the amplifying medium is found to be slight if spatial hole burning is neglected.
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