Beam-waveguide feed systems are used in large reflector antennas of deep-space networks. One of the main requirements for beam waveguides is to maintain the radiation pattern of the feed output beam, namely, the angular beam symmetry and zero crosspolarization level. Traditionally the Mizusawa's criteria are applied when designing a beam waveguide. However, the fullfilment of these criteria imposes constraints on the beam-waveguide geometry. It also provides, in addition to symmetry, the equality of the incident (input) and emergent (output) beamwidths, which is not always necessary. In this paper, we introduce the general criteria of symmetry and zero crosspolarization maintainance in two-mirror beam waveguides, allowing to transform the beamwidth. It is found within the geometrical optics approximation. The theoretical foundations of the developed approach is presented in the paper. As an example, a two-mirror beam waveguide synthesis is presented,which has the transformation coefficient of the input and output beamwidths K = 1.7. Good crosspolarization characteristics are confirmed by the calculation of the beam-waveguide radiation patterns with the method of integral equations.
