A method for obtaining non-Gaussian light beams with azimuthal field polarisation in a waveguide quasi-optical cavity is described. The method is based on the employment of polarisation-selective diffraction structures as laser mirrors. Efficient excitation of such beams at the output from an optically pumped waveguide HCOOH laser (λ = 0.4326 mm) with an inhomogeneous reflecting input and semitransparent output mirrors is confirmed theoretically and experimentally.