A quasi-optical mode converter has been designed to transform the TE/sub 22,6/ mode at 110 GHz to a Gaussian beam in free space. The converter consists of a rippled-wall waveguide launcher and two toroidal focusing reflectors. A full vector diffraction theory was developed to simulate the converter operation and predict the characteristics of the output beam. The simulation results were used to modify and improve the reflector design. The converter was built and tested on a 3-/spl mu/s pulsed gyrotron operating in the TE/sub 22,6/ mode at 110 GHz. Beam expansion and calorimetric efficiency measurements agreed well with diffraction theory predictions. Greater than 95% of the TE/sub 22,6/ power generated by the gyrotron was converted to a fundamental Gaussian beam and coupled into a corrugated waveguide. Four additional reflectors were built to transform the fundamental Gaussian beam into two similar Gaussian-like beams of approximately equal power level. The vector diffraction theory analysis suggested that simple sinusoidal and toroidal shaping mirrors can achieve high-efficiency beam splitting. Experiments showed that the beam splitting mirror relay successfully converted the fundamental Gaussian beam, produced by the launcher and two mirror relay, to two Gaussian-like beams. Calorimetric measurements indicated that 94% of the total power leaving the gyrotron was converted to the dual beam output with 52% of the power in the upper beam and 42% in the lower beam. The measured beam patterns and expansions were in good agreement with predictions of vector diffraction theory.