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A novel polarization converter using a triangular waveguide is proposed and analyzed by the imaginary-distance beam-propagation method based on Yee's mesh and the finite-difference time-domain method. The polarization conversion length is investigated as a function of relative refractive index difference. It is found, for a silicon core embedded in a silica cladding, that the conversion length is 2 mum, while the insertion loss is 0.5 dB at a wavelength of 1.55 mum. The extinction ratio is more than 20 dB over a wide wavelength range of 1.25 to 1.65 mum. Using a geometrically expanded model, the polarization conversion behavior is verified in the experiment at a microwave frequency of 15 GHz. Finally, reasonable polarization conversion is obtained with a modified structure, in which the two corners of the triangular waveguide are cut and the cut plane is aligned with a square input (output) waveguide.