A circular TE0n mode content analysis technique based on the multi-mode coupler with high mode selectivity is proposed. To improve the mode selectivity, a deformed waveguide, entitled the quad-polar waveguide, which discriminates the azimuthally symmetric TE-mode on the waveguide wall, is introduced. The influence of deformation on the TE01 and TE02 modes' field pattern, the corresponding transmission loss, and the power capacity in the quad-polar waveguide are analyzed. Based on the analysis, a dual-mode coupler of the circular TE01 and TE02 modes, consisting of an oversized deformed circular waveguide coupler and a pair of circular-to-quad-polar waveguide transitions, is designed for a high-power Ka-band gyrotron traveling-wave tube system. To verify the high mode selectivity of a quad-polar waveguide, a simple coupling with equal-radius and equal-interval holes are used. A prototype is fabricated and measured, and the results show that the coupling coefficient is -40 dB with the directivity of 27 dB for the TE01 mode, suppressing the unwanted mode TE02 mode with 53 dB. For the TE02 mode, the coupling coefficient is -40 dB with the directivity of 25 dB and suppresses the unwanted mode TE01 mode with 75 dB from 30 to 40 GHz.
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