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A ray-optical representation of the attenuation constants in circular hollow waveguides characterized by a surface impedance and admittance has been derived from the characteristic equation based on the boundary-value problems. It is shown that in the first order of approximation, the attenuation constants of all modes including hybrid modes can be derived as if the corresponding rays were meridional. The effect of the Goos-Hänchen shift is also considered, which is significantly different from that in an intuitive formula given in circular dielectric waveguides.
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Mitsunobu Miyagi (1985) studied this question.
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