The Faraday Rotation of Waves in a Circular Waveguide

Abstract

Exact solutions of the magnetic rotation of the guided waves in a circular waveguide of infinite length are described, whereby the rotational terms in both magnetization and electric polarization are considered. The normally degenerate modes of the circular guide are separated by the external magnetic field into two partial waves—i.e., the right-handed and left-handed circularly polarized waves, which are neither transverse-electric nor transverse-magnetic but are reduced to the TE- or TM-mode in the limit of vanishing magnetic field. The propagation constant of each partial wave is determined by a transcendental equation derived from the boundary conditions. Curves giving the frequency dependency of the propagation constants for both partial waves are shown for the quasi-TE₁₁-modes, and quasi-TM₁₁-modes for a special value of the coefficients of rotational terms. The dependence of the cutoff frequencies on these coefficients is also obtained. For TM-modes, the cutoff frequencies of both partial waves are found to coincide.