The symmetrized constitutive relations of Condon are used to find possible solutions in a waveguide formed from an isotropic chiral slab. Two eigenstates are found, related to positive and negative helicity plane-wave modes in an unbounded chiral medium. These eigenstates propagate along the slab, but are standing waves across the slab. Combinations of these eigenstates satisfy the boundary conditions when the slab is bounded by parallel conducting plates. The combinations are not transverse electric or transverse magnetic, but near cut-off these combinations correspond closely to TE or TM modes in achiral parallel-plate waveguides. Equations defining the dispersion relations are derived, and analytic solutions are obtained near cut-off and at high frequencies. At high frequencies one of the helicity eigenstates dominates, for all modes. Chirality of the slab medium splits the TE - TM degeneracy, but crossings of the dispersion curves are possible (and are demonstrated for a particular case).

A dielectric-clad waveguide is also considered. Analytic results are obtained for the low-frequency dispersion relations of the two fundamental modes. One of these modes approaches zero dispersion when the refractive index of the cladding tends to one of the indices of the two helicity eigenstates in the slab.