The expressions for the linear and cross-polarized reflection and transmission coefficients based on the invariant gyrotropic constitutive relations and the Drude–Born–Federov constitutive relations are compared. A physical interpretation for the first-order terms in the gyrotropic parameter and the chiral parameter is presented for normal and oblique angles of incidence. The analytical expressions for the linear cross-polarized or circular-like polarized reflection coefficients are proportional to the product of the gyrotropic measure, the tangent squared of the angle of refraction in the host medium, the round trip transmission coefficients for the horizontally and vertically polarized waves, and the polarization dependent reflection coefficients for a perfectly conducting mirror. These analytical results are consistent with the observed enhancement of the differential circular reflection for near-grazing incidence.
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