  It is generally believed that the right-handed circularly polarized (RCP) and
left-handed circularly polarized (LCP) waves in an isotropic chiral medium
propagate at different velocities, known as circular birefringence. Here we
show that this is not the case. After obtaining the refraction and reflection
coefficients of any elliptically polarized wave at the surface of a chiral
medium, we derive the conditions for single-mode refraction. By means of the
process of single-mode refraction, we demonstrate that both the refracted RCP
and the refracted LCP waves at normal incidence can be expressed as a coherent
superposition of a pair of orthogonal linearly polarized waves that are rotated
simultaneously. As a result, they must propagate at the same velocity as the
linearly polarized waves. A physical interpretation is also given in detail. In
particular, we show that the state of polarization of any elliptically
polarized wave in a chiral medium is rotated with propagation. Such a rotation
amounts to the rotation of polarization bases without involving the change of
the Jones vector. The rotation of the RCP and LCP waves, as special cases of
elliptically polarized waves, results in two opposite phases as if they
propagated at different phase velocities with their polarization states
transmitted unchanged.
