  Light traveling in time-dependent media has many extraordinary properties
which can be utilized to convert frequency, achieve temporal cloaking, and
simulate cosmological phenomena. In this paper, we focus on time-dependent
axion-type magnetoelectric (ME) media, and prove that light in these media
always has two degenerate modes with opposite circular polarizations
corresponding to one wave vector $\mathbf{k}$, and name this effect "time
circular birefringence" (TCB). By interchanging the status of space and time,
the pair of TCB modes can appear simultaneously via "time refraction" and "time
reflection" of a linear polarized incident wave at a time interface of ME
media. The superposition of the two TCB modes causes the "time Faraday effect",
namely the globally unified polarization axes rotate with time. A circularly
polarized Gaussian pulse traversing a time interface is also studied. If the
wave-vector spectrum of a pulse mainly concentrates in the non-traveling-wave
band, the pulse will be trapped with nearly fixed center while its intensity
will grow rapidly. In addition, we propose an experimental scheme of using
molecular fluid with external time-varying electric and magnetic fields both
parallel to the direction of light to realize these phenomena in practice.
