  Photonic structures and time-crystals, wherein time is incorporated as an
additional degree of freedom for light manipulation, have necessitated the
development of analytical and semi-analytical tools. However, such tools are
currently limited to specific configurations, leaving several unexplored
physical phenomena akin to photonic time-crystals elusive. In this
communication, using a coupled-wave theory approach, we unveil the occurring
light propagation phenomena in a time-periodic bi-isotropic medium whose
permittivity, permeability, and chirality parameter are periodic functions of
time. Contrary to their static counterparts, we demonstrate that the considered
dynamic medium couples only co-handed counter-propagating waves. In cases of
non-constant impedance, we prove that two first-order momentum gaps are formed
in the Brillouin diagram, resulting in parametric amplification with different
amplification factors and corresponding momenta for the right- and left-handed
modes, respectively. The presence of chirality plays a major role in
manipulating lightwave signals by controlling the center of resonance, the
corresponding bandwidth, and the amplification factor in a distinct fashion for
each mode. For a finite ``time-slab'' of the medium, we analytically derive the
scattering coefficients as functions of time and momentum, discussing how
extreme values of optical rotation grant access to the temporal analog of the
chirality-induced negative refraction regime. Finally, we demonstrate the
mechanism under which elliptical polarizations may change field orientation
whilst the electric field propagates in a momentum gap, thus simultaneously
showcasing parametric amplification.
