Light propagation in time-periodic bi-isotropic media

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.