Symmetries and conservation of spin angular momentum, helicity, and chirality in photonic time-varying media

Polarization-dependent dynamical properties of light as the spin angular momentum (SAM), helicity, and chirality are conserved quantities in free-space. Despite their similarities on account of their relationship with a circular state of polarization, SAM, helicity, and chirality emerge from distinct symmetries, which endows them with different physical meanings, properties, and practical applications. In this work, we investigate the behavior of such quantities in time-varying media (TVM), i.e., how a temporal modulation impacts their symmetries and conservation laws. Our results demonstrate that the SAM is conserved for any time modulation, helicity is only preserved in impedance-matched time modulations, while chirality is not conserved. In addition, the continuity equations highlight the dependence of the chirality with the energy content of the fields. These results provide additional insights into the similarities and differences between SAM, helicity, and chirality, as well as their physical meaning. Furthermore, our theoretical framework provides with a new perspective to analyze polarization-dependent light-matter interactions in TVM.