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

TL;DR

This paper explores how spin angular momentum, helicity, and chirality of light behave in time-varying media, revealing their distinct conservation laws and physical implications under different temporal modulations.

Contribution

It provides a theoretical analysis of the symmetries and conservation laws of SAM, helicity, and chirality in time-varying media, highlighting their differences and practical relevance.

Findings

SAM is conserved under any time modulation.

Helicity is preserved only in impedance-matched modulations.

Chirality is not conserved and depends on field energy.

Abstract

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.