Notes on Constraints for the Observation of Polar Kerr Effect in Complex Materials

While Kerr effect has been used extensively for the study of magnetic materials, it is only recently that its has shown to be a powerful tool for the study of more complex quantum matter. Since such materials tend to exhibit a wealth of new phases and broken symmetries, it is important to understand the general constraints on the possibility of observing a finite Kerr effect. In this paper we reviewed the consequences of reciprocity on the scattering of electromagnetic waves. In particular we concentrate on the possible detection of Kerr effect from chiral media with and without time-reversal symmetry breaking. We show that a finite Kerr effect is possible only if reciprocity is broken. Introducing the utilization of the Sagnac interferometer as a detector for breakdown of reciprocity via the detection of a finite Kerr effect, we argue that in the linear regime, a finite detection is possible only if reciprocity is broken. We then discuss possible Kerr effect detection for materials with natural optical activity, magnetism, and chiral superconductivity.