Polar magneto-optic Kerr and Faraday effects in finite periodic \texorpdfstring{$\mathcal{P}\mathcal{T}$}{PT}-symmetric systems

TL;DR

This paper investigates the anomalous Faraday and Kerr rotation effects in finite $ ext{PT}$-symmetric layered systems, revealing phase transition-like behavior, spectral singularities, and resonant enhancements of optical rotations.

Contribution

It introduces a nonperturbative approach to analyze Faraday and Kerr effects in $ ext{PT}$-symmetric structures, uncovering their spectral properties and relations under symmetry constraints.

Findings

Spectral singularities cause strong enhancement of rotation angles.

Faraday and Kerr angles exhibit phase transition-like behavior.

Resonant peaks in the spectrum coincide with transmission peaks, amplifying rotations.

Abstract

We discuss the anomalous behavior of the Faraday (transmission) and polar Kerr (reflection) rotation angles of the propagating light, in finite periodic parity-time ($\mathcal{P}\mathcal{T}$) symmetric structures, consisting of $N$ cells. The unit cell potential is two complex $\delta$-potentials placed on both boundaries of the ordinary dielectric slab. It is shown that, for a given set of parameters describing the system, a phase transition-like anomalous behavior of Faraday and Kerr rotation angles in a parity-time symmetric systems can take place. In the anomalous phase the value of one of the Faraday and Kerr rotation angles can become negative, and both angles suffer from spectral singularities and give a strong enhancement near the singularities. We also shown that the real part of the complex angle of KR, $\theta^{R}_1$, is always equal to the $\theta^{T}_1$ of FR, no matter what phase the system is in due to the symmetry constraints. The imaginary part of KR angles $\theta^{R^{r/l}}_2$ are related to the $\theta^{T}_2$ of FR by parity-time symmetry. Calculations based on the approach of the generalized nonperturbative characteristic determinant, which is valid for a layered system with randomly distributed delta potentials, show that the Faraday and Kerr rotation spectrum in such structures has several resonant peaks. Some of them coincide with transmission peaks, providing simultaneous large Faraday and Kerr rotations enhanced by an order one or two of magnitude. We provide a recipe for funding a one-to-one relation in between KR and FR.