Localized Single Frequency Lasing States in a Finite Parity-Time Symmetric Resonator Chain

TL;DR

This paper investigates how modulating both real and imaginary parts of the refractive index in finite parity-time symmetric resonator chains affects their band structure, symmetry breaking, and localized lasing modes, revealing edge effects and threshold behaviors.

Contribution

It introduces a comprehensive analysis of finite PT chains with combined index modulation, highlighting the impact on PT symmetry breaking and localized edge states, which was not previously explored.

Findings

Localized lasing modes occur at the edges of finite PT chains.

Threshold points are influenced by the type of index modulation.

Early PT symmetry breaking is caused by edge-localized termination states.

Abstract

In this paper a practical case of a finite periodic Parity Time chain made of resonant dielectric cylinders is considered. The paper analyzes a more general case where PT symmetry is achieved by modulating both the real and imaginary part of the material refractive index along the resonator chain. The band-structure of the finite periodic PT resonator chains is compared to infinite chains in order to understand the complex interdependence of the Bloch phase and the amount of the gain/loss in the system that causes the PT symmetry to break. The results show that the type of the modulation along the unit cell can significantly affect the position of the threshold point of the PT system. In all cases the lowest threshold is achieved near the end of the Brillouin zone. In the case of finite PT-chains, and for a particular type of modulation, early PT symmetry breaking is observed and shown to be caused by the presence of termination states localized at the edges of the finite chain resulting in localized lasing and dissipative modes at each end of the chain.