Parametric amplification and bidirectional invisibility in PT-symmetric time-Floquet systems

TL;DR

This paper demonstrates how parametric modulation in time-Floquet systems can induce PT-symmetry, enabling novel wave control phenomena like bidirectional invisibility and CPA/Laser operation without material gain.

Contribution

It introduces a new approach to PT-symmetry using parametric amplification in time-Floquet systems, linking Mathieu equation dynamics to PT-symmetric scattering.

Findings

Parametric slabs exhibit PT-symmetric scattering behavior.

PT-breaking threshold aligns with Mathieu instability.

Combined parametric slabs achieve bidirectional invisibility.

Abstract

Parity-Time (PT) symmetric wave devices, which exploit balanced interactions between material gain and loss, exhibit extraordinary properties, including lasing and flux-conserving scattering processes. In a seemingly different research field, periodically driven systems, also known as time-Floquet systems, have been widely studied as a relevant platform for reconfigurable active wave control and manipulation. In this article, we explore the connection between PT-symmetry and parametric time-Floquet systems. Instead of relying on material gain, we use parametric amplification by considering a time-periodic modulation of the refractive index at a frequency equal to twice the incident signal frequency. We show that the scattering from a simple parametric slab, whose dynamics follow Mathieu equation, can be described by a PT-symmetric scattering matrix, whose PT-breaking threshold corresponds to the Mathieu instability threshold. By combining different parametric slabs modulated out-of-phase, we create PT-symmetric time-Floquet systems that feature exceptional scattering properties, such as CPA/Laser operation and bidirectional invisibility. These bidirectional properties, rare for regular PT-symmetric systems, are related to a compensation of parametric amplification due to multiple scattering between two parametric systems modulated with a phase difference.