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

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 follows the 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 coherent perfect absorption (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.

Time-Varying Reactive Elements for Extreme Accumulation of Electromagnetic Energy

“…Generally speaking, the use of time-varying elements in electronic circuits [3][4][5][6][7][8][9][10][11] as well as time-varying material properties [12][13][14][15][16][17][18][19][20][21][22] (usually, time-varying permittivity) for engineering wave propagation has been attracting the attention of researchers since the 1960s. These studies mainly focused on achieving nonreciprocity, amplification, and frequency conversion.…”

Nonclassical light at exceptional points of a quantum PT -symmetric two-mode system

“…On the other hand, just one out of four frequenciesν j has a positive imaginary part, meaning the instability for the steady state in Eq. (29). Only if c ǫ = −c κ , all four frequenciesν j equal zero.…”

“…Enhanced sensing in such systems has been demonstrated [17,25]. Also PT -symmetric chaotic systems [26][27][28] and systems exhibiting bidirectional invisibility [29] have been addressed. * jan.perina.jr@upol.cz Balance between damping and amplification leads, among others, to considerable effective enhancement of both linear and nonlinear interactions in physical systems for suitable parameters, especially at and around exceptional points (EPs) [30,31].…”

Dynamically modulated perfect absorbers

“…We point out that our analysis involves scenarios for which strong non-Hermitian effects (like EPs etc) associated with the driving 44,50 are secondary as opposed to non-Hermiticity associated with material losses. Moreover, we assume that the material-related (non-radiative) losses are relatively weak and can be considered a small perturbation to the Hamiltonian of the isolated system.…”