  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.
