Non-Hermitian Floquet invisibility

Wave transport and scattering in open systems can be profoundly affected by non-Hermitian dynamics. In this work we consider wave scattering in a one-dimensional tight-binding lattice with a low-frequency harmonically vibrating complex site potential. Floquet scattering is shown to be suppressed in a range of the spectral lattice band, which is limited by a singularity in the spectral transmission/reflection amplitudes for inelastic scattering channels. Invisibility over the entire spectral band is found when the singularity is pushed at the edge of the Brillouin zone, which requires a modulation frequency larger than the width of the tight-binding lattice band. Remarkably, invisibility is found to persist for multiple oscillating lattice impurities.