We introduce a novel concept of the { \em pseudo} parity-time ($\mathcal{ PT}$) symmetry in periodically modulated optical systems with balanced gain and loss. We demonstrate that whether the original system is $\mathcal{ PT}$-symmetric or not, we can manipulate the property of the $\mathcal{ PT}$ symmetry by applying a periodic modulation in such a way that the effective system derived by the high-frequency Floquet method is $\mathcal{ PT}$ symmetric. If the original system is non-$\mathcal{ PT}$ symmetric, the $\mathcal{ PT}$ symmetry in the effective system will lead to quasi-stationary propagation that can be associated with the \emph{ pseudo $\mathcal{ PT}$ symmetry}. Our results provide a promising approach for manipulating the $\mathcal{ PT}$ symmetry of realistic systems.
Categories: physics.optics quant-ph