Virtual Parity-Time Symmetry

Parity-time (PT) symmetry has recently been opening exciting directions in photonics, yet the required careful balance of loss and gain has been hindering its widespread applicability. Here, we propose a gain-free route to PT symmetry by extending it to complex-frequency excitations that can mimic gain in passive systems. Based on the concept of virtual absorption, extended here to implement also virtual gain, we implement PT symmetry in the complex-frequency plane and realize its landmark effects, such as broken phase transitions, anisotropic transmission resonances, and laser-absorber pairs, in a fully passive, hence inherently stable, system. These results open a path to establish PT symmetry and non-Hermitian physics in passive platforms.