Non-Hermitian Linear Electro-Optic Effect Through Interactions of Free and Bound Charges

In recent years, there has been growing interest in non-Hermitian phenomena in low-symmetry conductors, particularly optical gain driven by electro-optic effects. Conventional semiclassical treatments typically attribute these effects to nonlinear interactions associated with the anomalous velocity of Bloch electrons. Here, we present a phenomenological microscopic model that not only recovers these anomalous-velocity contributions, but also incorporates interband effects that become significant at higher frequencies. Our model captures a wide range of nonlinear interactions while remaining consistent with passivity and microscopic reversibility. Using this broader framework, we study the nonlinear interactions between free and bound electrons as an alternative mechanism for optical gain. We show that, under non-equilibrium conditions in low-symmetry conductors, the linearized electromagnetic response can exhibit both nonreciprocity and gain, even without anomalous velocity contributions. Finally, we analyze the stability of electrically biased systems and highlight potential applications such as optical isolators and traveling-wave amplifiers.