Observing quantum control of up-conversion luminescence in Dy³⁺ ion doped glass from weak to intermediate shaped femtosecond laser fields

Controlling the up-conversion luminescence of rare-earth ions in real-time, in a dynamical and reversible manner, is very important for their application in laser sources, fiber-optic communications, light-emitting diodes, color displays and biological systems. In previous studies, the up-conversion luminescence control mainly focused on the weak femtosecond laser field. Here, we further extend this control behavior from weak to intermediate femtosecond laser fields. In this work, we experimentally and theoretically demonstrate that the up-conversion luminescence in Dy³⁺ ion doped glass can be artificially controlled by a π phase step modulation, but the up-conversion luminescence control behavior will be affected by the femtosecond laser intensity, and the up-conversion luminescence is suppressed by lower laser intensity while enhanced by higher laser intensity. We establish a new theoretical model (i.e. the fourth-order perturbation theory) to explain the physical control mechanism by considering the two- and four-photon absorption processes, and the theoretical results show that the relative weight of four-photon absorption in the whole excitation process will increase with the increase in laser intensity, and the interference between two- and four-photon absorptions results in up-conversion luminescence control modulation under different laser intensities. These theoretical and experimental works can provide a new method to control and understand up-conversion luminescence in rare-earth ions, and also may open a new opportunity to the related application areas of rare-earth ions.