Electromagnetic wave transformation in an oscillator medium with growing density

The model of a medium made of oscillators can describe various materials, including artificial ones made of meta-atoms. Here the transformation of an electromagnetic wave in such a medium with rapidly growing oscillator density is studied. The initial polariton is shown to be transformed not only into new polariton modes but also into natural oscillations of the existing and created oscillators. The oscillations produce zero net polarization but consume significant amount of the initial polariton energy. Although the boundary conditions at the temporal jump are sufficient to find the new polaritons, the description of the polarization oscillations requires integrating the material equations because the oscillations are uncoupled from the fields. Under some conditions, the spatial dependence of the amplitude of the oscillations can provide a snapshot of the electromagnetic field distribution at the moment of rapid density growth. Some subtle issues related to the continuity conditions at the density jump are also discussed.