Static-to-dynamic field conversion in a temporally switched Lorentz medium

We investigate static-to-dynamic electromagnetic field conversion in a temporally switched Lorentz medium initially subjected to an electrostatic field. An abrupt change of the oscillator strength drives the material away from its initial equilibrium, while the polarization retains memory of the pre-switch state and acts as the source of the resulting transient. We formulate the resulting initial-value problem in the Laplace domain and derive an analytical representation of the generated field in terms of the poles of the finite Lorentz slab. Material dispersion gives rise to a richer modal structure than in the nondispersive case, including families of slab-mode poles that accumulate toward the singularities associated with the Lorentz polarization dynamics. We further show that material memory governs the earliest stage of the transient, producing a smooth field onset and setting the velocity of the earliest propagating disturbance through the high-frequency permittivity. Because the temporal switch generates broadband spectral content, the transient samples positive-, near-zero-, and negative-permittivity regions of the post-switch material response, leading to qualitatively different spatial field distributions. These results reveal how material dispersion and memory fundamentally shape the generation and evolution of radiation produced from an initially static electromagnetic state.