Fig. 2: Analytical results for epsilon-positive -to- negative temporal boundary: step function of ε(t).

A, D, G, J Time-dependent permittivity, electric field, magnetic field, and instantaneous Poynting vector distributions as a function of space (x) and time (t) considering that relative ε of the entire medium is changed from a positive ε₁ = 1 to a negative real value ε₂ = −20 at t₁ = 37.1 T and is kept at this value (based on non-Foster concept) for t > t_1. (Note different ranges of scale bars are used in the two different temporal ranges to show details of the distributions.) B Space average of the instantaneous Poynting vector (blue) over one-wavelength distance (\({\int }_{0}^{{\lambda }_{0}}{S}_{{total}}\left(x,t\right){dx}\)) along with the momentum (red) as a function of time. C Phase of the E (blue) and H fields (green) along with their difference (yellow) for times t > t₁ calculated using the theory shown in the Supplementary Materials section 2. E, F Electric field, H, I magnetic field and (k, l) instantaneous Poynting vector distributions as a function of space (x) extracted from D, G, J at a time t = 37 T (second column) and t = 39 T (third column) corresponding to times before and after the change of permittivity from a positive to a negative value, respectively.