Fig. 3: Temporal aiming with monochromatic Gaussian beams.

a Schematic representation of an oblique incident Gaussian beam immersed in a time-dependent metamaterial. b Analytically derived angles of the instantaneous Poynting vector θ_2s (t > t₁) as a function of the incident angle θ_1k (t < t₁) when ε_r is changed from isotropic with ε_r1 = 10 to anisotropic \(\overline{\overline {\varepsilon _{r2}}}\) = [ε_r2x = 1, ε_r2z = 15] (black circles), along with the amplitude of the FW (E₂⁺/E₁) and BW (E₂⁻/E₁) electric fields (red and green circles, respectively). c–e Numerical results of the snapshot of the power-flow distribution and instantaneous Poynting vector (blue arrows) distributions for a Gaussian beam with a beam waist diameter D = 9λ before the change in ε_r (when ε_r1 = 10) at t = 30.2 T (t = t₁⁻) and after the change in the relative permittivity to \(\overline{\overline {\varepsilon _{r2}}}\) = [ε_r2x = 1, ε_r2z = 15] at t = 30.4 T (t = t₁⁺) and at t = 36.3 T (t > t₁), respectively. f–h Numerical results of the snapshot of the power-flow distribution and instantaneous Poynting vector (blue arrows) distributions at the same times as in panels c–e and using the same time-dependent ε_r(t) but considering a Gaussian beam with a beam waist diameter of D = 2λ. In all the numerical results, the incoming signal is switched off once the temporal boundary is induced at t = t₁ to appreciate the effect of using a time-dependent ε_r(t) on a signal already present in the medium