On the superluminal propagation of X-shaped localized waves

The generation and propagation of superluminal X-shaped pulses is investigated. We demonstrate that such pulses can be modelled using a spectral approach that produces time-limited Bessel beams. Special attention is given to calculating the velocities of the modelled pulsed Bessel beams. The velocities of the peaks of the resulting pulses depend on the shapes of the spatiotemporal distributions of the applied time-windows. The generation of pulsed Bessel beams is investigated for various set-ups; including circular arrays, annular slits and axicons. It is shown that superluminal pulsed Bessel beams undergo a delayed generation before they are launched; henceforth, the peak of these pulses travels at speeds exceeding that of light.