Controlling the Group Velocity of a Bessel Beam

Bessel beams are a family of beams resulting from interference between plane waves propagating at an angle <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\theta$</tex> in a conical geometry. The result is a needle-like intense central spot along the optical axis. In some applications, such as terahertz generation [1], controlling the group velocity of the Bessel beam is fundamental. It is well known that the group velocity of the Bessel beam is influenced by its spatio-temporal profile [2]. Two examples are the Bessel X-pulse and the pulsed Bessel beam with a velocity of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\frac{c}{\cos (\theta)}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$c \cos (\theta)$</tex> respectively [3]. However, Bessel pulses can have an infinite number of spatio-temporal profiles, and simulating their profile could give us the velocity of the Bessel beam. Although some existing programs can simulate spatio-temporal coupling in a setup [4], they are computationally intensive.