Methods for generating wideband localized waves of superluminal group velocity

Energy-flow velocities of nondiffracting localized waves

“…The first example of a superluminal scalar field with frequency-dependent Axicon angle is the so-called Focused X Wave (FXW) [18], possibilities of optical generation of which have been considered in Ref. [49]. The expression for the FXW reads…”

Photon Localization Revisited

“…Such wave with intriguing properties, named the focused X wave (FXW) (Besieris et al, 1998;, belongs to the so-called superluminal propagation-invariant localized waves. Although the FXW is not experimentally generated yet, a set-up based on a cylindrical diffraction grating has been proposed and its properties analyzed (Valtna et al, 2007). It should be noted here that there is nothing unphysical in the superluminality of the localized waves since a superluminal group velocity does not mean as if energy or information could be transmitted faster than c. This is an experimentally verified fact for the so-called Bessel-X pulse which is another representative of the family of superluminal waves (Alexeev et al, 2002;Bowlan et al, 2009;Saari et al, 2010;Saari & Reivelt, 1997).…”

Image formation of radially and temporally truncated Bessel beams

“…As already mentioned, a generalized localized wave field can be synthesized [11] which has its central intensity maximum moving at superluminal group velocity -the Focused-X-Wave (FXW, the term proposed in [12]). To avoid confusion, we note that the word focused here has nothing to do with optical focusing -it simply describes the shape of the wave function of the FXW.…”

“…To avoid confusion, we note that the word focused here has nothing to do with optical focusing -it simply describes the shape of the wave function of the FXW. The FXW can also be described as a superpostion of Bessel beams, but with another dispersion relation between the axial wavenumber and the frequency, which makes the angle θ frequency-dependent [11]. Here the Bessel beams' cone vertex angles as well as k-vector lengths vary -they are following a hyperbolic relation between the wave number's axial component k z and the radial component k ρ .…”