Spectral Index of OAM-Carrying Ultrafast Localized Pulses

We investigate the spectral degree of freedom of OAM-carrying localized waves, and its influence on their transverse intensity distribution. In particular, we focus our attention on two different families of spectra, namely exponentially decaying spectra, which are very tightly connected to fundamental X-waves, and Bessel-modulated spectra. For each class we show how it is possible, by suitable manipulating their spectrum, to structure their transverse intensity distribution, thus creating a radial structure similar to that of Laguerre-Gaussian beams. To complete our analysis, we investigate the impact of the two spectral functions on linear and angular momentum of such localized waves.