Metrics for localized beams and pulses

Geometric and energy metrics are here proposed to gauge the confinement properties of localized electromagnetic beams (e.g., Bessel beams) and pulses (e.g., X-waves) in both the nondispersive and dispersive cases. As is well known, the frequency superposition of Bessel beams sharing the same axicon angle leads to the generation of tightly bounded wavepackets, namely X-waves, with remarkable spatio-temporal confinement properties. In the nondispersive case, the axicon angle does not change with frequency, and these features can be predicted by closed-form expressions. Remarkably, it is found that the volumetric confinement of such pulses can be optimized for a specific axicon angle. Since the geometric metrics do not account for the unavoidable presence of energy tails outside the main spot, energy metrics are here introduced and compared with the purely geometric definition. Finally, the dispersive case is investigated, accounting for the typical wavenumber dispersion of radial waveguides. As a result, the axicon angle changes with the frequency, and fundamental limits exist for the maximum theoretical fractional bandwidth. Interestingly, design criteria based on approximate analytical expressions are derived to optimize the confinement, even in the dispersive case.