Space-frequency analysis of nondiffracting pulses

Abstract

A recently introduced method of producing nondiffracting space-time fields from ordinary diffracting solutions is here examined in the space-frequency domain. It is shown that in a 3D space the method leads to localized wavefields whose Fourier components are nondiffracting beams. Hence the nondiffracting pulses are spectral generalizations of the monochromatic conical waves, a property which provides novel insight into the physical analysis and the actual preparation of such localized space-time fields. In 2D, the resulting temporally varying wavefields are nonlocalized. The nondiffracting pulses obtained via the space-frequency synthesis of conical waves are illustrated with the help of broadband X waves and their temporal derivatives for which explicit expressions are derived. The relation of these fields to the previously known localized solutions is established.