Nature, diffraction-free propagation via space-time correlations, and nonlinear generation of time-diffracting light beams

摘要

We investigate the properties of the recently introduced time-diffracting (TD) beams in free space. They are shown to be paraxial and quasimonochromatic realizations of spatiotemporal localizedwaves traveling undistorted at arbitrary speeds. The paraxial and quasimonochromatic regime is shown to be necessary to observe what can properly be named diffraction in time. In this regime, the spatiotemporal frequency correlations for diffraction-free propagation are approximated by parabolic correlations. Time-diffracting beams of finite energy traveling at quasiluminal velocities are seen to form substantially longer foci or needles of light than the so-called abruptly focusing and defocusing needle of light or limiting TD beam of infinite speed. Exploring the properties of TD beams under Lorentz transformations and their transformation by paraxial optical systems, we realize that the nonlinear polarization of material media induced by a strongly localized fundamental pump wave generates a TD beam at its second harmonic, whose diffraction-free behavior as a needle of light in free space can be optimized with a standard 4f -imager system.