Conical wave packets: their propagation speed and their longitudinal fields

摘要

Abstract: We establish the distinction between free-space Bessel beams (the so-called `diffraction-free beams') and the guided modes of circular cylindrical geometry whose radial profiles take the form of Bessel functions. We explain why these two types of optical beams have different dispersion relations. A free-space Bessel beam can be produced by illuminating a mask with a single transparent ring placed at the focus of a lens; such a beam has group and phase velocities that are equal and larger than c, the speed of light in vacuo. We examine the propagation of polychromatic Bessel beams that can be produced when short pulses are illuminating a mask with one transmission ring; spectral modulation, temporal breakup and loss of fringe visibility can take place under such circumstances. Polychromatic Bessel beams are shown to constitute wave packets whose spatio-temporal field distributions are invariant upon propagation in vacuo; these wave packets have the shape of a double cone, and are sometimes called `X-pulses'. We present experimental evidence of loss of fringe visibility when very short pulses are used to generate such conical wave packets. The coherent superposition of multiple monochromatic Bessel beams can lead to a self-imaging phenomenon along the propagation axis when the spatial frequencies of the Bessel beams in the radial direction are properly selected. We specify the conditions for temporal self-imaging when a polychromatic single Bessel beam propagates in a dispersive medium. Spatio-temporal self-imaging is also possible when multiple polychromatic Bessel beams are propagated in a dispersive medium. We also examine the longitudinal fields associated to Bessel beams and conical wavepackets, and evaluate their suitability for partial acceleration.!23