Spatially and Temporally Nondiffracting Ultrashort Pulses

Abstract

During the last decade a number of novel exact solutions to the three-dimensional wave equation have been discovered, whose names in themselves — “splash modes,” “self-focus wave modes,” “directed-energy pulse trains,” “electromagnetic bullets,” “nondiffracting Bessel beams,” “nondiffracting X waves,” “slingshot pulses,” etc. — give an idea of localized or even particle-like properties of these exotic wave packets (see Refs.^1–4 and references therein). Unfortunately, so far the majority of them exists in formulae only, even if approximations of finite aperture and of finite invariant-propagation (“diffraction-free”) distance are considered. A serious obstacles in the way toward optical implementation of the most interesting and forward-propagating versions of these solutions is an ultra-wide-band spectral content needed for the temporal and spatial localization. This is why the experimental results in this emerging prospective field have been so far obtained in radio-frequency domain and in acoustic imaging, the latter being very intensively studied in the context of medical ultrasound diagnostics. The monochromatic Bessel beam is a remarkable exception. The field amplitude of an axisymmetric Bessel beam can be expressed as Ф_B ∝ J ₀(r k sinθ) exp[i (z k cosθ — ω t)], where J ₀ stands for the zeroth-order Bessel function, r is the transversal distance from the propagation axis z, k = ω /c is the wave number of the monochromatic light and θ is the tilt of the plane wave components with respect to the z axis. As a cylindrical counterpart of the ideal plane-wave solution, it has been rather well known in mathematical physics already since the last century. However, as recently as in 1987 it was demonstrated that the beam essentially maintains its propagation invariance property even in its physically realizable approximate versions: the beam possessing a central bright spot, e.g. of 70 μm FWHM, in the cross-section, shows no spread of this small spot over a distance of 70 cm.