Approximate fields of an ultra-short, tightly-focused, radially-polarized laser pulse in an under-dense plasma: a Bessel-Bessel light bullet

Abstract

Provided the intensity is not too high (for example, with I << 1018 W/cm2, for a wavelength of 1 μm), response of an under-dense plasma to the fields of a laser pulse can still be considered linear, and inhomogeneous wave equations for the vector and scalar potentials A and Φ, respectively, may be derived from Maxwell’s equations. A rigorous, but approximate, solution to the wave equation satisfied by a one-component, azimuthally symmetric, vector potential is developed using a Fourier transform method. It is found that an ultra-short and tightly-focused, radially-polarized laser pulse, described by this vector potential, propagates in the plasma like a laser bullet. The pulse is termed a Bessel-Bessel bullet because, to leading order in a power-series expansion, the vector potential, from which the pulse fields E and B are derived, is expressed in terms of a Bessel function of the first kind J0 and a spherical Bessel function of the first kind j0.