Fields of an ultrashort tightly focused radially polarized laser pulse in a linear response plasma

Analytic expressions for the fields of a radially polarized, ultrashort and tightly focused laser pulse propagating in a linear-response plasma are derived and discussed. The fields are obtained from solving the inhomogenous wave equations for the vector and scalar potentials, linked by the Lorenz gauge, in a plasma background. First the scalar potential is eliminated using the gauge condition, then the vector potential is synthesized from Fourier components of an initial uniform distribution of wavenumbers, and the inverse Fourier transformation is carried out term-by-term in a truncated series (finite sum). The zeroth-order term in, for example, the axial electric field component is shown to model a pulse much better than its widely used paraxial approximation counterpart. Some of the propagation characteristics of the fields are discussed and all fields are shown to have manifestly the expected limits for propagation in a vacuum.