Electromagnetic fields of an ultra-short tightly-focused radially-polarized laser pulse

•Analytic expressions for the fields of an ultra-short, tightly-focused, radially-polarized laser pulse are derived.•Analytic and numerical procedures are described for the derivation of the fields to any desired level of accuracy.•The fields are derived for two initial wavenumber distributions: a Gaussian and a Poissonian.•Fields to lowest-order of approximation are discussed using pulse lengths and waist radii comparable to a wavelength.

Fully analytic expressions, for the electric and magnetic fields of an ultrashort and tightly focused laser pulse of the radially polarized category, are presented to lowest order of approximation. The fields are derived from scalar and vector potentials, along the lines of our earlier work for a similar pulse of the linearly polarized variety. A systematic program is also described from which the fields may be obtained to any desired accuracy, analytically or numerically.