Fields of an ultrashort tightly-focused laser pulse

Analytic expressions for the electromagnetic fields of an ultrashort, tightly focused, linearly polarized laser pulse in vacuum are derived from scalar and vector potentials, using a small parameter which assumes a small bandwidth of the laser pulse. The derived fields are compared with those of the Lax series expansion and the complex-source-point approaches and are shown to be well-behaved and accurate even in the subcycle pulse regime. We further demonstrate that terms stemming from the scalar potential and due to a fast varying pulse envelope are non-negligible and may significantly influence laser-matter interactions.