Abstract
The three-dimensional optical pattern generated in a single pulse by a high-power free-electron-laser system when the ${e}^{\mathrm{\ensuremath{-}}}$-beam radius is small compared to the laser-beam radius is shown to be determined by the solution of a simple one-dimensional integral equation. This strong-diffraction-limit equation is of the convolution form and, while it is mostly easily solved numerically, it is shown to have nontrivial analytic solutions of interest.
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