Analytical solutions for the electromagnetic fields of tightly focused laser beams of arbitrary pulse length.

The analytical solution for a monochromatic focused laser beam was recently published [Opt. Lett.31, 1447 (2006)].

Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes.

The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer's finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier-Gegenbauer series.

Backscattering of an intense laser beam by an electron.

We present a novel, simple asymptotic expansion for the spectrum of radiation that is backscattered from a laser by a counterpropagating (or copropagating) electron. The solutions are presented in such a way that they explicitly show the relative merit of using an intense laser and of an energetic electron beam in x-ray production in the single particle regime. Simple scaling laws are given.