A boundary-value problem for Maxwell’s equations is formulated whose solutions represent ultrashort pulses of electromagnetic energy that travel along an axis. A paraxial approximation to the solution is introduced that, in the case of Gaussian boundary data, is expressed as a single integral over frequency. Calculations are presented for a pulse of Gaussian cross section and Gaussian time profile. A careful study is made of the error introduced by the paraxial approximation, and an error bound is derived.
© 1985 Optical Society of America
Jeffery Cooper and Egon Marx, "Free-space propagation of ultrashort light pulses," J. Opt. Soc. Am. A 2, 1711-1720 (1985)