Ultrashort free-electron laser pulse

Three-dimensional characteristics of short free-electron laser pulses are analyzed. When the optical pulse length is short, the growth rate and optical guiding will vary among the Fourier components comprising the pulse. Matched beam solutions of the wave equation, including diffraction and nonparaxial effects, are discussed. In certain limits a front to back asymmetry develops along the pulse as well as a frequency spread across it. In these limits the asymmetry and the frequency spread are relatively small unless the number of optical cycles in the pulse approaches unity.