Analytical method for calculating the electric field envelope of ultrashort pulses by approximating the wavenumber up to third order

摘要

For optical pulses shorter than 20 fs duration or highly dispersive materials in the visible range of the spectrum, high-order terms in the Taylor expansion for the wave vector, around the carrier frequency, should be considered. By expanding the wave vector near the center of optical frequency (omega)_(0) in a Taylor series up to the third-order approximation, we present an analytical method for calculating the electric field envelope of a pulse after it has propagated through a medium that contributes second- and third-order group velocity dispersion. To verify the method we present some examples for both 20 and 15 fs pulses propagating through pieces of glass made of low and high dispersive material. Limitations of the method are discussed.