Very short optical pulses: A new approximation method

Abstract

Very short optical pulses, traveling in sharp-line resonant absorbers without change of shape, are investigated with a new approximation techmque. Instead of employing the lang-pulse or slowly varying envelope assumption, we have developed a method of approximation based on a series expansion in powers of a small parameter which is related to the electric field strength. The principal advantages of the method are its ability to treat very short pulses, and the simplicity with which it can be extended, both from lower to higher levels of approximation, and from one type of steady-state pulse to another. In this paper we use the approximation method to study very short pulses which require retention of the second-derivative terms in the Maxwell envelope and phase equations. Corrections to the well-known McCall-Hahn results are easily found to first order in the small parameter. As expected, the corrections begin to be important only for picosecond and shorter pulses.

Pulse Propagation in Non-Local and Non-Linear Media

“…Crisp [80]. Marth, Holmes, and Eberly [81] went beyond the SVEA for the on resonance case, and developed a method of approximation based on a series expansion in powers of a small parameter which is related to the electric field amplitude. In this way, they studied Mathematical details and plots will be presented in Section 5.4, where we will re-derive their results from a uniform perturbation analysis and compare our new results to theirs.…”

“…The phase equation (5.2.20b) is a first-order linear differential equation for φ, from which one can derive a first integral [81]:…”

“…In Section 5.3, the coupled system of Maxwell-Bloch equations is solved perturbatively, based on a series expansion in powers of a small parameter which is related to the electric field amplitude. This method has already been presented for the on resonance case by Marth, Holmes, and Eberly[81] for the SIT problem in dilute gases. General expressions for the solitary waves and their phase modulations are derived for any incident carrier frequency ω and arbitrary pulse width τ.…”