On Solutions Describing Self-Induced Transparency of Ultra-Short Pulses

Abstract

Recent theoretical investigations [1–5] into systems of equations describing self-induced transparency (SIT) have revealed several interesting points concerning propagation of ultra-short pulses. The main theoretical reason for which these pulses are of interest appears in the fact that the standard theory of McCall and Hahn [6] is based on the slowly varying envelope assumption (SVEA) which cannot comprise a very good approximation for sufficiently short pulses. In the theory of ultra-short pulses in absorbers, attempts to get results better than the ones based on the original McCall-Hahn equations can be divided into two groups. The first group [4,5] offers systematic perturbation approaches in which ρ = Kξ/ω_o, or l/ω_oτ, is a small parameter. Here τ denotes the pulse length, ω_o is the resonant transition frequency for two-level atoms, K is the atomic dipole matrix element p in frequency units, i.e. p = ½ћK, and ξ is the envelope of the electric field. In another group [1–3] of papers one derives a system of equations which may be treated as an improved version of McCall and Hahn’s equations. These new equations can be solved in an analytic way yielding corrections to the known SIT solutions. There are a few conclusions which follow from both approaches and which agree between themselves confirming new features of solutions to the coupled Maxwell-Bloch equations.

Research partially supported by U.S. National Science Foundation and U.S. Energy Research and Development Administration.

Exchange scholar, U.S. National Academy of Science — Polish Academy of Sciences, 1977.

during the period August 1977 – August 1978.