Corresponding Author

Rabea, Rasha

Document Type

Original Article

Subject Areas

Mathematics, Statistics, Computer Science, Physics and Astronomy


Pulse propagation; semi-classical approach; Maxwell Bloch equations; non-linear equations; density matrix


The coherent propagation of two optical short pulses through a resonant medium consisting of two three-level atoms in the configuration is investigated. A self-consisting analytical solution without steady state or adiabatic approximations is presented. The electric field in the model studied consists of two co-propagating plane waves, each of which is in near resonance with a transition in the absorber. The density matrix of two three level atoms is studied. Also, the reduced density matrices are stated. The present approach for the semiclassical treatment of resonant coherent interactions in three-level atoms represents a generalization of the Maxwell- Bloch equations for a two-level system. The Maxwell-Bloch equations reduced to the non-linear pendulum equation. The solution shows that the two pulses can propagate simultaneously without loss under some conditions about the pulses and the medium. The propagation of the two pulses through the medium without any constrains approves the self -induced transparency (SIT) phenomenon.

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