Abstract
This research explore the behavior of soliton in Er +3 fiber laser medium by using a model that use the Quantum optics and three levels system . Starting from the equation of motion of the density operator, the researcher derive the nonlinear Schrödinger equation which include the detuning , Rabi frequency , the group velocity dispersion coefficient of the host fiber and γ the host nonlinearities and use analytic solutions to show that solitary waves can exist and be stable after four loops in ring cavity and the net gain depends on detuning and Rabi frequency
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