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Knowing the various physical mechanisms of the semiconductor optical amplifier (SOA) helps us to develop a more complete numerical model. It also enables us to simulate more realistically the static behavior of the SOA_s’ birefringence effect. This way, it allows us to study more precisely the behavior of SOA_s, and particularly the impact of the amplified spontaneous emission (ASE) or the pump and probe signals as well as the optical functions based on the non-linearity of the component. In static regime, the SOA_s possess a very low amplification threshold and a saturation power of the gain which mainly depends on the optical power injected into the active region. Beyond the optical input power, the SOA is in the saturated gain regime which gives it a nonlinear transmission behavior. Our detailed numerical model offers a set of equations and an algorithm that predict their behavior. The equations form a theoretical base from which we have coded our model in several files.cpp that the <strong>Language C++</strong> executes. It has enabled us, from the physical and geometrical parameters of the component, to recover all the relevant values ​​for a comprehensive study of SOA_s in static and dynamic regimes. In this paper, we propose to make a static characterization of the effect of the nonlinear polarization rotation by realizing a pump-probe assemblage to control the power and state of polarization at the entering of the SOA.

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The semiconductor optical amplifiers (SOA) are all-optical multifunctional devices. The improvement of their performance will, therefore, be of great importance for modern optical telecommunication systems. We propose in this article to develop a dynamic model that enables us to simulate the dynamic behavior of SOA's birefringence effects. The determination of a numerical model is a multidisciplinary activity that needs engineering skills, optimization and physics. This numerical model enables to describe the propagation of a picosecond optical pulse passing through the SOA and takes into account its polarization and the phenomenon of energy coupling between the eigenmodes of SOA (TE mode and TM mode). In this paper, we will, first of all describe the numerical algorithm of our model, and then we will propose to make a dynamic characterization of the effect of the nonlinear polarization rotation in the SOA, which will allow us to study the all-optical logic gates as well as all the other digital components based on the nonlinear effect of birefringence in SOA.

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