الفهرس 
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Abstract
The main purpose of this thesis is to discuss a new perspective on the chaotic behavior of two-photon laser in the presence of multi-intermediate states. The generalized equations for the density matrix for a two-photon laser have been obtained. This is followed by a study of the nonlinear dynamics of the system by using bifurcation diagrams and the Lyapunov exponent. The results show that the system dynamics is very sensitive to any variation in optical pumping. Also we have studied the case of asymmetry between the intermediate levels, as well as the case of the presence of two asymmetric intermediate levels . The results showed that there are various dynamic phenomena and behaviors of the system such as periodic, semi-periodic and chaotic behaviors. The thesis consists of four chapters as follows; Chapter one : It includes an introduction to the origin and nature of the laser and an overview why it is one of the important applications on the interaction of the electromagnetic field with the atom. There is also an outline of the thesis, in addition to its contents. Chapter two : This chapter consists of the derivation of Maxwell-Bloch equations that express the non-degenerate state of the two photon laser, followed by the study of the steady state. To clarify the extent to which this case is affected by the components of the optical cavity, a comparison was also made between the single-photon laser and the two-photon laser. At the end of the chapter, we analyze the linear stability of the system, and the results showed that the system was significantly stable with the change of coefficients optical cavity. At the end of the chapter there is a brief summary of the contents of the chapter. Chapter three : It deals with the derivation of Maxwell Schrodinger equations for the two photon laser followed by obtaining the general equations for the density matrix of the system in the presence of numbers of intermediate levels, then a special case of two intermediate levels is chosen for study and application of bifurcation and the Lyapunov exponent theory. The results showed the extent to which the system was affected by the presence of two asymmetric between intermediate levels, as well as with the gradient in the optical pumping, we have detected that system has different behaviors such as periodic and quasiperiodic behavior as well as chaotic behavior. At the end of the chapter there is a summary of the contents of the chapter. Chapter four : This chapter contains a summary of the thesis and includes future proposals for the study of the two-photon laser. The thesis ends with the presentation of the scientific research and references that were referred to during the thesis.