Nonlinear Dynamics of Coherent and Partially Coherent Optical Waves

In optics an important nonlinear effect is manifested by the fact that the refractive index, in addition to its frequency dependence, also depends on the intensity of the light. Nonlinear effects are present within a wide range of optical applications e.g. the fast growing fields of fiber-optic communication and all-optical signal processing. In recent years, the possibility of using sources with partial coherence has attracted strong interest as the degree of coherence plays a significant role for the propagation properties of the light and its interaction with the medium. Several approaches have been suggested for describing the nonlinear dynamics of partially coherent light and in this thesis we treat four of them, presenting their characteristic evolution equations and initial source conditions. An important feature of nonlinear wave propagation is the modulational instability. In this thesis the quasilinear evolution of the modulational instability beyond its initial linear stage is analyzed. A new exact solution of the Wigner-Moyal equation, which determines the evolution of partially coherent light beams in nonlinear media, is derived. This solution represents a dynamic self-similar soliton solution with a parabolic intensity profile. Similarly, using two different formalisms, exact self-similar solutions are also obtained for partially coherent beams propagating in logarithmically saturable media. Finally, the mutual interaction of coherent solitons and partially coherent soliton stripes in logarithmic saturable media are analyzed