Nonlinear Theory of Partially Coherent Optical Waves

Doctoral thesis, 2011

Nonlinear effects arise in optics as a consequence of the medium properties being modified by the presence of light. Of particular interest are situations where the effect of the nonlinearity can be described by an intensity dependent refractive index and the subsequent interplay with dispersion and diffraction. Nonlinear optics finds many important applications, e.g. within fiber-optical communication and all-optical signal processing. In recent years, the possibility of using partially coherent light has additionally attracted strong interest as the degree of coherence may significantly influence the propagation properties of the light and its interaction with the medium. The present thesis is concerned with the nonlinear theory of partially coherent optical waves. Several approaches have been suggested for describing the nonlinear dynamics of partially coherent light and in this thesis four of them are considered, along with their characteristic evolution equations and initial source conditions. It is shown that the evolution of partially coherent waves in noninstantaneous Kerr media can be treated in the framework of inverse scattering with the presentation of a generalized dressing method along with a recursion relation for generating an infinite number of invariants. The theory is applied by considering the modulation instability beyond its initial linear stage and a new parabolic solution of the Wigner-Moyal equation, which is one of the equations describing the evolution of partially coherent waves, is derived. Wave propagation in saturable logarithmic media is further considered by the derivation of a dynamic self-similar solution using two different formalisms and an analysis of the mutual interaction of coherent solitons as well as partially coherent soliton stripes. Finally, considerations are made of some aspects of the collapse and blow up phenomena of radially symmetric beams.