Numerical Research On Induced Focusing Of Optical Beams In Self-defocusing Media

It has been theoretically and experimentally demonstrated that in self-defocusing media, a weak beam (the probe)can be induced to focus by a strong beam (the pump) that propagates simultaneously with it. In the past decade, the phenomenon of induced focusing has attracted attention of many scholars. Up to now, most relative researches are on the cases in which the two beams copropagate with each other.In this thesis, induced focusing in self-defocusing media is explored thoroughly by numerical method. Firstly, it is simulated that a probe beam and a pump beam counter-propagate in a two-dimensional self-defocusing medium. The results show that the probe beam can be induced to focus due to cross-phase modulation from the pump beam under certain conditions. The effects of the beam parameters on the focusing are also discussed, and it is found that some of the parameters have optimum values which result in the strongest focusing of the probe beam. Further, comparison between copropagation and counter-propagation of two beams shows that some characteristics of focusing in these two configurations are different. Secondly, it is numerically simulated how a dark pump beam induces a bright probe beam(with the Gaussian profile spatially) to focus in two- and three-dimensional self-defocusing media, and the main factors that have influence on the focusing of the probe beam are also analyzed.The main achievement of this thesis is the thorough research for the first time by numerical method on the induced focusing from counter-propagation of two optical beams in self-defocusing media.There are six chapters in this thesis. In Chapter 1, the phenomenon and developments about induced focusing in self-defocusing media are summarized. In Chapter 2, the basic theory on the simultaneous propagation of two optical beam in nonlinear media is given briefly, and a couple of parameters for describing the focusing of a beam are introduced as well. In Chapter 3, how the split-step Fourier method is applied to simulate the co- and counter-propagation of two beams is presented. In Chapter 4, it is simulated that a probe beam and a pump beam counter-propagate in a two-dimensional self-defocusing medium and thorough analyses are made to the induced focusing in this configuration. How a dark pump beam induces abright probe beam to focus in two- and three-dimensional self-defocusing media is discussed in Chapter 5. A summary of the thesis is given in Chapter 6.