Abstract
Because the duration of light pulse in modern fiber communication systems is compressed to under the order of femto-second, such a short duration will make large amplitude. We need to consider the nonlinear effect because of the high light intensity when we propagate it in fiber. My thesis is on the basis of Nonlinear Schrödinger equation (NLSE) model, and then we will replace the original nonlinear term to different nonlinear terms with respect to different conditions. By this method we can observe more fantastic phenomenon which is attributed to different new nonlinear term. By the classification of the media, we call a medium “instantaneous” if it can response instantaneously to the emitting electromagnetic wave. Nevertheless, this property can only exist in the ideal medium by theory. Real media all need some relaxation time to response; therefore real media are “non-instantaneous”. In order to describe the non-instantaneous property, we replace the nonlinear term of the original NLSE to a non-instantaneous term with the parameter of relaxation time τ. We will use this new NLSE to observe the special propagation phenomenon of the swinging soliton and non-instantaneous MI. However, because NLSE is still a wave equation, the solution needs to be some specific type. My thesis will use variational method to find the specific solution of vortex pairs. At first, we will use the nonlocal medium for example. We can find the relationship of exciting power P and bean width w, and these specific solutions meet the original nonlocal NLSE. It is no different for the case of Kerr medium, although we let these specific solutions of vortex pairs be the perturbation of a background plane wave this time. And then we can derive the formula of the growth rate h2 of vortex pairs in accordance to the similar derivation of MI beforehand.