激光系统的Ginzburg-Landau方程及其相位扩散方程

讨论了激光系统Ginzburg-Landau方程的主要动力学行为,它描述激光系统的自发时空对称性破缺。当方程有非均匀静态解时,它存在合作频率锁定效应;而当方程有时空振荡解时,各横模仍有一个共同的光学载频。此模型还表明,混沌解可以发生在低抽运条件下。在较小失谐时,该方程的约化相位扩散方程能较精确地再现原方程的全程动力学行为。这说明在激光横向图形分布的自发形成中,电场的相位分布导引其动力学行为。 关键词：

LASER GINZBURG-LANDAU EQUATION AND ITS PHASE DIFFUSION EQUATION

The dynamical behavior of laser Ginzburg-Landau equation, which describes the sponta-neously spacial temporal symmetry breaking, has been investigated, In the case of inhomoge-neous stationary solution, it shows the cooperative frequency locking; and in the case of spa-tial-temporal oscillatory solution, all the transverse modes have a common optical carrier fre-quency. However, a chaotic solution can be generated at lower pumping, due to the diffraction of electro-magnetic field and nonlinearity. The numerical results show that, in the situation of small detuning, the reduced phase diffusion equation of this model can more precisely du-plicate its global dynamical behavior. It illustrates that the phase pattern of field guides the dy-namics in spontaneous formation of the transverse pattern of field.