高斯光束在对数型非线性介质中自诱导效应

The Effect of Self-induced Graded-refraction-index of Gaussian Beam Going through Logarithmically Saturable Nonlinear Media on the Propagation Feature

从标量Helmholtz方程出发,推导了对数饱和非线性介质中光场满足的非线性Schr dinger方程(NLSE)。通过与梯度折射率下的光场满足的方程比较,发现高斯光束在对数型饱和非线性介质中可自诱导梯度折射率。利用数值计算,详细地讨论了自诱导梯度折射率对高斯光束传输特性的影响。发现高斯光束在其自诱导的梯度折射率的影响下,呈振荡形式的准稳定的传输。光束注入介质中的初始状态,直接影响着光束的振荡形式(先发散还是先聚焦)、振荡深度(幅度)、振荡周期。得到高斯光束形成孤子的条件,以及若使高斯光束在对数饱和非线性介质中保持小损耗、高稳定的传输,应该使光束在阈值(孤子条件)附近注入介质的结论。

Nonlinear Schrodinger equation （NLSE） of optical field in logarithmically saturable nonlinear media is derived firstly from scalar Helmholtz equation. As comparing the equation of Gaussian beam in logarithmically storable nonlinear media with one of ordinary optical field in graded-refraction-index media, it＇s found that a graded-refraction-index will be induced itself when Gaussian beam passes through logarithmically saturable nonlinear media. By numerically analysing, the trait that self-induced gradedrefraction-index caused Gaussian beam being oscillating semi-stable form is found. And the beam oscillating feature is characterized by form, depth and period depend directly on the condition of inputting beam. It＇ s also found that in an threshold condition with which the inputting Gaussian beam satified , the beam will form soliton wave. And the Gaussian beam will keep propagating in logarithmically saturable nonlinear media with small consumption and high stability when the inputting beam has initial value around the threshold （ i. e soliton condition）.