非局域椭圆厄米—高斯空间光孤子与相移

研究了椭圆厄米-高斯光束在强非局域非线性介质中的传输特性。依据强非局域介质响应函数特征宽度远大于光束束宽的原理,对介质响应函数做两次泰勒级数展开,都近似取到二阶,得到了非局域非线性薛定谔方程对应的近似的拉格朗日密度函数。在此基础上,运用变分法得到了椭圆厄米-高斯光束各参量的演化方程、演化规律和两个临界功率。当光束、响应函数的椭圆率满足一定条件时,两个临界功率可以相等。当初始功率等于这一临界功率,光束从光腰处入射时,可得到椭圆厄米-高斯空间光孤子。进一步分析发现椭圆厄米-高斯空间光孤子的相移与介质椭圆率和孤子阶数有密切关系,当介质椭圆率和孤子阶数取不同值时,可产生大的正相移、零相移,甚至负相移。

Elliptical Hermite-Gaussian Spatial Optical Soliton and Phase Shift

The propagation properties of elliptical Hermite-Gaussian light beam in a strongly nonlocal nonlinear medium are studied.As the characteristic width of response function of strongly nonlocal media is much bigger than the beam width,the response function is expanded twice with Taylor series and the series are both preserved up to the second-orderterm,and the approximative Lagrangian density function corresponding to nonlocal nonlinear Schrdinger equation is thus obtained.Based on this,the evolution equations,evolution laws of elliptical Hermite-Gaussian light beam′s every variable and two critical powers are also derived using variational method.When the ellipticities of light beam and response function satisfy certain conditions,these two critical powers are equal.When the initial power is equal to the critical power and light beam is incident at the beam waist,the elliptical Hermite-Gaussian spatial optical soliton is obtained.Further studies point out that the phase shift of elliptical Hermite-Gaussian spatial optical soliton is closely connected with media′s ellipticity and soliton′s order.With different values of the media′s ellipticity and soliton′s order,large positive,zero even negative phase shift may come into being.