【摘要】 从非线性Schr d inger方程出发,应用数学解析的方法,详细讨论了在饱和非线性介质中(2+1)维空间光学孤子存在满足物理意义的自洽解的条件,给出数值计算所需要的边界条件。通过数值计算,给出了基模和一阶模在某一组参数下的部分模式的光场慢变包络、光强度的二维和三维分布的直观图形,以及相应能量(无量纲)。结果表明,孤子的存在不是任意的,而是依赖于一定的能量。当光脉冲能量不足以支持孤子的存在时,其解呈振荡形式,说明不存在孤子解。同时还给出介质的饱和参数、孤子在传播方向上的波矢k对孤子模式的影响等有意义的结论。更多还原

【Abstract】 High intensity laser beam transmitting in medium can result in amusing phenomena because of the nonlinear interaction between the laser pulse and the medium.Optical soliton is the just due to the balance(between) the medium responding nonlinearly to the intensity laser and the diffraction of the intensity laser beam,which have been a subject of many studies.The model for discussing optical soliton is nonlinear Schdinger equation(NLS),which is derived from Maxwell’s equations.The optical soliton,according to transverse coordinate and transmitting direction,can be divided into(n+1)D(n=1,2,3) spatial optical soliton that have n(dimensions) transverse coordinate and one transmitting direction.(2+1)D optical soliton modes are studied in this paper.Starting from nonlinear Schdinger equation(NLS),the condition that the(2+1)D spatial optical soliton in saturable nonlinear medium would be exist or not,and the boundary(conditions) for numerically calculating the modes were discussed by mathematical analysis method.By numerical analysis,the base-mode and one-order modes were given by pretty figures including slowly varying beam(envelope),beam intensity and three-dimension distribution of beam intensity,and the powers of each soliton were given(a.u.).The (results) indicate that the soliton is not arbitrary but depending on power,for example,if the beam power would not equal to soliton power,the soliton do not exist.This conclusion could be(evidenced) further in this paper,if(setting) the fitting starting value(equivalent to power of optical beam),the(solution) of Schdinger equation are existence,and if starting value is unfitting,then the solution behave surge,none solution.Meanwhile,the influence of the medium saturable nonlinear parameter and wave vector,which is the soliton transmitting in the direction of z,are studied.The results show that if the k,m,n is fixed on,the power is increasing with α becoming bigger.And if the α,m,n is fixed on,the location of biggest power shift to the position with small r value.The conclusions of this paper shows that the soliton has internal structure,and have the instructive action for the soliton researching.更多还原