轴不变光学系统中非线性传输的前向-后向方程
Forward-backward equations for nonlinear propagation in axially-invariant optical systems
摘要：
我们提出了一个新的一般框架来处理轴向不变的非线性光学系统，其中包括那些具有任何类型的线性或非线性横向不均匀性的电磁场的前向和后向分量。用最少的近似量，我们得到一个系统的两个一阶方程的前向和后向组件明确显示它们之间的非线性耦合。所使用的模态方法可以有效地减少原始问题的维数，从3+1（三个空间维度加一个时间维度）到1+1（一个空间维度加一个频率维度）。新的方程可以写成旋量的狄拉克形式，其中守恒量可以用一种优雅的方式计算。最后，这些新的方程固有地包含时空耦合，因此它们可以很容易地被具体化以处理纯时间或纯空间效应。以非线性正向脉冲传输和空间结构的非傍轴演化为例进行了分析。
英文摘要：
We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dirac-like form, out of which conserved quantities can be calculated in an elegant manner. Finally, these new equations inherently incorporate spatio-temporal couplings, so that they can be easily particularized to deal with purely temporal or purely spatial effects. Nonlinear forward pulse propagation and non-paraxial evolution of spatial structures are analyzed as examples.
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