Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface.
Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface.
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DOI：
10.1103/physreva.39.1809
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发表时间：
1989-02
期刊：
影响因子：
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通讯作者：
Alejandro B. Aceves;J. Moloney;Alan C. Newell
中科院分区：
文献类型：
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作者：
Alejandro B. Aceves;J. Moloney;Alan C. Newell
提出了一种理论，描述了全球的反射和传输特性的自聚焦通道传播的倾斜入射角的界面分离两个或两个以上的自聚焦非线性介质。代表自聚焦通道的非线性波包被表示为在等效势中运动的等效粒子。粒子的动力学由牛顿运动方程描述，通道的渐近传播路径从等效势的相关相图中读出。势的平衡，或等价地，相平面中的临界点，代表稳态（稳定或不稳定）非线性表面波。后者的稳定性直接来自对电势的简单检查。等效势的形状随入射光功率的变化而变化。我们的理论提供了非线性模拟著名的线性斯涅尔定律的反射和透射。理论的有效性的条件建立在参数空间中的广泛的数值解的非线性偏微分方程描述光束传输。本文的一个重要结论是，等效粒子理论的预测涵盖了广泛的物理参数空间。作为理论应用的一个例子，我们展示了如何设计一个全光角度或功率可调的空间扫描元件。接触与早期的数值研究光束传播和非线性表面波的稳定性在线性-非线性界面。
A theory is presented that describes the global reflection and transmission characteristics of a self-focused channel propagating at an oblique angle of incidence to an interface separating two or more self-focusing nonlinear dielectric media. The nonlinear wave packet representing the self-focused channel is represented as an equivalent particle moving in an equivalent potential. The dynamics of the particle is described by Newton’s equations of motion, with the asymptotic propagation paths of the channel being read off from the associated phase portraits of the equivalent potential. Equilibria of the potential, or equivalently, critical points in the phase plane, represent stationary (stable or unstable) nonlinear surface waves. Stability of the latter follows immediately from a simple inspection of the potential. The shape of the equivalent potential changes with the power in the incident beam. Our theory provides the nonlinear analog of the well-known linear Snell’s laws of reflection and transmission. Conditions on the validity of the theory are established in parameter space by extensive numerical solution of the nonlinear partial differential equation describing beam propagation. One important conclusion of the paper is that the predictions of the equivalent-particle theory encompass a wide physical parameter space. As an illustration of an application of the theory, we show how to design an all-optical angle or power adjustable spatial scanning element. Contact is made with earlier numerical studies of beam propagation and nonlinear surface-wave stability at a linear-nonlinear interface.