Opt Lett. 2018 Oct 15;43(20):5005-5008. doi: 10.1364/OL.43.005005.
It is commonly believed that the Hamiltonian approach applies only to linear systems, or nonlinear systems with proper linearization procedures. In this Letter, we show that the Hamiltonian approach based on linear coupled-mode theory applies very well for cross-mode modulation, i.e., field variation of the probe light induced by a strong co-propagating pump light in a degenerate mode group. By deriving eigenvalues and eigenvectors of the nonlinear system, evolution of the probe light can be obtained, which agrees with numerical simulations of multimode nonlinear Schrödinger equations. Using the Hamiltonian approach, a simple approach for determining the pump mode for realizing arbitrary mode conversion is discussed. Two concrete scenarios of the optically induced vector mode conversions within the LP-mode group are further exemplified.
人们通常认为哈密顿方法仅适用于线性系统，或者适用于具有适当线性化过程的非线性系统。在这封信中，我们表明，基于线性耦合模式理论的哈密顿方法非常适用于交叉模式调制，即强共传播泵光在简并模群中引起的探测光的场变化。通过导出非线性系统的特征值和特征向量，可以得到探测光的演化，这与多模非线性薛定谔方程的数值模拟结果一致。利用哈密顿方法，讨论了一种确定泵模以实现任意模式转换的简单方法。进一步举例说明了 LP 模式组内光诱导矢量模式转换的两个具体场景。
