Hamiltonian structure of propagation equations for ultrashort optical pulses
Hamiltonian structure of propagation equations for ultrashort optical pulses
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DOI：
10.1103/physreva.82.013812
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发表时间：
2010-07-13
影响因子：
2.9
通讯作者：
Demircan, A.
中科院分区：
文献类型：
--
作者：
Amiranashvili, Sh.;Demircan, A.
建立了超短光脉冲序列在非线性色散介质中传输的哈密顿框架。为此，将电场的二阶非线性波动方程变换为适当定义的复电场的一阶传播方程。然后，根据正常变量引入哈密顿公式，即，经典复场是指量子产生和湮灭算符。导出的z-传播哈密顿量考虑了前向波和后向波、任意介质色散和四波混频过程。作为一个简单的应用，我们获得了脉冲传播的运动积分。积分反映了脉冲传递的能量、动量和光子的时间平均通量。此外，脉冲形式的平稳非线性波被认为是。对于给定的能流，它们产生动量流的极值。简化的传播方程得到简化的哈密尔顿。特别地，对于单向传播，复电场简化为解析信号。全双向模型的解决方案进行了数值比较的分析信号的简化方程的预测和所谓的前向麦克斯韦方程。通过检验守恒定律，有效地检验了数值。
A Hamiltonian framework is developed for a sequence of ultrashort optical pulses propagating in a nonlinear dispersive medium. To this end a second-order nonlinear wave equation for the electric field is transformed into a first-order propagation equation for a suitably defined complex electric field. The Hamiltonian formulation is then introduced in terms of normal variables, i.e., classical complex fields referring to the quantum creation and annihilation operators. The derived z-propagated Hamiltonian accounts for forward and backward waves, arbitrary medium dispersion, and four-wave mixing processes. As a simple application we obtain integrals of motion for the pulse propagation. The integrals reflect time-averaged fluxes of energy, momentum, and photons transferred by the pulse. Furthermore, pulses in the form of stationary nonlinear waves are considered. They yield extremal values of the momentum flux for a given energy flux. Simplified propagation equations are obtained by reduction of the Hamiltonian. In particular, the complex electric field reduces to an analytic signal for the unidirectional propagation. Solutions of the full bidirectional model are numerically compared to the predictions of the simplified equation for the analytic signal and to the so-called forward Maxwell equation. The numerics is effectively tested by examining the conservation laws.