波包方法在谐振透射和反射光栅中的应用
Applications of the wave packet method to resonant transmission and reflection gratings
摘要：
利用Maxwell线性无源（色散和吸收）介质理论的时域数值算法，研究了飞秒激光脉冲在色散（Drude金属）和介质材料制成的共振透射和反射光栅上的散射。该算法是基于哈密顿形式主义的框架下，麦克斯韦方程组的无源介质被证明是等效的一阶方程，$\partial Ψ/\partial t = {\cal H}Ψ$，其中${\cal H}$是一个线性微分算子（哈密顿）作用于多维矢量$Ψ$建立的电磁感应和辅助物质场描述介质响应。初始值的问题，然后解决了一个修改的时间蛙跳法结合傅立叶伪谱方法应用于非均匀网格，这是由变量的变化，旨在提高采样效率附近的介质界面。该算法被证明是非常准确的，在相对较低的计算成本。与以前的理论和实验研究的光栅的一个很好的协议证明了使用我们的算法的数值模拟。此外，我们的算法允许看到在初始宽带波包的整个频率范围内的光栅中的电磁场的长离开共振激发的实时动态以及反射和透射波前的形成。
英文摘要：
Scattering of femtosecond laser pulses on resonant transmission and reflection gratings made of dispersive (Drude metals) and dielectric materials is studied by a time-domain numerical algorithm for Maxwell's theory of linear passive (dispersive and absorbing) media. The algorithm is based on the Hamiltonian formalism in the framework of which Maxwell's equations for passive media are shown to be equivalent to the first-order equation, $\partial Ψ/\partial t = {\cal H}Ψ$, where ${\cal H}$ is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector $Ψ$ built of the electromagnetic inductions and auxiliary matter fields describing the medium response. The initial value problem is then solved by means of a modified time leapfrog method in combination with the Fourier pseudospectral method applied on a non-uniform grid that is constructed by a change of variables and designed to enhance the sampling efficiency near medium interfaces. The algorithm is shown to be highly accurate at relatively low computational costs. An excellent agreement with previous theoretical and experimental studies of the gratings is demonstrated by numerical simulations using our algorithm. In addition, our algorithm allows one to see real time dynamics of long leaving resonant excitations of electromagnetic fields in the gratings in the entire frequency range of the initial wide band wave packet as well as formation of the reflected and transmitted wave fronts.
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