Department of Chemistry and Biochemistry, UCLA, Los Angeles, California 90095-1569, USA.
J Chem Phys. 2011 Aug 28;135(8):084121. doi: 10.1063/1.3626549.
We develop near-field (NF), a very efficient finite-difference time-dependent (FDTD) approach for simulating electromagnetic systems in the near-field regime. NF is essentially a time-dependent version of the quasistatic frequency-dependent Poisson algorithm. We assume that the electric field is longitudinal, and hence propagates only a set of time-dependent polarizations and currents. For near-field scales, the time step (dt) is much larger than in the usual Maxwell FDTD approach, as it is not related to the velocity of light; rather, it is determined by the rate of damping and plasma oscillations in the material, so dt = 2.5 a.u. was well converged in our simulations. The propagation in time is done via a leapfrog algorithm much like Yee's method, and only a single spatial convolution is needed per time step. In conjunction, we also develop a new and very accurate 8 and 9 Drude-oscillators fit to the permittivity of gold and silver, desired here because we use a large time step. We show that NF agrees with Mie-theory in the limit of small spheres and that it also accurately describes the evolution of the spectral shape as a function of the separation between two gold or silver spheres. The NF algorithm is especially efficient for systems with small scale dynamics and makes it very simple to introduce additional effects such as embedding.
我们开发了近场（NF）方法，这是一种非常有效的用于模拟近场区域电磁系统的有限差分时域（FDTD）方法。NF 本质上是准静态频域泊松算法的时间相关版本。我们假设电场是纵向的，因此仅传播一组时变极化和电流。对于近场尺度，时间步长（dt）比通常的 Maxwell FDTD 方法大得多，因为它与光速无关；相反，它由材料中的阻尼和等离子体振荡速率决定，因此在我们的模拟中，dt = 2.5 a.u. 是很好的收敛。时间的传播是通过类似于 Yee 方法的蛙跳算法完成的，每个时间步仅需要进行一次空间卷积。同时，我们还开发了一种新的、非常精确的 8 和 9 个 Drude 振子模型，以适应金和银的介电常数，这是因为我们使用了较大的时间步长。我们表明，在小球体的极限下，NF 与 Mie 理论一致，并且它还准确地描述了作为两个金或银球体之间距离函数的光谱形状的演化。NF 算法对于具有小尺度动力学的系统特别有效，并且可以非常简单地引入嵌入等附加效应。
