High Accuracy Algorithms for Computing Light Propagation in Dielectrics, Dispersive Matierials and Metamaterials

点击翻译按钮获取中文摘要

It is very difficult to compute the optical properties of structures (such as diffraction gratings) made out of metamaterials and dispersive materials. When the structure is neither symmetric nor infinitely periodic, there are no analytic solutions of Maxwell's equations, and it is necessary to use a numerical method. The finite difference time domain algorithm (FDTD) can handle arbitrary structures, but for dispersive materials recursive convolution (RC) must be added to the FDTD algorithm. This not only greatly increases the computational cost, but also the algorithm may become numerically unstable. For designing devices it is often sufficient to do a two-dimensional calculation.The high computational cost of two-dimensional calculations is also high, but in the TE mode (electric field, E, perpendicular to the incidence plane of an infinite plane wave) the electric and magnetic fields can be computed independently. Even when the electric permittivity varies with position, E is govern … More ed by the wave equation. We have developed a new RC-FDTD algorithm for the wave equation, which greatly reduces the computational cost of the TE mode. When RC is added to the FDTD algorithm, a physical model of the dispersion must be used, but unless the model parameters are carefully chosen the FDTD algorithm may become numerically unstable. We have carefully analyzed the stability of the FDTD algorithm, and have found the conditions that guarantee stability. We have done this for both the TE and TM mode (E perpendicular to the plane of incidence). In addition we have found out how to optimize the dispersion model parameters according to frequency to improve the accuracy of the calculation. Our new algorithm is more accurate than the usual one and is stable. We verified the accuracy of our new algorithm by computing the optical characteristics of large periodic structures 8 effectively infinite) and comparing with analytic solutions.We used our algorithm to study metallic gratings made of gold and silver in the infrared region. Less