Ren Qiang, Bao Huaguang, Campbell Sawyer D, Prokopeva Ludmila J, Kildishev Alexander V, Werner Douglas H
Opt Express. 2018 Oct 29;26(22):29005-29016. doi: 10.1364/OE.26.029005.
The discontinuous Galerkin time domain (DGTD) method and its recent flavor, the continuous-discontinuous Galerkin time domain (CDGTD) method, have been extensively applied to simulations in the radio frequency (RF) and microwave (MW) regimes due to their inherent ability to efficiently model multiscale problems. We propose to extend the CDGTD method to nanophotonics while exploiting its advantages which have already been established in the RF and MW regimes, such as domain decomposition, non-conformal meshing, high-order elements, and hp-refinement. However, at optical frequencies many materials are highly dispersive, so the modeling of nanophotonic devices requires accurate handling of different dielectric functions, including those of plasmonic elements, dielectrics, and tunable materials. In this paper, we propose a CDGTD method that incorporates a generalized dispersive material (GDM) model which is an efficient way to implement a wide range of optical dispersion models with a universal analytic function. Physics-based dispersion models, such as the Drude, Debye, Lorentz, and critical points as well as more complicated behavior founded on ab-initio principles can all be obtained as special cases of the universal GDM approach. The accuracy and convergence of this GDM-incorporated CDGTD are verified by numerical examples. The CDGTD method, equipped with the GDM model, paves the way to the efficient design and optimization of large scale photonic devices with a diverse range of optical dispersive materials.
间断伽辽金时域（DGTD）方法及其最新变体——连续 - 间断伽辽金时域（CDGTD）方法，因其具备有效模拟多尺度问题的内在能力，已被广泛应用于射频（RF）和微波（MW）领域的仿真。我们提议将CDGTD方法扩展至纳米光子学领域，同时利用其在RF和MW领域已确立的优势，如区域分解、非共形网格划分、高阶单元以及hp细化。然而，在光频下，许多材料具有高度色散性，因此纳米光子器件的建模需要精确处理不同的介电函数，包括等离子体元件、电介质和可调谐材料的介电函数。在本文中，我们提出一种结合广义色散材料（GDM）模型的CDGTD方法，这是一种利用通用解析函数实现广泛光学色散模型的有效方式。基于物理的色散模型，如德鲁德模型、德拜模型、洛伦兹模型和临界点模型，以及基于第一性原理的更复杂行为，都可以作为通用GDM方法的特殊情况得到。通过数值示例验证了这种结合GDM的CDGTD的准确性和收敛性。配备GDM模型的CDGTD方法为高效设计和优化具有多种光学色散材料的大规模光子器件铺平了道路。
