A new hybrid implicit-explicit FDTD method for local subgridding in multiscale 2-D TE scattering problems

The conventional finite-difference time-domain (FDTD) method with staggered Yee scheme does not easily allow including thin material layers, especially so if these layers are highly conductive. This paper proposes a novel subgridding technique for 2-D problems, based on a hybrid implicit-explicit scheme, which efficiently copes with this problem. In the subgrid, the new method collocates field components such that the thin layer boundaries are defined unambiguously. Moreover, aspect ratios of more than a million do not impair the stability of the method and allow for very accurate predictions of the skin effect. The new method retains the Courant limit of the coarse Yee grid and is easily incorporated into existing FDTD codes. A number of illustrative examples, including scattering by a metal grating, demonstrate the accuracy and stability of the new method

Birefringent dispersive FDTD subgridding scheme

A novel 2D finite difference time domain (FDTD) subgridding method is proposed, only subject to the Courant limit of the coarse grid. By making mu or epsilon inside the subgrid dispersive, unconditional stability is induced at the cost of a sparse, implicit set of update equations. By only adding dispersion along preferential directions, it is possible to dramatically reduce the rank of the matrix equation that needs to be solved

A hybrid Crank-Nicolson FDTD subgridding boundary condition for lossy thin-layer modelling

The inclusion of thin lossy, material layers, such as carbon based composites, is essential for many practical applications modeling the propagation of electromagnetic energy through composite structures such as those found in vehicles and electronic equipment enclosures. Many existing schemes suffer problems of late time instability, inaccuracy at low frequency, and/or large computational costs. This work presents a novel technique for the modeling of thin-layer lossy materials in FDTD schemes which overcomes the instability problem at low computational cost. For this, a 1D-subgrid is used for the spatial discretization of the thin layer material. To overcome the additional time-step constraint posed by the reduction in the spatial cell size, a Crank-Nicolson time-integration scheme is used locally in the subgridded zone, and hybridized with the usual 3D Yee-FDTD method, which is used for the rest of the computational domain. Several numerical experiments demonstrating the accuracy of this approach are shown and discussed. Results comparing the proposed technique with classical alternatives based on impedance boundary condition approaches are also presented. The new technique is shown to have better accuracy at low frequencies, and late time stability than existing techniques with low computational cost

Efficient HIE-FDTD method for designing a dual-band anisotropic terahertz absorption structure

The finite-difference time-domain (FDTD) method is considered to be one of the most accurate and common methods for the simulation of optical devices. However, the conventional FDTD method is subject to the Courant-Friedrich-Levy condition, resulting in extremely low efficiency for calculating two-dimensional materials (2DMs). Recent researches on the hybrid implicit-explicit FDTD (HIE-FDTD) method show that the method can efficiently simulate homogeneous and isotropic 2DMs such as graphene sheet; however, it is inapplicable to the anisotropic medium. In this paper, we propose an in-plane anisotropic HIE-FDTD method to simulate optical devices containing graphene and black phosphorus (BP) sheets. Numerical analysis shows that the proposed method is accurate and efficient. With this method, we present a novel multi-layer graphene-BP-based dual-band anisotropic terahertz absorption structure (GBP-DATAS) and analyze its optical characteristics. Combining the advantages of graphene and BP localized surface plasmons, the GBP-DATAS demonstrates strong anisotropic plasmonic resonance and high absorption rate in the terahertz band. © 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.Natural Science BasicResearch Program of Shaanxi Province (2020JM-515); KeyResearch and Development Projects of Shaanxi Province (2018GY-151); Natural Science Foundation of Fujian Province (2020J01294)

An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques

This work focuses on efficient full-wave solutions of multiscale electromagnetic problems in the time domain. Three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the Finite-Difference Time-Domain (FDTD) method on a nonuniform, staggered, tensor product grid: Newmark, Crank-Nicolson (CN) and Alternating-Direction-Implicit (ADI) implicitization. All of them are applied in preferable directions, alike Hybrid Implicit-Explicit (HIE) methods, as to limit the rank of the sparse linear systems. Both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous, possibly lossy, isotropic media. Numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed, relaxed limit. Apart from the theoretical contributions, new accomplishments such as the development of the leapfrog Alternating-Direction-Hybrid-Implicit-Explicit (ADHIE) FDTD method and a less stringent Courant-like time step limit for the conventional, fully explicit FDTD method on a nonuniform grid, have immediate practical applications. (C) 2017 Elsevier Inc. All rights reserved

Viability of Numerical Full-Wave Techniques in Telecommunication Channel Modelling

In telecommunication channel modelling the wavelength is small compared to the physical features of interest, therefore deterministic ray tracing techniques provide solutions that are more efficient, faster and still within time constraints than current numerical full-wave techniques. Solving fundamental Maxwell's equations is at the core of computational electrodynamics and best suited for modelling electrical field interactions with physical objects where characteristic dimensions of a computing domain is on the order of a few wavelengths in size. However, extreme communication speeds, wireless access points closer to the user and smaller pico and femto cells will require increased accuracy in predicting and planning wireless signals, testing the accuracy limits of the ray tracing methods. The increased computing capabilities and the demand for better characterization of communication channels that span smaller geographical areas make numerical full-wave techniques attractive alternative even for larger problems. The paper surveys ways of overcoming excessive time requirements of numerical full-wave techniques while providing acceptable channel modelling accuracy for the smallest radio cells and possibly wider. We identify several research paths that could lead to improved channel modelling, including numerical algorithm adaptations for large-scale problems, alternative finite-difference approaches, such as meshless methods, and dedicated parallel hardware, possibly as a realization of a dataflow machine

Soft-lithographical fabrication of three-dimensional photonic crystals in the optical regime

This dissertation describes several projects to realize low-cost and high-quality three-dimensional (3D) microfabrication using non-photolithographic techniques for layer-by-layer photonic crystals. Low-cost, efficient 3D microfabrication is a demanding technique not only for 3D photonic crystals but also for all other scientific areas, since it may create new functionalities beyond the limit of planar structures. We have developed an advanced microtransfer molding technique, called two-polymer microtransfer molding (2P-[mu]TM) that shows an extremely high yield in layer-by-layer microfabrication sufficient to produce highly layered microstructures. The use of two different photo-curable prepolymers, a filler and an adhesive, allows for fabrication of layered microstructures without thin films between layers. Second, we also had to develop an alignment technique. We studied the 1st-order diffracted moiré fringes of transparent multilayered structures comprised of irregularly deformed periodic patterns. We demonstrate the alignment method for the case of layer-by-layer microstructures using soft lithography. The alignment method yields high contrast of fringes even when the materials being aligned have very weak contrasts. The imaging method of diffracted moiré fringes is a versatile visual tool for the microfabrication of transparent deformable microstructures in layer-by-layer fashion. Third, we developed several methods to convert a polymer template to dielectric or metallic structures, for instance, metallic infiltration using electrodeposition, metallic coating using sputter deposition, dielectric infiltration using titania nano-slurry, and dielectric coating using atomic layer deposition of Titania. By several different developed techniques, high quality photonic crystals have been successfully fabricated; however, I will focus on a line of techniques to reach metallic photonic crystals in this dissertation since they are completely characterized at this moment. In addition to the attempts for photonic crystal fabrication, our non-photolithographic technique is applied for other photonic applications such as small optical waveguides whose diameter is comparable to the wavelength of guided light. By 2P-[mu]TM, we achieve low cost, high yield, high fidelity, and tailorable fabrication of small waveguides. Embedded semiconductor quantum-dots and grating couplers are used for efficient internal and external light source, respectively