Electromagnetic Finite Difference Time Domain Research Articles

Using high-resolution microscopy data to generate realistic structures for electromagnetic FDTD simulations from complex biological models.

Finite-difference time-domain (FDTD) electromagnetic simulations are a computational method that has seen much success in the study of biological optics; however, such simulations are often hindered by the difficulty of faithfully replicating complex biological microstructures in the simulation space. Recently, we designed simulations to calculate the trajectory of electromagnetic light waves through realistically reconstructed retinal photoreceptors and found that cone photoreceptor mitochondria play a substantial role in shaping incoming light. In addition to vision research and ophthalmology, such simulations are broadly applicable to studies of the interaction of electromagnetic radiation with biological tissue. Here, we present our method for discretizing complex 3D models of cellular structures for use in FDTD simulations using MEEP, the MIT Electromagnetic Equation Propagation software, including subpixel smoothing at mesh boundaries. Such models can originate from experimental imaging or be constructed by hand. We also include sample code for use in MEEP. Implementation of this algorithm in new code requires understanding of 3D mathematics and may require several weeks of effort, whereas use of our sample code requires knowledge of MEEP and C++ and may take up to a few hours to prepare a model of interest for 3D FDTD simulation. In all cases, access to a facility supercomputer with parallel processing capabilities is recommended. This protocol offers a practical solution to a significant challenge in the field of computational electrodynamics and paves the way for future advancements in the study of light interaction with biological structures.

Near-field analysis of strong coupling between localized surface plasmons and excitons

We simulate the near-field effects of strong coupling between molecular excitons and localized surface plasmons, supported by aluminum nanodisks. The simulations are done using a simple model of a two-level system, implemented in a commercial electromagnetic finite-difference time-domain solver. While the Rabi splitting is present in the near-field, its spectral gap is seen to be smaller than the one obtained in the far-field, although it follows a clear square root dependence on the molecular density as expected. Moreover, the energy exchange between the plasmonic mode and the excitonic material is evident in 'beats' within the electromagnetic near-field, which are out of phase with respect to the exciton population. Our results explicitly demonstrate the collective nature of strong coupling, which is expressed by the synchronized population oscillations at the collective Rabi frequency set by the number of molecules interacting with the plasmonic mode. This analysis sheds light on strong coupling effects in the near-field region using a versatile model, which provides a powerful tool to study strong coupling, near-field effects, and light-matter interactions in general.

Collocated electrodynamic FDTD schemes using overlapping Yee grids and higher-order Hodge duals

The collocated Lebedev grid has previously been proposed as an alternative to the Yee grid for electromagnetic finite-difference time-domain (FDTD) simulations. While it performs better in anisotropic media, it performs poorly in isotropic media because it is equivalent to four overlapping, uncoupled Yee grids. We propose to couple the four Yee grids and fix the Lebedev method using discrete exterior calculus (DEC) with higher-order Hodge duals. We find that higher-order Hodge duals do improve the performance of the Lebedev grid, but they also improve the Yee grid by a similar amount. The effectiveness of coupling overlapping Yee grids with a higher-order Hodge dual is thus questionable. However, the theoretical foundations developed to derive these methods may be of interest in other problems.

Extreme optical chirality of plasmonic nanohole arrays due to chiral Fano resonance

We study the physical origin of extreme optical chirality of subwavelength arrays of chiral holes in metal. We reconstruct the nanoscale relief of the hole arrays by the atomic-force microscopy and post-process the data to acquire an average unit-cell shape clear of noise and defects. For this shape, we perform the electromagnetic finite difference time domain simulations that reproduce all important features observed by the light-transmission experiments, including the notably strong circular dichroism and optical activity covering the whole range of possible values. To interpret the simulation results, we develop a chiral coupled-mode model which yields analytical expressions that fit accurately the numerical data in a broad wavelength range. Our conclusions undoubtedly link the extreme optical chirality to the plasmon resonances of chiral holes and the associated chiral Fano-type transmission resonance.

High Temperature 2-D Millimeter-Wave Radiometry of Micro Grooved Nuclear Graphite

ABSTRACTA dual 137 GHz heterodyne radiometer system was used to study grooved nuclear grade graphite (SGL Group NBG17) inside an electric furnace from room temperature to 1250°C. The millimeter wave radiometer views were collinear with the electric field of one polarized parallel, and the other perpendicular, to the grooves. The anisotropic emissivity was readily detected for 100 μm wide grooves of various depths with a spacing period of 0.76 mm. The emissivity in the 500 – 1250°C temperature range was found to be 5.1 ± 0.5% when the E-field was parallel to the grooves and a factor of 2 – 4 higher, depending on groove depth, in the perpendicular direction. The parallel surface emissivity which was identical to ungrooved surface emissivity corresponded to a 137 GHz surface resistance of 5.3 Ohms, which is about 2.5 times higher than the value predicted from frequency scaling dc surface resistance. The perpendicular emissivity had a modulation with groove depth at odd integral multiples of ¼λ, predicted by electromagnetic finite difference time domain analysis.

Analysis of the Role of Lead Resistivity in Specific Absorption Rate for Deep Brain Stimulator Leads at 3T MRI

Magnetic resonance imaging (MRI) on patients with implanted deep brain stimulators (DBSs) can be hazardous because of the antenna-effect of leads exposed to the incident radio-frequency field. This study evaluated electromagnetic field and specific absorption rate (SAR) changes as a function of lead resistivity on an anatomically precise head model in a 3T system. The anatomical accuracy of our head model allowed for detailed modeling of the path of DBS leads between epidermis and the outer table. Our electromagnetic finite difference time domain (FDTD) analysis showed significant changes of 1 g and 10 g averaged SAR for the range of lead resistivity modeled, including highly conductive leads up to highly resistive leads. Antenna performance and whole-head SAR were sensitive to the presence of the DBS leads only within 10%, while changes of over one order of magnitude were observed for the peak 10 g averaged SAR, suggesting that local SAR values should be considered in DBS guidelines. With rho(lead) = rho(copper) , and the MRI coil driven to produce a whole-head SAR without leads of 3.2 W/kg, the 1 g averaged SAR was 1080 W/kg and the 10 g averaged SAR 120 W/kg at the tip of the DBS lead. Conversely, in the control case without leads, the 1 g and 10 g averaged SAR were 0.5 W/kg and 0.6 W/kg, respectively, in the same location. The SAR at the tip of lead was similar with electrically homogeneous and electrically heterogeneous models. Our results show that computational models can support the development of novel lead technology, properly balancing the requirements of SAR deposition at the tip of the lead and power dissipation of the system battery.

Radar Response of Firn Exposed to Seasonal Percolation, Validation Using Cores and FDTD Modeling

We use ground-penetrating radars (GPRs), firn cores, and electromagnetic finite-difference time-domain (FDTD) numerical modeling to characterize the GPR response to a frozen high-arctic firn pack. As a result of extensive summertime percolation, the firn pack comprises a high fraction of ice layers, lenses, and vertical glands. We show that the GPR response on the firn pack mainly depends on the following: (1) the thickness of the ice layers; (2) the distance between layers; (3) the layer roughness; and (4) the presence or absence of elliptical ice lenses. Using 3-D FDTD modeling, we show that the GPR is not sensitive to typical ice glands, which implies that the GPR underestimates firn heterogeneity, such that firn stratigraphy in percolation and wet-snow zones could be incorrectly interpreted as being better preserved than it actually is. We find that thin ice layers (< 0.05 m) or multiple thin ice layers give a strong response. Thicker ice layers typically give a weaker backscatter per unit area, mainly due to the lack of interference of the reflections from the upper and lower interfaces, but are, due to their continuity, easily trackable. Ice layers with a thickness comparable to the GPR wavelength give 180deg phase-shifted upper and lower reflections and are, in general, separated by a band of low GPR response, due to the lack of permittivity contrast within the ice layers. Despite the ice lenses' relatively short horizontal correlation length, as inferred from cores, bands of high-amplitude clutter caused by these features can be traced over several kilometers in GPR profiles.

Flux limiting embedded boundary technique for electromagnetic FDTD

A general approach for incorporating embedded boundaries into an electromagnetic finite difference time domain (FDTD) code is presented. This algorithm is shown to satisfy Gauss’s law and enforces no magnetic monopoles while maintaining a globally second-order result (first-order at physical boundaries), with no added time-step restriction. Theoretically predicted superior results are shown with an 11% time-step reduction from the Courant stability limit. This is achieved through a physics-based flux limiting scheme near physical boundaries. Stability, local truncation error and energy conservation analysis are also provided.

Modeling elves observed by FORMOSAT‐2 satellite

The ISUAL experiment on the FORMOSAT‐2 satellite has confirmed the existence of ionization and Lyman‐Birge‐Hopfield (LBH) band emissions in elves. In this paper, an in‐depth study of the ISUAL recorded elves was carried out. Numerical simulation results of elves based on an electromagnetic finite difference time domain (FDTD) model of the emissions between 185–800 nm and of their spatial‐temporal evolution are presented. To account for the effect of atmospheric attenuation, three major attenuation mechanisms: O2, O3, and molecular Rayleigh scattering are considered. Validations of the electromagnetic FDTD model were conducted in three ways: by comparing the calculated and observed photon fluxes in the ISUAL spectrophotometric channels, by directly comparing the simulated and observed morphologies of elves, and by comparing the computed photon counts of the ISUAL Imager based on the derived peak currents for two elve‐associated NLDN (National Lightning Detection Network) cloud‐to‐ground discharges (CGs) with those recorded by the ISUAL Imager. In all three ways, very good agreement was achieved.

Microwave Modeling and Validation in Food Thawing Applications

Developing temperature fields in frozen cheese sauce undergoing microwave heating were simulated and measured. Two scenarios were investigated: a centric and offset placement on the rotating turntable. Numerical modeling was performed using a dedicated electromagnetic Finite Difference Time Domain (FDTD) module that was two-way coupled to the PHYSICA multiphysics package. Two meshes were used: the food material and container were meshed for the heat transfer and the microwave oven cavity and waveguide were meshed for the microwave field. Power densities obtained on the structured FDTD mesh were mapped onto the unstructured finite volume method mesh for each time-step/turntable position. On heating for each specified time-step the temperature field was mapped back onto the FDTD mesh and the electromagnetic properties were updated accordingly. Changes in thermal/electric properties associated with the phase transition were fully accounted for as well as heat losses from product to cavity. Detailed comparisons were carried out for the centric and offset placements, comparing experimental temperature profiles during microwave thawing with those obtained by numerical simulation.

Characterization of small planar antennas for UWB mobile terminals

AbstractThis paper presents an extensive investigations to characterize antennas for small UWB mobile terminals. Two small planar UWB antennas (slot antenna and printed monopole antenna) were designed, using a full‐wave electromagnetic finite difference time domain (FDTD) method. The UWB slot antenna has a size of 32 × 29 mm, the monopole antenna size is 20 × 36.75 mm. Both antennas were characterized using true UWB parameters, such as antenna transfer functions, fidelity, and pulse energy spread. We have investigated angular‐dependence of antenna characteristics over the entire radiation sphere. Spatially averaged transfer functions were introduced to disclose antenna characteristics for different solid angles in the radiation sphere. We have also shown the difference in transient characteristics of antenna in transmitting (Tx) and receiving (Rx) mode. Finally, we have investigated the Tx/Rx antenna system, where any relative orientation between Tx and Rx antenna was assumed to be equally probable. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Mie scattering calculation by FDTD employing a modified Debye model for Gold material

The parameters calculation for the modified Debye model in the electromagnetic finite difference time domain (FDTD) method is discussed. Validation for the selected parameters is done comparing the FDTD results with the Mie analytical solutions of a gold nanometer sphere under an optical plane wave incidence. Good agreement with an average relative error 6.7% has been demonstrated as to total electrical field amplitudes on the surface of the gold sphere. It indicates FDTD could be adopted in the optical region for a material even with a negative real relative permittivity particularly as metals.

Modeling microwave and hybrid heating processes including heat radiation effects

This paper presents an efficient simulation tool for conventional, microwave, and combined heating. Two heat-transfer mechanisms are included: conductive and radiant heat transfer. The conductive heat transfer is modeled by a finite-difference algorithm. A modeling technique for radiant heat transfer in nonuniform grids has been developed and is here presented for the first time. For the radiant heat transfer a finite-difference scheme is not applicable, as radiation from a material surface; is not bounded to the immediate vicinity, as is conductive heat transfer. Therefore, ray optical methods are used. Rays connecting mutually visible surfaces are obtained by a new fast method. Necessary, but acceptable simplifications allow fast computations. The algorithms are integrated conveniently together with an electromagnetic finite-difference time-domain program to one simulation tool. Representative simulations are presented for an oven heated conventionally, by microwaves, and by a combination of both.

Three-Dimensional Finite-Difference Time-Domain Analysis of Optical Disk Storage System

A rigorous three-dimensional optical electromagnetic finite-difference time-domain (FDTD) modeling for the accurate analysis of an optical disk storage system is detailed. In this model, not only the complex material properties of typical optical storage systems, such as the magneto-optical (MO) disk and the phase-change optical disk, but also the complex aperiodic disk structure is considered. Moreover, the model enables us to consider the high-numerical-aperture optical storage system, which is a necessity in the consideration of the near-field optical recording. Numerical investigations of the optical ROM, the phase-change optical disk and the MO disk are presented as examples to demonstrate the utility of the model.