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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

2004: Finite-Difference Time Domain Solution of Light Scattering by an Infinite Dielectric Column Immersed in an Absorbing Medium

The two-dimensional (2-D) finite-difference time domain (FDTD) method is applied to calculate light scattering and absorption by an arbitrarily shaped infinite column embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition (ABC) is used to truncate the computational domain. The single-scattering properties of the infinite column embedded in the absorbing medium, including scattering phase functions, extinction and absorption efficiencies, are derived using an area integration of the internal field. An exact solution for light scattering and absorption by a circular cylinder in an absorbing medium is used to examine the accuracy of the 2-D UPML FDTD code. With use of a cell size of 1/120 incident wavelength in the FDTD calculations, the errors in the extinction and absorption efficiencies and asymmetry factors from the 2-D UPML FDTD are generally smaller than approx .1%. The errors in the scattering phase functions are typically smaller than approx .4%. Using the 2-D UPML FDTD technique, light scattering and absorption by long noncircular columns embedded in absorbing media can be accurately solved.

Sun, W.↗
NASA NTRS2004

Examination of Surface Roughness on Light Scattering by Long Ice Columns by Use of a Two-Dimensional Finite-Difference Time-Domain Algorithm

Natural particles such as ice crystals in cirrus clouds generally are not pristine but have additional micro-roughness on their surfaces. A two-dimensional finite-difference time-domain (FDTD) program with a perfectly matched layer absorbing boundary condition is developed to calculate the effect of surface roughness on light scattering by long ice columns. When we use a spatial cell size of 1/120 incident wavelength for ice circular cylinders with size parameters of 6 and 24 at wavelengths of 0.55 and 10.8 mum, respectively, the errors in the FDTD results in the extinction, scattering, and absorption efficiencies are smaller than similar to 0.5%. The errors in the FDTD results in the asymmetry factor are smaller than similar to 0.05%. The errors in the FDTD results in the phase-matrix elements are smaller than similar to 5%. By adding a pseudorandom change as great as 10% of the radius of a cylinder, we calculate the scattering properties of randomly oriented rough-surfaced ice columns. We conclude that, although the effect of small surface roughness on light scattering is negligible, the scattering phase-matrix elements change significantly for particles with large surface roughness. The roughness on the particle surface can make the conventional phase function smooth. The most significant effect of the surface roughness is the decay of polarization of the scattered light.

Sun, W.↗
NASA NTRS2002

Finite-Difference Time Domain Solution of Light Scattering and Absorption by Particles in an Absorbing Medium

The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than similar to 2%. The errors in the scattering phase functions are typically less than similar to 5%. The errors in the asymmetry factors are less than similar to 0.l%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model.

Sun, W.↗
NASA NTRS1987

A finite difference-time domain technique for modeling narrow apertures in conducting scatterers

The finite difference-time domain (FDTD) technique has proven to be a valuable tool for the calculation of the transient and steady state scattering characteristics of relatively complex scatterer and source configurations. In spite of its usefulness, it exhibits serious deficiencies when used to analyze geometries that contain fine detail. An FDTD technique is described that utilizes Babinet's principle to decouple the regions on both sides of the aperture. The result is an FDTD technique that is capable of modeling apertures that are much smaller than the spatial grid used in the analysis and yet is not perturbed by numerical noise when used in the 'scattered field' mode. Numerical results are presented that show the field penetration through cavity-backed apertures that are much smaller than the spatial grid used during the solution.

Demarest, Kenneth R.↗
NASA NTRS1991

Finite difference time domain calculations of antenna mutual coupling

The Finite Difference Time Domain (FDTD) technique has been applied to a wide variety of electromagnetic analysis problems, including shielding and scattering. However, the method has not been extensively applied to antennas. In this short paper calculations of self and mutual admittances between wire antennas are made using FDTD and compared with results obtained using the Method of Moments. The agreement is quite good, indicating the possibilities for FDTD application to antenna impedance and coupling.

Luebbers, Raymond J.↗
NASA NTRS1991

Finite difference time domain calculations of antenna mutual coupling

The Finite Difference Time Domain (FDTD) technique was applied to a wide variety of electromagnetic analysis problems, including shielding and scattering. However, the method has not been exclusively applied to antennas. Here, calculations of self and mutual admittances between wire antennas are made using FDTD and compared with results obtained during the method of moments. The agreement is quite good, indicating the possibilities for FDTD application to antenna impedance and coupling.

Luebbers, Raymond J.↗
NASA NTRS1991

Finite difference time domain calculation of transients in antennas with nonlinear loads

Determining transient electromagnetic fields in antennas with nonlinear loads is a challenging problem. Typical methods used involve calculating frequency domain parameters at a large number of different frequencies, then applying Fourier transform methods plus nonlinear equation solution techniques. If the antenna is simple enough so that the open circuit time domain voltage can be determined independently of the effects of the nonlinear load on the antennas current, time stepping methods can be applied in a straightforward way. Here, transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain (FDTD) methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case, the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets, including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Luebbers, Raymond J.↗
NASA NTRS1993

Numerical modeling for an electric-field hyperthermia applicator

Hyperthermia, in conjunction with radiation and chemotherapy for treatment of cancers, is an area of current concern. Experiments have shown that hyperthermia can increase the potency of many chemotherapy drugs and the effectiveness of radiation for treating cancer. A combination of whole body or regional hyperthermia with chemotherapy or radiation should improve treatment results. Conventional methods for inducing whole body hyperthermia, such as exposing a patient in a radiant cabinet or under a hot water blanket, conduct heat very slowly from the skin to the body core. Thus a more efficient system, such as the three-plate electric-field hyperthermia applicator (EHA), is developed. This three-plate EHA has one top plate over and two lower plates beneath the patient. It is driven at 27.12 MHz with 500 Watts through a matching circuit. Using this applicator, a 50 kg pig was successfully heated to 42 C within 45 minutes. However, phantom and animal studies have indicated non-uniform heating near the side of the body. In addition, changes in the size and distance between the electrode plates can affect the heating (or electromagnetic field) pattern. Therefore, numerical models using the method of moments (MOM) or the finite difference time domain (FDTD) technique are developed to optimize the heating pattern of this EHA before it is used for human trials. The accuracy of the numerical modeling has been achieved by the good agreement between the MOM and FDTD results for the three-plate EHA without a biological body. The versatile FDTD technique is then applied to optimize the EHA design with a human body. Both the numerical and measured data in phantom blocks will be presented. The results of this study will be used to design an optimized system for whole body or regional hyperthermia.

Wu, Te-Kao↗
NASA NTRS2000

Radiative Properties of Cirrus Clouds in the Infrared (8-13 microns) Spectral Region

Atmospheric radiation in the infrared (IR) 8-13 microns spectral region contains a wealth of information that is very useful for the retrieval of ice cloud properties from aircraft or space-borne measurements. To provide the scattering and absorption properties of nonspherical ice crystals that are fundamental to the IR retrieval implementation, we use the finite-difference time domain (FDTD) method to solve for the extinction efficiency, single-scattering albedo, and the asymmetry parameter of the phase function for ice crystals smaller than 40 microns. For particles larger than this size, the improved geometric optics method (IGOM) can be employed to calculate the asymmetry parameter with an acceptable accuracy, provided that we properly account for the inhomogeneity of the refracted wave due to strong absorption inside the ice particle. A combination of the results computed from the two methods provides the asymmetry parameter for the entire practical range of particle sizes between 1 micron and 10000 microns over wavelengths ranging from 8 microns to 13 microns. For the extinction and absorption efficiency calculations, several methods including the IGOM, Mie solution for equivalent spheres (MSFES), and the anomalous diffraction theory (ADT) can lead to a substantial discontinuity in comparison with the FDTD solutions for particle sizes on the order of 40 microns. To overcome this difficulty, we have developed a novel approach called the stretched scattering potential method (SSPM). For the IR 8-13 microns spectral region, we show that SSPM is a more accurate approximation than ADT, MSFES, and IGOM. The SSPM solution can be further refined numerically. Through a combination of the FDTD and SSPM, we have computed the extinction and absorption efficiency for hexagonal ice crystals with sizes ranging from 1 to 10000 microns at 12 wavelengths between 8 and 13 microns Calculations of the cirrus bulk scattering and absorption properties are performed for 30 size distributions obtained from various field campaigns for midlatitude and tropical cirrus cloud systems. Parameterization of these bulk scattering properties is carried out by using second-order polynomial functions for the extinction efficiency and the single-scattering albedo and the power law expression for the asymmetry parameter. We note that the volume-normalized extinction coefficient can be separated into two parts: one is inversely proportional to effective size and is independent of wavelength, and the other is the wavelength-dependent effective extinction efficiency. Unlike conventional parameterization efforts, the present parameterization scheme is more accurate because only the latter part of the volume-normalized extinction coefficient is approximated in terms of an analytical expression. After averaging over size distribution, the single-scattering albedo is shown to decrease with an increase in effective size for wavelengths shorter than 10.0 microns whereas the opposite behavior is observed for longer wavelengths. The variation of the asymmetry parameter as a function of effective size is substantial when the effective size is smaller than 50 microns. For effective sizes larger than 100 microns, the asymmetry parameter approaches its asymptotic value. The results derived in this study can be useful to remote sensing applications involving IR window bands under cirrus cloud conditions.

Yang, Ping↗
NASA NTRS2001

Retrieval of Polar Stratospheric Cloud Microphysical Properties From Lidar Measurements: Dependence on Particle Shape Assumptions

Knowledge of particle sizes and number densities of polar stratospheric clouds (PSCs) is highly important, because they are critical parameters for the modeling of the ozone chemistry of the stratosphere. In situ measurements of PSC particles are rare. the main instrument for the accumulation of PSC data are lidar systems. Therefore the derivation of some microphysical properties of PSCS from the optical parameters measured by lidars would be highly beneficial for ozone research. Inversion of lidar data obtained in the presence of PSCs formed from crystalline particles type 11 and the various nitric acid tri Ydrrate (NAT) types cannot be easily accomplished, because a suitable scattering theory for small faceted crystals has not been readily available tip to now. As a consequence, the T-matrix method is commonly used for the interpretation of these PSC lidar data. Here the assumption is made that the optical properties of an ensemble of spheroids resemble those of crystalline PSCs, and microphysical properties of the PSC are inferred from the optical signatures of the PSC at two or more wavelengths. The problem with the T-matrix approach is that the assumption of spheroidal instead of faceted particles can lead to dramatically wrong results: Usually cloud particle properties are deduced from analysis of lidar profiles of backscatter ratio and depolarization ratio. The particle contribution to the backscatter ratio is given by the product of the particle number density and the backscattering cross section. The latter is proportional to the value of the particle's scattering phase function at 180 degrees scattering angle. At 180 degrees however, the phase functions of rough, faceted crystals and of spheroids with same maximum dimension differ by a factor of 6. From this it follows that for a PSC consisting of faceted crystals, the particle number density is underestimated by roughly the same factor if spheroidal particles are unrealistically assumed. We are currently developing a retrieval technique for determining the microphysical parameters of crystalline PSCs that takes into account the faceted shape of the PSC particles. This approach utilizes finite-difference time-domain (FDTD) calculations of particle optical properties. The accuracy and the free choice of the shape of the scattering particle make the FDTD technique a promising tool for the inversion of PSC lidar data. A first comparison of FDTD and T-matrix calculations will be presented.

Reichardt, Susanne↗
DOE OSTI2025

Decoupling Carrier Dynamics and Energy Transport in Ultrafast Near-Field Nanoscopy

Ultrafast near-field optical nanoscopy has emerged as a powerful platform to characterize low-dimensional materials. While analytical and numerical models have been established to account for photoexcited carrier dynamics, quantitative evaluation of the associated pulsed laser heating remains elusive. Here, we decouple the photocarrier density and temperature increase in near-field nanoscopy by integrating the two-temperature model (TTM) with finite-difference time-domain (FDTD) simulations. These results reveal that the electron–phonon coupling in a silicon film after femtosecond laser excitation is most pronounced within approximately 3 ps–substantially shorter than the photocarrier decay time scale at tens of picoseconds. Moreover, the coupled TTM-FDTD method indicates that ultrafast laser heating can cause up to a 14% variation in the near-field signal at a 220 μJ/cm 2 pump pulse fluence. Our numerical results are further validated by transient experiments, highlighting the potential of this method for investigations of carrier and thermal phenomena in emerging nanomaterials and nanodevices.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials

In this report we compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a dimensionless parameter. We begin with the simple and widely used finite difference time domain (FDTD) methods, and establish rigorous error bounds of them, which are valid up to the time at $O(1/\varepsilon)$. In the error estimates, we pay particular attention to how the errors depend explicitly on the mesh size $h$ and time step $\tau$ as well as the small parameter $\varepsilon$. Based on the results, in order to obtain "correct" numerical solutions up to the time at $O(1/\varepsilon)$, the $\varepsilon$-scalability (or meshing strategy requirement) of the FDTD methods should be taken as $h = O(\varepsilon^{1/2})$ and $\tau = O(\varepsilon^{1/2})$. To improve the spatial resolution capacity, we apply the Fourier spectral method to discretize the Dirac equation in space. Error bounds of the resulting finite difference Fourier pseudospectral (FDFP) methods show that they exhibit uniform spatial errors in the long-time regime, which are optimal in space as suggested by the Shannon's sampling theorem. Extensive numerical results are reported to confirm the error bounds and demonstrate that they are sharp.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Formation and optical properties of indium nanoparticle arrays for deep-UV plasmonics

We utilize a combined computational-experimental approach to examine the influence of indium nanoparticle (NP) array distributions on deep-ultraviolet (UV) plasmon resonances. For photon energies < 5.7 eV, analysis of ellipsometric spectra reveals an increase in silicon reflectance induced by indium NP arrays on silicon. For various energies in the range 5.7–7.0 eV, a decrease in reflectance is induced by the NP arrays. Similar trends in reflectance are predicted from finite-difference time-domain (FDTD) simulations using NP size distributions extracted from atomic-force micrographs as input. In addition, in the energy range of 7.4–9.2 eV, the FDTD simulations reveal reflectance minima, characteristic of localized surface plasmon resonances. Here, electron energy-loss spectroscopy collected from individual indium NPs reveals the presence of LSPR at ≈ 8 eV, further supporting the promise of indium NP arrays on silicon for deep-UV plasmonics.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Finite-frequency modeling of regional tropospheric infrasound using realistic atmospheres and terrain

Infrasonic waves have been observed to propagate to regional (greater than 15 km) distances through the troposphere. Infrasound propagation in the geometric acoustics approximation has shown that realistic terrain can scatter acoustic energy from tropospheric ducts; however, ray methods cannot intrinsically capture finite-frequency behavior such as diffraction. A two-dimensional finite-difference time-domain (FDTD) method has been developed to solve linearized equations for infrasound propagation with realistic terrain. Acoustic wave propagation over 100 km with both flat terrain and a Gaussian hill was first simulated in order to compare finite-frequency propagation with ray predictions. The effects of realistic terrain and atmospheres on infrasound signals from a 2012 surface explosion at the Utah Testing and Training Range are then investigated. Propagation through the troposphere is suggested by array processing results, but eigenrays are not predicted due to weak to nonexistent ducting conditions. FDTD modeling suggests that the inclusion of terrain and finite frequency effects helps explain much of the observed signal in a realistic scenario. Furthermore, these results suggest that geometric acoustics may underestimate propagation through the troposphere, and that recorded waveforms at regional distances may be noticeably affected by terrain.

58 GEOSCIENCES↗
DOE OSTI2024

Modeling aerosol transmission spectra from n(λ) and k(λ) infrared optical constants measurements of organic liquids and solids

The effects of light scattering and refraction play significantly different roles for aerosols than for bulk materials, making it challenging to identify aerosolized chemicals using traditional spectral methods or spectral reference libraries. Due to a potentially infinite number of particle morphologies, sizes, and compositions, constructing a database of laboratory-measured aerosol spectra is not a practical solution. Here, as an alternative approach, the measured n / k optical vectors of two example organic materials (diethyl phthalate and D-mannitol) are used in combination with particle absorption / scattering theory (Mie theory and FDTD) and the Beer-Lambert law to generate a series of synthetic infrared transmission / scattered light spectra. The synthetic spectra show significant differences versus simple slab transmission spectra, even for small changes in particle size (e.g., 5 vs. 10 µm) for both single particles and ensembles, potentially serving as useful reference data for aerosol sensing. For spherical single particles with diameters of 1 to 10 µm, FDTD simulations predict changes in the magnitudes of spectral shifts and the shapes of the peaks vs. particle size with only small deviations from Mie theory predictions, yet reliably capture the direction of the shifts. Typical spectral peak shifts in the longwave infrared correspond to Δλ ∼0.20 µm (∼34 cm -1 ) when compared to corresponding slab transmission spectra. Additionally, synthetic spectra generated from the n / k values derived using two different methods (KBr pellet transmission and single-angle reflectance) are compared using the Mie theory model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Influence of defects on the femtosecond laser damage resistance of multilayer dielectric gratings

Multilayer dielectric (MLD) gratings with high diffraction efficiency and a high laser-induced damage (LID) threshold for pulse compressors are key to scaling the peak and average power of chirped pulse amplification lasers. However, surface defects introduced by manufacturing, storage, and handling processes can reduce the LID resistance of MLD gratings and impact the laser output. The underlying mechanisms of such defect-initiated LID remain unclear, especially in the femtosecond regime. In this Letter, we model dynamic processes in interactions of a 20-fs near-infrared (NIR) laser pulse and a MLD grating design in the presence of cylindrically symmetrical nodules and particle contaminants and cracks at the surface. Utilizing a dynamic model based on a 2D finite difference in time domain (FDTD) field solver coupled with photoionization, electron collision, and refractive index modification, we study the simulation results for the damage site distribution initiated by defects of various types and sizes and its impact on the LID threshold of the grating design.

Zhang, Simin (ORCID:0000000174948230)↗
NASA NTRS1987

The electromagnetic modeling of thin apertures using the finite-difference time-domain technique

A technique which computes transient electromagnetic responses of narrow apertures in complex conducting scatterers was implemented as an extension of previously developed Finite-Difference Time-Domain (FDTD) computer codes. Although these apertures are narrow with respect to the wavelengths contained within the power spectrum of excitation, this technique does not require significantly more computer resources to attain the increased resolution at the apertures. In the report, an analytical technique which utilizes Babinet's principle to model the apertures is developed, and an FDTD computer code which utilizes this technique is described.

Demarest, Kenneth R.↗
NASA NTRS1991

Conical cut radar cross section calculations for a thin, perfectly conducting plate

Radar Cross Section (RCS) calculations for flat, perfectly conducting plates are readily available through the use of conventional frequency domain techniques such as the Method of Moments. However, if time domain scattering or wideband frequency domain results are desired, then the Finite Difference Time Domain (FDTD) technique is a suitable choice. In this paper, we present the application of the Finite Difference Time Domain (FDTD) technique to the problem of electromagnetic scattering and RCS calculations from a thin, perfectly conducting plate for a conical cut in the scattering angle phi. RCS calculations versus angle phi will be presented and discussed.

Luebbers, Raymond J.↗