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Field–potential finite-difference time-domain (FiPo FDTD) technique for computational electromagnetics

Modeling light–matter interactions at the nanoscale requires accurate handling of coupled quantum and electromagnetic systems. This coupling requires information about the electric scalar potential Φ and the magnetic vector potential A, which are not typically calculated in standard computational electromagnetics implementations. To that end, we have developed a field–potential finite-difference time-domain (FiPo FDTD) algorithm, which solves a set of first-order equations for Φ and A alongside equations for the electric and magnetic fields E and H. The FiPo Basic code is essentially conventional FDTD, but with an added module that calculates the potentials. The FiPo Hybrid code self-consistently calculates both fields and potentials and is particularly suitable for coupling with quantum electronic transport solvers because it can be sourced by the potentials themselves. To terminate the domain and mimic infinite space, we have derived and implemented a convolutional perfectly matched layer (CPML) absorbing boundary condition for FiPo FDTD whose performance is on par with state-of-the-art CPMLs for standard FDTD. We present FiPo simulation results on several example systems.

Avazpour, L. [University of Wisconsin-Madison, WI ↗

Local Explosion Detection and Infrasound Localization by Reverse Time Migration Using 3-D Finite-Difference Wave Propagation

Infrasound data are routinely used to detect and locate volcanic and other explosions, using both arrays and single sensor networks. However, at local distances (< km) topography often complicates acoustic propagation, resulting in inaccurate acoustic travel times leading to biased source locations when assuming straight-line propagation. Here we present a new method, termed Reverse Time Migration-Finite-Difference Time Domain (RTM-FDTD), that integrates numerical modeling into the standard RTM back-projection process. Travel time information is computed across the entire potential source grid via FDTD modeling to incorporate the effects of topography. The waveforms are then back-projected and stacked at each grid point, with the stack maximum corresponding to the likely source. We apply our method to three volcanoes with different network configurations, source-receiver distances, and topography. At Yasur Volcano, Vanuatu, RTM-FDTD locates explosions within ~20 m of the source and differentiates between multiple vents. RTM-FDTD produces a more accurate location for the two Yasur subcraters than standard RTM and doubles the number of detected events. At Sakurajima Volcano, Japan, RTM-FDTD locates the source within 50 m of the active vent despite notable topographic blocking. The RTM-FDTD location is similar to that from the Time Reversal Mirror method, but is more computationally efficient. Lastly, at Shishaldin Volcano, Alaska, RTM and RTM-FDTD both produce realistic source locations (<50 m) for ground-coupled airwaves recorded on a four-station seismic network. We show that RTM is an effective method to detect and locate infrasonic sources across a variety of scenarios, and by integrating numerical modeling, RTM-FDTD produces more accurate source locations and increases the detection capability.

58 GEOSCIENCES↗

Finite-difference time-domain methods

The finite-difference time-domain (FDTD) method is a widespread numerical tool for full-wave analysis of electromagnetic fields in complex media and for detailed geometries. Applications of the FDTD method cover a range of time and spatial scales, extending from subatomic to galactic lengths and from classical to quantum physics. Technology areas that benefit from the FDTD method include biomedicine — bioimaging, biophotonics, bioelectronics and biosensors; geophysics — remote sensing, communications, space weather hazards and geolocation; metamaterials — sub-wavelength focusing lenses, electromagnetic cloaks and continuously scanning leaky-wave antennas; optics — diffractive optical elements, photonic bandgap structures, photonic crystal waveguides and ring-resonator devices; plasmonics — plasmonic waveguides and antennas; and quantum applications — quantum devices and quantum radar. This Primer summarizes the main features of the FDTD method, along with key extensions that enable accurate solutions to be obtained for different research questions. Additionally, hardware considerations are discussed, plus examples of how to extract magnitude and phase data, Brillouin diagrams and scattering parameters from the output of an FDTD model. Furthermore, the Primer ends with a discussion of ongoing challenges and opportunities to further enhance the FDTD method for current and future applications.

42 ENGINEERING↗

Topanga: A kinetic ion plasma code for large-scale ionospheric simulations on magnetohydrodynamic timescales

Topanga is a kinetic ion code developed for simulating large-scale plasma phenomena in the Earth's ionosphere on magnetohydrodynamic timescales. It is a domain-decomposed parallel code that runs on high-performance computing platforms. Features of Topanga include spherical geometry for simplified boundary conditions and computational efficiency; a hybrid plasma model with inertia-less fluid electrons, kinetic ions, and an electric field specified via an Ohm's law; a Maxwell-FDTD (finite difference time domain) plasma model which retains the displacement current in Maxwell's equations and models electron currents in the ionosphere with a tensor conductivity; sponge-layer boundary conditions for absorption of electromagnetic and plasma waves incident on the domain boundaries; and a novel mixed-implicit algorithm for evolving the EM fields inside the Maxwell-FDTD region that is stable over many orders of magnitude in the electron–ion collision frequency. We verify the numerical methods used in Topanga on a pair of test problems. The first test involves modeling a three-dimensional collisionless shock using the hybrid set of equations. The second test involves modeling a spherical TEM mode in vacuum using the Maxwell-FDTD set of equations. Finally, we demonstrate how using the combined set of hybrid and Maxwell-FDTD equations to model the Starfish Prime high-altitude nuclear test recovers a “missing” EM signal on the ground that is not present when using only the hybrid set of equations. The magnitude of this signal in the simulation containing the Maxwell-FDTD region agrees well with the E3a portion of the magnetohydrodynamic electromagnetic pulse from Starfish Prime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗

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↗

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↗

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↗

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↗

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)↗

Origin of high optical contrast in zinc-zinc oxide electrodeposits for dynamic windows

The control of solar light and heat emission through windows is an important strategy for increasing the energy efficiency of buildings. Reversible Zn electrodeposition has recently emerged as a promising method for constructing electronically tintable robust dynamic windows. In Zn electrodeposits formed from dimethyl sulfoxide (DMSO) electrolytes during device tinting, we observe extraordinary absorption that is in excess of what is predicted by the Beer-Lambert law for a uniform Zn thin film. Here, the charge required to electroplate these films is abnormally low, significantly less than previously reported dynamic windows based on reversible metal electrodeposition, which facilitates the construction of large-area devices that switch uniformly. Finite-difference time-domain (FDTD) simulations are used to investigate the origin of this enhanced absorption, which arises from plasmonic effects among the Zn nanoparticles and ZnO dendrites in the film. The dielectric ZnO dendrites promote absorption via slit-like Zn-dielectric-Zn structures that from hybrid surface plasmon resonance at metal walls. Through these investigations, we provide design principles to construct low-charge and high-contrast metal and metal oxide-based dynamic windows.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Plasmonic Core–Shell–Satellites with Abundant Electromagnetic Hotspots for Highly Sensitive and Reproducible SERS Detection

In this work, we develop a Ag@Al2O3@Ag plasmonic core–shell–satellite (PCSS) to achieve highly sensitive and reproducible surface-enhanced Raman spectroscopy (SERS) detection of probe molecules. To fabricate PCSS nanostructures, we employ a simple hierarchical dewetting process of Ag films coupled with an atomic layer deposition (ALD) method for the Al2O3 shell. Compared to bare Ag nanoparticles, several advantages of fabricating PCSS nanostructures are discovered, including high surface roughness, high density of nanogaps between Ag core and Ag satellites, and nanogaps between adjacent Ag satellites. Finite-difference time-domain (FDTD) simulations of the PCSS nanostructure confirm an enhancement in the electromagnetic field intensity (hotspots) in the nanogap between the Ag core and the satellite generated by the Al2O3 shell, due to the strong core–satellite plasmonic coupling. The as-prepared PCSS-based SERS substrate demonstrates an enhancement factor (EF) of 1.7 × 107 and relative standard deviation (RSD) of ~7%, endowing our SERS platform with highly sensitive and reproducible detection of R6G molecules. We think that this method provides a simple approach for the fabrication of PCSS by a solid-state technique and a basis for developing a highly SERS-active substrate for practical applications.

47 OTHER INSTRUMENTATION↗

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗

Investigation on the AgPt and AgPd hybrid alloy nanoparticles (HANPs) for the hybrid MoS 2 /ZnO/HANP UV photodetector application

We report hybrid photodetectors made of two or more nanomaterial components can offer the high potential for advanced photodetection applications with enhanced light absorption, improved efficiency and structural tunability. A hybrid UV photodetector (PD) configuration incorporating the plasmonic hybrid alloy nanoparticles (HANP), ZnO quantum dots (QDs) and MoS 2 nanoflakes, namely MoS2/ZnO/HANP PD, is demonstrated. The optimized MoS 2 /ZnO/HANP PD exhibits a high photocurrent of 5.66 mA at 0.34 mW/mm 2 under 385 nm illumination with two orders of improvement from the bare ZnO, which is one of the highest photocurrents by the ZnO-based PDs. It also demonstrates high figure-of-merits with the responsivity of 14,523 mA/W, detectivity of 8.13 x 10 11 jones, and external quantum efficiency (EQE) of 4,680 %, outperforming most of the ZnO-based hybrid architectures. The enhanced photoresponse is primarily attributed to the significantly enhanced hot electron generation by the AgPd HANPs and photocarrier collection through the ZnO QD layer. MoS 2 nanoflakes also provide additional photon absorption sites and boost the photo-carrier transfer process. HANPs are grown by adapting a dual-step solid-state dewetting process (SSD) approach and the superiority of AgPd HANPs is confirmed by systematic investigation, FDTD simulation and comparison of AgPt and AgPd HANPs.

MoS2↗

Investigating relationship between surface topography and emissivity of metallic additively manufactured parts

Due to the direct relationship between thermal history and mechanical behavior, in situ thermal monitoring is key in gauging quality of parts produced with additive manufacturing (AM). Accurate monitoring of temperatures in an AM process requires knowledge of environment and object parameters including object emissivity. The emissivity is dependent on several variables, including: wavelength, material composition, temperature, and surface topography. Researchers have been concerned with the thermal emissivity dependence on temperature since large ranges are seen in metal powder bed processes, but there is also an extensive range of surfaces produced by AM. This work focused on discovering what roughness characteristics control thermal emissivity through investigation of prototypic 316 stainless steel AM samples produced with a range of build conditions on a laser powder bed fusion machine. Through experimental measurements of emissivity using hemispherical directional reflectance (HDR), guided by simulations using a finite-difference time-domain (FDTD) Maxwell solver, it was found that combinations of existing roughness parameters describing both height and slope of the surface correlate well with emissivity changes. Furthermore, these parameters work well due to their apt description of surface features encouraging internal reflection, which is the phenomenon that increases emissivity when a surface falls under the geometric optical region conditions.

36 MATERIALS SCIENCE↗