Finite-difference Time-domain Results Research Articles

Boosting biodiesel production over silicon heterojunction with visible light irradiation

Renewable energy sources offer greater reliability and resilience compared to traditional sources. Biodiesel, derived from renewable resources that absorb carbon dioxide during growth and production, boasts a significantly lower carbon footprint than petroleum-based diesel fuel. Heterojunction photocatalysts have emerged as a promising solution for environmental challenges. This study focused on efficient biodiesel production using visible light-irradiated Si/MgO heterojunctions. The XPS analysis confirmed the crucial role of surface functionality in achieving high photocatalytic efficiency. Transesterification occurs through SiH and SiOH bond formation on the catalyst. Finite-difference time-domain (FDTD) predicts the structure–activity relationship, showing stronger plasmonic nearfields in Si/MgO due to distinct dielectric constants. The Si/MgO photocatalyst exhibited superior photocatalytic activity under visible light, consistent with FDTD results. Biodiesel production was attained to 96% yield using 2 wt% catalysts, a 12:1 M ratio of methanol to Jatropha curcas oil, and a 3.5 hrs reaction time. Therefore, the work provided valuable insights into the mechanism of efficient plasmonic photocatalysis, paving the way for future advancements in novel high-performance photocatalysts.

Penentuan Density Matrix Sistem Kuantum Satu Partikel Dimensi Satu dengan Metode Discretized Path Integral (DPI)

A mixed quantum system can be represented by a density matrix. By knowing the density matrix of the system, other thermodynamic properties of the system such as Helmholtz free energy and entropy can be determined. Computation of the density matrix of a one-dimensional single-particle quantum system using the discretized path integral(DPI) method is presented. The results of the DPI method were validated using the finite difference time domain (FDTD) method for a particle in an infinite square well and harmonic oscillator potentials. The results of density matrix, Helmholtz’s free energy and entropy have shown that the DPI method produces correct numerical values compared to the FDTD results. Then, the DPI method is used in the double-well potential by giving variations in barrier potential and temperature of the system. The results show that the particle will be tunneling when the barrier potential energy is more than the kinetic energy of the particle. The particle also can tunnel easily if the system has the higher temperature.

Consistent FDTD Modeling of Dispersive Dielectric Media via Multiple Debye Terms Derived Rigorously by Padé Approximants

An finite-difference time-domain (FDTD) scheme for simulating wave propagation inside Cole-Cole (CC), Havriliak-Negami (HN), or Raicu (R) dispersive media is proposed. The main difficulty in FDTD implementations for such media is the fact that the time-domain polarization relations are fractional integro-differential equations. To circumvent this difficulty, the dispersive susceptibility of the medium is modeled by Padé approximants. It is proven that under certain conditions the Padé approximant is equal to a weighted sum of Debye terms, while the physical restrictions for positive weights and relaxation times are fulfilled with certainty. Hence, a set of first-order auxiliary differential equations (ADEs), which approximate the original fractional polarization relation, is derived and directly embedded in the FDTD scheme. In contrast to previous works, the derivation of the Debye expansion of the original dispersive permittivity is carried out in a straightforward manner without involving nonlinear optimization techniques. Comparisons between analytical and FDTD results of the reflection and transmission coefficients as well as of the transfer functions inside the dispersive media illustrate the efficiency of the proposed scheme, over wideband frequency domains.

Modeling of surface roughness in deeply etched photonic MEMS mirrors and filters

We study the impact of the surface roughness on the response of deeply etched silicon Bragg mirrors and resonators. The transfer matrix method is extended to account for the roughness in multilayered systems. The model is first verified numerically using the finite difference time domain (FDTD) method for surface roughness values up to 80 nm at a wavelength of 1550 nm. The response of the mirrors and filters having an RMS roughness of 30 nm is calculated by the developed model and compared with the numerical results of the FDTD results, and it shows a good agreement. Then the model results are compared with the experimental data of a Bragg mirror and filter, fabricated by the deep reactive ion etching Bosch process of silicon on an insulator wafer; they show a very good agreement in the insertion loss and 3-dB bandwidth due to the roughness model. Finally, the transmission, 3-dB bandwidth and quality factor of the optical filters based on single, double, and triple silicon layer mirrors are examined using the model and accounting for Gaussian beam excitation. The presented model can be used to guide the requirements on the fabrication quality of optical surfaces and the choice of the optimum number of layers.

A Finite-Difference Time-Domain Formulation for Modeling Air Ionization Breakdown Streamers

A numerical model based on the finite-difference time-domain (FDTD) method is developed for calculating discharge currents and fields produced due air ionization between two electrodes. Electric conductivity σ of the ionized channel between two electrodes is calculated using non-linear equations, i.e., σ is obtained using functions of time. The functions for calculating σ are adapted and proposed in this work for each stage of the plasma formation and disrupting processes. The proposed numerical model is validated by making comparisons among the obtained FDTD results and experimental data published in literature. In order to perform the validation procedures, an experimental setup from literature is numerically reproduced using the proposed FDTD methodology.

An Adaptive and Highly Accurate FDTD Mesh Generation Technique for Objects with Complex Edge Structures

In this paper, a triangular facets based, highly accurate, and adaptive finite-difference time-domain (FDTD) mesh generation technique is presented. There are two innovations in the implementation of this technique. One is adaptive mesh lines placement method. The mesh lines are automatically set to be dense where the object has fine structure and sparse where the object has rough structure based on the incremental placement of the triangular mesh vertices. The other is ray column tracing method. Ray columns in the normal direction of the coordinate plane are employed to intersect the surface facets to make the mesh generation results highly accurate. The generating FDTD results of the numerical examples show that the proposed technique can well-restore objects with complex edge structures. The simulation results are in good agreement with the theoretical results.

FDTD simulation of Ag-decorated ZnO nanorods for optimization of 3D SERS substrates

Surface enhanced Raman spectroscopy (SERS) is becoming an effective method of detecting organic molecules, and three-dimensional (3D) SERS substrates are promising in practical applications. To optimizing 3D SERS substrates, the extinction spectra and local electromagnetic fields of Ag-decorated ZnO nanorods (Ag-ZnO-NR) were studied by a finite-difference time-domain (FDTD) method. The diploe local surface plasmonic resonance (LSPR) was found to split into high- and low-frequency two branches, in which the low-frequency mode is predominant in contributing to the Raman enhancement, while the ZnO-NR radius and Ag-layer thickness play important roles in tuning the LSPR frequencies. Both of high- and low-frequency LSPRs were enhanced with the increase in the Ag-ZnO-NR length while the intensity of local electromagnetic field depends on the Ag-ZnO-NR density. The FDTD results were discussed with a comparison to the experimental data obtained from flower-like Ag-ZnO-NR 3D SERS substrates. In addition, the extinction spectra of Ag nanotube and Ag-decorated TiO2 and SiO2 nanorods were calculated and the refractive index of dielectric materials was found to be capable of tuning the LSPR of 3D SERS substrates as well. The principle revealed in this work is helpful for design and optimization of 3D SERS substrates.

Plasmonic all-optical metal–insulator–metal switches based on silver nano-rods, comprehensive theoretical analysis and design guidelines

In this paper, all-optical plasmonic switches are proposed and analyzed. These structures consist of a rectangular resonator filled with a Kerr-type material (AuSiO2) which is coupled to isolated metal–insulator–metal plasmonic waveguides. The resonators contain periodic arrays of nano-rods with rectangular and triangular patterns. The horizontal and vertical waveguides are used for data and control signals, respectively. Using two separate paths for the data and control signals results in suitable isolation between the signals. The finite difference time domain (FDTD) method is used for numerical investigation of the designed structures. To provide more insight, the FDTD results of the building blocks of the switches are compared with transmission line method results. The most important benefits of the proposed topologies are requiring lower pump intensities, needing smaller footprints and having isolated data and control ports. The proposed switch needs a pump intensity equal to 193.2 mW/μm2 and requires a 0.593 μm2 footprint area. A 11.3 dB contrast ratio exists between the On and Off states of the switch. Based on the mentioned advantages, these switches have the potential to be used in complex integrated optical circuits.

A Drude-Two-CP-FDTD method for Drude-critical points model of metal nanofilms

Based on Drude-critical points (Drude-Two-CP) model for a dispersive media, a finite-difference time-domain (FDTD) method for metal nanofilms is proposed. By establishing the corresponding relationship between Drude-Two-CP model and Drude–Lorentz model, the conversion coefficients between the two models are calculated. And we modify the Drude-Two-CP model into the form of standard Lorentz model. The transformation relationship between the two models is conducive to the modular programming of FDTD. Formula deduction and calculation results show that Drude-Two-CP model has higher fitting accuracy and fitting formulas are more complex. Using the proposed FDTD method, we have calculated the reflection, transmission and extinction coefficients of gold and aluminium nanofilms. The results show that the FDTD results are in good agreement with those of Drude-Two-CP model, which are better than those of Drude–Lorentz model. Therefore, the Drude-Two-CP-FDTD method proposed in this paper is helpful for improving the accurate modelling and calculation of nano-optical structures.

Realization of a plasmonic optical switch using improved nano-disk resonators with Kerr-type nonlinearity: A theoretical and numerical study on challenges and solutions

In this paper, a novel all-optical plasmonic switch is presented. For the proposed structure, a nano-disk resonator coupled to parenthesis-shaped adjunctions and perpendicular metal–insulator–metal waveguides are used. The insulator which is used here, is an optically nonlinear Kerr-type material (InGaAsP). The data and control pulses are injected to the horizontal and vertical waveguides, respectively. Allocating two separate waveguides for the data and control signals prevents these signals from interfering with each other. One of the main benefits of the proposed switch is that a single wavelength can be used for the data and control signals. It prevents the amplitude modulation of the output signal and eliminates the need for harmonic suppression filters. The finite difference time domain (FDTD) method is used for numerical investigation of the switch. Based on the numerical simulations, the switch can operate for control pulses as narrow as 3 ps at 1028 nm. In addition to FDTD, analytical formulas have also been presented to model the switch, which are in excellent agreement with FDTD results. To provide a better perspective, besides the conventional frequency domain analysis, the time domain simulations are also presented. The main advantages of the proposed topology are: the ability to use an identical wavelength for data and control pulses (which originates from the novel resonator shape), having separate and isolated input and output data and control ports, requiring a small footprint area of 1.37μm2, the simplicity of fabrication due to its simple and symmetric structure and finally the robustness of the design, where other nonlinear materials with higher Kerr indices can also be easily used to redesign the switch.

Fabrication of large-scale freestanding THz wire grid polarizers by femtosecond laser micromachining

High-performance THz polarizers, as a quasi-optical device to manipulate THz waves, are highly demanded for THz spectroscopy and imaging applications. In this work, we have employed the femtosecond laser micro-machining technique to fabricate freestanding THz wire grid polarizers with two kinds of reinforced line structures which weaken the effects of gravity sagging and entanglement of long free wires, thus enabling large-scale processing. The effect of the reinforced lines on the polarizers were simulated by the Finite-Difference Time-Domain (FDTD) method, and the performances of the polarizer were characterized by THz time-domain spectroscopy and compared with that of a commercial wire gird polarizer. The calculated transmittance is in good agreement with the FDTD results. The degree of polarization and the extinction ratio of the polarizer with discontinuous reinforced lines are better than those of a commercial wire grid polarizer.

Lightning Surge Analysis of a Transmission Line Tower With an XLPE Power Cable and Metallic Cleats Using the FDTD Method

A direct lightning strike to a transmission line tower may cause overvoltages and insulation failures, and to avoid unexpected insulation failures and protect power equipment, it is necessary to install effective lightning protection measures. To design effective countermeasures, the prediction of lightning surge phenomena is required. The finite-difference time-domain (FDTD) method, one of the full-wave numerical approaches, which do not require the assumption of the transversal electromagnetic mode, has been an effective tool for predicting electromagnetic transient phenomena in 3-D structures, such as transmission line towers. In this article, using a technique for representing coaxial cables in the FDTD method, we simulate a reduced-scale model of a transmission line tower with a power cable, calculate the surge phenomena in the tower model when a surge current is injected into the top of the tower, and compare the FDTD results with the measured results for validation. Furthermore, we propose a technique for simulating the influence of using metallic cleats to fix a power cable to a transmission line tower for FDTD simulations in a 3-D arrangement, and we calculate surge phenomena in practical cross-linked polyethylene power cables placed over a ground plane and installed in a real-scale 77 kV transmission line tower. The FDTD results are validated through the comparison with measured results obtained in a previous study.

Earth Current and GPR Distributions Due to Lightning and Effect of a Distribution Line

This article investigates the transient characteristics of earth currents and grounding potential rises (GPRs) produced by lightning strikes directly to the earth and to a vertical conductor with a grounding electrode. Influences of the earth depth and the distance from the lightning channel are discussed based on a field test and finite-difference time-domain (FDTD) computed results. The validity of the FDTD is confirmed in comparison with the field test results. Based on the FDTD results, a large portion of the lightning current is observed to flow along the earth surface during a transient period. The current density is roughly proportional to 1/ r 2 ( r : distance from the lightning base) for the lightning to the earth surface, and 1/ Lr for the lightning to a vertical conductor with a grounding electrode of length L . The GPR shows similar characteristics. Electromagnetic field radiated from the lightning to the earth contributes to the peak of the earth-surface current, and it becomes dominant when r is larger than 10 m. The pole grounding of a distribution line nearby the lightning absorbs a portion of the lightning current and, thus, the current density becomes larger toward the distribution pole.

Design and analysis of thin optical lens composed of low-index subwavelength structures.

We design a polarization-insensitive subwavelength optical lens capable of focusing plane waves of visible wavelength using traditional optical materials such as glass. Using analytical effective medium theory and finite difference time domain (FDTD) method, the phase of transmission of arrayed subwavelength inclusions is studied with respect to their size and shape. It is shown that the phase relations can be accurately predicted using an analytical method, simplifying the design process. A guideline is established for selecting a set of subwavelength inclusions so that complete phase coverage can be achieved. Analytical calculation of focal length using diffraction equations (Fresnel or Rayleigh-Sommerfeld) along with effective medium approximation is done and compared with FDTD and experimental results, showing high accuracy. Large-scale optical lenses with subwavelength thickness are designed and their performance analyzed using an analytical approach. The optical lenses show high focusing efficiency at small numerical apertures, insensitivity to polarization angle, and robustness to uncertainty in their structural parameters. This work shows that using an analytical method, thin optical lenses with subwavelength structure can be designed and studied.

FDTD Analysis of Nearby Lightning Surges Flowing Into a Distribution Line via Groundings

This paper investigates lightning surges on a distribution line reported using a finite-difference time-domain (FDTD) method. FDTD simulation results show a satisfactory agreement with measured lightning currents when lightning strikes ground nearby a distribution line. The current and voltage characteristics along the line, which were not measured in the test, are calculated by the FDTD simulation. Parametric analysis shows that lightning currents and voltages are dependent on the lightning position, distance from the lightning to the nearest pole, and pole grounding resistance. A large portion of phase-wire voltage is induced by the lightning channel current, and correspondingly, a large portion of phase-wire current is produced by the induced voltage. When the lightning channel is inclined, the peak current and voltage vary by +10% to -10% depending on the inclined angle. The effect of neutral wire position in the line is also investigated, and the induced voltage at the nearest pole to the lightning can be effectively suppressed by installing two neutral wires above and under the phase wires. EMTP simulation results agree qualitatively well with the measurement and FDTD results.

Electromagnetic disturbances in gas-insulated substations and VFT calculations

This paper is focused on the oscillating frequencies of very-fast transients (VFTs) generated by disconnector and circuit breaker operations in gas-insulated substations (GISs) related to electromagnetic disturbances (EMDs). Test results of the VFT amplitudes and oscillating frequencies are summarized, and the measured results have shown that there is no significant difference of the frequencies in the high-voltage main circuits and the low-voltage control circuits in the GISs. Modeling of GIS elements for VFT simulations by EMT-type software are explained, and simulation examples are demonstrated in comparison with test results. Also, FDTD (finite-difference time-domain) computations are performed, and the calculated results are compared with EMTP simulation results. If proper modeling is adopted, EMTP and FDTD results show a reasonable agreement.

Cylindrical optical resonators: fundamental properties and bio-sensing characteristics

In this paper, detailed theoretical analysis of cylindrical resonators is demonstrated. As illustrated, these kinds of resonators can be used as optical bio-sensing devices. The proposed structure is analyzed using an analytical method based on Lam's approximation. This method is systematic and has simplified the tedious process of whispering-gallery mode (WGM) wavelength analysis in optical cylindrical biosensors. By this method, analysis of higher radial orders of high angular momentum WGMs has been possible. Using closed-form analytical equations, resonance wavelengths of higher radial and angular order WGMs of TE and TM polarization waves are calculated. It is shown that high angular momentum WGMs are more appropriate for bio-sensing applications. Some of the calculations are done using a numerical non-linear Newton method. A perfect match of 99.84% between the analytical and the numerical methods has been achieved. In order to verify the validity of the calculations, Meep simulations based on the finite difference time domain (FDTD) method are performed. In this case, a match of 96.70% between the analytical and FDTD results has been obtained. The analytical predictions are in good agreement with other experimental work (99.99% match). These results validate the proposed analytical modelling for the fast design of optical cylindrical biosensors. It is shown that by extending the proposed two-layer resonator structure analyzing scheme, it is possible to study a three-layer cylindrical resonator structure as well. Moreover, by this method, fast sensitivity optimization in cylindrical resonator-based biosensors has been possible. Sensitivity of the WGM resonances is analyzed as a function of the structural parameters of the cylindrical resonators. Based on the results, fourth radial order WGMs, with a resonator radius of 50 μm, display the most bulk refractive index sensitivity of 41.50 (nm/RIU).

Three-dimensional Plasmonic Fields of Gold Nanostar Arrays: Beyond the Near-field

Background The performance of plasmonic nanostructures is based on optical properties and the intensity of the electric field. The nature of the nearfields around coinage metal nanoparticles has been well-studied. However, how to project the enhanced electric field to several hundred nanometers distance might be more convenient for the real applications. Methods In this paper, we examine whether an array of gold nano-stars may be used as enhancement of the electric field to the several hundred nanometers distance. Electron beam lithography was used to fabricate gold nano-star arrays. Near-field optical properties of these arrays were then obtained using near-field scanning optical microscopy (NSOM). The near-field optical properties were also explored with finite-difference time-domain (FDTD) simulations. Results In the model, a scanning electron microscope image of actual nano-stars was used to build the FDTD targets of 40 nm thickness. The incident wavelength was 532 nm in both simulation and experiment. In the simulations the near-field optical intensity distribution was studied with monitors positioned at various distances (0, 1 and 2 μm above the top surface of a nano-star). The FDTD results were found to be consistent with the experimental NSOM results. Conclusion We found that the field enhancement is not only localized to the individual nanostars but also projected several hundred nanometers into the space. Such an array could be potential used to probe the intracellular environment of an adjacent cell or near-field imaging.

Scattering based hyperspectral imaging of plasmonic nanoplate clusters towards biomedical applications.

A new optical scattering contrast-agent based on polymer-nanoparticle encapsulated silver nanoplates (PESNs) is presented. Silver nanoplates were chosen due to the flexibility of tuning their plasmon frequencies. The polymer coating preserves their physical and optical properties and confers other advantages such as controlled contrast agent delivery. Finite difference time domain (FDTD) simulations model the interaction of light with the nanoplates in different orientations in the cluster. Hyperspectral dark field microscopy (HYDFM) observes the scattering spectra of the PESNs. An unsupervised sequential maximum angle convex cone (SMACC) image analysis resolves spectral endmembers corresponding to different stacking orientations of the nanoplates. The orientation-dependent endmembers qualitatively agree with the FDTD results. For contrast enhancement, the uptake and spatial distribution of PESNs are demonstrated by an HYDFM study of single melanoma cells to result in an enhanced contrast of up to 400%. A supervised spatial mapping of the endmembers obtained by the unsupervised SMACC algorithm reveals spatial distributions of PESNs with various clustering orientations of encapsulated nanoplates. Our study demonstrates tunability in plasmonics properties in clustered metal nanoparticles and its utility for the development of scatter-based imaging contrast agents for a broad range of applications, including studies of single cells and other biomedical systems.

Gate-Tunable mid-Infrared Plasmonic Planar Band-Stop Filters Based on a Monolayer Graphene

In this paper, the graphene ribbon bus waveguide side-coupled a coplanar short graphene strip, constructed on a monolayer graphene with substrates by spatially varying external gates, is proposed and investigated numerically by using the finite-difference time-domain (FDTD) method. Simulated results exhibit that the outstanding mid-infrared band-stop filtering effect is realized based on the edge mode resonance in the short strip acting as a perfect Fabry-Perot resonator. By changing the locations of gate voltages to vary the size of the short graphene strip, not only the Fabry-Perot resonance mode is tuned effectively but also the original rectangular-loop resonance mode appears. The changes in the coupling distance and substrates are also used for modulating the transmission spectrum. FDTD results are in excellent agreement with the coupled-mode theory (CMT). The simple structure without doubt is a real electrically controlled plasmonic device. Our studies will support the fabrication of planar nano-integrated plasmonic circuits for mid-infrared optical processing.