Finite-difference Frequency-domain Research Articles

Real-Time Modeling of Forward-Looking Synthetic Aperture Ground Penetrating Radar Scattering From Rough Terrain

Ground penetrating radar (GPR) is a viable tool for fast and high fidelity detection of concealed explosive threats. The radar effectiveness is limited by scattering from rough terrain which considerably obscures the buried target response. To calculate the rough ground scattering, a 3-D full-wave algorithm such as finite-difference frequency-domain (FDFD) method is required but is often prohibitive for multiple frames when the GPR antennas are distant from the target region. This paper presents a real-time 3-D modeling of a moving platform forward-looking GPR scattering from rough terrain located at great electrical distances from the GPR antenna. For a synthetic aperture, the computational domain of the focal region is reduced to a very small subset of the entire observed volume, and the surface clutter is computed via a mere multiplication of a precomputed impulse response matrix of the rough ground with the matrix characterizing the GPR transmitting signal. For a vehicle-mounted GPR detection system, this results in a significant reduction of complexity and saving of computation resources. The effectiveness of the algorithm is evaluated through an implementation of 3-D Monte Carlo simulation for various rough surface parameters. Our developed model compares well with the direct FDFD results, and can be used for lossy and frequency-dispersive soils.

Electromagnetic Uncertainty Analysis Using Stochastic FDFD Method

This paper presents a novel stochastic finite-difference frequency-domain (S-FDFD) method that incorporates the statistical variations of electrical properties directly into the FDFD algorithm by using the delta method approximation. The method is validated through two examples—a 1-D bioelectromagnetic layered model and specific absorption rate in a 2-D slice of a human head model. Comparisons between the single run S-FDFD results and those of the Monte Carlo method (the benchmark in statistical simulations) show that the S-FDFD method can predict the mean and variance of electromagnetic fields with a fair degree of accuracy in a computationally efficient way. Our numerical experiment also shows that the accuracy is highly dependent on the approximation for the correlation coefficients of the variance equations.

Design and modelling of all-normal dispersion As39Se61 chalcogenide photonic crystal fiber for flat-top coherent mid-infrared supercontinuum generation

Abstract We report numerical investigation of mid-infrared supercontinuum (SC) generation in all-normal dispersion (ANDi) As39Se61 chalcogenide photonic crystal fiber (PCF). Numerical results, obtained by using the Finite-Difference Frequency-Domain (FDFD) method, indicate that desirable dispersion properties can be achieved by adjusting the air holes diameter and ANDi regime is obtained over the entire wavelength range with a PCF pitch and air holes diameter of 1.8 µm and 0.7 µm, respectively. Besides, the optimized design has a nearly zero dispersion wavelength of 3.45 µm and exhibits high Kerr nonlinearity of 5.89 w−1 m−1. By pumping 50 fs duration laser pulses at 3.45 µm, we demonstrate the generation of a broad, ultraflat-top and highly coherent SC spectrum extending from 2.43 µm to 4.85 µm at 4 dB spectral flatness and from 1.95 µm to 6.58 µm at 8 dB, by employing very low energy pulses of 50 pJ and 250 pJ, respectively. Owing to its remarkable optical characteristics, the proposed SC source based on As39Se61 chalcogenide glass PCF is found to be suitable for various potential mid-infrared applications such as optical coherence tomography, mid-infrared spectroscopy and metrology.

Numerical investigation of a broadband coherent supercontinuum generation in Ga8Sb32S60 chalcogenide photonic crystal fiber with all-normal dispersion

All normal dispersion (ANDi) and highly nonlinear chalcogenide glass photonic crystal fiber (PCF) is proposed and numerically investigated for a broad, coherent and ultra-flat mid-infrared supercontinuum generation. The proposed PCF consists of a solid core made of Ga8Sb32S60 glass surrounded by seven rings of air holes arranged in a triangular lattice. We show by employing the finite difference frequency domain (FDFD) method that the Ga8Sb32S60 PCF dispersion properties can be engineered by carefully adjusting the air holes diameter in the cladding region and ANDi regime is achieved over the entire range of wavelengths with a zero chromatic dispersion around 4.5 μm. Moreover, we demonstrate that injecting 50 fs width and 20 kW peak power laser pulses (corresponding to a pulse energy of 1.06 nJ) at a pump wavelength of 4.5 μm into a 1 cm long ANDi Ga8Sb32S60 PCF generates a broad, flat-top and perfectly coherent SC spectrum extending from 1.65 μm to 9.24 μm at the 20 dB spectral flatness. These results make the proposed Ga8Sb32S60 PCF an excellent candidate for various important mid-infrared region applications including mid-infrared spectroscopy, medical imaging, optical coherence tomography and materials characterization.

Application of the pseudospectral method to the finite difference frequency domain method

Application of the pseudospectral method in numerical calculations is well established. The method is used in several disciplines, from geology to applied mathematics. The pseudospectral method also appears in computational electromagnetism. Its implementation already has been carried out for the finite element method and finite difference time domain method. In this study, we implement the pseudospectral method for the finite difference frequency domain (FDFD) method, and hence the resulting method is called the pseudospectral frequency domain (PSFD) method. The PSFD method is compared to the FDFD method in terms of the numerical phase velocity and anisotropy. The method is extended for the nonlinear process PSFD (NL-PSFD) of second-harmonic generation. It is shown how a plane wave source at oblique incidence can be implemented, and its performance for tilted quasi-phase-matched grating is discussed. Finally, a specific method is deduced from NL-PSFD for large-volume simulation, where only second-order nonlinearity is spatially structured, and a two-dimensional nonlinear photonic crystal is simulated.

Three-Dimensional Transient Electromagnetic Numerical Simulation Using FDFD Based on Octree Grids

The transient electromagnetic method (TEM) has been widely used as a geophysical exploration method in recent years. When Maxwell's equations are discretized in the time domain by the direct solution method, the initial field is used as a substitute for the source, so the electromagnetic response of a shallow three-dimensional anomalous body cannot be calculated. Maxwell's equations in the frequency domain are simple in form, and the current source can be directly added without calculating the initial field. However, large linear equations must be calculated. The coefficient matrix is large, and the calculation speed is slow, which limits their application. Based on Yee grids, this paper combines octree grids with the finite-difference frequency-domain (FDFD) method. Ensuring a sufficiently large computational area, octree grids are used to refine the area of anomalous bodies, while coarse grids are still used to reduce the total number of grids and improve the efficiency. In the numerical simulation, the vacancy positions are set to zero to solve the data storage problem of the coarse grids and fine grids. The binary paraboloid interpolation method is used to solve the electromagnetic field component transfer problem at the intersection of the coarse grid and fine grid. Finally, the electromagnetic response curve in the time domain is obtained by a frequency-time transformation. By comparing the calculation results of typical models, the correctness of the FDFD method based on octree grids is verified. By comparing the computational time of complex anomalous bodies for Yee grids and octree grids, it can be concluded that the efficiency of the FDFD method based on octree grids is improved to a certain extent.

Two-dimensional plasma-wave interaction in an helicon plasma thruster with magnetic nozzle

An axisymmetric, finite difference frequency domain model is used to study the wave propagation and power absorption in a helicon plasma thruster operating inside a laboratory vacuum chamber. The magnetic field is not purely axial and the plasma beam is cylindrical in the source and divergent in the magnetic nozzle. The influence of the magnetic field strength, plasma density, electron collision frequency and geometry on the wavefields and the power absorption maps is investigated, showing different power deposition patterns. The electromagnetic radiation is not confined to the source region but propagates into the nozzle divergent region, and indeed the power absorption there is not negligible. For the impedance at the antenna, the reactance is rather constant but the resistance is very dependent on operation parameters; optimal parameter values maximizing the resistance are found.

Transformation optics based on unitary vectors and Fermat's principle for arbitrary spatial transformation design.

A methodology of designing an arbitrary transformation using transformation optics (TO) based on unitary vectors and Fermat's principle is presented. The TO equation is derived in terms of grid coordinates. The geometry of the transformed space is stored in the grid coordinates rather than the transformation functions. This allows the crafting of an arbitrary transformation by combining several transformation templates together. The touch interface is employed to intuitively apply the transformations. The resulting material parameters are calculated from the proposed method and verified using the anisotropic finite-difference frequency-domain method. Five examples are presented to demonstrate the capability of this method.

Effects of key factors on the heat insulation performance of a hollow block ventilated wall

A hollow block ventilated wall can be cooled down in the summer and warmed in the winter by utilizing the air that flows through cavities. The heat transferred between the outdoor and indoor environments can also be removed. However, neither simulations nor experimental studies on the hollow block ventilated wall have been complete, and factors that affect the thermal insulation performance of hollow block ventilated walls need to be identified. In this paper, the frequency-domain finite-difference method and the Number of Transfer Units method are adopted to build the coupled three-dimensional heat transfer model for investigating the temperature distribution on wall surfaces and the exhaust airflow. Experiments are carried out to validate the three-dimensional model, and comparisons prove that the model has considerable accuracy. In addition, both the numerical and experimental studies show that the hollow block ventilated wall can significantly reduce the heat transferred from outdoor environments to indoor rooms through ventilation in the summer. The effects of influential factors, including the airflow velocity, the inlet temperature of the airflow and the cavity size, on the thermal insulation performance of the hollow block ventilated wall are investigated based on the heat transfer model. Results show that the temperature of the inner surface of the hollow block ventilated wall at four orientations is reduced and ranges from 24.8 to 27.0 °C during a typical summer day. The heat flux through the inner surface is reduced by 55.08%, 55.07%, 56.03% and 55.19% respectively for the east, west, south, and north hollow block ventilated walls, indicating the energy saving potential of hollow block ventilated walls. The most critical factor is the cavity size. When the cavity dimension is constant, the influence of the airflow velocity on thermal insulation is much larger compared to the airflow temperature, and the suggested airflow rate is 1.3 m/s. Results show that a higher airflow rate, higher inlet airflow temperature, and larger cavity size, enable the hollow block ventilated wall to achieve better thermal insulation performance.

Application of the Finite-Difference Frequency-Domain (FDFD) method on radiowave propagation in urban environments

In this work a Finite-Difference Frequency-Domain (FDFD) propagation method for complex urban environments is proposed. The formulation starts from the discretization of the Helmholtz equation for the magnetic field instead of the usual separate one order derivative Ampere's and Faraday's laws. The Stretched Coordinate Perfectly Matched Layer (SCPML) is used as an absorbing boundary condition. These procedures produce less field components to estimate and achieve high wave absorption at the computation domain boundaries. The main goal is the rigorous prediction of VHF/SHF signals in real urban scenarios through the evaluation of several propagation mechanisms: direct rays, diffraction, reflection and refraction effects. The method is validated through an analytic problem and preliminary results are generated by two case studies: a cellular system measurement campaign and an idealized urban scenario.

Review and accuracy comparison of various permittivity-averaging schemes for material discontinuities in the two-dimensional FDFD method: implementation using efficient computer graphics techniques.

Several known and widely used averaging techniques aiming to improve the accuracy of the two-dimensional finite-difference frequency-domain (FDFD) method, in the presence of material discontinuities, are reviewed, numerically tested, and compared with respect to their accuracies. Furthermore, all averaging techniques are rigorously and efficiently implemented using the Supercover Digital Differential Analyzer algorithm and a modified Liang-Barsky algorithm suitably adapted from computer graphics applications. The FDFD with Gaussian blurring; the FDFD with volume-polarized effective permittivity; the FDFD with volume-polarized effective permittivity on shifted cells; and the FDFD with anisotropic smoothing [FDFD (AS)] are compared with respect to their accuracies (for both TE and TM polarization), in the case of scattering by an infinite homogeneous cylinder (for which analytical solution exists) comprising a lossless dielectric, a high-index, low-loss dielectric, or a metal. Sample plots of the relative errors are presented for various field components. Absolute error norms (L2 and L∞) are also presented for both polarizations and for two grid-cell sizes for quantitative comparisons. The results show that the FDFD (AS) prevails in accuracy mainly because it satisfies the boundary conditions at the cylinder's boundary the best. However, for the high-index dielectrics and metals, even the FDFD without any averaging gives very good results for the field components parallel to the uniformity direction. However, the FDFD (AS) is always more accurate when the in-plane field components are sought.

A generalized average-derivative optimal finite-difference scheme for 2D frequency-domain acoustic-wave modeling on continuous nonuniform grids

The frequency-domain finite-difference (FDFD) method is an effective tool for implementing frequency-domain seismic modeling, inversion, and migration. However, the computational cost for the FDFD method dealing with large models is prohibitive, limiting its application. As a common strategy to improve the computational efficiency, a nonuniform grid is usually adopted in the time-domain finite-difference method instead of the FDFD method. We have developed a generalized average-derivative optimal scheme (GADOS) that can perform frequency-domain acoustic-wave modeling on continuous nonuniform grids in the vertical and horizontal directions. Before we begin the calculations, we optimize numerous stencils in which the grid spacing ratios are different to obtain a large dictionary composed of many groups of optimal coefficients. We consider the continuous nonuniform grids as a gathering of nonuniform nine-point stencils (i.e., the stencil of the GADOS) and select the proper weighted coefficients for every stencil to ensure that the numerical dispersion is minimal in the global area. All the phase-velocity errors of the GADOS for different grid spacing ratios are less than [Formula: see text] even if the number of grid points per wavelength is as small as four after the weighted coefficients are optimized by minimizing the numerical dispersion. Compared with the average-derivative optimal scheme (ADOS), simulating seismic waves with the GADOS on nonuniform grids reduce the computational cost with the premise of ensuring sufficient accuracy. Several numerical examples are presented to illustrate the feasibility and efficiency of the GADOS on continuous nonuniform grids.

A discontinuous-grid finite-difference scheme for frequency-domain 2D scalar wave modeling

The discontinuous-grid method can greatly reduce the storage requirement and computational cost in finite-difference modeling, especially for models with large velocity contrasts. However, this technique is mostly applied to time-domain methods. We have developed a discontinuous-grid finite-difference scheme for frequency-domain 2D scalar wave modeling. Special frequency-domain finite-difference stencils are designed in the fine-coarse grid transition zone. The coarse-to-fine-grid spacing ratio is restricted to [Formula: see text], where [Formula: see text] is a positive integer. Optimization equations are formulated to obtain expansion coefficients for irregular stencils in the transition zone. The proposed method works well when teamed with commonly used 9- and 25-point schemes. Compared with the conventional frequency-domain finite-difference method, the proposed discontinuous-grid method can largely reduce the size of the impedance matrix and number of nonzero elements. Numerical experiments demonstrated that the proposed discontinuous-grid scheme can significantly reduce memory and computational costs, while still yielding almost identical results compared with those from conventional uniform-grid simulations. When tested for a very long elapsed time, the frequency-domain discontinuous-grid method does not show instability problems as its time-domain counterpart usually does.

Accelerating convergence of an iterative solution of finite difference frequency domain problems via schur complement domain decomposition.

We show that iterative solution of Maxwell's equations using the finite-difference frequency-domain method can be significantly accelerated by using a Schur complement domain decomposition method. We account for the improvement by analyzing the spectral properties of the linear systems resulting from the use of the domain decomposition method.

Finite-Difference Complex-Frequency-Domain Method for Optical and Plasmonic Analyses

The finite-difference frequency-domain (FDFD) method is one of the most effective methods for obtaining the frequency responses of specific optical components, such as thin films and guided wave structures. This letter describes an efficient algorithm based on the FDFD method to perform optical and plasmonic analyses. Solutions to the Maxwell's equations in the complex-frequency-domain are obtained by the finite-difference scheme and are numerically transformed into the time domain using the fast inverse Laplace transform. Reliable time and frequency responses of electromagnetic waves can be obtained through a simple and fast procedure. Furthermore, the time increment and observation time can be selected freely, while maintaining the accuracy. These are verified by performing the electric near-field analyses of a metallic cylinder. The computational results by our method are compared with the exact solution and the finite-difference time-domain (FDTD) method. Some details of performing inverse Laplace transform are also discussed.

Adaptive 9-point frequency-domain finite difference scheme for wavefield modeling of 2D acoustic wave equation

Adaptive 9-point frequency-domain finite difference scheme for wavefield modeling of 2D acoustic wave equation

A Linear Method for Shape Reconstruction Based on the Generalized Multiple Measurement Vectors Model

In this paper, a novel linear method for shape reconstruction is proposed based on the generalized multiple measurement vectors (GMMV) model. Finite difference frequency domain (FDFD) is applied to discretized Maxwell's equations, and the contrast sources are solved iteratively by exploiting the joint sparsity as a regularized constraint. Cross validation (CV) technique is used to terminate the iterations, such that the required estimation of the noise level is circumvented. The validity is demonstrated with an excitation of transverse magnetic (TM) experimental data, and it is observed that, in the aspect of focusing performance, the GMMV-based linear method outperforms the extensively used linear sampling method (LSM).

Numerical simulation of nonlinear second harmonic wave generation by the finite difference frequency domain method

Nonlinear second harmonic wave generation (SHG) has been thoroughly examined in one dimension both analytically and numerically. Recently, the application of advanced domain poling techniques enabled the fabrication of two-dimensional (2D) patterns of the sign of the nonlinear coefficient in certain nonlinear crystals, such as LiNbO3 and LiTaO3. This method can be used to achieve quasi phase matching in SHG and hence amplification of the second harmonic fields in 2D. In this study we present a true vectorial numerical method for the simulation of SHG by extending the finite difference frequency domain method (FDFD). Our nonlinear method (NL-FDFD) operates directly on the electromagnetic fields, uses two meshes for the simulation (for ω and 2ω fields), and handles the nonlinear coupling as an interaction between the two meshes. Final field distributions can be obtained by a small number of iteration steps. NL-FDFD can be applied in arbitrarily structured linear media with an arbitrarily structured χ(2) component both in the small conversion efficiency and the pump depleted cases.

Plasmon polaritons in cubic lattices of spherical metallic nanoparticles

We theoretically investigate plasmon polaritons in cubic lattices of spherical metallic nanoparticles. The nanoparticles, each supporting triply-degenerate localized surface plasmons, couple through the Coulomb dipole-dipole interaction, giving rise to collective plasmons that extend over the whole metamaterial. The latter hybridize with photons forming plasmon polaritons, which are the hybrid light-matter eigenmodes of the system. We derive general analytical expressions to evaluate both plasmon and plasmon-polariton dispersions and the corresponding eigenstates. These are obtained within a Hamiltonian formalism, which takes into account retardation effects in the dipolar interaction between the nanoparticles and considers the dielectric properties of the nanoparticles as well as their surrounding. Within this model we predict polaritonic splittings in the near-infrared to the visible range of the electromagnetic spectrum that depend on polarization, lattice symmetry, and wave-vector direction. Finally, we show that the predictions of our model are in excellent quantitative agreement with conventional finite-difference frequency-domain simulations, but with the advantages of analytical insight and significantly reduced computational cost.

Adjoint-based optimization of active nanophotonic devices.

We show that the adjoint variable method can be combined with the multi-frequency finite-difference frequency-domain method for efficient sensitivity calculations, enabling the systematic optimization of active nanophotonic devices. As a proof of principle demonstration, we have optimized a dynamic isolator structure in two-dimensions, resulting in the reduction of the length of the modulated regions by a factor of two, while retaining good performance in the isolation ratio and insertion loss.