Time-domain Physical Optics Research Articles

Exact Evaluation of Time-Domain Physical Optics Integral for High-Order Triangles

In this work, a method for the exact evaluation of time domain physical optics (PO) integral on high-order triangles is presented. The presented method is based on the recently developed method for quadratic triangles. Specifically, the PO integral on the surface of the high-order triangle is reduced to a line integral on the intersection of the high-order triangle and the plane formed by the incidence and observation directions in barycentric coordinates of the triangle. Then, the intersecting curve is parametrized in terms of one of the barycentric coordinates of the high-order triangle. At last, the line integral is evaluated exactly using the suitable order Gauss Legendre quadrature rule (GLQR). The validity of the proposed method is demonstrated via analyzing transient scattering from a unit sphere and a flower-shaped scatterer modeled with high-order triangles using PO approximation.

Efficient GPU implementation of the time-domain shooting and bouncing rays method on electrically large complex target

In order to rapidly obtain the scattered echo from large complex target, we have developed a high-frequency simulation tool through the combination of time-domain shooting and bouncing rays (TDSBR) method and time-domain physical optics (TDPO). For ray tracing is time consuming, compute unified device architecture (CUDA) and OptiX from Nvidia are used to reduce computational time. The closed-form expression of TDPO integral is adopted to predict the far field of the illuminated area. A new TDPO integral expression is derived based on the original expression for ray tube integral area in multiple bounce scattering. The simulation results are compared with full-wave method to demonstrate the accuracy of our method. Finally, this improved TDSBR-TDPO method is used to simulate the scattering echo from complex realistic targets and the results are also discussed. The simulation time and hardware configuration are given to show the efficiency of our work.

An ISAR Imaging Framework for Large and Complex Targets Using TDSBR

An inverse synthetic aperture radar (ISAR) imaging framework is proposed to process transient scattered echoes into ISAR images. First, the time-domain shooting and bouncing ray (TDSBR) method is developed to simulate the transient scattering echoes. Then, based on the electromagnetic scattering echo expressions, the ISAR imaging formula is derived. In order to improve the imaging efficiency, we use Gaussian modulation pulse to replace the traditional linear frequency modulation pulse and propose an improved matched filtering method. Finally, some ISAR images are presented to demonstrate the accuracy and efficiency of the proposed method. Besides, by comparing with time-domain physical optics(TDPO) method, we also analyze the effect of multiple scattering contribution calculated by TDSBR on the image emphatically.

A Fast, Hybrid, Time-Domain Discontinuous Galerkin-Physical Optics Method for Composite Electromagnetic Scattering Analysis

To accelerate the solution of transient electromagnetic scattering from composite scatters, a novel hybrid discontinuous Galerkin time domain (DGTD) and time-domain physical optics (TDPO) method is proposed. The DGTD method is used to solve the accurate scattering field of the multi-scale objects region, and a hybrid explicit-implicit time integration method is also used to improve the efficiency of multi-scale problems in the time domain. Meanwhile, the TDPO method is used to accelerate the speed of surface current integration in an electrically large region. In addition, the DGTDPO method considers the mutual coupling between two regions, and effectively reduces the number of numerical calculations for the other space of the composite target, thereby significantly reducing the computer memory consumption. Numerical results certified the high efficiency and accuracy of the hybrid DGTDPO. According to the results, in comparison with the DGTD algorithm in the entire computational domain, the DGTDPO method can reduce computing time and memory by 90% and 70% respectively. Meanwhile, the normalized root mean square deviation (NRMSD) of the time-domain, high-frequency approximation method is over 0.2, and that of the DGTDPO method is only 0.0971. That is, compared with the approximation methods, the hybrid method improves the accuracy by more than 64%.

Scattering Prediction of Target Above Layered Rough Surface Based on Time-Domain Ray Tracing Modeling

In the past, most of the transient electromagnetic (EM) analyses focused on the scattering from the target. The transient scattering from rough surface was rarely studied, especially for the layered rough surface. When the target is above the rough surface, it needs to solve the composite transient scattering from the rough surface and the target above it. In this article, we mainly focus on the time-domain (TD) analysis for transient scattering from the target and layered rough surface based on time-domain ray tracing (TDRT) modeling. Applying geometrical optics (GO), the multiple bounces of the transient EM waves between layered rough surfaces and target are traced to obtain the incident field of the irradiated surfaces. Then considering the particularity of the layered rough surface, we modify TD Gordon integral and reduce the TD physical optics (TDPO) integral to closed-form expressions to improve the computing efficiency. To demonstrate the efficiency and accuracy of the proposed algorithm, the transient scattering simulations of the composite model involving target and layered rough surface are compared with frequency-domain ray tracing (FDRT) with inverse fast Fourier transform (IFFT), as well as the results obtained by the multilevel fast multipole algorithm (MLFMA) of FEKO in conjunction with IFFT (IFFT-MLFMA). The characteristics of transient scattering from the composite model are further studied to show the physical phenomenon of scattering mechanisms. Specifically, the transient scattering from the composite model for different parameters is simulated for sensitivity investigation of the transient scattering to the variations in the related parameters.

ISAR Image Algorithm Using Time-Domain Scattering Echo Simulated by TDPO Method

In this letter, we propose an inverse synthetic aperture radar (ISAR) imaging method using time-domain (TD) scattering echo simulated by time-domain physical optics (TDPO) method. First, the TD pulse plane wave is taken as the incident wave and the transient scattering echo data matrix is obtained by using the TDPO method under different look angles of the target. Then, demodulation, pulse compression, and azimuth inverse fast Fourier transform (FFT) are performed on the echo data matrix to obtain the ISAR image under small bandwidth small angle. In this letter, considering the fact of TD pulse signals emitted by radar, electromagnetic scattering modeling method is adopted to obtain more accurate TD scattering echoes. This method combines the electromagnetic scattering algorithm and radar imaging algorithm effectively and is closer to practical application. Finally, ISAR images are given to verify the feasibility and fidelity of the presented method.

Analysis of multilayered homogeneous dielectric targets by using time‐domain physical optics method

An improved time-domain physical optics (TDPO) method is proposed to simulate multilayered dielectric structures, in which the characteristic matrix theory of multilayered medium is implemented. In order to accurately calculate the total reflection coefficient on the surface of the multilayered medium, a series of two-dimensional characteristic matrices are established. Based on the characteristic matrices, the total reflection coefficient can be directly derived, instead of summing up the multiple reflected and refracted waves, which is insensitive to the number of the number of the layers and the polarization of the incident wave. Numerical examples are given to validate effectiveness of the proposed TDPO method. It states that this method has much higher computational efficiency, without the loss of accuracy.

Near-Field Finite-Zone Focused Radiation From Reflector Antenna With Continuously Tapered Ellipsoidal Surface Curvatures

In this paper, a design of reflector antennas to produce near-field focused (NFF) radiation is presented. Instead of focusing the radiation at a single focal point, which results in an ellipsoidal reflector, this new reflector antenna application concept designates a finite zone, especially a finite curved surface, for NFF illumination. This finite zone may consist of several subzones for multi-NFF radiation. The design concept employs equal path lengths of wave propagation from the feed’s phase center toward the focal zone via reflections from the reflector’s surface in a one-to-one correspondence, which results in a confluence of reflection points found from a set of ellipsoidal surfaces. Based on a definition of the mapping mechanism to extract the reflection points to form the reflector, the field can be properly focused in the target zone by the concept of geometric optics (GO). In this paper, the basic theoretical concept is first summarized with a design equation developed for easy implementation. The focus property is demonstrated by a time-domain physical optics (TD-PO) analysis of spherical wave illumination with a transient-step field behavior to show the focusing responses of electromagnetic scattering from the reflector. The focusing characteristics of the frequency domain (FD) are also shown by PO simulation at 20 GHz.

Near-Field Scattering Prediction Based on Refined Time-Domain High-Frequency Method

The theoretical implementation aspects of near-field wideband electromagnetic (EM) scattering prediction based on refined time-domain physical optics (TDPO) and time-domain equivalent edge currents (TDEEC) integral are proposed in this letter. First, the closed-form expressions in far-field assumption of TDPO and TDEEC integrals are derived based on a Radon transform interpretation. Then, to solve the difficulties of the traditional TDPO and TDEEC in the near-field scattering computation, a refined integral representation is formulated. Afterward, by introducing the concept of the locally expanded approximations both in phase and amplitude, a more accurate expression of the Green function in frequency domain and time domain is developed. In this way, the near-field versions of TDPO and TDEEC are proposed to predict the scattered EM field of electronically large target in the near-field zone while retaining the simplicity of the conventional forms. The validity and applicability of the proposed refined TD method in near-field calculation are demonstrated by some numerical examples in the last part.

Hybrid Time-Domain PTD and Physical Optics Contour Integral Representations for the Near-Field Backscattering Problem

Time-domain physical optics (TDPO) contour integral representations are developed for backscattered near fields from a perfectly conducting surface illuminated by a dipole source. The proposed representations are derived from the TDPO surface integral representations by introducing two theorems: surface gradient and surface divergence theorems. The proposed representations are free from singularities for all the source/observer positions in which the dipole antenna is located. In addition, the time-domain physical theory of diffraction is introduced to modify the physical optical field considering the effect of the edge diffraction. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.

The Study on Near-Field Scattering of a Target Under Antenna Irradiation by TDSBR Method

An efficient time domain shooting and bouncing ray (TDSBR) method is proposed to analyze the transient near-field scattering from an electrically large complex object illuminated by a far-field antenna source. The time-domain far-field incident sources can be derived by a convolution of pulsed excitation with the inverse Fourier transform of frequency domain (FD) far-fields radiated from an antenna. In order to obtain accurate near-field scattering results, time domain physical optics (TDPO) near-field integral representations are proposed and reduced to closed-form expressions to improve computing efficiency by applying locally expanded Green function approximation. Different from the plane wave incident situation, in the case of antenna radiation, the incident fields of each individual facet in the ray path are represented by the radiation fields from the equivalent mirror antenna derived in this paper. Since the radiation fields naturally contains the time delay term, the complicated processing of the time delay problem can be avoided by solving the equivalent mirror antenna radiation fields. It is simpler and more accurate than the traditional time domain geometrical optics (TDGO) method. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.

Range Distance Requirements for Large Antenna Measurements for Square Aperture With Uniform Field Distribution

Frequency dependences of the field for constant angle of observation measured by different probes at different distances are discussed. We consider the case of the square aperture antenna with the uniform field distribution. The analysis is based on time-domain physical optics method of field calculation. We show and explain the effect of sidelobe reduction when a big square probe is placed at a finite distance from square aperture antenna. Errors of the sidelobe levels of the antenna radiation pattern (ARP) in the cases of different sizes of the probe placed at different distances are shown. We show an optimal probe size and an optimal measurement distance between antennas. We also show and explain the effect of a large distortion of the ARP first zero, measured by the big probe at the finite distance.

Evaluation of Passive Intermodulation Using Full-Wave Frequency-Domain Method With Nonlinear Circuit Model

Passive intermodulation (PIM) arising from metallic contact junctions on the reflector antenna may cause the degradation of a satellite communication system. A time-domain method such as time-domain physical optics (TD-PO) can solve the nonlinear problems of PIM; however, the error accumulation is unacceptable in the analysis of electrically large objects. The rigorous full-wave frequency-domain method of electrically large objects is not suitable because it only can be applied at single frequency. An equivalent circuit model coupled with full-wave frequency-domain method is proposed to solve the PIM problems of electrically large objects. The responses of the nonlinearities at metal–insulator–metal (MIM) contacts are analyzed by the circuit method; the electromagnetic field distribution is evaluated by the rigorous full-wave frequency-domain method. Finally, the analysis of PIM on a reflector antenna illuminated by a practical horn is performed to exemplify the usefulness of the method presented in this paper.

Closed-Form Time Domain PO Expressions of the Electric Field Scattered From PEC Objects Illuminated by an Electric Dipole

In this study, a time domain analytical expression is derived for the electric field scattered from PEC objects illuminated by an infinitesimal electric dipole via physical optics (PO). It is assumed that the observer resides at infinity while no limitations on the distance of the illuminating dipole to the scatterer are imposed. The scatterer is modeled with triangular facets. The scalar potential contribution of the dipole on the induced surface currents is not neglected. The efficacy of the derived analytical expression is demonstrated through several numerical examples.

EFFICIENT EVALUATION OF NEAR-FIELD TIME-DOMAIN PHYSICAL-OPTICS INTEGRAL USING LOCALLY EXPANDED GREEN FUNCTION APPROXIMATION

A time-efficient method is proposed to calculate the near-field time-domain physical-optics (TD-PO) integral to analyze the transient electromagnetic fields scattered from three-dimensional perfectly conducting objects under the illumination of a pulsed plane wave. It is shown that the TD- PO integral can be reduced to a close-form expression by introducing locally expanded Green-function approximations used in conjunction with the surface partitioning. As a result, the near-field TD-PO response to a general pulsed plane wave excitation is derived by a convolution of the excitation waveform with the TD-PO impulse response, which can be performed in a closed form. To satisfy the causality, i.e., the transient field cannot travel away from the sources faster than the speed of light, the high-order derivative of a modulated-Gaussian wave is specified as the excitation waveform. The efficiency and accuracy of the proposed near-field formulas are validated through numerical examples.

Passive inter-modulation scattering analysis of reflector considering contact nonlinearity

Passive inter-modulation (PIM) is a form of nonlinear distortion caused by the inherent nonlinearities of the passive devices and components in RF/microwave system. It will degenerate the performance of communication system with broad-band channel and high-sensitivity receiver. Therefore, it is necessary to construct a model to simulate this process in order to predict the level of PIM. This paper is aimed at constructing some plate models with one-dimensional and two-dimensional contact nonlinearity sections illuminated by two-tone waves, and calculating the scattered field at a fixed-point in space using time-domain physical optics method. By taking fast Fourier transform (FFT), we get the spectrum of the scattered field and then analyze the generated PIM products. At the end of this paper, some numerical examples are presented to show the influence rules of the relative factors on PIM. The results indicate the variation of the level of PIM with the number of the nonlinear regions, the nonlinear spacing, and the incident power levels.

Time-Domain Analysis of a Rectangular Reflector Antenna

Rectangular reflector antennas have motivated the time-domain analysis of electromagnetic scattering problems. The asymptotic time domain physical-optics (TDPO) is applied to the analysis of a rectangular reflector illuminated by a Gaussian-impulse. The effects of time-delayed mutual coupling between points on the surface will be ignored as a result of utilizing the TDPO method for determining the equivalent surface-current density on the reflector. Finally, in this work the scattered signals at the specular reflection point, at the edges, and at the corners can be clearly distinguished.

Time-Domain Physical Optics Method for the Analysis of Wide-Band EM Scattering from Two-Dimensional Conducting Rough Surface

Time-domain physical optics (TDPO) method is extended to investigate electromagnetic (EM) scattering from two-dimensional (2D) perfectly electrically conducting (PEC) rough surface in both time domain and frequency domain. The scheme requires relatively small amounts of computer memory and CPU time, and has advantage over the Kirchhoff Approximation (KA) method in obtaining transient response of rough surface by a program run. The 2D Gaussian randomly rough surface is generated by Monte Carlo method and then is partitioned into small triangle facets through the meshing preprocess. The accuracy of TDPO is validated by comparing the numerical results with those obtained by the KA method in both backward and specular directions. The transient response and its frequency distribution of radar cross section (RCS) from rough surface is shown, respectively. The scattering results from rough surface with different size in the specular direction are given. The influence of the root mean square height (σ) and correlation length (l) on electromagnetic scattering from PEC rough surface is discussed in detail. Finally, the comparisons of backscattering results at different incident angles are presented and analyzed.

Investigation on Time- and Frequency-Domain Responses of Some Complex Composite Structures in the Presence of High-Power Electromagnetic Pulses

Investigation on time- and frequency-domain responses of some complex composite structures in the presence of high-power electromagnetic pulses (EMP) is carried out in this paper. An efficient hybrid numerical method is proposed and implemented for studying an EMP penetrating through arbitrary apertures on a perfectly conducting (PEC) screen, coupled with conical spiral wire and even with Yagi-Uda antennas. This method effectively combines the time-domain integral equation (TDIE) with time-domain physical optics (TDPO), where hybrid TDIE-TDPO equations are solved by marching-on-in-time scheme (MOT). In its implementation, the antennas, wire-surface junctions, and the small part of the solid platform in the vicinity of the junctions are assigned to the TDIE region; nevertheless, a small part of the PEC screen in the vicinity of the apertures is set to be the TDIE region, while the remainder of the solid platform and the PEC screen is in the TDPO one. Our developed numerical algorithm is sufficiently verified in both time and frequency domains for predicting input admittance, S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> and S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">21</sub> parameters, directivities, excited transient current responses as well as backward scattered fields of different antennas mounted on a PEC platform. These results are useful for further evaluating electromagnetic environments of some complex communication.

HYBRID TDIE-TDPO METHOD USING WEIGHTED LAGUERRE POLYNOMIALS FOR SOLVING TRANSIENT ELECTROMAGNETIC PROBLEMS

An e-cient and stable hybrid method, based on the time-domain integral equation (TDIE) and time-domain physical optics (TDPO), is developed for investigating transient radiation and scattering from perfectly electrical conducting (PEC) objects. It at flrst requires partitioning the PEC object surface into TDIE and TDPO regions, respectively. Then, a set of hybrid TDIE-TDPO equations is derived and solved using an adaptive marching-on-in- degree (MOD) method. The fast Fourier transforms (FFT)-based blocking scheme is further implemented into the proposed algorithm so as to reduce N 2 O dependence of the traditional MOD method to NO log 2 (NO), where NO is the highest order of the weighted Laguerre polynomials used for computation. Under such circumstances, its computational cost, in comparison with the full TDIE-MOD solver, is reduced signiflcantly. Several numerical examples are presented to demonstrate its accuracy and e-ciency in solving some typical transient electromagnetic problems.