Plane Wave Spectrum Research Articles

Efficient single-frequency millimeter-wave three-dimensional imaging for rapid target identification

Compared to broadband systems, single-frequency millimeter-wave (SFQ-MMW) imaging systems can significantly simplify system complexity, but can only obtain two-dimensional information of the target. Moreover, the position of the reference plane must be adjusted in real time during the imaging process to obtain a high-quality focusing effects. Therefore, this paper proposes a SFQ-MMW three-dimensional imaging algorithm. In the plane wave spectrum domain, the propagation operator is used as a focusing term to accurately locate the target focus. Only single-frequency echo data is required to retrieve information and reconstruct high-quality images. This method can significantly improve the efficiency of near-field millimeter wave measurement and imaging. This work facilitates applications in rapid target identification and characterization. The performance of this method was tested through numerical simulation. Finally, validation was performed on real data in an independently developed system. The results show that the test results are in line with expectations, and the imaging efficiency has been significantly improved.

Research on the efficient EM modeling method from multilayered anisotropic medium-metal composite targets

The paper presents a high-frequency modeling approach tailored for the electromagnetic (EM) scattering characteristics from electrically large radar targets coated with multi-layered anisotropic mediums (MLAMs). The approach begins by deriving the plane-wave spectrum expression for the incident EM field within MLAMs. It then employs spectral domain full-wave analysis method (SDFWAM) to obtain an analytical representation of the scattering field, further leveraging saddle point evaluation (SPE) to derive asymptotic solutions in the spatial domain. By integrating principles of physical optics (PO) and the tangent plane approximation, the far-field scattering characteristics of target enveloped in the specified medium are efficiently delineated. Validations against standard structure and the Misty satellite model reveal the method's pronounced alignment with the method of moments – finite element method (MoM-FEM) hybrid numerical algorithm, underscoring its notable computational efficiency. Furthermore, in conjunction with scattering sources decomposition technique, the approach is applied to optimize the radar cross-section (RCS) of the Su-57 aircraft, achieving precise and intelligent RCS control at minimal material cost. In conclusion, this research offers pivotal technological and theoretical foundations for EM scattering prediction, stealth design, and performance assessment in radar target domains.

Reactive Near-Field to 3-Meter Far-Field Transformation Based on Deep Convolutional Neural Networks and Plane Wave Spectrum

Reactive Near-Field to 3-Meter Far-Field Transformation Based on Deep Convolutional Neural Networks and Plane Wave Spectrum

Transmission across a ribbon containing a square [formula omitted] impurity

We study the spectrum and transmission coefficient of plane waves propagating along square ribbons of varying widths, containing a square-shaped, PT-symmetric impurity region. We start with a zero-width ribbon (1D chain) and place a PT symmetric dimer. The spectrum is computed numerically and the instability gain is computed as a function of the gain/loss dimer strength. The transmission coefficient is obtained in closed form and examined as a function of wavevector and the gain/loss parameter. Next, we study a ribbon in a narrow ladder configuration containing a square PT impurity. As before, we compute the instability gain numerically and the transmission coefficient in closed form for the two possible input modes. Finally, we repeat the calculations for a wider ladder ribbon containing a Lieb-like impurity in a PT configuration. For all cases and transmission channels, we obtain transmission divergences in wavevector-gain/loss parameter space, whose number increases with the width of the ribbon.

Physical temperature sensing of targets with shelters under indoor scenes by a revised Ku band microwave radiometer

This work is aimed to solve technical difficulties for microwave radiometers in Ku band and above under indoor scenes to detect physical temperatures of targets with shelters. Firstly, a revised microwave radiometer in Ku-band is developed with a novel calibration scheme. Secondly, in order to the designed radiometer pocess a high temperature accuracy for targets with shelters, crucial technical difficulties are investigated: 1) The long-neglected impact on temperature sensitivity of the single channel radiometer by the frequency stability of LO is analyzed and a LO with high frequency stability and small volume is designed. 2) The calibration accuracy deterioration caused by the receiver's nonideality is analyzed, and a novel calibration algorithm is proposed. 3) the method of plane wave spectrum (PWS) is proposed to derive the planar electric field in near field of the horn antenna for temperature inversion. 4) A more complete microwave thermal radiation transmission model of clothed human body is proposed. Thirdly, several experiments are set up and show that the designed radiometer can track physical temperatures of targets sheltered by cotton cloth relatively accurately, so that methods proposed for indoor near field applications are confirmed effective. Noteworthily, it is the first time in the microwave passive sensing domain that our work systematically proposes the temperature inversion theory for physical temperatures of targets with shelters accurately in noncontact under indoor scenes, and the design scheme for the microwave radiometer optimized portable along with a high temperature sensitivity applied for microwave security and medical monitoring.

Plane-Wave Spectrum Analysis of Spherical Wave Absorption and Reflection by Metasurface Absorber

Plane-Wave Spectrum Analysis of Spherical Wave Absorption and Reflection by Metasurface Absorber

Scaled-Model Radar Cross-Section Measurement: The Influence of the Scattered Field under Gaussian Beam Illumination-A Theoretical Analysis.

At microwave frequencies, radar cross-section (RCS) measurements are usually performed by placing the target in the far-field region of the antenna. The wavefront of the radiating field from the antenna can be approximated as planar, ensuring that the incident field and the power interact with the target independently of the antenna. However, for electrically large targets, the required distance becomes significant, posing challenges for implementation. Scaled-model RCS measurements offer an alternative solution. RCS measurements at terahertz and optical frequencies typically require a collimated beam as the source, where the intercepted power and RCS become dependent on the excitation. To address this dependency, researchers have proposed modifying the RCS definition to account for the intercepted power and to analytically formulate the scattering problem. However, such modifications require prior knowledge of the target's geometry and material properties, which are often not readily available in practice. This also limits the study to only canonical targets. In this paper, we propose an alternative approach for modelling the intercepted power. The Gaussian beam is decomposed into a number of plane waves travelling to different directions using the theory of plane wave spectrum. The scattering problem is solved using the full-wave method of moment. Through theoretical proofs and numerical examples involving spheres and a non-canonical target, with a scaled-model aircraft, we demonstrate that the original RCS definition can serve as a good approximation for scaled measurements, provided that the beam waist is approximately four times the target's dimensions. These findings provide valuable guidelines for radar engineers when performing scaled measurements using collimated beams. The results, which match those obtained from full-model measurements, enable us to predict the RCS of full-scale targets. This capability facilitates various target-related applications, such as target characterization, classification, detection, and even recognition.

Design and measurements of 6 x 6 m collimator reflector with rounded edges

Compact antenna test range (CATR) is designed to form a plane wave at a small distance from the aperture of the collimator reflector, which allows measurements to be made under far field conditions in a compact anechoic chamber. Currently, collimators are in demand due to the technical re-equipment of the industry for the production of 4G, 5G and Internet of Things stuff. The typical size of a quiet zone for these needs is 1–1.5 m. Along with antenna pattern measurements, collimators are widely used for RCS measurements. In the latter case, the measured objects may have dimensions several times larger than the average size of the quiet zone. Manufacturing, installation and adjustment of collimator reflector of several meters in size is a non-trivial task that requires separate study for each project. An incorrect choice of the reflector geometry can lead to an increase in mass and size, which entails an increase in production costs and the anechoic chamber designed for the CATR. In addition, increase in mass imposes additional requirements on the rigidity of the rack to which the reflector is attached, and the foundation under the collimator. As a rule, large-sized reflectors consist of a dozen fragments, which leads to the need to have special adjustment mechanisms for precision tuning of the reflector fragments. These and other problems need to be solved when developing large CATR. The article presents the issues faced by the LLC «RadioLine» in the process of manufacturing and setting up a collimator stand with a 6 x 6 m reflector. The issues of choosing the geometry of the reflector, its focal length have been highlighted. It has been shown how the agreement of the results of three-dimensional modeling of the reflector and production capabilities has been carried out. The features of the design of the reflector rack are touched upon, in particular, the appropriateness of using two materials: one for the base, and the second for the truss, which is connected to the reflector. After discussing the design features, a scheme for measuring the electromagnetic field distribution in a quiet zone, approaches to improving the quality of the RF characteristics of the CATR have been presented. It is noted that in the process of setting up the collimator, in order to determine the directions to the sources of diffraction, it is useful to apply the recalculation of the measured electromagnetic field in the quiet zone into the plane wave spectrum. At the end of the article, quiet zone cuts have been shown at frequencies of 0.75 GHz, 8.2 GHz and 50 GHz. Average peak-to-peak ripple of the amplitude-phase distribution in the operating frequency range of the CATR is 1 dB in amplitude and 10 degrees in phase.

Hybrid OTA Chamber for Multidirectional Testing of Wireless Devices: Plane Wave Spectrum Generator Design and Experimental Demonstration

This article investigates practical implementation aspects of a novel hybrid chamber concept that has been recently introduced for over-the-air (OTA) testing of wireless devices. The chamber allows to synthesize a spectrum of plane waves (PWs) incident on a device under test (DUT) from a wide range of angles of arrival (AoAs) through exploiting multiple field scattering inside the overmoded waveguide (WG) chamber. An optimal design approach for the plane wave spectrum generator (PWSG) array inside the chamber is presented considering: 1) array antenna impedance matching for the desired test zone (TZ) quality and AoAs’ range; 2) an operational frequency bandwidth of the test environment and an instantaneous signal bandwidth; and 3) the impact of PWSG excitation errors. A robust linearly constrained minimum variance (LCMV) beamformer is formulated to realize the desired test environment over a wide frequency band, while accounting for the varying number of the WG propagating modes as excited by PWSG array. Numerical simulations and measurements with the first prototype of the hybrid chamber for FR1 frequency band (~3.5 GHz) are presented. This prototype includes a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${7\times 7}$ </tex-math></inline-formula> bowtie antenna element PWSG array, a 1.00 m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times1.25$ </tex-math></inline-formula> m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times1.75$ </tex-math></inline-formula> m metal WG chamber, an off-line optimal array beamforming setup, and a planar scanner for TZ characterization.

Fractionality and PT symmetry in a square lattice

We study the spectral stability of a 2D discrete Schr\"{o}dinger equation on a square lattice, in the simultaneous presence of a fractional Laplacian and $\cal{PT}$ symmetry. For that purpose, we compute the plane-wave spectrum in closed form, as a function of the gain/loss parameter and the fractional exponent. Examination of the spectrum reveals that an increase of the gain/loss parameter favors the early appearance of complex eigenvalues, thus is, the onset of a broken ${\cal PT}$ symmetry. On the other hand, as the fractional exponent decreases from unity, at a critical value a gap opens up separating the upper and lower bands, and the spectrum becomes real. Further decrease of the exponent increases the width of the gap and the system remains in the $\cal{PT}$-symmetric phase down to a vanishing value of the fractional exponent. Examination of the density of states and the participation ratio reinforce these observations and lead one to conclude that, unlike the standard, non-fractional case where the binary lattice is always in the broken $\cal{PT}$ phase, for the fractional case it is possible to have a symmetric $\cal{P}{\cal T}$ phase in the presence of a finite gain/loss parameter and a small enough fractional exponent.

Fast Spectral-Domain Computation of Radiation Integrals Over Tilted Planes Using Unequally-Spaced Fast Laplace Transforms

A plane-wave spectrum method is presented for the fast computation of radiation integrals for source and observation plates, which can be arbitrarily tilted and separated by an intermediate-to-far-field distance. The method expedites the direct and inverse transforms between spatial and spectral domains using unequally spaced fast Laplace transforms. These fast algorithms allow one to combine fast Fourier transforms (FFTs) and contour deformation in the complex plane with controllable accuracy and computation times close to that of a single 2-D FFT. Hence, scattering interactions between plates of sizes up to thousands of wavelengths can now be computed within seconds using current desktop computers. The fast method is validated here for the case of radio propagation in a canyon street modeled with electrically large facets using the physical optics approximation.

Characteristics of an Airy beam at a dielectric interface

A full analytical theory for the reflection and transmission of an Airy beam impinging on a dielectric surface is presented. Based on the plane-wave angular spectrum expansion, the analytical expressions for the reflected and transmitted fields comprising beam modes are derived. To improve the calculation accuracy, the actual beam field retains up to the second-order terms. The influences of decay factor and beam width on the intensity distributions of the incident, reflected, and transmitted beams are studied. In addition, we investigate the effects of decay factor and beam width on the beam shift of the reflected beam near the Brewster angle. There is a giant negative lateral shift near the Brewster angle. Results show that the beam shift decreases and increases with increasing decay factor and beam width, respectively. A comparison with the beam shifts of Airy beams incident on the interface and dielectric slab at the Brewster angle is also discussed. The beam shift of the dielectric slab exists an abrupt increase. Finally, an Airy beam incident from air to the left-handed material (LHM) is considered. Results indicate that the imaging position of the incident Airy beam in the LHM is affected by the incident angle and negative refractive index. Our results may provide some theoretical support for the applications of Airy beams in detection and imaging.

Scattering by Arbitrary Cross-Section Cylinders Based on the T-Matrix Approach and Cylindrical to Plane Waves Transformation

Multiple scattering of parallel cylinders with arbitrary cross section is computed using the T-matrix of each single scatterer and the general translational matrix for cylindrical waves. Usually, the recommended golden rule to compute the translational matrix is Graf’s addition theorem. However, this approach cannot be properly implemented for some geometries, such as in a two-cylinder case when the center of one of them falls within the minimum circular cylinder that circumscribes the other one. In order to overcome this limitation, a transformation between cylindrical waves and plane waves, followed by propagation of the latter, is proposed. The new approach succeeds due to an adequate truncation of the evanescent plane wave spectrum. This strategy is demonstrated by studying the scattering of three infinite elliptic metallic cylinders for different electrical sizes and observing the convergence of the results as a function of the truncated spectrum. Finally, to conclusively show the interest and applicability of the approach, two more complex problems are treated: a group of infinite elliptic metallic cylinders where two different sizes are combined and a practical real-life filter in substrate integrated waveguide (SIW) technology, including several groups of rectangular dielectric cylinders.

Fast Computation of Electromagnetic Scattering From Dielectric Objects Using Quadrilateral Piecewise Sinusoidal Basis and Characteristic Basis Function Method

A method of moments (MoM)-based procedure is developed to calculate the scattering from homogeneous dielectric bodies. The technique uses quadrilaterals for the approximation of geometry and piecewise sinusoidal (PS) basis functions for the approximation of surface currents. The notable advantage of the PS basis is its radiated fields can be expressed in closed-form. The proposed approach therefore circumvents the need to use Green’s function in formulating the integral equations. Combined with a simple testing procedure, the matrix filling time is reduced and the concern of singularity is removed. To further reduce the computational complexity and enhance the performance, a characteristic basis function method (CBFM) is implemented and embellished with a new characteristic basis function (CBF) generation strategy. Specifically, a cubical surface bounding the entire target is first specified and discretized. A set of auxiliary sources are then defined in a manner similar to that done for a scattering body. These auxiliary sources are defined once and shared by different blocks. In comparison to the traditional plane wave spectrum (PWS) method, the CBFs generated by the new approach are valid not only for plane wave excitations but also for localized excitations. Numerical results are provided to validate the efficacy of the proposed algorithm.

Use of a Set of Wearable Dielectric Scatterers to Improve Electromagnetic Transmission for a Body Power Transfer System

In this paper we present an accurate analytical solution of the scattering of a plane-wave by dielectric cylinders placed above a multilayered medium. An analytical approach is used to solve the scattered field by the cylinders in each medium through expansions into cylindrical waves, expressed through plane-wave spectra. The multilayer models a biological tissue consisting of skin, fat and muscle covered by a cotton textile. Several numerical examples are presented considering the electrical parameters of the biological and textile tissues at the millimeter frequency range (24 GHz). The results show that it is possible to obtain an intensification of the electric field in the underlying tissues in case of TM polarization of the incident wave, finding an interesting application for the charging of implantable or wearable devices.

Simulation and Analysis of Electromagnetic Scattering from Anisotropic Plasma-Coated Electrically Large and Complex Targets

An efficient physical optics (PO) calculation method is proposed for the electromagnetic (EM) scattering of electrically large targets coated with magnetized plasma characterized by asymmetric tensor dielectric parameters. The outer surface of the arbitrarily shaped target is discretized into triangular elements. According to the principle of tangent plane approximation and by using the plane wave spectrum expansion method, the scattered field from one triangular element is derived as a double integral in the spectral domain. To obtain the solution in the spatial domain, the saddle point method is used to asymptotically calculate the integral. Then, the equivalent surface currents (ESCs) are constructed by calculating the surface field at the outer surface of the planar model, from which the PO solution is derived by using the Stratton–Chu integral. Moreover, to interpret the field propagation process in the plasma layer quantitatively, the total scattered field of the coated planar model is decomposed into the superposition of different mode field components. It is observed that the scattered fields demonstrate an inherent cross-polarization phenomenon due to the nonreciprocal constitutive relation of the plasma, which is a distinct feature and is different from the general anisotropic medium whose dielectric parameters can be diagonalized. The effectiveness of the proposed method is verified by numerical results. Furthermore, the proposed algorithm consumes less calculation time and memory as compared to commercial full solvers.

Reflection and transmission of an Airy beam in a dielectric slab

The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method. Based on the plane-wave angular spectrum expansion and Fresnel approximation, the analytical expressions of the reflected field, internal field as well as transmitted field in each region are obtained. Through numerical simulations, the intensity distributions of the incident beam, reflected beam, internal beam as well as transmitted beam are presented at oblique incidence. Besides, we also compare the intensity distributions of the geometrical-optics beam field, the first order beam mode field and the actual beam field, which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab. Meanwhile, the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated. Finally, the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail. The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.

Scattering Characteristics of an Electrically-Large Aircraft Object Illuminated by Bessel Vortex Beams

Based on the excellent and broad prospect of the vortex beams in military application, it is necessary to evaluate the scattering characteristics of classical Bessel beam upon a perfect electrical conductor (PEC) blunt cone model of aircraft structure. First, a Bessel beam is expanded by a series of plane wave spectra. Then, combining the physical optics (PO) method, the scattered field of the object fitted by facet elements can be calculated. The amplitude, phase, and orbital angular momentum (OAM) spectra of scattered field for different object attitudes are discussed in detail. The results show that the backward scattering still retains good OAM characteristics, and which are distorted with the increase of oblique angle. Besides, the backscattering radar cross section (BRCS) of aircraft are also calculated and analyzed, and the scattering results of degenerated zero-order Bessel beam and plane wave are compared to verify the correctness of the proposed theory. Compared with plane waves, object scattering of vortex beams provides a new degree of freedom, providing more information for object detection.

Inverse Imaging Using Total Field Measurements

Most microwave inverse imaging algorithms rely on measurements of both the total and the incident electric field in order to estimate the dielectric properties of an unknown scattering object (SO). We propose a new technique to jointly estimate the incident field and relative permittivity of a heterogeneous dielectric object from measurements of the total electric field alone. For the first task, we express the incident field as a collection of plane waves and estimate the wave coefficients from the given data by leveraging the sparsity of the plane wave spectrum and obtain the solution via a constrained reweighted <inline-formula> <tex-math notation="LaTeX">$L_{1}$ </tex-math></inline-formula> norm minimization technique. Subsequently, we estimate the permittivity and geometry of the SO using a twofold subspace optimization method. We evaluate the performance of our algorithm on synthetically generated object and experimental data. For synthetic objects, the accuracy in reconstruction of the incident field and the relative permittivity is &#x2248;93&#x0025; for field measurements with a 15-dB signal-to-noise ratio, while the accuracy obtained for an experimental data set was &#x2248;90&#x0025;.

Absorbed/Epithelial Power Density Assessment Using Plane-Wave Spectrum Method From Inside the Skin Tissue Above 6 GHz

In this paper, the idea of measurement inside the human skin liquid-filled phantom for 5G technologies is examined. Measurement inside the skin tissue phantom is almost off the table due to the shallow penetration depth of fields at millimeter and quasi-millimeter waves. Antenna-body interactions should be considered for absorbed power density (APD) assessment when the device is close to the human body. These effects can be considered to a large extent by measuring within the liquid phantom. The reconstruction technique is used to determine APD at the human skin surface using the backward plane-wave spectrum method through sampling the E-field at the specific distance within the phantom. The reconstruction errors were obtained using a planar array antenna at 10 to 60 GHz frequencies. These errors were no larger than 9.4%, 7.35%, 7.8% at 10, 24, and 60 GHz for assessing the maximum spatially-averaged power density for a separation distance between the device and tissue phantom larger than 1 mm. At last, the measuring requirement for the electric field was also investigated. The results suggest that the coupling/multiple-reflection effects are negligible when the separation distance between antenna and body is larger than λ.