Search Results (37)

The Feynman path integral formalism for non-relativistic quantum mechanics is revisited. A comparison is made with cases of light propagation (Huygens’ principle) and Brownian motion. The difficulties for a physical model applying Feynman’s formalism are pointed out. A reformulation is proposed, where the transition probability of a particle from one space-time point to another one is the sum of probabilities of the possible paths. As an application, Born approximation for scattering is derived within the formalism, which suggests an interpretation involving the stochastic motion of a particle rather than the square of a wavelike amplitude. Full article

The evolution of telecommunications and radars in the terrestrial and space domains is introducing new specifications for antennas that have difficulty meeting today’s phased arrays. Breakthrough technologies must be introduced to push back the limits not only in beam steering and beam forming, but also in frequency bandwidth, conformation, and multifunctionality. Indeed, the representation of radiating surfaces (Huygens) by arrays of point sources (a century ago!) is the poorest approximation of the rigorous solution, with well-known limitations. The proposed approach starts from the rigorous expression of the field radiated by any antenna obtained using the equivalence principle on any closed surface Sc surrounding the antenna. Important approximations are introduced to apply this rigorous result to the design of beam-agile multisource antennas that require sampling of the radiating Sc surface. The proposed approach samples the Sc surface by slicing it into small piecewise surfaces. For the fabrication of these small surfaces, structures called “pixels” deduced from the s have been designed. Many applications are proposed and compared with array solutions. Full article

In the existing studies of slope stability under seismic excitation, the non-uniform spatiotemporal dynamic response and amplification effect caused by the slope scale are often overlooked. In order to analyze the dynamic response of large-scale slopes under non-uniform seismic excitation, this study presents an analytical model based on the Hilbert’s best approximation problem (BAP), taking into account the scale of slopes under seismic incidence. A methodology for differentiating between the plane wave assumption of Huygens’ principle and BAP principle is proposed. A Stoneley equation considering the scale of the slope on the interface is proposed to analyze the non-uniform spatiotemporal dynamic response. Meanwhile, the Knott equation is subjected to non-uniform seismic waves and adopted to describe the amplification factor of spectral response accelerations (SRA). To visually represent the non-uniform spatiotemporal dynamic response and amplification effect, numerical models based on the finite difference method (FDM) are established to simulate the non-uniform incidence of seismic waves. The numerical simulation results show that the non-uniform dynamic response cannot be disregarded in cases where $L/h>4:20$. Slopes of this scale subjected to seismic wave incidence satisfy the BAP principle. Conversely, the dynamic response exhibits uniformity in cases where $L/h<1:20$, which is in accordance with the plane wave assumption of Huygens’ principle. Full article

Axial flow fans, used for heat dissipation in electronic equipment, may generate significant electromagnetic interference during PWM speed regulation. Due to its multiple radiation sources and relatively smaller size compared to the equipment, the radiation prediction model for equipment-level EMC analysis often involves a huge number of grids, which leads to computational difficulties and inefficiencies, and thus an equivalent modeling method for the electromagnetic radiation of PWM fan is presented. First, a detailed field-circuit coupling model of the radiation from winding and driving circuits is established using the time-domain finite-integral method with non-uniform grids. Then, a near-field hexahedron is defined to surround the fan, and the electromagnetic field of all its surfaces is derived based on the Huygens principle and calculated. Finally, the hexahedron encapsulating all radiation sources within the fan can be used in a higher level simulation as replicable and reusable equivalent sources. The proposed method is validated by a numerical example and actual measurements and applied to predict the radiation emissions within an electronic enclosure. The results show that the equivalent model can reduce 81.4% computation time and maintain good consistency in comparison to the detailed field-circuit coupling model. Full article

The present study is concerned with the power transfer efficiency enhancement using a combination of the multi-hop node (MHN) and the Intelligent Reflecting Surface (IRS)-based passive beamforming technologies. The primary objective is to ensure a high RF-DC converter power conversion efficiency (PCE) used at the receiving end, which is difficult to achieve due to path loss and multi-path propagation. An electronically tunable reconfigurable reflectarray (RRA) designed to operate at the sub-GHz ISM band (865.5 MHz) is utilized to implement the IRS concept. Both the MHN and RRA were developed and studied in our earlier research. The RRA redirects the reflected power-carrying wave amplified by the MHN toward the intended receiver. It comprises two layers: the RF layer containing tunable phase shifters and the ground plane. Each phase shifter comprises two identical eight-shaped metal patches coupled by a pair of varactor diodes used to achieve the reflection phase tuning. The phase gradient method is used to synthesize the RRA phase profiles, ensuring different desired reflection angles. The RRA prototype, composed of 36 phase shifters, is employed in conjunction with the MHN equipped with two antennas and an amplifier. The RRA parameter optimization is accomplished by randomly varying the varactor diode voltages and measuring the corresponding received power levels until the power reflected in the desired direction is maximized. Two measurement scenarios are examined: power transmission without and with the MHN. In the first scenario, the received power is calculated and measured at several distinct beam steering angles for different distances between the Tx antenna and RRA. The same procedure is applied to different distances between the RRA and MHN in the second scenario. The effect of slight deviations in the operating frequency from the designed one (865.5 MHz) on the RRA performance is also examined. Additionally, the received power levels for both scenarios are estimated via full-wave analysis performed using the full-wave simulation software Ansys HFSS 2023 R1. A Huygens’ surface equivalence principle-based model decomposition method was developed and employed to reduce the CPU time. The calculated results are consistent with the measured ones. However, some discrepancies attributed to the adverse effect of RRA diode biasing lines, manufacturing tolerances, and imperfection of the indoor environment model are observed. Full article

Charged quasiparticles, which are constrained to move on a plane, interact by means of electromagnetic (EM) fields which are not subject to this constraint, living, thus, in three-dimensional space. We have, consequently, a hybrid situation where the particles of a given system and the EM fields (through which they interact) live in different dimensions. Pseudo-Quantum Electrodynamics (PQED) is a U(1) gauge field theory that, despite being strictly formulated in two-dimensional space, precisely describes the real EM interaction of charged particles confined to a plane. PQED is completely different from QED(2 + 1), namely, Quantum Electrodynamics of a planar gauge field. It produces, for instance, the correct $1/r$ Coulomb potential between static charges, whereas QED(2 + 1) produces $lnr$ potential. In spite of possessing a nonlocal Lagrangian, it has been shown that PQED preserves both causality and unitarity, as well as the Huygens principle. PQED has been applied successfully to describe the EM interaction of numerous systems containing charged particles constrained to move on a plane. Among these are p-electrons in graphene, silicene, and transition-metal dichalcogenides; systems exhibiting the Valley Quantum Hall Effect; systems inside cavities; and bosonization in (2 + 1)D. Here, we present a review article on PQED (also known as Reduced Quantum Electrodynamics). Full article

We derive the analytical expressions for root-mean-square (rms) beam wander (BW) and relative BW of a twisted electromagnetic elliptical vortex (TEEV) beam propagating through non-Kolmogorov atmospheric turbulence with the help of the extended Huygens–Fresnel principle and the second-order moments of the Wigner distribution function (WDF). Our numerical findings demonstrate that the BW of a TEEV beam with a small ellipticity, a large topological charge as well as a small waist width and initial coherent length is less affected by the turbulence. It can be also found that the effect of turbulence with a larger outer scale of turbulence, a generalized exponent parameter, and a generalized structure parameter on BW is more obvious. It is interesting to find that the effect of atmospheric turbulence on BW for a TEEV beam can be effectively reduced by regulating jointly the symbols and sizes of the twisted factor and topological charge. Therefore, modulation of the structure parameters of a TEEV beam provides a new way to mitigate turbulence-induced beam wander. Our work will be useful for free-space optical communications, remote sensing, and lidar distance measurement. Full article

The resolving power of metalens telescopes rely on their aperture size. Flat telescopes are advancing with the research on super-resolution confocal metalenses with large aperture. However, the aperture sizes of metalenses are usually bound within hundreds of micrometers due to computational and fabrication challenges, limiting their usage on practical optical devices like telescopes. In this work, we demonstrated a two-step designing method for the design of dual-band far-field super-resolution metalens with aperture sizes from the micro-scale to macro-scale. By utilizing two types of inserted unit cells, the phase profile of a dual-wavelength metalens with a small aperture of 100 μm was constructed. Through numerical simulation, the measured FWHM values of the focal spots of 5.81 μm and 6.81 μm at working wavelengths of 632.8 nm and 1265.6 nm were found to all be slightly smaller than the values of 0.61 λ/NA, demonstrating the super-resolution imaging of the designed metalens. By measuring the optical power ratio of the focal plane and the incident plane, the focusing efficiencies were 76% at 632.8 nm and 64% at 1265.6 nm. Based on the design method for small-aperture metalens, far-field imaging properties through the macro metalens with an aperture of 40 mm were simulated by using the Huygens–Fresnel principle. The simulation results demonstrate confocal far-field imaging behavior at the target wavelengths of 632.8 nm and 1265.6 nm, with a focal length of 200 mm. The design method for dual-band far-field super-resolution metalens with a large aperture opens a door towards the practical applications in the dual-band space telescope system. Full article

In this paper, we propose a new method based on Huygens’ principle for calculations of transmission spectra with weak coupling and we call this method an improved Huygens’ principle. The original Huygens’ principle for metamaterial can only deal with transmission spectra without coupling between metamaterial structures. Our improved Huygens’ principle can give the approximate calculations of transmission spectra while considering coupling by employing the original Huygens’ principle. We demonstrate our method by employing full-wave simulations and experimental results. Full article

We investigate the evolution properties of a partially coherent Laguerre–Gaussian vector vortex (LGVV) beam through inhomogeneous atmospheric turbulence. Analytical formulae for the elements of a cross-spectral density matrix of a partially coherent LGVV beam propagating in turbulence are derived with the help of the extended Huygens–Fresnel principle. Our outcomes demonstrate that the normalized initial profile of a partially coherent beam with concentric dark rings gradually evolves into a Gaussian-like beam profile in turbulence. We also find that the beam is emitted at a large zenith angle and quickly converts to a Gaussian-like beam. Furthermore, it is also shown that a propagation beam with a large topological charge has a stronger ability to resist atmospheric turbulence. In order to confirm our numerical results, we combine the complex screen method and multi-phase screen method to simulate the propagation of a partially coherent LGVV beam in atmospheric turbulence. It is indicated that the simulation results are in good agreement with theoretical predictions. Our results will pave the way for the development of free-space optical communications and remote sensing. Full article

An estimation of the electric sources in the heart was conducted using a novel method, based on Huygens’ Principle, aiming at a direct estimation of equivalent bioelectric sources over the heart’s surface in real time. The main scope of this work was to establish a new, fast approach to the solution of the inverse electrocardiography problem. The study was based on recorded electrocardiograms (ECGs). Based on Huygens’ Principle, measurements obtained from the surfaceof a patient’s thorax were interpolated over the surface of the employed volume conductor model and considered as secondary Huygens’ sources. These sources, being non-zero only over the surface under study, were employed to determine the weighting factors of the eigenfunctions’ expansion, describing the generated voltage distribution over the whole conductor volume. With the availability of the potential distribution stemming from measurements, the electromagnetics reciprocity theorem is applied once again to yield the equivalent sources over the pericardium. The methodology is self-validated, since the surface potentials calculated from these equivalent sources are in very good agreement with ECG measurements. The ultimate aim of this effort is to create a tool providing the equivalent epicardial voltage or current sources in real time, i.e., during the ECG measurements with multiple electrodes. Full article

Suppressing the impact of atmospheric turbulence on laser beam propagation is a bottleneck problem in the application of free space optical communications, with the primary difficulty being the lack of a quantitative description of the effect of turbulence on a laser beam. In this paper, we propose a quantitative description of the effect of turbulence and express a quantitative analysis of the effect of atmospheric turbulence on Bessel–Gaussian beam based on the extended Huygens–Fresnel principle. The results of numerical analysis confirm the validity of the theoretical description. This study also shows that the influence of turbulence is stronger when the annular shape of the Bessel–Gaussian beam is more obvious. The method also provides theoretical guidance for reverse engineering the amplitude and phase distribution of the initial laser beam, thereby effectively reducing the impact of atmospheric turbulence on laser beam propagation. Full article

A light ray in space is characterized by two vectors: (i) a transverse spatial vector associated with the point where the ray intersects a given spherical cap; (ii) an angular-frequency vector which defines the ray direction of propagation. Given a light ray propagating from a spherical emitter to a spherical receiver, a linear equation is established that links its representative vectors on the emitter and on the receiver. The link is expressed by means of a matrix which is not homogeneous, since it involves both spatial and angular variables (having distinct physical dimensions). Indeed, the matrix becomes a homogeneous rotation matrix after scaling the previous variables with appropriate dimensional coefficients. When applied to diffraction, in the framework of a scalar theory, the scaling operation results directly in introducing fractional-order Fourier transformations as mathematical expressions of Fresnel diffraction phenomena. Linking angular-frequency vectors and spatial frequencies results in an interpretation of the notion of a spherical angular spectrum. Accordance of both homogeneous and non-homogeneous ray matrices with the Huygens–Fresnel principle is examined. The proposed ray-matrix representation of diffraction is also applied to coherent imaging through a lens. Full article

Novel techniques, such as microwave imaging, have been implemented in different prototypes and are under clinical validation, especially for breast cancer detection, due to their harmless technology and possible clinical advantages over conventional imaging techniques. In the prospective study presented in this work, we aim to investigate through a multicentric European clinical trial (ClinicalTrials.gov Identifier NCT05300464) the effectiveness of the MammoWave microwave imaging device, which uses a Huygens-principle-based radar algorithm for image reconstruction and comprises dedicated image analysis software. A detailed clinical protocol has been prepared outlining all aspects of this study, which will involve adult females having a radiologist study output obtained using conventional exams (mammography and/or ultrasound and/or magnetic resonance imaging) within the previous month. A maximum number of 600 volunteers will be recruited at three centres in Italy and Spain, where they will be asked to sign an informed consent form prior to the MammoWave scan. Conductivity weighted microwave images, representing the homogeneity of the tissues’ dielectric properties, will be created for each breast, using a conductivity = 0.3 S/m. Subsequently, several microwave image parameters (features) will be used to quantify the images’ non-homogenous behaviour. A selection of these features is expected to allow for distinction between breasts with lesions (either benign or malignant) and those without radiological findings. For all the selected features, we will use Welch’s t-test to verify the statistical significance, using the gold standard output of the radiological study review. Full article

Based on the extended Huygens–Fresnel principle and infinitely long phase screen, the scintillation index and the aperture averaging effect of partially coherent beams in computational ghost imaging (CGI) with a finite bucket detector through atmospheric turbulence is investigated analytically and numerically. The signal–to–noise ratio (SNR) is used to evaluate the image quality of computational ghost imaging. It is found that a strong phase modulation effect due to increasing turbulence intensity, leads to a degradation in image quality, as well as an increase in the scintillation index. In addition, the scintillation–saturation phenomenon occurs for strong turbulence. On the other hand, reducing the propagation distance, and the degree of source coherence results in a decrease in the scintillation index and an improvement of image quality. However, deteriorating the degree of beam source coherence could weaken the aperture averaging effect. Thus, the optimal beam and bucket detector aperture size require a trade–off between the scintillation index, the aperture averaging effects, and the image quality in CGI. Full article