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2023 Photonics & Electromagnetics Research Symposium (PIERS)最新文献

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Image Spectrum Decomposition of Ice-Sounding Data in Stratified Medium for Back Projection Algorithm 分层介质中冰探数据图像频谱分解的反投影算法
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221278
Chengfeng Lv, T. Hao
Image formation of synthetic aperture radar, which virtually observes the scenes and identifies targets along the predetermined trajectory, can be applied to ice-sounding data in the time domain, to map subglacial topographic structures with less sidelobe clutters. However, complex signal transmission path within stratified media limits the efficiency and accuracy of focusing. Here, we present the method to analyze the wavenumber support region by decomposing in the spectrum domain the combined vector formed from multi-paths in stratified media. This assists to determine the lowest Nyquist sampling rate, which essentially accelerates the reconstruction of aliased-free images and can be inherently inserted into the fast factorized back projection algorithm framework, based on divide-and-conquer scheme, recursively yielding low-to-high quality images. With this technique, along-track motion perturbations of flights and unknown tomography variations, can be accommodated at the additional but neglectable computational expenses. Results from real ice-sounding data in Antarctica are presented to validate the promising performance of the proposed method.
合成孔径雷达成像可以虚拟地观测场景并沿预定轨迹识别目标,可应用于时域冰探数据,以较少的副瓣杂波绘制冰下地形结构。但分层介质中复杂的信号传输路径限制了聚焦的效率和精度。本文提出了在谱域对分层介质中多路径形成的组合矢量进行分解来分析波数支持域的方法。这有助于确定最低的奈奎斯特采样率,从本质上加快了无混叠图像的重建,并且可以固有地插入到基于分治方案的快速分解反投影算法框架中,递归地生成从低到高质量的图像。利用这种技术,飞行的沿轨道运动扰动和未知的断层扫描变化,可以在额外的但可忽略的计算费用中得到适应。最后给出了南极测冰实测数据的结果,验证了该方法的良好性能。
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引用次数: 0
A Study on Machine Learning Assisted Accelerated Design of Microwave Structures 机器学习辅助微波结构加速设计研究
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221453
Zhao Zhou, Zhaohui Wei, Jian Ren, Nan Sun, Jiali Kang, Ying-Zheng Yin, M. Shen
An increasing number of researchers devote to applying machine learning for ac-celerating design of microwave structures (e.g., antenna, metasurface, filter, etc.), inspired by the great potential that machine learning shows in many fields, such as image/speech/digits recognition, self-driving, text processing, etc. Despite the fact that machine learning based design has been widely validated to be accurate and well-behaved, machine learning based design methods are often doubted in terms of efficiency, because a large amount of simulation works are mandatory to be executed previously for preparing sufficient training data. In that sense, machine learning based design seems not to be efficient, as it takes more simulation works in total than conventional optimization algorithm based design methods. This paper investigates the efficiency of machine learning based design compared with typical optimization algorithm based design, and a generic solution is proposed for reducing the burden of data preparation to improve the efficiency of machine learning based design. By qualitatively analyzing the required simulation cycles during the whole design process, we propose efficiency measures to demonstrate and compare the efficiency of machine learning based design and typical optimization algorithm based design in the context of metasurface design. According to the comparison result, machine learning based design outperforms other methods in terms of efficiency when it comes to high-bit metasurface design, while optimization algorithm based design is more efficient for low-bit meta-surface. Based on the observation, we introduced an improved design approach that combines the advantages of optimization algorithms and machine learning. The qualitative analysis and improved design approach mayalso bring inspiration to the design of other microwave structures. Investigating on improved data acquisition method for reducing required simulation and training data is a promising direction for further boosting machine learning based accelerated design of microwave structures.
越来越多的研究人员致力于将机器学习应用于微波结构(如天线、元表面、滤波器等)的加速设计,受到机器学习在许多领域显示出的巨大潜力的启发,如图像/语音/数字识别、自动驾驶、文本处理等。尽管基于机器学习的设计已经被广泛证明是准确和良好的,但基于机器学习的设计方法在效率方面经常受到质疑,因为为了准备足够的训练数据,之前必须执行大量的模拟工作。从这个意义上说,基于机器学习的设计似乎效率不高,因为它比传统的基于优化算法的设计方法总共需要更多的模拟工作。本文研究了基于机器学习的设计与基于典型优化算法的设计的效率比较,并提出了一种通用的解决方案来减少数据准备的负担,从而提高基于机器学习的设计效率。通过定性分析整个设计过程中所需的仿真周期,我们提出了效率度量,以展示和比较基于机器学习的设计和基于典型优化算法的设计在元表面设计背景下的效率。对比结果表明,基于机器学习的设计在高位元表面设计效率上优于其他方法,而基于优化算法的设计在低位元表面设计效率更高。基于观察,我们引入了一种改进的设计方法,该方法结合了优化算法和机器学习的优点。定性分析和改进的设计方法对其他微波结构的设计也有一定的启发作用。研究改进的数据采集方法以减少所需的模拟和训练数据,是进一步推进基于机器学习的微波结构加速设计的一个有希望的方向。
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引用次数: 0
Quantum Photonics Enhances Continuous Variable Quantum Key Distribution 量子光子学增强连续可变量子密钥分配
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221470
Lang Li, Tao Wang, Peng Huang, Guihua Zeng
Continuous-variable quantum key distribution (CV-QKD) technology has the characteristics of high channel capacity and well compatibility with existing optical communication infrastructures, and has become an important implementation method of quantum secure communication. Quantum photonics technology provides a promising solution for the construction of low-cost, miniaturized, portable, scalable and highly stable CV-QKD systems that can be deployed at large scale [1]. Therefore, it is of great significance to research and build a chip-based CV-QKD system with higher integration, higher system performance and higher practical security for the development of high-performance and practical quantum secure communication technology. This paper mainly reports the latest progress of the research of on-chip CV-QKD system in terms of system practical security [2] and integration of high-performance light sources [3].
连续变量量子密钥分发(CV-QKD)技术具有信道容量大、与现有光通信基础设施兼容性好等特点,已成为量子保密通信的重要实现方式。量子光子学技术为构建低成本、小型化、便携、可扩展、高稳定且可大规模部署的CV-QKD系统提供了一种很有前景的解决方案[1]。因此,研究和构建一种集成度更高、系统性能更高、实用安全性更高的基于芯片的CV-QKD系统,对于发展高性能实用的量子安全通信技术具有重要意义。本文主要报道片上CV-QKD系统在系统实用安全性[2]和高性能光源集成[3]方面的最新研究进展。
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引用次数: 0
Motion of a Charge Density and the Speed of Light in Vacuum Revisited 真空中电荷密度和光速的运动
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221362
N. Yener
As an extension of affirmative past work by the author on the feasibility of an infinite speed of light, this note focuses on the consequences of an infinite speed of light $c$ for a charge density in a motion that starts abruptly in time. In previous work it was proved that the scalar and vector potentials need to be non-retarded or speed of light must be infinite for such a charge density in order that Maxwell's equations be satisfied by the scalar and vector potentials. Here it is found that for this abruptly starting motion of a charge density function Maxwell's equations will fail even if the potentials are not retarded. For even though an infinite $c$ is sufficient for the Lorenz condition on the potentials to be satisfied when $t > 0$, it is not at $t=0$. Then there arises the problem of facing unsatisfied Maxwell's equations and hence the necessity of having to introduce additional source terms into these equations to render them satisfied. It is seen that with inclusion of electric charge and current density terms this objective cannot be attained, and magnetic charge and current density terms are needed as the only means. The steps for the determination of the required magnetic sources are given. The problem is seen to be reduced to that of solving an inverse source problem for Poisson's equation. The obtained electric and magnetic fields with the introduced magnetic sources are non-retarded. The obtained results apply to the case of a continuous charge distribution as well as a point charge.
作为作者过去关于无限光速可行性的肯定工作的延伸,这篇笔记着重于无限光速对在时间上突然开始的运动中的电荷密度的影响。在以前的工作中,证明了标量势和矢量势必须是非延迟的,或者对于这样的电荷密度,光速必须是无限的,这样标量势和矢量势才能满足麦克斯韦方程。这里发现,对于这种突然开始的电荷密度函数运动,麦克斯韦方程组将失效,即使电势没有迟滞。因为即使无限的c足以满足势的洛伦兹条件,当t=0时,它并不满足。然后就出现了面对不满足的麦克斯韦方程组的问题,因此必须在这些方程中引入额外的源项以使它们满足。可见,如果包含电荷和电流密度项,则无法达到这一目标,而需要磁荷和电流密度项作为唯一的手段。给出了确定所需磁源的步骤。这个问题被看作是解泊松方程的逆源问题。所引入的磁源所得到的电场和磁场是无延迟的。所得结果不仅适用于点电荷分布,也适用于连续电荷分布的情况。
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引用次数: 2
Deep Reinforcement Learning-based Auto-tuning Algorithm for Cavity Filters 基于深度强化学习的空腔滤波器自调谐算法
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221259
Daniel Poul Mtowe, Seongho Son, D. Ahn, Dong Min Kim
Over the past few decades, the tuning of cavity filters has often been done by trial and error, using human experience and intuition, due to the imprecision of the design and manufacturing tolerances, which often results in detuning the filters and requiring costly post-production fine-tuning. Various techniques using optimization and machine learning have been investigated to automate the process. The superiority of a deep reinforcement learning approach, which can properly explore various possibilities and operate them in the desired way according to the well-defined reward, has motivated us to apply it to our problem. To meet the demand for an automatic tuning algorithm for cavity filters with high accuracy and efficiency, this study proposes an automatic tuning algorithm for cavity filters based on the deep reinforcement learning. For the efficiency of the tuning process, we limit the order of the elements to be tuned, inspired by the experience of experts based on domain knowledge. In addition, the coarse tuning process is performed first, followed by the fine tuning process to improve the tuning accuracy. The proposed method has demonstrated the ability of the deep reinforcement learning to learn the complex relationship between impedance values of equivalent circuit elements and S-parameters to effectively satisfy filter design requirements within an acceptable time range. The performance of the proposed automatic tuning algorithm has been evaluated through simulation experiments. The effectiveness of the proposed algorithm is demonstrated by the fact that it is able to tune a detuned filter from random starting point to meet its design requirements.
在过去的几十年里,由于设计和制造公差的不精确,腔滤波器的调谐通常是通过尝试和错误来完成的,这通常会导致滤波器失谐并需要昂贵的后期微调。已经研究了使用优化和机器学习的各种技术来实现该过程的自动化。深度强化学习方法的优势在于,它可以正确地探索各种可能性,并根据明确定义的奖励以期望的方式操作它们,这促使我们将其应用于我们的问题。为了满足高精度、高效率的空腔滤波器自动调谐算法的需求,本研究提出了一种基于深度强化学习的空腔滤波器自动调谐算法。为了提高调优过程的效率,我们借鉴了专家基于领域知识的经验,限制了需要调优的元素的顺序。此外,首先进行粗调,然后进行微调,以提高调谐精度。该方法证明了深度强化学习能够学习等效电路元件阻抗值与s参数之间的复杂关系,从而在可接受的时间范围内有效满足滤波器设计要求。通过仿真实验对所提出的自动调谐算法的性能进行了评价。该算法能够从随机起始点调整失谐滤波器以满足其设计要求,证明了该算法的有效性。
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引用次数: 0
Development and Characterisation of a Stent-Like Z-Shaped Wireless Implantable Sensor for Aneurysm Size Detection 用于动脉瘤大小检测的支架状z形无线植入式传感器的研制与表征
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221356
Nuno P. Silva, Bilal Amin, Eoghan Dunne, Martin O'Halloran, A. Elahi
Abdominal aortic aneurysm (AAA) is a dilation of the aorta artery larger than the normal diameter of the artery (> 3 cm) in the abdominal region. Endovascular abdominal aortic repair (EVAR) is the main treatment option for AAA, that involves deploying a graft into the diseased portion of the aorta artery. Hence, creating a new pathway for blood flow and preventing the risk of rupture. This treatment requires follow-up routine on the first and sixth month, and yearly afterwards; which is time-consuming, costly, and resource-demanding for healthcare systems. An alternative approach to traditional imaging modalities used in the follow-up routine is the implantation of a wireless sensor. In this study, a novel wireless implantable sensor with a stent-like Z-shaped configuration is proposed with the objective of tracking the growth of the aneurysm. The proposed sensor is based on an inductor that is designed in a sequential ring of six struts inspired by stent-struts. The inductor has the ability to expand and contract with a change in the diameter of the aneurysm. This study aims to characterise the electrical characteristics of the inductor as the inductor expands with a growing abdominal aortic aneurysm. An analytical expression was developed to define the geometric changes in the inductor that occur over the growth of the aneurysm, and are responsible for the changes in the electrical characteristics of the inductor. Electrical characteristics, including inductance, resistance, and quality factor, were observed in the numerical and experimental evaluation of the performance of the inductor with varying radii. The experimental and numerical results showed that an increase of radius from 5 to 50 mm resulted in an increase of 77% and 106% of inductance, respectively. Moreover, the average percentage difference between the numerical and experimental inductance values was found to be 10%. The resistance of the sensor remains constant during expansion. The preliminary findings of this study showed that the proposed sensor can be used to track the corresponding expansion of the aortic aneurysm over time.
腹主动脉瘤(AAA)是腹主动脉的扩张,其直径大于正常动脉直径(> 3cm)。腹主动脉血管内修复(EVAR)是AAA的主要治疗选择,包括将移植物植入病变的主动脉。因此,为血液流动创造了一条新的途径,防止了破裂的风险。这种治疗需要在第一个月和第六个月进行常规随访,之后每年一次;这对医疗保健系统来说既耗时又昂贵,而且需要资源。在随访常规中使用的传统成像方式的替代方法是植入无线传感器。在这项研究中,我们提出了一种新型的无线植入式传感器,具有类似支架的z形结构,目的是跟踪动脉瘤的生长。所提出的传感器基于一个电感器,该电感器设计在六个支柱的连续环中,灵感来自支架支柱。电感器有能力随着动脉瘤直径的变化而扩张和收缩。这项研究的目的是描述电感器随着腹主动脉瘤的增长而膨胀时的电特性。开发了一个解析表达式来定义在动脉瘤生长过程中电感器的几何变化,并负责电感器电特性的变化。在数值和实验中对不同半径的电感器进行了性能评估,包括电感、电阻和品质因子。实验和数值结果表明,当半径从5 mm增加到50 mm时,电感分别增加77%和106%。此外,数值电感值与实验电感值之间的平均百分比差异为10%。传感器的电阻在膨胀过程中保持恒定。本研究的初步结果表明,所提出的传感器可用于跟踪相应的主动脉瘤随时间的扩张。
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引用次数: 0
Aircraft Optical Video Transmission Communication based on the Forward Error Correction Codes 基于前向纠错码的飞机光视频传输通信
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221478
A. Krotov, Mihail Krotov, S. Matsenko, T. Salgals, V. Bobrovs
Modern aircraft information and telecommunication systems are segmented into two separate networks: data transmission and video networks. This differs from the typical approach for modern telecommunications in which all types of traffic are transmitted through one network (for example, access NGN-IMS networks). The external aircraft electromagnetic environment is constantly becoming more complicated: the high intensity of the electromagnetic field $(E_{mf})$ due to the increase of radio frequencies quantity and their frequencies spectrum expansion, which occupies a band from 10 kHz to 3 GHz that affects the quality of service of electronic devices on board. A new method of image representation with forward error correction (FEC) codes was developed and considered. The method decreases the Bit Error Ratio (BER) for asymmetric data transmission via fiber optics and computational complexity for video correction. The paper investigates the superior performance of Low-Density Parity-Check (LDPC-) based on Irregular Repeat-Accumulate (IRA) codes over regular LDPC codes for the same code rate with Gaussian noise to match a certain signal-to-noise ratio (SNR). The LDPC FEC codes are simulated with code rates $R_{c}in{1/2}$ from the digital video broadcasting by satellite - second-generation (DVB-S2) standard. This setup has 17 low-data network subscribers and one highly loaded network section for video transmission. This approach makes it possible to increase the load in the asymmetric networks for aircraft onboard electronic systems and to ensure the quality of video images in the pickup environment to avionics during operation, for example, radar devices.
现代飞机信息和电信系统分为两个独立的网络:数据传输和视频网络。这与现代电信的典型方法不同,在现代电信中,所有类型的流量都通过一个网络传输(例如,接入NGN-IMS网络)。飞机外部电磁环境不断复杂化:由于无线电频率数量的增加及其频谱的扩展,电磁场强度高$(E_{mf})$,占据了从10khz到3ghz的频段,影响了机上电子设备的服务质量。提出并考虑了一种基于前向纠错码的图像表示方法。该方法降低了非对称光纤传输的误码率和视频校正的计算复杂度。在具有高斯噪声的相同码率下,研究了基于不规则重复累加码的低密度奇偶校验(LDPC-)在匹配一定信噪比(SNR)方面优于规则LDPC码的性能。采用卫星第二代数字视频广播(DVB-S2)标准的码率$R_{c}in{1/2}$对LDPC FEC码进行了仿真。该设置有17个低数据网络用户和一个用于视频传输的高负载网络部分。这种方法可以增加机载电子系统的非对称网络负载,并确保在操作期间航空电子设备(例如雷达设备)的拾取环境中视频图像的质量。
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引用次数: 0
Low-symmetrical Topological Graphene Metasurfaces with Quantum Valley and Spin Hall Effects 具有量子谷和自旋霍尔效应的低对称拓扑石墨烯超表面
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221238
Long Chen, Z. Lan, Xiong Wei Wu, Qian Ma, J. You, T. Cui
As topological phases in the physics of condensed matter have evolved over the last few years, topological photonics began to emerge and therefore attracted wide attention. Photonic crystals provide an excellent platform for the study of topological phenomena, combining the flexibly tuned symmetries of photonic crystals with the macroscopic properties of classical photonic systems. Graphene's special physical properties make it an excellent candidate for the realization of topological photonic systems at terahertz (THz) and mid-infrared (MIR) frequencies. Topological valley transport based on graphene plasmons was studied, as well as bilayer systems for valley and layer pseudospin studies. However, high point group symmetry topological systems have been the focus of most of the relevant studies to date. In this paper, it is shown for the first time that graphene plasmonic crystals with $C_{1v}$ symmetry are able to open the Dirac cone, leading to topological band gap. Subsequently, a domain-wall interface will be constructed and quantum valley Hall plasmons will be demonstrated in a monolayer graphene metasurface. In a graphene metasurface consisting of two layers, we also demonstrate quantum pseudospin Hall plasmons. Further exploration of the Dirac points protected by low-symmetry and their promising practical applications will be facilitated by the initial study and demonstration of the low-symmetric $C_{2v}$ and $C_{1v}$ point groups. Furthermore, this new low point group symmetry design principle is extendable to other classical waves.
近年来,随着凝聚态物理中拓扑相的发展,拓扑光子学开始出现并引起了广泛的关注。光子晶体将光子晶体的灵活调谐对称性与经典光子系统的宏观特性相结合,为拓扑现象的研究提供了一个很好的平台。石墨烯的特殊物理性质使其成为实现太赫兹(THz)和中红外(MIR)频率拓扑光子系统的优秀候选者。研究了基于石墨烯等离子体的拓扑谷输运,以及谷和层伪自旋的双层系统。然而,高点群对称拓扑系统一直是迄今为止大多数相关研究的焦点。本文首次证明了具有$C_{1v}$对称性的石墨烯等离子体晶体能够打开狄拉克锥,从而导致拓扑带隙。随后,将构建畴壁界面,并在单层石墨烯超表面上展示量子谷霍尔等离子体。在由两层组成的石墨烯超表面中,我们也展示了量子伪自旋霍尔等离子体。低对称$C_{2v}$和$C_{1v}$点群的初步研究和论证,将有助于进一步探索低对称保护的狄拉克点及其有前景的实际应用。此外,这种新的低点群对称设计原理可推广到其他经典波中。
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引用次数: 0
MXene-GST-Graphene-Si Composited Tunable Surface Plasmon Resonance-Based Refractive Index Sensor Operated at Infrared Optical Wavelength 基于mxene - gst -石墨烯-硅复合可调谐表面等离子体共振的红外折射率传感器
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221392
V. Vekariya, Vishal P. Sorathiya, K. Jadav
We proposed the numerical study and analysis of a tunable surface plasmon resonance-based refractive index sensor for the infrared frequency spectrum. The proposed structure was formed using Au-Si-Graphene-GeSbTe(GST)-MXene-BK7 composited material structure. The proposed design has been numerically simulated over the infrared wavelength of $1.3 mu mathrm{m}$ to $2.5 mu mathrm{m}$. This structure can be tunable with different temperature values because of the state of the phase material GST. The GST material provides two forms of tunability: amorphous state (aGST) and crystalline state (cGST). This design is numerically investigated over the optical refractive index of 1 to 2.4, covering the standard refractive index of biomarker concentrations such as haemoglobin, urine, cortisol, cancerous etc. The proposed structure's tunable behaviour will help design a biosensor structure and its point of care device for a wide range of biosensing or refractive index sensing applications.
提出了一种基于表面等离子体共振的可调谐红外光谱折射率传感器的数值研究和分析。该结构采用au - si -石墨烯- gesbte (GST)-MXene-BK7复合材料结构形成。在$1.3 mu mathrm{m}$到$2.5 mu mathrm{m}$的红外波长范围内对所提出的设计进行了数值模拟。由于相材料GST的状态,这种结构可以在不同的温度值下进行调节。GST材料提供两种形式的可调性:无定形(aGST)和晶态(cGST)。该设计在1至2.4的光学折射率范围内进行了数值研究,涵盖了血红蛋白、尿液、皮质醇、癌症等生物标志物浓度的标准折射率。所提出的结构的可调行为将有助于设计生物传感器结构及其护理点设备,用于广泛的生物传感或折射率传感应用。
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引用次数: 0
Motion of a Charge Density, Necessary Magnetic Sources and Solution of Maxwell's Equations including Magnetic Sources by Employing Potentials 电荷密度的运动,必要的磁源和麦克斯韦方程组包括磁源的利用势解
Pub Date : 2023-07-03 DOI: 10.1109/PIERS59004.2023.10221536
N. Yener
We treat the problem of determining the magnetic sources that have been shown to come into existence when an electric charge density abruptly starts an arbitrary motion and hence an infinite speed of light becomes necessary for the satisfaction of the Lorenz condition for the scalar and vector potentials. The change that the Poynting theorem equation undergoes when an infinite speed of light constraint is enforced is the basis for the development and also use is made of the fact that the required magnetic and electric charge density functions share the same support and the same velocity in their motion. Reference to Green's functions in the source region is made to obtain the solution for the magnetic sources. The magnetic sources are computed to be in the form $m=Zrho$ and $vec{M}=Zvec{J}$ where $Z$ is the wave impedance of the lossless, simple medium which can be vacuum. Also, the solution of Maxwell's equations incorporating the magnetic charge and current densities is given in terms of potentials with an infinite speed of propagation for the waves emitted by the charge functions. The magnetic scalar potential is a summation in the form of an integral of monopole moments. For $t > 0$ even though the resulting differential equations involve biharmonic operators, particular solutions of these equations are essentially solutions of Poisson's equations. When $t > 0$ the same Lorenz condition for the case with no magnetic sources appears also in this case with magnetic sources. The solutions for the potentials at $t=0$ where the Lorenz condition fails are obtained using the Helmholtz theorem.
我们处理确定磁源的问题,当电荷密度突然开始任意运动时,磁源已被证明是存在的,因此,无限光速成为满足标量势和矢量势的洛伦兹条件所必需的。当施加无限光速约束时,Poynting定理方程所经历的变化是发展的基础,并且利用了所需的磁和电荷密度函数在其运动中具有相同的支撑和相同的速度这一事实。参考源区域的格林函数,得到磁源的解。磁源的计算形式为$m=Zrho$和$vec{M}=Zvec{J}$,其中$Z$是可以是真空的无损简单介质的波阻抗。同时,结合磁荷和电流密度的麦克斯韦方程组的解以电荷函数发射的波具有无限传播速度的势的形式给出。磁标量势是单极矩积分形式的和。对于$t > 0$,即使得到的微分方程包含双调和算子,这些方程的特解本质上是泊松方程的解。当$t > 0$没有磁源的情况下同样的洛伦兹条件也出现在有磁源的情况下。利用亥姆霍兹定理得到了在$t=0$处洛伦兹条件失效的势的解。
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引用次数: 2
期刊
2023 Photonics & Electromagnetics Research Symposium (PIERS)
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