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We have developed a circuit to demonstrate the phase relationships between resistive and reactive elements in series RLC circuits. We utilize a differential amplifier to allow the phases of the three elements and the current to be simultaneously displayed on an inexpensive four channel oscilloscope. We have included a novel circuit that provides a visual indication of the magnitude and direction of the voltage or current using LEDs. This allows the phase relationships to be demonstrated directly using the very intuitive measurement of the brightness of a light. [ABSTRACT FROM AUTHOR]

An electronic circuit for controlling RLC experiments is shown. This arrangement does not employ a function generator, which makes it more suitable when a wide range of R, L and C values is required and a relatively high current is involved. This circuit can be used for driven and undriven DC experiments. [ABSTRACT FROM AUTHOR]

This paper investigates a highly selective frequency selective rasorber (FSR) utilizing interdigitated resonators, characterized by a passband exhibiting low insertion loss (IL) and the introduction of a second-order passband response in the lossless layer enhances selectivity on both sides of the passband. The lossy unit is implemented by inserting interdigitated resonators on an octagonal ring loaded with lumped resistors, while the lossless layer is constructed with a five-layer structure. Simulation results demonstrate a low IL value of 0.78 dB at 3.5 GHz. At vertical incidence, the S 21>−3 dB bandwidth ranges from 3.41 to 3.67 GHz, and the S 11<−10 dB range spans from 2.2 to 8.2 GHz, obtaining two absorption bands on either side of the passband, with absorption rates exceeding 80%. The operating frequency bands are 1.95–3.27 GHz and 3.8–8.4 GHz. The designed FSR exhibits polarization insensitive. To validate simulation results, a prototype FSR was fabricated and tested, with experimental data aligning with simulation results. [ABSTRACT FROM AUTHOR]

This paper presents machine learning classification on simulated data of permeable conducting spheres in air and seawater irradiated by low frequency electromagnetic pulses. Classification accuracy greater than 90% was achieved. The simulated data were generated using an analytical model of a magnetic dipole in air and seawater placed 1.5–3.5 m above the center of the sphere in 50 cm increments. The spheres had radii of 40 cm and 50 cm and were of permeable materials, such as steel, and non-permeable materials, such as aluminum. A series RL circuit was analytically modeled as the transmitter coil, and an RLC circuit as the receiver coil. Additive white Gaussian noise was added to the simulated data to test the robustness of the machine learning algorithms to noise. Multiple machine learning algorithms were used for classification including a perceptron and multiclass logistic regression, which are linear models, and a neural network, 1D convolutional neural network (CNN), and 2D CNN, which are nonlinear models. Feature maps are plotted for the CNNs and provide explainability of the salient parts of the time signature and spectrogram data used for classification. The pulses investigated, which expand the literature, include a two-sided decaying exponential, Heaviside step-off, triangular, Gaussian, rectangular, modulated Gaussian, raised cosine, and rectangular down-chirp. Propagation effects, including dispersion and frequency dependent attenuation, are encapsulated by the analytical model, which was verified using finite element modeling. The results in this paper show that machine learning methods are a viable alternative to inversion of electromagnetic induction (EMI) data for metallic sphere classification, with the advantage of real-time classification without the use of a physics-based model. The nonlinear machine learning algorithms used in this work were able to accurately classify metallic spheres in seawater even with significant pulse distortion caused by dispersion and frequency dependent attenuation. This paper presents the first effort towards the use of machine learning to classify metallic objects in seawater based on EMI sensing. [ABSTRACT FROM AUTHOR]

The wideband absorption and transmission of frequency-selective rasorber (FSR) remain a persistent challenge in the application of radar devices. In this article, a novel high performance wideband FSR design based on cross bend resonators was proposed. The FSR consists of an upper absorption lossy layer, which offers broad absorption and transmission bands, and a lower bandpass frequency-selective surface that enables a highly selective transmission of incident electromagnetic wave. Full wave simulation results showed that this novel design achieves an absorption bandwidth of 83.7% with more than 90% absorptivity in the frequency range of 5.2–12.7 GHz. Furthermore, the passband's fractional bandwidth for the insertion loss (IL) less than −3 dB is 33.9%, ranging from 14.9 to 21 GHz, with the minimum IL recorded at 0.69 dB at 17.7 GHz. To further verify the proposed method, a prototype FSR with 10 × 10 units of 120 mm × 120 mm was fabricated and the performance of the FSR was tested. The experiment results were in good agreement with the simulated results, and it showed a significant monostatic radar cross-section reduction in the frequency range of 5.3 GHz to 18.3 GHz compared with a metallic plane of the same size. [ABSTRACT FROM AUTHOR]

The measured voltage at the inductor in an RLC series circuit connected to a sinusoidal electromotive force depends on the current and the impedance. The latter does not only include the inductive reactance only but also the ohmic resistance of the inductor. This fact has a clear consequence on the result of the measurement as the measured voltage at the inductor is not in counterphase with the measured voltage at the capacitance as shown in theory where ideal inductors are usually considered. In this work, the resistance of a coil in an RLC circuit is obtained from the direct measurements of the phase of the voltage at the coil at resonance and the resonant frequency for different values of capacitance. This value is compared with the resistance of the coil determined directly with an ohmmeter. The agreement between both values is very good. The conventional signal generator has been replaced by a smartphone which is a very familiar device for the students. The smartphone can provide the necessary voltage supply for the experiment to be carried out successfully. [ABSTRACT FROM AUTHOR]

In this work three examples of textbook circuits (resistor-capacitor, resistor-inductor and resistor-inductor-capacitor) have been modeled by employing the Euler method for the approximate solution of differential equations using algorithms implemented in the Python programming language. The aim of this work was to demonstrate how simple, yet highly effective, algorithms can be neatly implemented in one of the currently most popular programming languages for scientific applications. At the same time, the visualization of the results allows for a detailed introduction to the properties of the circuits most frequently commented on in all the relevant textbooks. Our code, as provided to the reader, includes detailed comments, and can easily be modified to model other similar systems. Instructions on how to prepare tasks for students have been also provided. [ABSTRACT FROM AUTHOR]

A flexible extra broadband metamaterial absorber (MMA) stacked with five layers working at 2 GHz–40 GHz is investigated. Each layer is composed of polyvinyl chloride (PVC), polyimide (PI), and a frequency selective surface (FSS), which is printed on PI using conductive ink. To investigate this absorber, both one-dimensional analogous circuit analysis and three-dimensional full-wave simulation based on a physical model are provided. Various crucial electromagnetic properties, such as absorption, effective impedance, complex permittivity and permeability, electric current distribution and magnetic field distribution at resonant peak points, are studied in detail. Analysis shows that the working frequency of this absorber covers entire S, C, X, Ku, K and Ka bands with a minimum thickness of 0.098 λ max (λ max is the maximum wavelength in the absorption band), and the fractional bandwidth (FBW) reaches 181.1%. Moreover, the reflection coefficient is less than −10 dB at 1.998 GHz–40.056 GHz at normal incidence, and the absorptivity of the plane wave is greater than 80% when the incident angle is smaller than 50°. Furthermore, the proposed absorber is experimentally validated, and the experimental results show good agreement with the simulation results, which demonstrates the potential applicability of this absorber at 2 GHz–40 GHz. [ABSTRACT FROM AUTHOR]

Conventional frequency selective surface (FSS) absorbers design is time-consuming, involving multiple electromagnetic (EM) simulations for parameter scanning. A novel reverse design method is proposed utilizing evolutionary deep learning (EDL) based on an improved bacterial foraging optimization (IBFO) algorithm and a deep belief network. It establishes the relationship between the geometric structure and EM response. The combination of IBFO and EDL facilitates an efficient optimization for structural parameters, mitigating the 'one-to-many' problem and accelerating the design process. An optically transparent FSS absorber with an ultra-bandwidth of 8–18 GHz is designed to verify the proposed method's capability. The simulation and experimental results demonstrate that the absorber displays exceptional characteristics such as polarization insensitivity and robustness under a 45° oblique incidence angle, making it a suitable candidate for radar stealth and photovoltaic solar energy applications. The proposed method can be applied to the design and optimization of various absorbers and complex EM devices. [ABSTRACT FROM AUTHOR]

In this paper, a lightweight high-efficiency circularly polarized (CP) all-metal antenna design method is presented for satellite industry applications. The proposed antenna is composed of a rectangular waveguide feeder, a high-order mode cavity and a metasurface circular polarizer (MCP). The cavity high-order mode TE440 is directly excited by four coupling slots in the waveguide. The MCP is placed on the cavity to generate the CP radiation. Due to the introduction of high-order mode technology and MCP, all metal walls inside the antenna can be removed, which are necessary in conventional waveguide structures, and weight is thereby significantly reduced. To reflect the weight advantage, a conventional metal wall-loaded waveguide antenna of the same size is designed. The measured results show that the proposed antenna has wider impedance and axial ratio bandwidths, and higher radiation efficiency. In particular, the proposed antenna is 40% lighter than the comparative one, indicating that it is more applicable to satellite platforms with limited loading capacities. [ABSTRACT FROM AUTHOR]

The rapid development of surveillance technology has driven the research of multispectral stealth. Demand for infrared and microwave radar compatible stealth is becoming increasingly urgent in military applications. Herein, a versatile metamaterial absorber is designed and fabricated to simultaneously achieve ultra-broadband radar scattering reduction, low infrared emission, and high optical transparency. The designed structure consists of an infrared stealth layer, radar absorption layers, and backing ground. The infrared stealth layer employs specifically indium tin oxide (ITO) square patches, while the radar absorption layers can be obtained by stacking different size ITO patterned films of the same structure with high surface resistances, realizing broadband microwave stealth performance in the 1.98–18.6 GHz frequency range with an incident angle of 45°. The broad radar stealth and low infrared emissivity of 0.283 are consistent with the simulations and calculations. Furthermore, the designed structure exhibits characteristics such as polarization insensitivity, wide incident angles, optical transparency, and flexibility, allowing for a wide range of applications in various environments. [ABSTRACT FROM AUTHOR]

The resonance characteristics of vibrating structures change when they are immersed in fluids and these changes can be related to the parameters density and viscosity of Newtonian liquids. The various suitable structures, vibration modes, transduction principles, and signal analysis methods lead to an immense variety of sensor systems reported in the literature. In this review, we focus on the basic similarities between various electromechanical transducers and their evaluation methods and show that despite the apparent differences, a common design route can be followed. It is outlined that single vibration modes can be approximated by damped harmonic oscillators where the hydrodynamic loading is accounted for by a general model. The two common classes of sensors, the piezoelectric and the electrodynamic, can be described by dual circuits such that the same resonance estimation method can be applied. Also, the limitations associated with this unified approach are discussed. Furthermore, aspects concerning interface circuits and accuracy-limiting factors, such as noise and interference, are reviewed. [ABSTRACT FROM AUTHOR]

A novel hybrid structure with high responsivity and efficiency is proposed based on an L-shaped frame nano-antenna (LSFNA) array for solar energy harvesting application. So, two types of LSFNAs are designed and optimized to enhance the harvesting characteristics of traditional simple electric dipole nano-antenna (SEDNA). The LSFNA geometrical dimensions are optimized to have the best values for the required input impedance at three resonance wavelengths of λres = 10 μm, 15 μm, and 20 μm. Then the LSFNAs with three different sizes are modeled like a planar spiral-shaped array (PSSA). Also, a fractal bowtie nano-antenna is connected with the PSSA in the array gap. This proposed hybrid structure consists of two main elements: (I) Three different sizes of the LSFNAs with two different material types are designed based on the thin-film metal–insulator–metal diodes that are a proper method for infrared energy harvesting. (II) The PSSA gap is designed based on the electron field emission proposed by the Fowler–Nordheim theory for the array rectification. Finally, the proposed device is analyzed. The results show that the PSSA not only has an averaged 3-time enhancement in the harvesting characteristics (such as return loss, harvesting efficiency, etc.) than the previously proposed structures but also is a multi-resonance wide-band device. Furthermore, the proposed antenna takes up less space in the electronic circuit and has an easy implementation process. [ABSTRACT FROM AUTHOR]

Rotary-dependent metasurfaces incorporating with kirigami configuration feature unique properties that offer alternative and active solutions in reconfigurable structures and devices providing diverse platforms to control electromagnetic (EM) waves on the deep subwavelength scale. Herein, a transformable metasurface using a switchable rotating kirigami configuration that absorbs EM waves at different frequency regions and overcomes several fundamental limitations of conventional metasurfaces, including non-reconfigurability, narrow bandwidth operation, and sensitive polarization, is introduced. By rotating kirigami-pixels in predestinated orientations, the absorption bandwidths can be mechanically switched to cover the S, C, X and Ku bands. The concept and physical phenomena were confirmed by numerical simulations, theoretical analysis, and experiments. Such a switchable metasurface promotes an impressive approach to realize reconfigurable meta-devices that are lightweight, cost-effective and flexible. [ABSTRACT FROM AUTHOR]

Herein, we discuss the conditions for excitation of symmetry-protected toroidal dipole modes in all-dielectric metasurfaces composed of trimer or twin-trimer clusters of dielectric disks. Such metasurfaces permit enhanced light–matter interaction due to spatially confined light in resonant systems with a high-quality factor. To describe characteristics of toroidal modes existing in the clusters, we use the magnetic dipole moments approximation, group-theoretical methods, group representation theory, symmetry-adapted linear combination method, and circuit theory. To validate the obtained theoretical results, we fulfill both full-wave numerical simulations and microwave experiments. In particular, we have shown that the toroidal dipole mode appears as a quasi-dark state of the trimer. It can be excited in the metasurface by the field of a linearly polarized wave, providing the symmetry of the trimer is properly reduced. In the metasurface, the properties of the toroidal dipole mode are determined primarily by the parameters of a single trimer and are not a consequence of the periodicity of the array. The coupling of the toroidal dipole modes in the twin-trimers can appear in both bonding and anti-bonding fashion resulting in different orders of the net toroidal dipole moment. Due to the unique field configuration of these modes, the proposed metasurfaces can be considered as a platform for efficient light–matter interaction for enhanced absorption, non-linear switching, and sensing. [ABSTRACT FROM AUTHOR]

We propose a scheme to realize various non-Hermitian topological phases in a topolectrical (TE) circuit network consisting of resistors, inductors, and capacitors. These phases are characterized by topologically protected exceptional points and lines. The positive and negative resistive couplings Rg in the circuit provide loss and gain factors which break the Hermiticity of the circuit Laplacian. By controlling Rg, the exceptional lines of the circuit can be modulated, e.g. from open curves to closed ellipses in the Brillouin zone. In practice, the topology of the exceptional lines can be detected by the impedance spectra of the circuit. We also considered finite TE systems with open boundary conditions, the admittance spectra of which exhibit highly tunable zero-admittance states demarcated by boundary points (BPs). The phase diagram of the system shows topological phases that are characterized by the number of their BPs. The transition between different phases can be controlled by varying the circuit parameters and tracked via the impedance readout between the terminal nodes. Our TE model offers an accessible and tunable means of realizing different topological phases in a non-Hermitian framework and characterizing them based on their boundary point and exceptional line configurations. [ABSTRACT FROM AUTHOR]

Infrared (IR) and terahertz plasmons in two-dimensional (2D) materials are commonly excited by metallic or dielectric grating couplers with deep-submicron features fabricated by e-beam lithography. Mass reproduction of such gratings at macroscopic scales is a labor-consuming and expensive technology. Here, we show that localized plasmons in graphene can be generated on macroscopic scales with couplers based on randomly oriented particle-like nanorods (NRs) in close proximity to graphene layer. We monitor the excitation of graphene plasmons indirectly by tracking the changes in reflection/absorption spectra of methylene blue (MB) or polymethyl methacrylate(PMMA) molecules deposited on the structure. Hybridization of spectrally broad graphene plasmon and narrow molecular oscillators results in enhanced oscillator strengths and Fano scattering related lines asymmetry in reflection spectra. [ABSTRACT FROM AUTHOR]

Chipless RFID sensors attract attention to structural health monitoring (SHM) because of its advantages of being low-cost, wireless, passive, and having multiple resonances for sensing. Its application for corrosion sensing, however, receives little attention and faces challenges in terms of sensitivity and reliability. This paper proposes a chipless RFID sensor for corrosion characterization based on frequency selective surface (FSS) and feature fusion. An FSS pattern on a substrate is designed to generate three resonances within 2–6 GHz. The ability of the FSS to characterize corrosion thickness was simulated and validated in the experiments. The experimental results using dedicated corrosion undercoating samples show that the FSS based chipless RFID sensor can be used to characterize corrosion, where the three resonance frequency features provide sensitivity and consistent monotonic relations to the corrosion progression. Furthermore, feature fusion using simple sum and confidence weighted averaging (CWA) can enhance the sensitivity and reliability of the sensor. With the low-profile and printability of the sensor, this work paves the way for smart coatings for corrosion sensing and monitoring on metallic structures. [ABSTRACT FROM AUTHOR]

In this article, it is shown how a smartphone can be used together with an e-textile structure, such as smart clothing, or any other smart home textile structure, smart composite, etc, to power it and to send and receive data generated by the e-textile by using the magnetic induction phenomenon through textile materials. This has been achieved using the NFC communication protocol and NFC compatible fully textile antennas without any electronic components such as resistors, inductors or capacitors. Our NFC antennas have been realized by embroidery and geometrical shapes using conductive threads. All the antennas realized have been tested to show their capacity to send the power and to send and receive data from sensors, in particular by testing their resonant frequencies, which are 13.7 MHz and 13.83 MHz, and their quality factor, which are 45 and 55, respectively. The approach used in this work facilitates the design and production of smart textiles and their reliability and washability, as they do not need any more to be equipped with power supplies such as batteries and data acquisition and interface cards, that are not laundering and cleaning friendly and are very difficult to be realized on flexible structures making them textile compatible. Therefore, we believe that in the future, a smartphone placed in specific locations in our clothing (pockets) equipped with our antennas will help the development and the market readiness of future generations of smart textile structures. The realized prototypes will enable to create a sensor network by acting as a current extension transmitting power and data. [ABSTRACT FROM AUTHOR]

This paper presents the analytical modeling, simulation and experimental validation of sensitivity, temperature variation and active controllability of MEMS geometric anti-spring (GAS) devices. Two models, the elasticity model and the thermal drift model, were proposed and analyzed, based on the study of asymmetrical and symmetrical geometric anti-spring structures. With the elasticity model, structural optimization led to analytical frequency-prestress design formula and a dedicated MEMS structure. An independent pre-stress and frequency shift effect is the result of thermal changes, so a thermal drift analytical model was built for the geometric anti-spring device, showing thermal sensitivities of 82.5 ppm/°C and 58.4 ppm/°C for the 3-spring and 4-spring devices, respectively. The analytical model was validated by both finite element analyses and experimental measurements. The designed devices (3-springs and 4-springs) were tested afterward in a dedicated setup, for both positive and negative electrostatically induced pre-stresses. Without electrical compensation, the thermal drift of the symmetrical 4-spring GAS device, for temperatures in the range +25°C to +110°C, is about 2138 ppm, and it is reduced to only 8.35 ppm when the electrostatic temperature compensation is active. Similarly, the asymmetrical structure has an uncompensated thermal sensitivity of its resonant frequency of 2254 ppm in the temperature operation range, and it is reduced to 51.5 ppm with electrical compensation within the easily controlled range of the temperature span, from +25°C to +75°C. As a result, although the benefits of the asymmetrical structure would lead to a higher sensitivity, trade-offs related to thermally-induced drift behavior and controllability also should be taken into consideration in the selection of the structural topology and application environment. [ABSTRACT FROM AUTHOR]

We present a general physics laboratory exercise that centres around the use of the electrocardiogram sensor as an application of circuits and electronic signal filtering. Although these topics are commonly taught in the general physics classroom, many students consider topics such as alternating current as unrelated to their future professions. This exercise provides the motivation for life science and pre-health majors to learn concepts such as voltage, resistance, alternating and direct current, RLC circuits, as well as signal and noise, in an introductory undergraduate physics lab. [ABSTRACT FROM AUTHOR]

The motion of charged particles can be interfaced with electric circuitry via the current induced in nearby pick-up electrodes. Here we show how the rotational and translational dynamics of levitated objects with arbitrary charge distributions can be coupled to a circuit and how the latter acts back on the particle motion. The ensuing cooling rates in series and parallel RLC circuits are determined, demonstrating that quadrupole ion traps are well suited for implementing all-electric cooling. We derive the effective macromotion potential for general trap geometries and illustrate how consecutive rotational and translational resistive cooling of a microscale particle can be achieved in linear Paul traps.

We present an easily reproducible, open-source, sound card based experimental set-up to support transfer function measurement. Our system is able to visualize the signals of mechanical and electrical resonances and their spectra in real time. We give a brief description of the system, and show some examples of electrical and mechanical resonance experiments that are supported by the system. The theoretical background, experimental set-up, component selection and digital signal processing are all discussed, and more detailed information (building instructions, software download) is provided on a dedicated web page (www.noise.inf.u-szeged.hu/edudev/RealTimeAnalysisOfResonances/). The experimental set-up can support the undergraduate and graduate education of students of physics, physics education and engineering by means of experimental demonstrations and laboratory exercises. The very low cost, high efficiency and transparent system provides a scalable experimental environment that can be easily built in several instances. [ABSTRACT FROM AUTHOR]

An electromagnetic shunt damper (EMSD) is composed of an electromagnetic damper connected to one or more RLC shunt circuits. Through a theoretical comparison, this paper reveals the similarity and difference between an EMSD and a tuned mass damper (TMD), both of which are resonant-type vibration absorbers. The equivalent mass, stiffness and damping coefficient of the EMSD are derived based on the transfer functions of structures with a TMD or an EMSD, and the functions of circuit capacitance and inductance are discussed accordingly. The optimal parameters of the RLC circuit in the EMSD are obtained through H∞ optimization. Despite their different optimal parameters, the EMSD and TMD exhibit comparable control performance with the same equivalent mass ratio. The dynamic analogy between these two types of dampers offers a new perspective for understanding novel EMSDs, given that TMDs have previously been extensively studied. The potentials and constraints of the EMSD are further discussed through numerical case studies in which EMSD control performance is examined in different situations. [ABSTRACT FROM AUTHOR]

We introduce a family of soft-matter capacitors and inductors composed of microchannels of liquid-phase gallium–indium–tin alloy (galinstan) embedded in a soft silicone elastomer (Ecoflex® 00-30). In contrast to conventional (rigid) electronics, these circuit elements remain electronically functional even when stretched to several times their natural length. As the surrounding elastomer stretches, the capacitance and inductance of the embedded liquid channels change monotonically. Using a custom-built loading apparatus, we experimentally measure relative changes in capacitance and inductance as a function of stretch in three directions. These experimental relationships are consistent with theoretical predictions that we derive with finite elasticity kinematics. [ABSTRACT FROM AUTHOR]

In this work, attention was focused on the inductive contribution to the real part of admittance G(T , f ) in (Fe0.45Co0.45Zr0.10)x(PZT)(1-x) nanocomposite films deposited in a mixed argon-oxygen atmosphere. The observed G(x, f, T ) dependences for the films on the dielectric side of the insulator-metal transition demonstrated the negative capacitance (NC) effect that was maximal for the nanocomposites with 0.40 < x < 0.60, where the metallic FeCoZr nanoparticles were totally oxidized. The NC effect was explained by a specially developed model for the ac hopping conductance of the electrons between the fully oxidized nanoparticles embedded in the PZT matrix. In accordance with the model, under the determined conditions the observed structure of nanocomposites led to an increase in the hopping electron mean lifetime on nanoparticles and hence to the possibility of positive angles of the phase shifts ϑ and a proper NC (inductive-like contribution) effect. [ABSTRACT FROM AUTHOR]

We seek to illustrate Fano interference in a classical coupled oscillator by using classical analogues of the atom-laser interaction. We present an analogy between the dressed state picture of coherent atom-laser interaction and a classical coupled oscillator. The Autler-Townes splitting due to the atom- laser interaction is analogous to the splitting of normal-mode frequencies of a coupled oscillator. Using this analogy, we simulate and experimentally demonstrate Fano interference and the associated phenomena in threelevel atoms in a coupled electrical resonator circuit. This work aims to highlight analogies between classical and quantum systems for students at the postgraduate and graduate levels. Also, the reported technique can be easily realized in undergraduate laboratories. [ABSTRACT FROM AUTHOR]

This paper describes an electromagnetic field analogue of the classical Brayton-Moser formulation. It is shown that Maxwell's curl equations constitute a pseudo-gradient system with respect to a single electromagnetic mixed-potential functional and a metric defined by the constitutive relations of the fields. Besides its use for the generation of power-based Lyapunov functionals for stability analysis and Poynting-like flow balances, the electromagnetic mixed-potential formulation suggests a family of alternative variational principles. This yields a novel Lagrangian boundary control system formulation admitting nonzero energy flow through the boundary. The corresponding symplectic Hamiltonian system is still associated with the total electromagnetic field energy. [ABSTRACT FROM AUTHOR]