In this paper, the propagation of TEM waves along a coaxial waveguide with a step discontinuity on its outer wall is investigated rigorously by applying the direct Fourier transform and reducing the problem into the solution of a modified Wiener–Hopf equation. The solution for the field terms are determined in terms of an infinite number of unknown coefficients, which satisfy an infinite set of linear algebraic equations. These equations are solved numerically and the effect of area ratio is presented graphically at the end of the analysis. The same problem is also analyzed by applying the mode-matching technique and the results of the two approaches are compared. It is observed numerically that the Wiener–Hopf technique provides a better convergence than the mode-matching technique.
A new simplified formula is derived for the absorption cross section of small dielectric ellipsoidal particles embedded in lossy media. The new expression leads directly to a closed form solution for the optimal conjugate match with respect to the surrounding medium, i.e. the optimal permittivity of the ellipsoidal particle that maximizes the absorption at any given frequency. This defines the optimal plasmonic resonance for the ellipsoid. The optimal conjugate match represents a metamaterial in the sense that the corresponding optimal permittivity function may have negative real part (inductive properties), and can not in general be implemented as a passive material over a given bandwidth. A necessary and sufficient condition is derived for the feasibility of tuning the Drude model to the optimal conjugate match at a single frequency, and it is found that all the prolate spheroids and some of the (not too flat) oblate spheroids can be tuned into optimal plasmonic resonance at any desired center frequency. Numerical examples are given to illustrate the analysis. Except for the general understanding of plasmonic resonances in lossy media, it is also anticipated that the new results can be useful for feasibility studies with e.g. the radiotherapeutic hyperthermia based methods to treat cancer based on electrophoretic heating in gold nanoparticle suspensions using microwave radiation.
In this paper, quantitative dielectric image reconstruction based on broadband microwave measurements is investigated. A time-domain-based algorithm is derived where Debye model parameters are reconstructed in order to take into account the strong dispersive behavior found in biological tissue. The algorithm is tested with experimental and numerical data in order to verify the algorithm and to investigate improvements in the reconstructed image resulting from the improved description of the dielectric properties of the tissue when using broadband data. The comparison is made in relation to the more commonly used conductivity model. For the evaluation, two examples were considered, the first was a lossy saline solution and the second was less lossy tap water. Both liquids are strongly dispersive and used as a background medium in the imaging examples. The results show that the Debye model algorithm is of most importance in the tap water for a bandwidth of more than 1.5 GHz. Also the saline solution exhibits a dispersive behavior but since the losses restrict the useful bandwidth, the Debye model is of less significance even if somewhat larger and stronger artifacts can be seen in the conductivity model reconstructions
The all spectrum absorption efficiency appears in the physical bounds on antennas expressed in the polarizability dyadics. Here, it is shown that this generalized absorption efficiency is close to 1/2 for small idealized dipole antennas and for antennas with a dominant resonance in their absorption. Also, the usefulness of this parameter is analyzed for estimation of antenna performance. The results are illustrated with numerical data for several antennas.
The objective of this paper is to review some recently developed sum rules and physical bounds in scattering and antenna theory. The sum rules are based on identities for Herglotz functions that relate the quantity of interest integrated over all wavelengths with its static polarizability dyadics. They are transformed to physical bounds by applying variational principles for the polarizability dyadics together with various estimates of the integrals. The theoretical findings are exemplified by numerical results for several configurations.
In this paper, we introduce a ﬁrst order accurate resonance model based on a second order Pade approximation of the reﬂection coeﬃcient of a narrowband antenna. The resonance model is characterized by its Q factor, given by the frequency derivative of the reﬂection coeﬃcient. The Bode-Fano matching theory is used to determine the bandwidth of the resonance model and it is shown that it also determines the bandwidth of the antenna for suﬃciently narrow bandwidths. The bandwidth is expressed in the Q factor of the resonance model and the threshold limit on the reﬂection coeﬃcient. Spherical vector modes are used to illustrate the results. Finally, we demonstrate the fundamental diﬃculty of ﬁnding a simple relation between the Q of the resonance model, and the classical Q deﬁned as the quotient between the stored and radiated energies, even though there is usually a close resemblance between these entities for many real antennas.
In this paper, the inverse scattering problem of amultilayer structure is analysed with the Fisher information matrix and the Cramer–Rao lower bound (CRLB). The CRLB quantifies the ill-posedness of the inverse scattering problem in terms of resolution versus estimation accuracy based on the observation of noisy data. The limit for feasible inversion is identified by an asymptotic eigenvalue analysis of the Toeplitz Fisher information matrix and an application of the sampling theorem. It is shown that the resolution is inversely proportional to the bandwidth of the reflection data and that the CRLB increases linearly with the number of slabs. The transmission data give a rank-1 Fisher information matrix which can approximately reduce the CRLB by a factor of 4. Moreover, the effect of dispersive material parameters and simultaneous estimation of two material parameters are analysed. The results are illustrated with numerical examples.
The high Q-factor (low bandwidth) and low efficiency make the design of small antennas challenging. Here, convex optimization is used to determine current distributions that provide upper bounds on the antenna performance. Optimization formulations for maximal gain Q-factor quotient, minimal Q-factor for superdirectivity, and minimum Q for given far-fields are presented. The effects of antennas embedded in structures are also discussed. The results are illustrated for planar geometries.
This paper provides a general framework for electromagnetic (EM) modeling, sensitivity analysis, computation, and measurements regarding the wave propagation characteristics of high-voltage direct-current (HVDC) power cables. The modeling is motivated by the potential use with transient analysis, partial-discharge measurements, fault localization and monitoring, and is focused on very long (10 km or more) HVDC power cables with transients propagating in the low-frequency regime of about 0-100 kHz. An exact dispersion relation is formulated together with a discussion on practical aspects regarding the computation of the propagation constant. Experimental time-domain measurement data from an 80-km-long HVDC power cable are used to validate the electromagnetic model, and a mismatch calibration procedure is devised to account for the connection between the measurement equipment and the cable. Quantitative sensitivity analysis is devised to study the impact of parameter uncertainty on wave propagation characteristics. The sensitivity analysis can be used to study how material choices affect the propagation characteristics, and to indicate which material parameters need to be identified accurately in order to achieve accurate fault localization. The analysis shows that the sensitivity of the propagation constant due to a change in the conductivity in the three metallic layers (the inner conductor, the intermediate lead shield, and the outer steel armor) is comparable to the sensitivity with respect to the permittivity of the insulating layer. Hence, proper modeling of the EM fields inside the metallic layers is crucial in the low-frequency regime of 0-100 kHz.
This paper presents a stable and efficient fullwave cable model and a detailed study of the relatedmodel uncertainties regarding the wave propagation characteristics of very long HVDC power cables at low frequencies. The model can be used to predict the dispersion characteristics of the cable with respect to its electromagnetic parameters, or as an inverse problem to estimate some parameters of the cable (armour permeability, metal layer conductivities, temperature, length, etc.) based on measurements. The electromagnetic model is based on a magnetic frill generator that can be calibrated to the current measured at the input of the cable, and a layer recursive computation of the axial-symmetric fields. Measurements of pulse propagation on an 82 km long HVDC power cable over a bandwidth of 100 kHz have been used to validate the model. The main conclusion of the study is that the conductivity (and thus the temperature) of the conductor and the lead sheath are of utmost importance to achieve an accurate model. At the same time, some parameters are in principle insignificant regarding the dispersion characteristics in the low-frequency regime, such as the permittivity and the conductivity of the semi-conducting screens. The paper contains an investigation and a discussion on the electromagnetic properties of all layers of a typical HVDC power cable.
This paper addresses electromagnetic wave propagation in High Voltage Direct Current (HVDC) power cables. An electromagnetic model, based on long (10 km or more) cables with a frequency range of 0 to 100 kHz, is derived. Relating the frequency to the propagation constant a dispersion relation is formulated using a recursive approach. The propagation constant is found numerically with normalized residue calculation. The paper is concluded with a sensitivity analysis of the propagation constant with respect to the electrical parameters ε_{r} (the real relative permittivity) and σ (the conductivity)
In this report, we propose the application of the Cramer Rao Lower Bound (CRLB) as a performance measure for optimal design of experimental setups in electrical impedance tomography. In particular, we focus on the optimum positioning of electrodes. Cramer Rao Bound is bounded from below by the inverse of the Fisher information matrix (FIM). FIM incorporates all aspects of the forward problem, statistical properties of the measurement noise, and multi-frequency data. We consider the application of CRB in both the deterministic as well as the Bayesian setting. We first present the CRB for the case of the unbiased estimator and then the Bayesian Cramer Rao Bound (BCRB) for the case of the biased estimator. All CRB computations are performed using a measured noise model from a clinical experiment.
The purpose of this paper is to establish a formal mathematical framework for the electromagnetic wave propagation in an arbitrary cavity. The walls of the cavity are not assumed perfectly conducting and we use the transmission boundary conditions for the tangential fields. Our main tool is the Laplace transform. The focus here is on the modeling and detailed proofs or calculations are not provided.
A passive approximation problem is formulated where the target function is an arbitrary complex valued continuous function defined on an approximation domain consisting of a closed interval of the real axis. The approximating function is any Herglotz function with a generating measure that is absolutely continuous with Hölder continuous density in an arbitrary neighborhood of the approximation domain. The norm used is induced by any of the standard L^{p}-norms where 1 ≤ p ≤ ∞. The problem of interest is to study the convergence properties of simple Herglotz functions where the generating measures are given by finite B-spline expansions, and where the real part of the approximating functions are obtained via the Hilbert transform. In practice, such approximations are readily obtained as the solution to a finite- dimensional convex optimization problem. A constructive convergence proof is given in the case with linear B-splines, which is valid for all L^{p}-norms with 1 ≤ p ≤ ∞. A number of useful analytical expressions are provided regarding general B-splines and their Hilbert transforms. A typical physical application example is given regarding the passive approximation of a linear system having metamaterial characteristics. Finally, the flexibility of the optimization approach is illustrated with an example concerning the estimation of dielectric material parameters based on given dispersion data.
This paper describes the ongoing research on approximation of frequency dielectric spectroscopy measurement data. The algorithm based on passive approximation, Hilbert transform and Tikhonov regularization for non-uniformly sampled data is derived. The interpolation and extrapolation problems with application to the dielectric spectroscopy measurement data are solved using convex optimization.
This paper presents a model based technique to estimate the complex valued permeability of cable armour steel. An efficient analytical model is derived for the linearized mutual impedance of a transformer coil built on a core of magnetic armour steel. A numerical residue calculation is used to solve the related inverse problem based on impedance data. The analytical model is validated using commercial finite element (FEM) software to establish that edge effects can be neglected. The numerical residue calculation is investigated by studying its convergence based on a simple rectangular quadrature rule in comparison to the composite Simpson's rule. When there are no measurement errors, both methods converge with an unexpected high order (superconvergence). However, in practice the estimation performance will be governed by measurement and model errors. Assuming that there are Gaussian measurement errors, the present performance of the estimation technique is quantified and investigated by means of the Cramér-Rao lower bound. In future, the proposed method will be useful as an input to general calculations of power losses in three-phase power cables.
This report is intended as a tutorial on electromagnetic modeling to measure and estimate the complex valued relative permeability of magnetic steel. The main application is with the estimation of the electromagnetic material parameters of the armour wires used with high-voltage AC power cables.
When the magnetic field intensity is sufficiently far from saturating the magnetic steel, the magnetic hysteresis phenomena can be approximated by using a linearization approach based on a complex valued (and frequency and amplitude dependent) relative permeability. In the report it is demonstrated how the complex valued permeability of magnetic steel can be efficiently estimated in the presence of a strong skin-effect. This is achieved by using a simple transformer coil built on the magnetic steel to be tested and by efficient numerical modeling based on waveguide theory and complex analysis. Numerical computations based on the Finite Element Method (FEM) and the commercial software COMSOL are employed to establish when edge effects can be ignored in the simplified analytical model.
We present a simple classical (random) signal model reproducing Born's rule. The crucial point of our approach is that the presence of detector's threshold and calibration procedure have to be treated not as simply experimental technicalities, but as the basic counterparts of the theoretical model. We call this approach threshold signal detection model (TSD). The experiment on coincidence detection which was done by Grangier in 1986 [22] played a crucial role in rejection of (semi-)classical field models in favour of quantum mechanics (QM): impossibility to resolve the wave-particle duality in favour of a purely wavemodel. QM predicts that the relative probability of coincidence detection, the coefficient g((2)) (0); is zero (for one photon states), but in (semi-) classicalmodels g((2)) (0) >= 1 : In TSD the coefficient g((2)) (0) decreases as 1/epsilon(2)(d); where epsilon(d) > 0 is the detection threshold. Hence, by increasing this threshold an experimenter can make the coefficient g((2)) (0) essentially less than 1. The TSD-prediction can be tested experimentally in new Grangier type experiments presenting a detailed monitoring of dependence of the coefficient g((2)) (0) on the detection threshold. Structurally our model has some similarity with the prequantum model of Grossing et al. Subquantum stochasticity is composed of the two counterparts: a stationary process in the space of internal degrees of freedom and the random walk type motion describing the temporal dynamics.
We show that quantum probabilities for photon detection can be reproduced by a model in which classical random fields interact with detectors of the threshold type. This approach is applied to the old problem of distinguishing classical and quantum light sources with the aid of the coefficient of second-order coherence g^{(2)} (0) ( the problem of "existence of photon"). In our classical random field model, we obtain an estimate of this coefficient implying that it becomes strictly less than one for sufficiently small value of parameter is an element of = (epsilon) over bar/epsilon(d), where (epsilon) over bar (pulse) is the average energy of pulses (photons) emitted by a source and epsilon(d) is the detection threshold. This prediction can in principle be tested experimentally. Thus in the presented model experimental technicalities (such as e. g. the detection thresholds) are lifted to the level of the fundamental entities of theory.
The electromagnetic fields of a single optic fibre mode are quantized based on the observationthat these fields can be derived from a scalar harmonic oscillator function depending on onlytime and the axial wavenumber. Asymptotic results for both the one-photon probabilitydensity and two-photon correlation density functions within the forward light cone arepresented, showing an algebraic decay for large times or distances. This algebraic decay,increasing the uncertainty in the arrival time of the photons, also remains in the presence ofdispersion shift, in qualitative agreement with experimental results. Also presented are explicitformulae to be used in parameter studies to optimize quantum optic fibre communications.
We obtain Born's rule from the classical theory of random waves in combination with the use of thresholdtype detectors. We consider a model of classical random waves interacting with classical detectors and reproducing Born's rule. We do not discuss complicated interpretational problems of quantum foundations. The reader can select between the "weak interpretation," the classical mathematical simulation of the quantum measurement process, and the "strong interpretation," the classical wave model of the real quantum (in fact, subquantum) phenomena.
The distance dependence of the probability of observing two photons in a waveguide is investigated and the Glauber correlation functions of the entangled photons are considered. First the case of a hollow waveguide with modal dispersion is treated in detail: the spatial and temporal dependence of the correlation functions is evaluated and the distance dependence of the probability of observing two photons upper bounds and asymptotic expressions valid for large distances are derived. Second the generalization to a real fibre with both material and modal dispersion, allowing dispersion shift, is discussed.
This paper gives a detailed derivation of the classical electromagnetic modes of a layered circularly symmetrical dielectric waveguide. The corresponding Hamilton function is derived by using suitable canonical observables and the standard analogy to the classical harmonic oscillator. The derivation is generic in the sense that it can be used as an "algorithm" to compute the electromagnetic field of the waveguide. The associated Hamilton operator can then be obtained by using the standard quantization procedure where the canonical observables are replaced by the corresponding operators i.e., the creation and the annihilation operators of the photon (or equivalently, the position and the momentum operators of the harmonic oscillator) and by taking the appropriate commutation relations into account.
The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) that limit the bit rate for long distances and examines the assumption used in this exploration that losses can be ignored. Propagation of photons in optical fibers is modelled using methods of quantum electrodynamics. We define the "photon duration" as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper: the linear dependence of photon duration on the distance when losses can be ignored. This effect puts the limit to joint increasing of the photon flux and the distance from the source and it has consequences for quantum communication. Once quantum communication develops into a real technology (including essential decrease of losses in optical fibres), it would be appealing to engineers to increase both the photon flux and the distance. And here our "photon flux/distance effect" has to be taken into account. This effect also may set an additional constraint to the performance of a loophole free test of Bell's type-to close jointly the detection and locality loopholes.
This paper presents a digital directional coupler (DDC) that separates forward- and backward-traveling waves on a transmission line. Based on two independent wideband measurements of voltage and current and on frequency-domain digital wave splitting using a fast Fourier transform (FFT), the DDC is a versatile device for direction separation. A practical procedure is described for the calibration of the digital processor with respect to the particular transmission line and the voltage and current sensors that are being used. As an experiment, a DDC was designed and implemented using low-cost wideband sensors and was installed with medium-voltage equipment in a power distribution station. Partial discharge (PD) measurements were conducted on cross-linked polyethylene (XLPE)-insulated power cables to illustrate the directional separation capabilities of the DDC.
A mathematical framework is introduced for optimization of antenna near-field imaging problems, based on the multipole expansion of the electromagnetic field, the Fisher information to quantify the quality of data and use of modern interior point convex optimization techniques. We consider the general problem of optimizing the measurement sensor allocation for parameter estimation in distributed systems, and in particular the problem of optimizing the measurement set-up for antenna near-field estimation. As an application example for antenna near-field imaging, we consider a relevant measurement set-up using cylindrical probing coordinates. The convex optimization problem is examined using duality theory, and it is shown that several structural properties of the optimal measurement problem can be exploited in developing an efficient interior point optimization method. In particular, we show that the cylindrical measurement set-up yields a Fisher information matrix with block diagonal structure, a feature which can be directly exploited in the optimization algorithm by reducing the number of dual decision variables.
This conference illuminates and benefits from relations between different types of waves, i.e., quantum physics methods in classical wave modeling. The proceedings are intended for researchers and graduate students in fundamental as well as applied sciences. The preface classifies and summarizes the conference giving relations between the papers.
This paper discusses criteria for establishing uniqueness of wave propagation problems. Causality, or passivity that implies causality, is adopted as the fundamental principle. It is stressed that radiation conditions are not applicable for waveguide modes that carry no active power. The Jones' criteria for causality in the frequency domain, which covers the convectively unstable case, are presented and analysed, the vanishing absorption principle, VAP, in particular. It is proposed to use L^{2} for a lossy medium but a weighted L^{2} for the lossless case.
With the purpose of source localization in high voltage direct current submarine power cables general layered waveguide models are investigated. It is concludes that the non-discrete modes can usually be ignored in comparison with the least attenuated discrete mode. Only a finite number of discrete modes are of importance for a band limited signal. Accurate analytical expressions are derived in the time domain for both discrete and non-discrete electromagnetic waveguide modes for large distances together with an error analysis.
This paper presents accurate analytical expressions in the time domain for discrete electromagnetic waveguide modes for large distances together with a discussion of the errors. The main application is source localization for high voltage direct current submarine power cables. The research behind this paper is part of the project “Fundamental wave modelling for signal estimation on lossy transmission lines” funded by the Swedish Research Council and ABB High Voltage Cables AB in Sweden.
There are two optic fibre properties in particular that obstruct the transfer over long distances in quantum communications. One of them is dispersion, which reduces the maximum bit rate. In classical communication with modern highly purified fibres, dispersion is the major limiting factor. The other property is the material loss that causes fluctuations in addition to a general annihilation with distance of photons. It is believed that losses are the major limiting factor in quantum communication over long distances if the bit rate is not an issue. Of major interest in quantum communication is the photon source. It is therefore a high priority to develop methods for the determination of properties like initial temporal modes, repeatability, independence of sequentially emitted photons, etc., for a source emitting single photons in a given spatial mode. In the current paper we suggest that the source properties can be estimated using statistics of the run times of the photons. This requires that the fibre is modelled with sufficient accuracy. To simplify the analysis, it is assumed that the fibre losses can be neglected and that the photons are independent and identically generated. Energy detection in one spin state is employed, making the modelling scalar. The one photon initial temporal mode is found by maximizing a maximum-likelihood function based on running time statistics. Unfortunately, this optimization problem is, in general, not convex. However, for photon detection in the so-called asymptotic radiation zone, where the probability density can be determined to a sufficient degree with asymptotic methods, the optimization problem is convex. In the current paper, quantum tomography in fibres based on this convex optimization method is presented, and its generalization to more complicated situations like the introduction of losses in the modelling is discussed.
For the purpose of determining the twist of a homogeneous, locally reacting, uniaxial cylinder, an inverse microwave scattering theory is presented. Remote measurements of the spiral grain of trees and logs are the prime application. Based on practical considerations, it is assumed that the transmitting and receiving antennas are collocated, requiring a three-dimensional modelling. A general theory is first developed, followed by an asymptotic analysis assuming that the distance from the antennas to the cylinder is many wavelengths and many cylinder radii. In this way, a substantial reduction of the numerical complexity, to the level of the two-dimensional case, is achieved. The error of the determined twist angle as function of inherent parameters of the problem using a CramEacuter-Rao analysis is given. The results from numerical simulations show that this error is low enough for determining the grain angle. Presented parameter studies of the error can be used for minimizing the errors in a measurement set up, of particular interest for non-sophisticated instruments and non-ideal laboratory conditions, by selecting optimum parameters such as frequency and antenna gain. Finally, it is stated that the model has a great potential for developing efficient algorithms for measuring the twist angle.
An inverse microwave scattering theory is presented for the determination of twist of a homogeneous locally reacting uniaxial cylinder. The prime application is remote measurements of spiral grain of trees and logs. From practical considerations, the transmitting and receiving antennas are near each other
requiring a three-dimensional modelling. First a general theory is developed. Then asymptotic formulae are derived assuming that the distance from the antennas to the cylinder is many wavelengths and many cylinder radii granting a substantial reduction of the numerical complexity compared to the twodimensional case. Finally, the error of the determined twist angle as function of inherent parameters of the problem is given using a Cramer Rao analysis.