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.
We investigate TE-wave propagation in a hollow waveguide with a graded dielectric barrier, using an equivalent model of the waveguide filled with a stratified medium. General formulae for the electric field components of the TE-waves, applicable to hollow waveguides with arbitrary cross sectional shapes, are presented. As an illustration, we obtain the exact analytical results for the electric field components in a rectangular waveguide, as well as the exact analytical results for reflection and transmission coefficients which are valid for waveguides of arbitrary cross sectional shapes.
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.
Objective: Newborns with lung immaturity often require continuous monitoring and treatment of their lung ventilation in intensive care units, especially if born preterm. Recent studies indicate that electrical impedance tomography (EIT) is feasible in newborn infants and children, and can quantitatively identify changes in regional lung aeration and ventilation following alterations to respiratory conditions. Information on the patient-specific shape of the torso and its role in minimizing the artefacts in the reconstructed images can improve the accuracy of the clinical parameters obtained from EIT. Currently, only idealized models or those segmented from CT scans are usually adopted. Approach: This study presents and compares two methodologies that can detect the patient-specific torso shape by means of wearable devices based on (1) previously reported bend sensor technology, and (2) a novel approach based on the use of accelerometers. Main results: The reconstruction of different phantoms, taking into account anatomical asymmetries and different sizes, are produced for comparison. Significance: As a result, the accelerometers are more versatile than bend sensors, which cannot be used on bigger cross-sections. The computational study estimates the optimal number of accelerometers required in order to generate an image reconstruction comparable to the use of a CT scan as the forward model. Furthermore, since the patient position is crucial to monitoring lung ventilation, the orientation of the phantoms is automatically detected by the accelerometer-based method.
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 finite union of closed and bounded intervals on the real axis. The norm used is a weighted L-p-norm where 1 <= p <= infinity. The approximating functions are Herglotz functions generated by a measure with Holder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are Holder continuous functions given by the density of the measure and its Hilbert transform, respectively. In practice, it is useful to employ finite B-spline expansions to represent the generating measure. The corresponding approximation problem can then be posed as a finite-dimensional convex optimization problem which is amenable for numerical solution. A constructive proof is given here showing that the convex cone of approximating functions generated by finite uniform B-spline expansions of fixed arbitrary order (linear, quadratic, cubic, etc.) is dense in the convex cone of Herglotz functions which are locally Holder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, typical physical application examples are included regarding the passive approximation and optimization of a linear system having metamaterial characteristics, as well as passive realization of optimal absorption of a dielectric small sphere over a finite bandwidth.
An optimal plasmonic resonance and the associated Fröhlich resonance frequency are derived for a thin layer in a straight waveguide in TM mode. The layer consists of an arbitrary composite material with a Drude type of dispersion. The reflection and transmission coefficients of the layer are analyzed in detail. To gain insight into the behavior of a thin plasmonic layer, an asymptotic expansion to the first order is derived with respect to the layer permittivity.
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.
Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary optimization techniques. The first version is formulated in terms of polarization currents (or equivalent currents) inside the scatterer and generalizes previous results given for a lossless medium. The corresponding bound is referred to here as a variational bound and is valid for an arbitrary geometry with a given material property. The second version is formulated in terms of the T-matrix parameters of an arbitrary linear scatterer circumscribed by a spherical volume and gives a new fundamental upper bound on the total absorption of an inclusion with an arbitrary material property (including general bianisotropic materials). The two bounds are fundamentally different as they are based on different assumptions regarding the structure and the material property. Numerical examples including homogeneous and layered (core-shell) spheres are given to demonstrate that the two bounds provide complimentary information in a given scattering problem.
We introduce the set of quasi-Herglotz functions and demonstrate that it has properties useful in the modeling of non-passive systems. The linear space of quasi-Herglotz functions constitutes a natural extension of the convex cone of Herglotz functions. It consists of differences of Herglotz functions, and we show that several of the important properties and modeling perspectives of Herglotz functions are inherited by the new set of quasi-Herglotz functions. In particular, this applies to their integral representations, the associated integral identities or sum rules (with adequate additional assumptions), their boundary values on the real axis and the associated approximation theory. Numerical examples are included to demonstrate the modeling of a non-passive gain media formulated as a convex optimization problem,where the generating measure is modeled by using a finite expansion of B-splines and point masses.
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.
Non-passive approximation is presented as a tool to study the realizability of amplifying media. As an interesting physical example, we derive first a suitable approximation of the plasmonic singularity of a dielectric sphere with respect to a hypothetical amplifying background medium. A non-passive approximation based on convex optimization is then employed to investigate the necessary bandwidth requirements to achieve the approximate pole singularity.
Convex optimization has emerged as a well-suited tool for passive approximation. Here, it is desired to approximate some pre-defined non-trivial system response over a given finite frequency band by using a passive system. This paper summarizes some explicit results concerning the Hilbert transform of general B-splines of arbitrary order and arbitrary partitions that can be useful with the convex optimization formulation. A numerical example in power engineering is included concerning the identification of some model parameters based on measurements on high-voltage insulation materials.
Objective: This paper defines a method for optimizing the breath delineation algorithms used in Electrical Impedance Tomography (EIT). In lung EIT the identification of the breath phases is central for generating tidal impedance variation images, subsequent data analysis and clinical evaluation. The optimisation of these algorithms is particularly important in neonatal care since the existing breath detectors developed for adults may give insufficient reliability in neonates due to their very irregular breathing pattern. Approach: Our approach is generic in the sense that it relies on the definition of a gold standard and the associated definition of detector sensitivity and specificity, an optimisation criterion and a set of detector parameters to be investigated. The gold standard has been defined by 11 clinicians with previous experience with EIT and the performance of our approach is described and validated using a neonatal EIT dataset acquired within the EU-funded CRADL project. Main results: Three different algorithms are proposed that are improving the breath detector performance by adding conditions on 1) maximum tidal breath rate obtained from zero-crossings of the EIT breathing signal, 2) minimum tidal impedance amplitude and 3) minimum tidal breath rate obtained from Time-Frequency (TF) analysis. As a baseline the zero crossing algorithm has been used with some default parameters based on the Swisstom EIT device. Significance: Based on the gold standard, the most crucial parameters of the proposed algorithms are optimised by using a simple exhaustive search and a weighted metric defined in connection with the Receiver Operating Characterics (ROC). This provides a practical way to achieve any desirable trade-off between the sensitivity and the specificity of the detectors.
Spectral analysis based on short-time Fourier transform (STFT) using Kaiser window is proposed to examine the frequency components of neonates EIT data. In this way, a simultaneous spatial-time-frequency analysis is achieved.
The objective of this paper is to report our investigation demonstrating that the phase angle information of complex impedance could be a simple indicator of a breath cycle in chest Electrical Impedance Tomography (EIT). The study used clinical neonatal EIT data. The results show that measurement of the phase angle from complex EIT data can be used as a complementary information for improving the conventional breath detection algorithms.
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.