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Frequency domain sweeps of array antennas are well-known to be time-intensive, and different surrogate models have been used to improve the performance. Data-driven model order reduction algorithms, such as the Loewner framework and vector fitting, can be integrated with these adaptive error estimates, in an iterative algorithm, to reduce the number of full-wave simulations required to accurately capture the requested frequency behavior of multiport array antennas. In this work, we propose two novel adaptive methods exploiting a block matrix function which is a key part of the Loewner framework generating system approach. The first algorithm leverages an inherent matrix parameter freedom in the block matrix function to identify frequency points with large errors, whereas the second utilizes the condition number of the block matrix function. Both methods effectively provide frequency domain error estimates, which are essential for improved performance. Numerical experiments on multiport array antenna S-parameters demonstrate the effectiveness of our proposed algorithms within the Loewner framework., Comment: 10 pages, 12 figures

In this paper, the bounds on the Q-factor, a quantity inversely proportional to bandwidth, are derived and investigated for narrow-band phased array antennas. Arrays in free space and above a ground plane are considered. The Q-factor bound is determined by solving a minimization problem over the electric current density. The support of these current densities is on an element-enclosing region, and the bound holds for lossless antenna elements enclosed in this region. The Q-factor minimization problem is formulated as a quadratically constrained quadratic optimization problem that is solved either by a semi-definite relaxation or an eigenvalue-based method. We illustrate numerically how these bounds can be used to determine trade-off relations between the Q-factor and other design specifications: element form-factor, size, efficiency, scanning capabilities, and polarization purity., Comment: 12 pages, 11 figures

In this paper, the Q-factor expression for periodic arrays over a ground plane is determined in terms of the electric current density within the array's unit cell. The expression accounts for the exact shape of the array element. The Q-factor formula includes integration only over a volume of an element in a unit cell, and can thus be efficiently implemented numerically. The examples show good agreement between the proposed Q-factor, the full-wave-calculated tuned fractional bandwidth, and the input-impedance-based formula by Yaghjian and Best (2005) for the array of tilted dipoles and the loops array., Comment: 5 pages, 4 figures

In this paper, we study optimization of multi-tone signals for wireless power transfer (WPT) systems. We investigate different non-linear energy harvesting models. Two of them are adopted to optimize the multi-tone signal according to the channel state information available at the transmitter. We show that a second-order polynomial curve-fitting model can be utilized to optimize the multi-tone signal for any RF energy harvester design. We consider both single-antenna and multi-antenna WPT systems. In-band co-existing communication links are also considered in this work by imposing a constraint on the received power at the nearby information receiver to prevent its RF front end from saturation. We emphasize the importance of imposing such constraint by explaining how inter-modulation products, due to saturation, can cause high interference at the information receiver in the case of multi-tone signals. The multi-tone optimization problem is formulated as a non-convex linearly constrained quadratic program. Two globally optimal solution approaches using mixed-integer linear programming and finite branch-and-bound techniques are proposed to solve the problem. The achieved improvement resulting from applying both solution methods to the multi-tone optimization problem is highlighted through simulations and comparisons with other solutions existing in the literature.

The Q-factor for lossless three-dimensional structures with two-dimensional periodicity is here derived in terms of the electric current density. The derivation in itself is shape-independent and based on the periodic free-space Green's function. The expression for Q-factor takes into account the exact shape of a periodic element, and permits beam steering. The stored energies and the radiated power, both required to evaluate Q-factor, are coordinate independent and expressed in a similar manner to the periodic Electric Field Integral equation, and can thus be rapidly calculated. Numerical investigations, performed for several antenna arrays, indicate fine agreement, accurate enough to be predictive, between the proposed Q-factor and the tuned fractional bandwidth, when the arrays are not too wideband (i.e., when $Q\geq 5$). For completeness, the input-impedance Q-factor, proposed by Yaghjian and Best in 2005, is included and agrees well numerically with the derived Q-factor expression. The main advantage of the proposed representation is its explicit connection to the current density, which allows the Q-factor to give bandwidth estimates based on the shape and current of the array element., Comment: 14 pages, 7 figures. Updated proof in Appendix C, minor updates in the text and figures

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 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., Comment: 23 pages, 5 figures. Updated Introduction and Sections 2.1 and 2.4. Restructured and updated Section 5. New numerical example in Section 5.3

This paper presents a study of transmission through arrays of periodic sub-wavelength apertures. Fundamental limitations for this phenomenon are formulated as a sum rule, relating the transmission coefficient over a bandwidth to the static polarizability. The sum rule is rigorously derived for arbitrary periodic apertures in thin screens. By this sum rule we establish a physical bound on the transmission bandwidth which is verified numerically for a number of aperture array designs. We utilize the sum rule to design and optimize sub-wavelength frequency selective surfaces with a bandwidth close to the physically attainable. Finally, we verify the sum rule and simulations by measurements of an array of horseshoe-shaped slots milled in aluminum foil., Comment: 10 pages, 11 figures. Updated Introduction and Conclusions

Considerable time is often spent optimizing antennas to meet specific design metrics. Rarely, however, are the resulting antenna designs compared to rigorous physical bounds on those metrics. Here we study the performance of optimized planar meander line antennas with respect to such bounds. Results show that these simple structures meet the lower bound on radiation Q-factor (maximizing single resonance fractional bandwidth), but are far from reaching the associated physical bounds on efficiency. The relative performance of other canonical antenna designs is compared in similar ways, and the quantitative results are connected to intuitions from small antenna design, physical bounds, and matching network design., Comment: 10 pages, 15 figures, 2 tables, 4 boxes

This paper presents a method to estimate the static electric polarizability of two-dimensional infinitely periodic metal patch arrays with dielectric substrate. The main features of the proposed method is its numerical efficiency and a deep insight into the physics of the fields interacting with the structure. We provide derivation and analysis of the method, and its verification against two another commercial solver-based approaches for various structure geometries. Additionally, we suggest the guidelines for applying the method to bandwidth optimization of frequency selective structures and illustrate this with an example., Comment: 4 pages, 2 figures. Updates: -Added verification by variational approach -Minor updates of the text -Added the guidelines for the method's applications -Removed Fig. 1c

Far-field shaping of small antennas is a challenge and the realizations of non-dipole radiation of small to intermediate sized antennas are difficult. Here we examine the antenna bandwidth cost associated with such constraints, and in certain cases we design antennas that approach the bounds. Far-field shaping is in particular interesting for Internet-of-things (IoT) and Wi-Fi applications since e.g. spatial filtering can mitigate package loss through a reduction of mutual interference, and hence increase the power efficiency of the devices. Even a rather careful far-field shaping of smaller antennas can be associated with a steep reduction in the best available bandwidth. It is thus important to develop constraints that a small antenna can support. We describe a power front-to-back ratio, and a related, beam-shaping constraint that can be used in optimization for the minimum Q-factor. We show that such a non-convex Q-factor optimization can be solved with the semi-definite relaxation technique. We furthermore show that certain of the above optimized non-standard radiation patterns can be realized with a multi-position feeding strategy with a moderate loss of Q-factor: $Q_\text{antenna}\leq 1.61Q_\text{optimal}$.

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 $\text{L}^p$-norm where $1\leq p\leq\infty$. The approximating functions are Herglotz functions generated by a measure with H\"{o}lder continuous density in an arbitrary neighborhood of the approximation domain. Hence, the imaginary and the real parts of the approximating functions are H\"{o}lder 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 H\"{o}lder continuous in a neighborhood of the approximation domain, as mentioned above. As an illustration, a typical physical application example is included regarding the passive approximation and optimization of a linear system having metamaterial characteristics.

This paper revisit and extend the interesting case of bounds on the Q-factor for a given directivity for a small antenna of arbitrary shape. A higher directivity in a small antenna is closely connected with a narrow impedance bandwidth. The relation between bandwidth and a desired directivity is still not fully understood, not even for small antennas. Initial investigations in this direction has related the radius of a circumscribing sphere to the directivity, and bounds on the Q-factor has also been derived for a partial directivity in a given direction. In this paper we derive lower bounds on the Q-factor for a total desired directivity for an arbitrarily shaped antenna in a given direction as a convex problem using semi-definite relaxation techniques (SDR). We also show that the relaxed solution is also a solution of the original problem of determining the lower Q-factor bound for a total desired directivity. SDR can also be used to relax a class of other interesting non-convex constraints in antenna optimization such as tuning, losses, front-to-back ratio. We compare two different new methods to determine the lowest Q-factor for arbitrary shaped antennas for a given total directivity. We also compare our results with full EM-simulations of a parasitic element antenna with high directivity., Comment: Correct some minor typos in the previous version

The accuracy of two equivalent antenna representations, near-field sources and far-field sources, are evaluated for an antenna installed on a simplified platform in a series of case studies using different configurations of equivalent antenna representations. The accuracy is evaluated in terms of installed far-fields and surface currents on the platform. The results show large variations between configurations. The root-mean-square installed far-field error is 4.4% for the most accurate equivalent representation. When using far-field sources, the design parameters have a large influence of the achieved accuracy. There is also a varying accuracy depending on the type of numerical method used. Based on the results, some recommendations on the choice of sub-domain for the equivalent antenna representation are given. In industrial antenna applications, the accuracy in determining e.g. installed far-fields and antenna isolation on large platforms are critical. Equivalent representations can reduce the fine-detail complexity of antennas and thus give an efficient numerical descriptions to be used in large-scale simulations. The results in this paper can be used as a guideline by antenna designers or system engineers when using equivalent sources.

Polymer nanocomposite dielectrics are promising materials for electrical insulation in high voltage applications. However, the physics behind their performance is not yet fully understood. We use density functional theory to investigate electronic properties of the interfacial area in magnesium oxide-polyethylene nanocomposite. Our results demonstrate polyethylene conduction band matching with conduction bands of different surfaces of magnesium oxide. Such band bending results in long range potential wells of up to 2.6 eV deep. Furthermore, the fundamental influence of silicon treatment on magnesium oxide surface properties is assessed. We report a reduction of the surface-induced states at the silicon-treated interface. The simulations provide information used to propose a new model for charge trapping in nanocomposite dielectrics., Comment: arXiv admin note: substantial text overlap with arXiv:1604.05984

Electric and magnetic current densities are an essential part of electromagnetic theory. The goal of the present paper is to define and investigate stored energies that are valid for structures that can support both electric and magnetic current densities. Stored energies normalized with the dissipated power give us the Q factor, or antenna Q, for the structure. Lower bounds of the Q factor provide information about the available bandwidth for passive antennas that can be realized in the structure. The definition that we propose is valid beyond the leading order small antenna limit. Our starting point is the energy density with subtracted far-field form which we obtain an explicit and numerically attractive current density representation. This representation gives us the insight to propose a coordinate independent stored energy. Furthermore, we find here that lower bounds on antenna Q for structures with e.g. electric dipole radiation can be formulated as convex optimization problems. We determine lower bounds on both open and closed surfaces that support electric and magnetic current densities. The here derived representation of stored energies has in its electrical small limit an associated Q factor that agrees with known small antenna bounds. These stored energies have similarities to earlier efforts to define stored energies. However, one of the advantages with this method is the above mentioned formulation as convex optimization problems, which makes it easy to predict lower bounds for antennas of arbitrary shapes. The present formulation also gives us insight into the components that contribute to Chu's lower bound for spherical shapes. We utilize scalar and vector potentials to obtain a compact direct derivation of these stored energies. Examples and comparisons end the paper., Comment: Minor updates to figures and text

Polymer-based nanocomposite dielectrics are expected to become essential in future generations of high voltage electrical insulation. However, the physics behind their performance is not yet understood. Here we investigate electronic properties of the interfacial area in magnesium oxide-polyethylene nanocomposite. We use density functional theory to calculate densities of states for MgO (100) and hydroxylated MgO (111) interfaces with polyethylene. We evaluate the role of silicon-based nanoparticle surface modification at the electronic level and propose a new theory for charge trapping in nanocomposites., Comment: This paper has been withdrawn by the author due to a mistake in performed calculations

Electric and magnetic currents are essential to describe electromagnetic stored energy, as well as the associated quantities of antenna Q and the partial directivity to antenna Q-ratio, D/Q, for general structures. The upper bound of previous D/Q-results for antennas modeled by electric currents is accurate enough to be predictive, this motivates us here to extend the analysis to include magnetic currents. In the present paper we investigate antenna Q bounds and D/Q-bounds for the combination of electric- and magnetic-currents, in the limit of electrically small antennas. This investigation is both analytical and numerical, and we illustrate how the bounds depend on the shape of the antenna. We show that the antenna Q can be associated with the largest eigenvalue of certain combinations of the electric and magnetic polarizability tensors. The results are a fully compatible extension of the electric only currents, which come as a special case. The here proposed method for antenna Q provides the minimum Q-value, and it also yields families of minimizers for optimal electric and magnetic currents that can lend insight into the antenna design., Comment: 27 pages 7 figures

This letter defines a physical bound based array figure of merit that provides a tool to compare the performance of both single and multi-band array antennas with respect to return-loss, thickness of the array over the ground-plane, and scan-range. The result is based on a sum-rule result of Rozanov-type for linear polarization. For single-band antennas it extends an existing limit for a given fixed scan-angle to include the whole scan-range of the array, as well as the unit-cell structure in the bound. The letter ends with an investigation of the array figure of merit for some wideband and/or wide-scan antennas with linear polarization. We find arrays with a figure of merit >0.6 that empirically defines high-performance antennas with respect to this measure., Comment: Minor changes. Included a pre-page to comply with Journal requirements. Added a few more antennas for which we calculated the array figure of merit

Decomposition of the electromagnetic energy into its stored and radiated parts is instrumental in the evaluation of antenna Q and the corresponding fundamental limitations on antennas. This decomposition is not unique and there are several proposals in the literature. Here, it is shown that stored energy defined from the difference between the energy density and the far field energy equals the new energy expressions proposed by Vandenbosch for many cases. This also explains the observed cases with negative stored energy and suggests a possible remedy to them. The results are compared with the classical explicit expressions for spherical regions where the results only differ by ka that is interpreted as the far-field energy in the interior of the sphere. Numerical results of the Q-factors for dipole, loop, and inverted L-antennas are also compared with estimates from circuit models and differentiation of the impedance. The results indicate that the stored energy in the field agrees with the stored energy in the Brune synthesized circuit models whereas the differentiated impedance gives a lower value for some cases. The corresponding results for the bandwidth suggest that the inverse proportionality between bandwidth and Q depends on the relative bandwidth or equivalent the threshold of the reflection coefficient. The Q from the differentiated impedance and stored energy are most useful for relative narrow and wide bandwidths, respectively.

The capacitance of the circular parallel plate capacitor is calculated by expanding the solution to the Love integral equation into a Fourier cosine series. Previously, this kind of expansion has been carried out numerically, resulting in accuracy problems at small plate separations. We show that this bottleneck can be alleviated, by calculating all expansion integrals analytically in terms of the Sine and Cosine integrals. Hence, we can, in the approximation of the kernel, use considerably larger matrices, resulting in improved numerical accuracy for the capacitance. In order to improve the accuracy at the smallest separations, we develop a heuristic extrapolation scheme that takes into account the convergence properties of the algorithm. Our results are compared with other numerical results from the literature and with the Kirchhoff result. Error estimates are presented, from which we conclude that our results is a substantial improvement compared with earlier numerical results., Comment: 15 pages, 3 figures

Linear acoustic wave-splitting is an often used tool in describing sound-wave propagation through earth's subsurface. Earth's subsurface is in general anisotropic due to the presence of water-filled porous rocks. Due to the complexity and the implicitness of the wave-splitting solutions in anisotropic media, wave-splitting in seismic experiments is often modeled as isotropic. With the present paper, we have derived a simple wave-splitting procedure for an instantaneously reacting anisotropic media that includes spatial variation in depth, yielding both a traditional (approximate) and a `true amplitude' wave-field decomposition. One of the main advantages of the method presented here is that it gives an explicit asymptotic representation of the linear acoustic-admittance operator to all orders of smoothness for the smooth, positive definite anisotropic material parameters considered here. Once the admittance operator is known we obtain an explicit asymptotic wave-splitting solution., Comment: 20 pages

The equations for the electromagnetic field in an anisotropic media are written in a form containing only the transverse field components relative to a half plane boundary. The operator corresponding to this formulation is the electromagnetic system's matrix. A constructive proof of the existence of directional wave-field decomposition with respect to the normal of the boundary is presented. In the process of defining the wave-field decomposition (wave-splitting), the resolvent set of the time-Laplace representation of the system's matrix is analyzed. This set is shown to contain a strip around the imaginary axis. We construct a splitting matrix as a Dunford-Taylor type integral over the resolvent of the unbounded operator defined by the electromagnetic system's matrix. The splitting matrix commutes with the system's matrix and the decomposition is obtained via a generalized eigenvalue-eigenvector procedure. The decomposition is expressed in terms of components of the splitting matrix. The constructive solution to the question on the existence of a decomposition also generates an impedance mapping solution to an algebraic Riccati operator equation. This solution is the electromagnetic generalization in an anisotropic media of a Dirichlet-to-Neumann map., Comment: 45 pages, 2 figures

We study solutions close to solitary waves of the pseudo-relativistic Hartree equation describing boson stars under the influence of an external gravitational field. In particular, we analyze the long-time effective dynamics of such solutions. In essence, we establish a (long-time) stability result for solutions describing boson stars that move under the influence of an external gravitational field., Comment: 57 pages, 4 figures

We study the nonlinear equation $i \partial_t \psi = (\sqrt{-\Delta + m^2} - m) \psi - ( |x|^{-1} \ast |\psi|^2 ) \psi$ on $\RR^3$, which is known to describe the dynamics of pseudo-relativistic boson stars in the mean-field limit. For positive mass parameters, $m > 0$, we prove existence of travelling solitary waves, $\psi(t,x) = e^{i t \mu} \sol_{v}(x-vt)$, with speed $|v| < 1$, where $c=1$ corresponds to the speed of light in our units. Due to the lack of Lorentz covariance, such travelling solitary waves cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with $v=0$). To overcome this difficulty, we introduce and study an appropriate variational problem that yields the functions $\sol_v \in \Hhalf(\RR^3)$ as minimizers, which we call boosted ground states. Our existence proof makes extensive use of concentration-compactness-type arguments. In addition to their existence, we prove orbital stability of travelling solitary waves $\psi(t,x) = e^{it \mu} \sol_v(x-vt)$ and pointwise exponential decay of $\sol_v(x)$ in $x$., Comment: 30 pages

We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We study the long time behaviour of solutions with initial conditions close to a stable, B=0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave, whose centre and scale evolve according to a certain dynamical law involving the function B(t,x), plus an H^1-small fluctuation., Comment: 19 pages

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval., Comment: 42 pages, 2 figures

We study the behavior of solitary-wave solutions of some generalized nonlinear Schr\"odinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing inertial motions of stable solitary waves. We construct solutions of the equations with a non-vanishing external potential corresponding to initial conditions close to one of these solitary wave solutions and show that, over a large interval of time, they describe a solitary wave whose center of mass motion is a solution of Newton's equations of motion for a point particle in the given external potential, up to small corrections corresponding to radiation damping., Comment: latex2e, 41 pages, 1 figure