Theoretical and computational electromagnetics

One of the most time-consuming tasks associated with developing and using computer models in electromagnetics is that of verifying software performance and vali- dating the model results. Some of the errors that occur in modeling, the need for quantitative error measures, and some of the validation tests such as convergence behavior and boundary- condition checks are discussed. Use of model-based para- meter estimation to develop error estimates or to control uncertainty in an observable is illustrated. It is recommended that the Computational ElectroMagnetics community adopt a policy of requiring some minimal standards concerning the ac- curacy of numerical results accepted for journal articles and meeting presentations.

Electricity production is a major problem for deep space exploration. The possibility of using radioisotope elements with a very long life as an energy source was investigated in the framework of an EU project “SpaceTRIPS”. For this, a two-stage system was tested, the first in which thermal energy is converted into mechanical energy by means of a thermoacoustic process, and the second where mechanical energy is converted into electrical energy by means of a magnetohydrodynamic generator (MHD). The aim of the present study is to develop an analytical model of the MHD generator. A one-dimensional model is developed and presented that allows us to evaluate the behavior of the device as regards both electromagnetic and fluid-dynamic aspects, and consequently to determine the characteristic values of efficiency and power.

Electricity production is a major problem for deep space exploration. The possibility of using radioisotope elements with a very long life as an energy source was investigated in the framework of an EU project “SpaceTRIPS”. For this, a two-stage system was tested, the first in which thermal energy is converted into mechanical energy by means of a thermoacoustic process, and the second where mechanical energy is converted into electrical energy by means of a magnetohydrodynamic generator (MHD). The aim of the present study is to develop an analytical model of the MHD generator. A one-dimensional model is developed and presented that allows us to evaluate the behavior of the device as regards both electromagnetic and fluid-dynamic aspects, and consequently to determine the characteristic values of efficiency and power.

Optical pulling force (OPF) can make a nanoparticle (NP) move against the propagation direction of the incident light. Long-distance optical pulling is highly desired for nano-object manipulation, but its realization remains challenging. We propose an NP-in-cavity structure that can be pulled by a single plane wave to travel long distances when the spherical cavity wrapping the NP has a refractive index lower than the medium. An electromagnetic multipole analysis shows that NPs made of many common materials can receive the OPF inside a lower index cavity. Using a silica-Au core-shell NP that is encapsulated by a plasmonic nanobubble, we experimentally demonstrate that a single laser can pull the Au NP-in-nanobubble structure for ~0.1 mm. These results may lead to practical applications that can use the optical pulling of NP, such as optically driven nanostructure assembly and nanoswimmers.

We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics to cloaks with a surface of revolution. We derive the expression of the transformation matrix and show that one of its eigenvalues vanishes on the inner boundary of the cloaks, while the other two remain strictly positive and bounded. The validity of our approach is confirmed by finite edge-elements computations for a non-convex cloak of varying thickness.

By applying the Transmission-Line Super Theory (TLST) to a practical transmission-line configuration (two risers and a horizontal part of the line parallel to the ground plane) it is elaborated under which physical and geometrical conditions the horizontal part of the transmission-line can be represented by a classical telegrapher equation with a sufficiently accurate description of the physical properties of the line. The risers together with the part of the horizontal line close to them are treated as separate lines using the TLST. Novel frequency and local dependent reflection coefficients are introduced to take into account the action of the bends and their radiation. They can be derived from the matrizant elements of the TLST solution. It is shown that the solution of the resulting network and the TLST solution of the entire line agree for certain line configurations. The physical and geometrical parameters for these corresponding configurations are determined in this paper.

In this paper, we investigate the effects of the dielectric insulation on the input impedance and admittance characteristics of coated thin-wire helical antennas, using the quasi-static moment-method approach described elsewhere by Adekola et al. [1]. For the dielectric insulation modeled by a Schelkunuff's volume polarization current, the unknown quantity is the electric field in the dielectric region due to the distribution of current along the axis of the un-insulated wire, which is also an unknown quantity. The quasi-static approach assumes that both unknowns are related in the manner specified by Richmond and Newman [2], and Lee and Balmain [3], so that the problem then becomes completely solved, when using the method of moments, the unknown current distribution is obtained. One interesting feature of the paper is the demonstration that the circuit-geometric character of the moment-methods enables the formulation for the coated elliptical cylindrical helical antenna to serv...

We make precise some results on the cloaking of displacement fields
in linear elasticity. In the spirit of transformation media theory, the transformed governing equations in Cosserat and Willis frameworks are shown to be equivalent to certain high contrast small defect problems for the usual Navier equations. We discuss near-cloaking for elasticity systems via a regularized transform and perform numerical experiments to illustrate our near-cloaking results. We also study the sharpness of the estimates from [H. Ammari, H. Kang, K. Kim and H. Lee, J. Diff. Eq. 254, 4446-4464 (2013)], wherein the convergence of the solutions to the transmission problems is investigated, when the Lamé parameters in the inclusion tend to extreme values. Both soft and hard inclusion limits are studied and we also touch upon the finite frequency case. Finally, we propose an approximate isotropic cloak algorithm for a symmetrized Cosserat cloak.

In 1918 Albert Einstein wrote in a letter to Walter Dällenbach against his own theory of optical force: “It has long been known that the values I had derived with Laub at the time are wrong; Abraham, in particular, was the one who presented this in a thorough paper. The correct strain tensor has incidentally already been pointed out by Minkowski”. Unfortunately after almost 100 years, it is still not clear why Einstein wrote so regarding the theory of optical/electromagnetic force (the optical stress tensor (ST)) associated with Lorentz force. The electromagnetic force is one of the four fundamental interactions (other three: the strong interaction, the weak interaction and gravitation) in nature. In spite of experiencing much progress from 1970, research on optical/electromagnetic forces has so far revealed only the partial nature of light-matter interaction. For example, inside a material media an appropriate description of photon momenta (i.e. the Abraham-Minkowski dilemma) and an appropriate description of stress tensors along with Lorentz /volumetric forces (known as Minkowski, Abraham, Chu, Einstein-Laub and Ampere/Nelson forces) are still matters of great controversy. In this thesis, physics and applications of Lorentz force along with stress tensors and photon momenta have been investigated in details with special interest in tractor beam effect, plasmonic objects, chiral objects and the objects embedded in a generic material medium. At first, we have considered simpler case: application of Lorentz force for the objects placed in air. Specifically we demonstrate how the mechanism of Lorentz force can be used in a tractor beam-like effect for pulling multiple Rayleigh particles placed outside a dielectric hollow core waveguide and coupler. We also represent the Lorentz force analysis for plasmonic off-axis and on-axis spherical heterodimers and it is shown that the reversal of longitudinal binding force can be easily controlled by forced symmetry breaking. Though it is commonly believed that plasmonic forces mostly arise from the surface force and Fano resonance can be a promising way to achieve binding force reversal, our study based on Lorentz force dynamics suggests notably opposite proposals for the case of plasmonic spherical heterodimers. Next, we have also considered objects those are embedded in a material medium. The fundamental results/proposals of this thesis are presented afterwards. We have shown that the well-known Lorentz force leads to inconsistent result (pushing force) instead of the experimentally observed optical pulling force as observed in interfacial tractor beam experiments. As one of the major contributions of this thesis, we identify the ‘exact’ reasons why the well-known distinct Lorentz/volumetric forces fail not only for interfacial tractor beam experiment but also for several other major radiation pressure experiments performed up to date. Later, we demonstrate that it is still possible to establish different equivalent time-averaged Lorentz / volumetric force formulas based on the fulfilment of just two ‘consistency conditions’. Based on those proposed ‘consistency conditions’, finally, we demonstrate that by modifying the Einstein-Laub or Chu formulation; time-averaged STs and volume forces are obtainable, which can overcome the aforementioned inconsistencies. For example- these modified formulations can yield the ‘correct’ time averaged force similar to Minkowski’s force for almost all the previous real experiments. Specially, our proposed modified Einstein-Laub ST can be considered as an efficient mathematical toolkit, an alternative of time and memory consuming volumetric forces, to yield the internal bulk force of a chiral or achiral object embedded in complex material backgrounds (i.e. homogeneous, heterogeneous, bounded etc.). Later, we have also shown an interesting application of modified Lorentz force to control the reversal of optical binding force of plasmonic cubes placed over plasmonic substrate due to strong Fano resonance. Finally, based on our proposals throughout the thesis, at the end of this thesis we propose a new hypothesis named as the ‘existence domain’. ‘Existence domain’ is the region either outside of a scattering body taking only its exterior fields into account, or in its interior considering only the inside fields. Though almost all the time averaged distinct STs and volumetric force laws are restricted to the idea of ‘existence domain’, we demonstrate that the stress tensor, volumetric force and photon momentum of Minkowski are free from such and other restrictions both in instantaneous and time averaged situations. After almost 100 years of Einstein’s prediction, this thesis, most probably, finally answers why only Minkowski’s theory of optical force and photon momentum remains consistent in all circumstances. Proposals presented in this thesis can be very effective for resolving not only the dilemma of distinct stress tensors and optical Lorentz/ volumetric forces but also for settling the controversy of Abraham-Minkowski photon momenta. This thesis may also open a new window for optical pulling force/tractor beams along with the novel manipulation process of plasmonic dimers.

— Spherical induction motors hold great potential for numerous applications where design of multi-degree of freedom drive systems is needed, such as mechatronic systems, robotics, automotive industry and medical applications. Namely, spherical induction motor can operate in several degrees of freedom due to its specific design features. In addition, the drives where spherical motors are used might be lighter, smaller, more responsive and more cost-effective. Over the past few years scientific research is directed towards development of a spherical motor that could outperform conventional single-axis induction motors. The primary goal of this paper was to model and to analyze spherical induction motors and to compare their performance characteristics to the conventional induction motors. The modeling and analysis was based on 3D finite element method by using commercial software environment Flux Cedrat. Our simulation results showed that spherical induction motors do not achieve the same or at least comparable performance as the conventional induction motor; hence for the time being cannot replace traditional single-axis/single degree of freedom induction motors. We identified the main disadvantages of the spherical machines that need to be improved in order to meet the requirements for their massive use and production.

The current paper seeks to evaluate the performance of the quarter-wave transformer-based impedance matching technique implemented by means of reduced-height waveguide structures with each section being a quarter-wavelength long electrically, with comparison between performances based on number of sections used for impedance matching. The two-step impedance matching technique has been compared to its six-step variant, by comparing the impedance variation from input to output section in both cases, to enable optimization of power transfer and reduction of standing-wave formation due to significant variation in impedance between two successive sections, which is significant in case of two-step impedance matching by two quarter-wave sections.

This paper introduces a modified enhanced transmission-line theory to account for higher-order modes while using a standard transmission line equation solver or equivalently a Baum, Liu and Tesche (BLT) equation solver. The complex per-unit-length parameters as defined by Nitsch et al. are first cast into an appropriate per-unit-length resistance, inductance, capacitance and conductance (RLCG) form. Besides, these per-unit-length parameters are modified to account for radiation losses with reasonable approximations. This modification is introduced by an additional per-unit-length resistance. The reason and explanations for this parameter are provided. Results obtained with this new formalism are comparable to those obtained using an electromagnetic full-wave solver, thus extending the capability of conventional transmission line solvers.

We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics to cloaks with a surface of revolution. We derive the expression of the transformation matrix and show that one of its eigenvalues vanishes on the inner boundary of the cloaks, while the other two remain strictly positive and bounded. The validity of our approach is confirmed by finite edge-elements computations for a non-convex cloak of varying thickness.

This paper proposes a radial dependent dispersive finite-difference time-domain method for the modeling of electromagnetic cloaking structures. The permittivity and permeability of the cloak are mapped to the Drude dispersion model and taken into account in dispersive FDTD simulations. Numerical simulations demonstrate that under ideal conditions, objects placed inside the cloak are ‘invisible’ to external electromagnetic fields. However for the simplified cloak based on linear transformations, the back scattering has a similar level to the case of a PEC cylinder without any cloak, rendering the object still being ‘visible’. It is also demonstrated numerically that the simplified cloak based on high-order
transformations can indeed improve the cloaking performance.