Real and Complex Analysis

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Methods Of Modern Mathematical Physics

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Electrodynamics Of Continuous Media

Introduction to Electromagnetic Compatibility

Functions of One Complex Variable

We study the behavior of solitary-wave solutions of some generalized nonlinear Schrodinger 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 consider 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.

Solitary Wave Dynamics in an External Potential

Physical bounds on the directivity Q-factor quotient and optimal current distributions are determined for antennas of arbitrary shape and size using an optimization formulation. A variational approach offers closed form solutions for small antennas expressed in the polarizability of the antenna structure. Finite sized antennas are solved using Lagrangian parameters in a method of moments formulation. It is also shown that the optimal charge density for a small antenna can be generated by several current densities. Numerical examples for small and large antennas are used to illustrate the results.

/pdf/physical-bounds-and-optimal-currents-on-antennas-1lik9luw51.pdf

Physical Bounds and Optimal Currents on Antennas

The present thesis considers two different subjects in the research area of electromagnetics. The first part is concerned with antenna design and the second with radar absorbers and rasorber.In the first part, a novel excitation technique for cylindrical dielectric resonator antennas is introduced to produce circular polarization. The exciter is a tape helix that is wound around the dielectric resonator and is fed by a coaxial probe. The helix excites the HE11σ modes in phase quadrature in the cylindrical dielectric resonator antenna. The height of the helix is determined using the Hansen-Woodyard condition for an end-fire array based on the phase velocity of the surface wave traveling along the dielectric resonator side wall. This phase velocity is estimated from the phase velocity in an infinitely long dielectric rod with the same permittivity and radius as the dielectric resonator antenna. The helical exciter is required to operate in the helix axial mode. The height of the helix is usually taller than the height of the dielectric resonator core. Using this type of excitation, a 3 dB axial-ratio bandwidth of 6.4% was achieved for a sample design with dielectric constant er ~ 11. The achieved 3 dB axial-ratio bandwidth is greater than that typical of other reported single feed cylindrical dielectric resonator antennas. A prototype of the sample design is fabricated and measured and a good agreement between simulation and measurement is observed. Furthermore, two approaches for the enhancement of the 3 dB axial ratio bandwidth are proposed: removing the central portion of the cylindrical dielectric resonator and using stacked cylinders. The advantages and limitations of each approach are discussed. Another perspective on the proposed design is to consider the antenna as a helix with a dielectric resonator core. In this perspective, the effects of the dielectric core on the helix antenna are discussed.The second part of the thesis is concerned with the design of thin wideband electromagnetic planar absorber for X- and KKu-band which also has a polarization sensitive transparent window at frequencies lower than L-band. The design is based on a two layer capacitive circuit absorber with the backmetal layer replaced with a polarization sensitive frequency selective surface. The structure is studied for normally incident waves with two orthogonal linear polarizations. The structure is optimized to have high transparency at low frequencies for one of the polarizations and at the same time good absorption efficiency for both polarizations at the high-frequency band. For one of the polarizations a -1.9 dB transmission with a transmission loss of less than 10% at 1 GHz as well as a 2.25:1 (75%) bandwidth of -20 dB reflection reduction are achieved. For the other polarization we obtained more than 3:1 (100%) bandwidth of -19 dB absorption. Compared with our earlier design based on a Jaumann absorber, we succeed in significantly reducing the transmission loss at the transparent window. Furthermore, the module of absorption quality is extensively improved. The improvements are based on using periodic arrangements of resistive patches in the structure design. The investigation of the structure for oblique angles of incidence and non-ideal materials is also accomplished.

Design of a wideband rasorber with a polarisation-sensitive transparent window

Although the stored energy of an antenna is instrumental in the evaluation of antenna Q and the associated physical bounds, it is difficult to strictly define stored energy. Classically, the stored energy is either determined from the input impedance of the antenna or the electromagnetic fields around the antenna. The new energy expressions proposed by Vandenbosch express the stored energy in the current densities in the antenna structure. These expressions are equal to the stored energy defined from the difference between the energy density and the far field energy for many but not all cases. Here, the different approaches to determine the stored energy are compared for dipole, loop, inverted L-antennas, and bow-tie antennas. We use Brune synthesized circuit models to determine the stored energy from the input impedance. We also compare the results with differentiation of the input impedance and the obtained bandwidth. The results indicate that the stored energy in the fields, currents, and circuit models agree well for small antennas. For higher frequencies, the stored energy expressed in the currents agrees with the stored energy determined from Brune synthesized circuit models whereas the stored energy approximated by differentiation of input impedance gives a lower value for some cases. The corresponding results for the bandwidth suggest that the inverse proportionality between the fractional bandwidth and Q-factor depends on the threshold level of the reflection coefficient.

https://lup.lub.lu.se/search/files/96358182/Gustafsson_Jonsson2015_AntennaQ.pdf

Antenna Q and Stored Energy Expressed in the Fields, Currents, and Input Impedance

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 energy expressions proposed by Vandenbosch for many but not all 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 the electrical size ka that is interpreted as the far-field energy in the interior of the sphere.

/pdf/stored-electromagnetic-energy-and-antenna-q-1zssraa78f.pdf

B. L. G. Jonsson

Papers

Solitary Wave Dynamics in an External Potential

Physical Bounds and Optimal Currents on Antennas

Design of a wideband rasorber with a polarisation-sensitive transparent window

Antenna Q and Stored Energy Expressed in the Fields, Currents, and Input Impedance

Stored Electromagnetic Energy and Antenna Q