Daniel Sjöberg

A Floquet--Bloch Decomposition of Maxwell's Equations Applied to Homogenization

Using Bloch waves to represent the full solution of Maxwell’s equations in periodic media, we study the limit where the material’s period becomes much smaller than the wavelength. It is seen that for steady-state fields, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the non-vanishing Bloch waves, providing a new means of homogenization. The representation is valid for an arbitrary wave vector in the first Brillouin zone.

Physical bounds on the all-spectrum transmission through periodic arrays

We show that the blockage in transmission of a screen with a periodic microstructure integrated over all wavelengths is bounded by the static polarizability per unit area of the screen. Physical bounds on the co-polarized transmission coefficient over a wavelength interval are presented using only information from the zero-frequency properties of the microstructure. The theoretical results are compared to and verified by measurements on a screen composed of a large number of split ring resonators printed on a dielectric substrate.

Physical Bounds and Sum Rules for High-Impedance Surfaces

High-impedance surfaces are artificial surfaces synthesized from periodic structures. The high impedance is useful as it does not short circuit electric currents and reflects electric fields without phase shift. Here, a sum rule is presented that relates frequency intervals having high impedance with the thickness of the structure. The sum rule is used to derive physical bounds on the bandwidth for high-impedance surfaces composed by periodic structures above a perfectly conducting ground plane. Numerical examples are used to illustrate the result, and show that the physical bounds are tight.

Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition

We find effective, or homogenized, material parameters for Maxwell’s equations when the microscopic scale becomes small compared to the scale induced by the frequencies of the imposed currents. After defining a singular value decomposition of the non-selfadjoint partial differential operator, we expand the electromagnetic field in the modes corresponding to the singular values, and show that only the smallest singular values make a significant contribution to the total field when the scale is small. The homogenized material parameters can be represented with the mean values of the singular vectors through a simple formula, which is valid for wavelengths not necessarily infinitely large compared to the unit cell. (Less)

Optical Theorem and Forward Scattering Sum Rule for Periodic Structures

Based on energy conservation, an optical theorem is constructed for a slab having an arbitrary periodic microstructure in a plane. A sum rule for low pass structures is derived using analytic properties of Herglotz functions based on causality and passivity. The sum rule relates the total cross section to the static polarizability per unit cell, and quantifies the interaction between the slab and electromagnetic fields possible over all wavelengths. The results are illustrated with several numerical and experimental examples.

Performance Analysis of Millimeter-Wave Phased Array Antennas in Cellular Handsets

This letter discusses the usage of high-gain steerable antenna arrays operating at millimeter-wave (mmWave) frequencies for future cellular networks (5G). Based on the probable outline of the 5G networks, a method for characterizing phased array antennas in cellular handsets has been introduced. For analyzing the performance, the total scan pattern of the array configuration together with its respective coverage efficiency are essential to consider in order to compare different antenna designs and topology approaches with each other. Two design approaches and subarray schemes of these have been considered in order to illustrate the relevance of such a characterization method. The results show the importance of evaluating potential array antennas in such manners. The method can be applied to much more complex system models, where polarization diversity, hand and body effect, and statistical modeling of the channel may be included.

Scattering from a thin magnetic layer with a periodic lateral magnetization: application to electromagnetic absorbers

A magnetized thin layer mounted on a PEC surface is considered as an alternative for an absorbing layer. The magnetic material is modeled with the Landau-Lifshitz-Gilbert equation, with a lateral static magnetization having a periodic variation along one lateral direction. The scattering problem is solved by means of an expansion into Floquet-modes, a propagator formalism and wave- splitting. Numerical results are presented, and for parameter values close to the typical values for ferro- or ferrimagnetic media, reflection coefficients below −20 dB can be achieved for the fundamental mode over the frequency range 1-4 GHz, for both polarizations. It is found that the periodicity of the medium makes the reflection properties for the fundamental mode almost independent of the azimuthal direction of incidence, for both normally and obliquely incident waves.

Analysis of Wave Propagation in Stratified Structures Using Circuit Analogues, with Application to Electromagnetic Absorbers.

This paper presents an overview of how circuit models can be used for analysing wave propagation in stratified structures. Relatively complex structures can be analysed using models which are accessible to undergraduate students. Homogeneous slabs are modelled as transmission lines, and thin sheets between the slabs are modelled as lumped elements. It is seen that electric material properties act as shunt elements, and magnetic material properties act as series elements. When the sheets have periodic patterns, they can be represented with resonant circuits. When designing, for instance, an absorber for electromagnetic waves, the circuit models can be used as a starting point to derive a basic, stable design, which can later be optimized using full wave simulations if necessary.

Slot-Coupled Millimeter-Wave Dielectric Resonator Antenna for High-Efficiency Monolithic Integration

A readily mass-producible, flip-chip assembled, and slot-coupled III-V compound semiconductor dielectric resonator antenna operating in the millimeter-wave spectrum has been fabricated and characterized. The antenna has a 6.1% relative bandwidth, deduced from its 10 dB return loss over 58.8–62.5 GHz, located around the resonance at 60.5 GHz. Gating in the delay-domain alleviated the analysis of the complex response from the measured structure. The radiation efficiency is better than

DETERMINATION OF PROPAGATION CONSTANTS AND MATERIAL DATA FROM WAVEGUIDE MEASUREMENTS

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