21 research outputs found

    EM modelling of periodic structures using green's functions

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    Master'sMASTER OF ENGINEERIN

    Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

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    The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135885/1/srtan_1.pd

    Multiple Volume Scattering in Random Media and Periodic Structures with Applications in Microwave Remote Sensing and Wave Functional Materials

    Full text link
    The objective of my research is two-fold: to study wave scattering phenomena in dense volumetric random media and in periodic wave functional materials. For the first part, the goal is to use the microwave remote sensing technique to monitor water resources and global climate change. Towards this goal, I study the microwave scattering behavior of snow and ice sheet. For snowpack scattering, I have extended the traditional dense media radiative transfer (DMRT) approach to include cyclical corrections that give rise to backscattering enhancements, enabling the theory to model combined active and passive observations of snowpack using the same set of physical parameters. Besides DMRT, a fully coherent approach is also developed by solving Maxwell’s equations directly over the entire snowpack including a bottom half space. This revolutionary new approach produces consistent scattering and emission results, and demonstrates backscattering enhancements and coherent layer effects. The birefringence in anisotropic snow layers is also analyzed by numerically solving Maxwell’s equation directly. The effects of rapid density fluctuations in polar ice sheet emission in the 0.5~2.0 GHz spectrum are examined using both fully coherent and partially coherent layered media emission theories that agree with each other and distinct from incoherent approaches. For the second part, the goal is to develop integral equation based methods to solve wave scattering in periodic structures such as photonic crystals and metamaterials that can be used for broadband simulations. Set upon the concept of modal expansion of the periodic Green’s function, we have developed the method of broadband Green’s function with low wavenumber extraction (BBGFL), where a low wavenumber component is extracted and results a non-singular and fast-converging remaining part with simple wavenumber dependence. We’ve applied the technique to simulate band diagrams and modal solutions of periodic structures, and to construct broadband Green’s functions including periodic scatterers.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137141/1/srtan_1.pd

    Diffraction by a penetrable wedge

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    New approaches to the problem of diffraction by a penetrable wedge are introduced in this thesis. The motivation has been to add to the power the Geometrical Theory of Diffraction by obtaining diffraction coefficients for corners of penetrable bodies

    Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

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    Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

    Contribution to Integral Equation Techniques for Solving Electromagnetic Problems

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    Surface Mixed Potential Integral Equation (MPIE) formulations together with the Method of Moments (MoM) are widely used to solve electromagnetic problems. An accurate evaluation of the Green functions (GF) associated to the integral equation and of the coupling integrals needed to fill the MoM matrix are the cornerstone steps in the implementation of integral equation algorithms. This thesis is mainly focused on these two topics. The main intended application of our MPIE-MoM formulation is the analysis of enclosed structures, with the shield being materialized by rectangular cavities with perfect conducting (PEC) walls. GFs for rectangular cavities constitute a classic research topic, where there is still a lot of room for improvements. In this area, three main original results are presented in this thesis. Firstly, the exponential convergence of the modal series is ensured via a sophisticated coordinate permutation method. In second place, a study which allows setting the relationship between cavity resonances, excited modes and GF components' singularities, is fully developed. Finally, a novel hybrid method, to compute the GF static part is introduced. This method combines in a new original way both, the modal and image expansions of the cavity GFs. The discretization of the MPIE via the method of moments leads to a matrix equation. In the Galerkin version of the MoM, the matrix elements are given by four-dimensional integrals over source and observer surface domains of the GFs multiplied by some basis and test functions. These so-called coupling integrals invoke the integration of the GF singularity, which in the MPIE case is of the weak type (1/R). The accurate integration of this singularity is a very challenging topic, which has been tackled following many different strategies. Here, the closed analytical expressions of the 4D integral over rectangular domains of this singularity are presented. The problem related to the integration of the GF singularity on arbitrary shaped domains is solved through a hybrid numerical-analytical technique based on an original integral transformation and using by the first time double exponential (DE) numerical integration rules. The thesis concludes with several numerical examples and benchmarks of practical interest. They ascertain the validity of strategies, concepts and results of this thesis and they strongly hint to the development of future competitive computer tools

    Modeling of Long-Term Multipactor Evolution in Microwave Components Including Dielectric Layers

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    Multipactor is a resonant vacuum discharge occurring in microwave components of satellite systems as well as in particle accelerators. Due to its undesirable effects, multipactor analysis constitutes a mandatory step in the design of modern satellite components and in performance studies of particle accelerators. To this end, the development of computational techniques for multipactor prediction attracts intense interest in the scientific community. The phenomenon evolves in two distinct phases: first, a fast growth of the electron population and, second, a steady state during which the population reaches a saturation level and remains almost constant. State-of-the-art computational models focus on the precise prediction of the initial multipactor phase, which defines whether the discharge occurs or not. However, a clear overview of the phenomenon also requires the analysis of the longterm multipactor evolution. Due to the high complexity introduced by considering saturation mechanisms, long-term multipactor evolution remains still unclear for many configurations of highly practical importance. Such a case is the multipactor analysis in the presence of dielectrics, a case dealt within this thesis. Motivated by the challenging nature of analyzing the multipactor steady state, this work aims to provide its own contribution to the modeling and the analysis of long-term multipactor evolution. For this, a sophisticated computational tool has been developed for the full-3D multipactor analysis, taking into account saturation mechanisms. In order to get a fast overview of the phenomenon, a generalized single-electron model has been developed which allows a multipactor analysis in any configuration with unidirectionallike electric field. Based on this 1D model, qualitative studies considering the effect of lowenergy electron collisions and of single-sided multipactor in non-uniform coaxial fields have been performed. As a further step, a multiple-particle, full-3D model able to consider the stochastic nature of the secondary emission phenomenon has been developed. The singleelectron model nicely supplements the robust 3D analysis by providing fast estimations for the most likely cases in which multipactor occurs. Saturation mechanisms have been considered, too, for both 1D and 3D approximations. Taking into account the induced charges on the metallic boundaries, a fast analysis of longterm multipactor is provided by the 1D model for the parallel plate and coaxial line cases. The saturation study is boosted in the 3D analysis by taking into account the mutual Coulomb interaction between particles. The developed multipactor model has been properly adapted in order to study long-term multipactor in the case of dielectric-loaded waveguides. Space charge effects as well as the effect of the surface charge developed on the dielectric layer have been both considered in the analysis. Particularly, in order to efficiently take into account the effect of the induced charges, a novel image method for the evaluation of the 3D Green function in multi-layered media has been developed. For the first time, a saturation steady state is identified in parallel plates loaded with a dielectric layer

    Electromagnetic Modeling for Radar Remote Sensing of Snow-Covered Terrain

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    This thesis investigates the radar remote sensing of snow-covered terrain for estimation of snow equivalent water on global scale. The importance and impact of this research stems from the fact that water from snowmelt is the major source of water for inland cities and agriculture during summer. This effort is focused on developing a physics-based model for snow and a fully coherent polarimetric scattering model for snow above ground. Both the physical model and the forward polarimetric scattering model present a significant improvement compared to the existing models for snowpack. Computer-generated snow media are constructed using 3-D spatial exponential correlation functions, along with Lineal-Path functions that serve to preserve the connectivity of the snow particles. A fully-coherent model is presented through the use of the Statistical S-matrix Wave Propagation in Spectral-Domain (SSWaP-SD) technique. The SSWaP-SD depends on the discretization of the medium into thin slabs. Several realizations of a thin snow slab are solved numerically to form the statistics of the scattering matrix representing such a thin snow layer. For each thin slab of the snow-pack, a corresponding polarimetric N-port (representing different directions of scattering) S-matrix is generated. These S-matrices are cascaded using the SSWaP-SD method to calculate the total forward and backward bistatic scattered fields in a fully coherent way. The SSWaP-SD, in conjunction with a Method of Moments (MoM) code based on the Discrete-Dipole Approximation (DDA), is chosen to leverage both the time-efficient computations of the DDA and the full-coherency of the SSWaP-SD method, simultaneously. In addition to the MoM-DDA, a Finite Element Method (FEM) based on commercial software is used for cross-comparison and validation. The simulation results of the backscattering from an arbitrary thick snow layer are presented and validated with measurements. The underlying rough ground surface response is then estimated through both an analytical technique based on the Physical Optics (PO) method and a numerical solver based on MoM using a commercial full-wave solver. Finally, the complete response is then calculated by cascading the S-matrices representing the snow and the rough surface responses. The simulation results of the backscattering are presented using a Monte-Carlo process, which show very good agreement with measurements.PHDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/167972/1/mzaky_1.pd
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