Yuriy K. Sirenko

An FFT-Accelerated FDTD Scheme with Exact Absorbing Conditions for Characterizing Axially Symmetric Resonant Structures

An accurate and e-cient flnite-difierence time-domain (FDTD) method for characterizing transient waves interactions on axially symmetric structures is presented. The method achieves its accuracy and e-ciency by employing localized and/or fast Fourier transform (FFT) accelerated exact absorbing conditions (EACs). The paper details the derivation of the EACs, discusses their implementation and discretization in an FDTD method, and proposes utilization of a blocked-FFT based algorithm for accelerating the computation of temporal convolutions present in nonlocal EACs. The proposed method allows transient analyses to be carried for long time intervals without any loss of accuracy and provides reliable numerical data pertinent to physical processes under resonant conditions. This renders the method highly useful in characterization of high-Q microwave radiators and energy compressors. Numerical results that demonstrate the accuracy and e-ciency of the method are presented.

Modern Theory of Gratings

The principal results of modern electromagnetic theory of gratings are reviewed briefly in this chapter. The model initial boundary value problems and boundary value problems are formulated and supplied with basic equations, domains of analysis, boundary and initial conditions, and the condition providing their unambiguous resolution are determined. The analytic relations between problems in time and frequency domains are found out. The problems connected with the consideration of gratings as open periodic resonators and waveguides are formulated and analyzed. The actual essential results of spectral theory of gratings and resonant scattering theory by periodic structures are presented in concise form. 1.1 The Formulation of Boundary Value and Initial Boundary Value Problems in the Theory of Diffraction Gratings 1.1.1 Fundamental Equations The initial boundary value problems and boundary value problems for the system of differential Maxwell equations form the corner stone of time domain and frequency domain electromagnetic theory. The solutions to these problems provide us with results, describing physical phenomena of spatio–temporal and spatial–frequency transformations of electromagnetic fields occurring in a large variety of structures: gratings, wave-guiding units, open resonators, radiating elements in antennas, etc. The adequacy and accuracy of the results depend in an essential way on the quality of the mathematical problems formulation and on the possibility of detailed analytic investigation of the solutions before the start of their numerical determination. In this chapter, we describe the problems of electromagnetic theory of gratings resulting from following system of equations: η0rot H = ε E ∂t + σ E + J, rot E = −η0μ H ∂t , (1.1) div ( μ H = 0 , div ε E = ρ, (1.2) 1 Y.K. Sirenko, S. Ström (eds.), Modern Theory of Gratings, Springer Series in Optical Sciences 153, DOI 10.1007/978-1-4419-1200-8_1, C

TIME-DOMAIN ANALYSIS OF OPEN RESONATORS. ANALYTICAL GROUNDS

The paper is concerned with the development and mathematical justification of the methodology for applying the timedomain methods in the study of spectral characteristics of open electrodynamic resonant structures.

Controlled Changes in Spectra of Open Quasi-Optical Resonators

The e-ciency of difierent ways for controlled changes of spectral characteristics of open electrodynamic resonant structures are studied and evaluated in the paper.

Explicit Conditions for Virtual Boundaries in Initial Boundary Value Problems in the Theory of Wave Scattering

This paper deals with the problem of finding a correct way of restricting the computational domain in the FDTD-method in its application to the analysis of transient wave processes in infinite homogeneous regions containing compact inhomogeneities. The formulation of the explicit ABCs (Absorbing Boundary Conditions) in such a way that they do not distort the physical model simulated by the mathematics, and the incorporation of these ABCs in the computational scheme form the basis of the approach presented here. A number of numerical results are given, illustrating in particular the performance of the exact ABCs in comparison with lower order approximations.

COMPRESSION AND RADIATION OF HIGH-POWER SHORT RF PULSES. II. A NOVEL ANTENNA ARRAY DESIGN WITH COMBINED COMPRESSOR/RADIATOR ELEMENTS

The paper discusses the radiation of compressed high power short RF pulses using two difierent types of antennas: (i) A simple monopole antenna and (ii) a novel array design, where each of the elements is constructed by combining a compressor and a radiator. The studies on the monopole antenna demonstrate the possibility of a high power short RF pulses e-cient radiation even using simple antennas. The studies on the novel array design demonstrate that a reduced size array with lower pulse distortion and power decay can be constructed by assembling the array from elements each of which integrates a compressor and a radiator. This design idea can be used with any type of antenna array; in this work it is applied to a phased array.

Simulation and Analysis of Transient Processes in Open Axially-symmetrical Structures: Method of Exact Absorbing Boundary Conditions

Present day methodologies for mathematical simulation and computational experiment are generally implemented in electromagnetics through the solution of boundary-value (frequency domain) problems and initial boundary-value (time domain) problems for Maxwell’s equations. Most of the results of this theory concerning open resonators have been obtained by the frequency-domain methods. At the same time, a rich variety of applied problems (analysis of complex electrodynamic structures for the devices of vacuum and solid-state electronics, model synthesis of open dispersive structures for resonant quasioptics, antenna engineering, and high-power electronics, etc.) can be efficiently solved with the help of more universal time-domain algorithms. The fact that frequency domain approaches are somewhat limited in such problems is the motivation for this study. Moreover, presently known remedies to the various theoretical difficulties in the theory of non-stationary electromagnetic fields are not always satisfactory for practitioners. Such remedies affect the quality of some model problems and limit the capability of time-domain methods for studying transient and stationary processes. One such difficulty is the appropriate and efficient truncation of the computational domain in so-called open problems, i.e. problems where the computational domain is infinite along one or more spatial coordinates. Also, a number of questions occur when solving far-field problems, and problems involving extended sources or sources located in the far-zone. In the present work, we address these difficulties for the case of 0 TE n and 0 TM n -waves in axially-symmetrical open compact resonators with waveguide feed lines. Sections 2 and 3 are devoted to problem definition. In Sections 4 and 5, we derive exact absorbing conditions for outgoing pulsed waves that enable the replacement of an open problem with an equivalent closed one. In Section 6, we obtain the analytical representation for operators that link the nearand far-field impulsive fields for compact axially-symmetrical structures and consider solutions that allow the use of extended or distant sources. In Section 7, we place some accessory results required for numerical implementation of the approach under

Modeling and analysis of transients in periodic gratings. II. Resonant wave scattering

In this paper we represent a number of new physical results obtained using time domain methods and based on equivalent replacement of initially open electrodynamic problems with closed ones. These results prove the high efficiency and reliability of the approach, being grounded in our companion paper in this issue.

Nonstationary Model Problems for Waveguide Open Resonator Theory

ABSTRACT The paper takes a fresh look at rigorous approaches and algorithms for model problems of electromagnetic theory of waveguide discontinuities. Numerical experiment is still the main tool for investigation the resonant wave scattering phenomena, which are characteristic for such structures. The mathematical approaches employed for such purposes have to fit certain requirements for accuracy, efficiency and versatility, for ability to be focused on particular details of various practically interesting regimes. The approaches for analysis of transient processes in waveguide open resonators considered herein satisfy all these requirements. They rely on the description of scattering properties of discontinuities in regular waveguides in terms of transform operators related to “evolutionary basis” of nonstationary signals, which are qualitatively the same for all guiding structures. The prototypes of such approaches in frequency domain (FD) have been verified by large body of boundary value problems (BVP...

COMPRESSION AND RADIATION OF HIGH-POWER SHORT RF PULSES. I. ENERGY ACCUMULATION IN DIRECT-FLOW WAVEGUIDE COMPRESSORS

Proper design of e-cient microwave energy compressors requires precise understanding of the physics pertinent to energy accumulation and exhaust processes in resonant waveguide cavities. In this paper, practically for the flrst time these highly non-monotonic transient processes are studied in detail using a rigorous time-domain approach. Additionally, in∞uence of the geometrical design and excitation parameters on the compressors performance is quantifled in detail.