Analysis of Electromagnetic Fields and Waves: The Method of Lines

The Method of Lines (MOL) is a versatile approach to obtaining numerical solutions to partial differential equations (PDEs) as they appear in dynamic and static problems. This method, popular in science and engineering, essentially reduces PDEs to a set of ordinary differential equations that can be integrated using standard numerical integration methods. Its significant advantage is that the analysis algorithms follow the physical wave propagation and are therefore efficient. This is because the fields on the discretisation lines are described by generalised transmission line (GTL) equations. With this formulation we have a connection to the well known transmission line theory and resulting in an easy understanding.
The method of lines is a very accurate and powerful way to analyze electromagnetic waves, enabling a full–wave solution without the computational burden of pure finite element or finite difference methods.
With Analysis of Electromagnetic Fields and Waves, Reinhold Pregla describes an important and powerful method for analyzing electromagnetic waves. This book:
Describes the general analysis principles for electromagnetic fields.Includes applications in microwave, millimetre wave and optical frequency regions.Unifies the analysis by introducing generalised transmission line (GTL) equations for all orthogonal coordinate systems and with materials of arbitrary anisotropy as a common start point.Demonstrates a unique analysis principle with the numerical stable impedance/admittance transformation and a physical adapted field transformation concept that is also useful for other modelling algorithms.Includes chapters on Eigenmode calculations for various waveguides, concatenations and junctions of arbitrary number of different waveguide sections in complex devices, periodic structures (e.g. Bragg gratings, meander lines, clystron resonators, photonic crystals), antennas (e.g. circular and conformal). Enables the reader to solve partial differential equations in other physical areas by using the described principles.Features an accompanying website with program codes in Matlab© for special problems.
Analysis of Electromagnetic Fields and Waves will appeal to electromagnetic field practitioners in primary and applied research as well as postgraduate students in the areas of photonics, micro– and millimetre waves, general electromagnetics, e.g. microwave integrated circuits, antennas, integrated and fibre optics, optoelectronics, nanophotonics, microstructures, artificial materials

Spis treści:
Preface.
1 THE METHOD OF LINES.
1.1 INTRODUCTION.
1.2 MOL: FUNDAMENTALS OF DISCRETISATION.
1.2.1 Qualitative description.
1.2.2 Quantitative description of the discretisation.
1.2.3 Numerical example.
2 BASIC PRINCIPLES OF THE METHOD OF LINES.
2.1 INTRODUCTION.
2.2 BASIC EQUATIONS.
2.2.1 Anisotropic material parameters.
2.2.2 Relations between transversal electric and magnetic fields – generalised transmission line (GTL) equations.
2.2.3 Relation to the analysis with vector potentials.
2.2.4 GTL equations for 2D structures.
2.2.5 Solution of the GTL equations.
2.2.6 Numerical examples.
2.3 EIGENMODES IN PLANAR WAVEGUIDE STRUCTURES WITH ANISOTROPIC LAYERS.
2.3.1 Introduction.
2.3.2 Analysis equations for eigenmodes in planar structures.
2.3.3 Examples of systemequations.
2.3.4 Impedance/admittance transformation in multilayered structures.
2.3.5 System equation in transformed domain.
2.3.6 System equation in spatial domain.
2.3.7 Matrix partition technique: two examples.
2.3.8 Numerical results.
2.4 ANALYSIS OF PLANAR CIRCUITS.
2.4.1 Discretisation of the transmission line equations.
2.4.2 Determination of the field components.
2.5 FIELD AND IMPEDANCE/ADMITTANCE TRANSFORMATION.
2.5.1 Introduction.
2.5.2 I mpedance/admittance transformation in multilayered and multisectioned structures.
2.5.3 Impedance/admittance transformation with finite differences.
2.5.4 Stable field transformation through layers and sections.
3 ANALYSIS OF RECTANGULAR WAVEGUIDE CIRCUITS.
3.1 INTRODUCTION.
3.2 CONCATENATIONS OF WAVEGUIDE SECTIONS.
3.2.1 LSM and LSE modes in circular waveguide bends.
3.2.2 LSM and LSE modes in straight waveguides.
3.2.3 Impedance transformation at waveguide interfaces.
3.2.4 Numerical results for concatenations.
3.2.5 Numerical results for waveguide filters.
3.3 WAVEGUIDE JUNCTIONS.
3.3.1 E–plane junctions.
3.3.2 H–plane junctions.
3.3.3 Algorithm for generalised scattering parameters.
3.3.4 Special junctions: E–plane 3–port junction.
3.3.5 Matched E–plane bend.
3.3.6 Analysis of waveguide bend discontinuities.
3.3.7 Scattering parameters.
3.3.8 Numerical results.
3.4 ANALYSIS OF 3D WAVEGUIDE JUNCTIONS.
3.4.1 General description.
3.4.2 Basic equations.
3.4.3 Discretisation scheme for propagation between A and B.
3.4.4 Discontinuities.
3.4.5 Coupling to other ports.
3.4.6 Impedance/admittance transformation.
3.4.7 Numerical results.
4 ANALYSIS OF WAVEGUIDE STRUCTURES IN CYLINDRICAL COORDINATES.
4.1 INTRODUCTION.
4.2 GENERALISED TRANSMISSION LINE (GTL) EQUATIONS.
4.2.1 Material parameters in a cylindrical coordinate system.
4.2.2 GTL equations for z–direction.
4.2.3 GTL equations for φ–direction.
4.2.4 Analysis of circular (coaxial) waveguides with azimuthally–magnetised ferrites and azimuthallymagnetised solid plasma.
4.2.5 GTL equations for r–direction.
4.3 DISCRETISATION OF THE FIELDS AND SOLUTIONS.
4.3.1 Equations for propagation in z–direction.
4.3.2 Equations for propagation in φ–direction.
4.3.3 Solution of the wave equat ions in z– and φ–direction.
4.3.4 Equations for propagation in r –direction.
4.4 SOLUTION IN RADIAL DIRECTION.
4.4.1 Discretisation in z –direction – circular dielectric resonators.
4.4.2 Discretisation in z –direction – propagation in φ–direction.
4.4.3 Discretisation in φ–direction – eigenmodes in circular multilayered waveguides.
4.4.4 Eigenmodes of circular waveguides with magnetised ferrite or plasma – discretisation in r –direction.
4.4.5 Waveguide bends – discretisation in r –direction.
4.4.6 Uniaxial anisotropic fibres with circular and noncircular cross–section – discretisation in φ–direction.
4.5 DISCONTINUITIES IN CIRCULAR WAVEGUIDES – ONE–DIMENSIONAL DISCRETISATION IN RADIAL DIRECTION.
4.5.1 Introduction.
4.5.2 Basic equations for rotational symmetry.
4.5.3 Solution of the equations for rotational symmetry.
4.5.4 Admittance and impedance transformation.
4.5.5 Open ending circular waveguide.
4.5.6 Numerical results for discontinuities in circular waveguides.
4.5.7 Numerical results for coaxial line discontinuities and coaxial filter devices.
4.5.8 Non–rotational modes in circular waveguides.
4.5.9 Numerical results and discussion.
4.6 ANALYSIS OF GENERAL AXIALLY SYMMETRIC ANTENNAS WITH COAXIAL FEED LINES.
4.6.1 Introduction.
4.6.2 Theory.
4.6.3 Regions with crossed lines.
4.6.4 Two special cases.
4.6.5 Port relations of section D.
4.6.6 Numerical results.
4.6.7 Further structures and remarks.
4.7 DEVICES IN CYLINDRICAL COORDINATES –TWO–DIMENSIONAL DISCRETISATION.
4.7.1 Discretisation in r– and φ–direction.
4.7.2 Numerical results.
4.7.3 Discretisation in r– and z–direction.
4.7.4 Discretis