This book explores spatial harmonic analysis (SHA) for characterizing and analyzing external magnetic fields in technical systems. Its strong emphasis on addressing real engineering challenges and a practical focus on both spherical and spheroidal harmonics set it apart, with the latter being valuable for analyzing objects with high aspect ratios. The content is particularly applicable to naval and spacecraft applications, as well as the rapidly growing field of autonomous unmanned vehicles, including aerial, surface, and underwater vehicles. In these contexts, precise control of magnetic signatures is crucial for navigation, detection avoidance, and overall operational effectiveness. The author presents multiple original concepts, including fast algorithms for spheroidal harmonic functions, which make them computationally feasible for real-world applications. Additionally, the use of magnetic energy as a general metric for the magnetic intensity of a given device is explored, as well as isodynamic surfaces to identify regions of maximum magnetic field extension.
Magnetic Signatures: Advanced Analysis for Modern Systems combines rigorous mathematical foundations with practical implementation strategies, making it an essential resource for designing and operating magnetically sensitive systems across various domains.
Introduction.- Theoretical Basis for Description of External
Electromagnetic Fields.- the Electric Field.- the Spatial Harmonic Analysis
in Electrostatics: Basic Concepts.- the Magnetic Field.- Fundamentals of the
Electromagnetic Theory: Maxwell's Equations.- Analytical Simulation of VLF or
Static Sources.- VLF Magnetic Multipoles.- Characterization of Sources by
Evaluation of Magnetic Energy.- Prolate Spheroidal Magnetic Multipoles.- the
Spatial Harmonic Characterization of an Elongated VLF Source.- the Spatial
Harmonic Characterization of a Flattened VLF Source.- Complex VLF or Static
Magnetic Sources: Numerical Simulation and Spatial Harmonic Analysis.- Hybrid
Fem-Sha Coupling Strategy.-Spheroidal Harmonic Analysis Using FEM Results.-
Simulations Using SHA-FEM Coupling.- Measurement Procedures for Spatial
Harmonic Analysis.- Spatial Harmonic Analysis Using Axisymmetric Sensor
Arrangements.- Generation of the Selective Functions Using Gram-Schmidt
Orthonormalization.- Prolate Spheroidal Multipole Analysis Using a Prolate
Spheroidal Array.- Generation of the Selective Functions for a Prolate
Spheroidal Array with Axial Magnetic Sensors: Indirect Method.- Oblate
Spheroidal Multipole Analysis Using Axisymmetric Arrays.- Selective Functions
of the Rectangular Planar Array of Sensors.- Generation of the Selective
Functions for a Non-Axisymmetric Rectangular Planar Array by the Forward
Orthonormalization.- Modeling of Sensor Noise, Misplacement and
Misorientation.- Addendum A: Application of Recurrence Relations for
Spherical Harmonic Analysis.- Addendum B: Application of Recurrence Relations
for Spheroidal Harmonic Analysis.- Addendum C: Coordinate Systems and Vector
Transformations.- Metric Coefficients.- Vector Transforms.
Alexander V. Kildishev, PhD, is a Professor of Electrical and Computer Engineering at the Elmore Family School of Electrical and Computer Engineering at Purdue University. His research focuses on theoretical and numerical modeling in the field of nanophotonics. Professor Kildishev has made significant contributions in several areas, including negative refractive index metamaterials, optical artificial magnetic structures, loss compensation in metamaterials, plasmonic nanolasers, optical metasurfaces, optical cloaks, and hyperlenses. He has been recognized on the Highly Cited Researchers List, which highlights outstanding researchers whose work includes multiple highly cited papers that rank in the top 1% by citations in the cross-field category for 2018, 2022, and 2023 in Web of Science (WOS). Additionally, Professor Kildishev is a Fellow of Optica (OSA) and serves on the editorial boards of Advanced Optical Materials and Advanced Photonics.
