Field quantities — A geometrical perspective

Several geometrical modalities of representing electromagnetic (EM) field quantities are reviewed. The shortcomings arising from the representation as local vector functions are examined. Alternative geometrical frameworks that are capable to more accurately model the physics of the EM field are discussed. The study is intended to bring conceptual clarifications and to present incentives for including alternative perspectives within the scope of (basic) EM courses.

[1]  E. Tonti.  Finite Formulation of the Electromagnetic Field , 2001 .

[2]  Ioan E. Lager,et al.  The Space-Time Integrated Model of Electromagnetic Field Computation , 2002 .

[3]  I. T. Rekanos,et al.  FDTD Modeling of Havriliak-Negami Media , 2012, IEEE Microwave and Wireless Components Letters.

[4]  D. Cavallo,et al.  Closed-Form Analysis of Artificial Dielectric Layers—Part I: Properties of a Single Layer Under Plane-Wave Incidence , 2014, IEEE Transactions on Antennas and Propagation.

[5]  Alain Bossavit,et al.  Yee-like schemes on staggered cellular grids: a synthesis between FIT and FEM approaches , 2000 .

[6]  Timo Euler.  Consistent discretization of maxwell's equations on polyhedral grids , 2007 .

[7]  R. Hansen.  Phased Array Antennas , 2009 .

[8]  Eng Leong Tan,et al.  A Split-Step FDTD Method for 3-D Maxwell's Equations in General Anisotropic Media , 2010, IEEE Transactions on Antennas and Propagation.

[9]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[10]  Enzo Tonti,et al.  The Mathematical Structure of Classical and Relativistic Physics: A General Classification Diagram , 2013 .

[11]  S. D. Gedney,et al.  A Discontinuous Galerkin Finite Element Time-Domain Method Modeling of Dispersive Media , 2012, IEEE Transactions on Antennas and Propagation.

[12]  Ali Akbarzadeh-Sharbaf,et al.  Finite-Element Time-Domain Solution of the Vector Wave Equation in Doubly Dispersive Media Using Möbius Transformation Technique , 2013, IEEE Transactions on Antennas and Propagation.

[13]  F. Teixeira.  Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media , 2008, IEEE Transactions on Antennas and Propagation.

[14]  Xiaoyu Xu,et al.  Dual Discrete Geometric Methods in Terms of Scalar Potential on Unstructured Mesh in Electrostatics , 2014, IEEE Transactions on Magnetics.

[15]  B. Mashhoon,et al.  Space-Time-Matter: Modern Kaluza-Klein Theory , 1998 .

[16]  Robert J. Mailloux,et al.  Phased Array Antenna Handbook , 1993 .

[17]  Cibelle Celestino Silva,et al.  Polar and axial vectors versus quaternions , 2002 .

[18]  Ioan E. Lager,et al.  Finite formulation and domain-integrated field relations in electromagnetics - a synthesis , 2003 .

[19]  Leonor Godinho,et al.  An Introduction to Riemannian Geometry , 2014 .

[20]  L. Felsen,et al.  Radiation and scattering of waves , 1972 .

[21]  A. Einstein.  The Meaning of Relativity , 1946 .

[22]  Ioan E. Lager,et al.  Application of the domain-integrated field relations method to the solution of large scale static and stationary magnetic field problems , 2002 .

[23]  A. T. Hoop.  Handbook of radiation and scattering of waves , 1995 .

[24]  Nathan Marcuvitz.  Waveguide Handbook , 1951 .

[25]  D. Baldomir,et al.  Differential forms and electromagnetism in 3-dimensional Euclidean space R3 , 1986 .

[26]  D. Cavallo,et al.  Closed-Form Analysis of Artificial Dielectric Layers—Part II: Extension to Multiple Layers and Arbitrary Illumination , 2014, IEEE Transactions on Antennas and Propagation.

[27]  G. Deschamps.  Electromagnetics and differential forms , 1981, Proceedings of the IEEE.

[28]  F. Teixeira,et al.  Differential Forms, Galerkin Duality, and Sparse Inverse Approximations in Finite Element Solutions of Maxwell Equations , 2007, IEEE Transactions on Antennas and Propagation.

[29]  P. Hammond,et al.  Geometry of Electromagnetic Systems , 1996 .

[30]  Constantine A. Balanis,et al.  Antenna Theory: Analysis and Design , 1982 .

[31]  I. T. Rekanos,et al.  FDTD Schemes for Wave Propagation in Davidson-Cole Dispersive Media Using Auxiliary Differential Equations , 2012, IEEE Transactions on Antennas and Propagation.

[32]  A. T. de Hoop.  Electromagnetic Field Theory in $(N+1)$ -Space-Time: A Modern Time-Domain Tensor/Array Introduction , 2013, Proceedings of the IEEE.