TY - JOUR
T1 - A note on volterra differential constitutive operators and locality considerations in electromagnetic theory
AU - Censor, Dan
AU - Melamed, Timor
N1 - Funding Information:
Dan Censor obtained his B.Sc. in Electrical Engineering, cum laude, at the Israel Institute of Technology, Haifa, Israel in 1962. He was awarded M.Sc. (EE) in 1963 and D.Sc. (Technology) in 1967 from the same institute. Since 1987, he has been a tenured full professor in the Department of Electrical and Computer Engineering at Ben Gurion University of the Negev. He was a founding member of Israel URSI National Committee. His main areas of interest are electromagnetic theory and wave propagation. In particular, he studies electrodynamics and special relativity, wave and ray propagation in various media, theories and applications of Doppler effect in various wave systems, scattering by moving objects, and application to biomedical engineering.
PY - 2002/1/1
Y1 - 2002/1/1
N2 - Macroscopic Maxwell's theory for electrodynamics is an indeterminate set of coupled, vector, partial differential equations. This infrastructure requires the supplement of constitutive equations. Recently a general framework has been suggested, taking into account dispersion, inhomogeneity and nonlinearity, in which the constitutive equations are posited as differential equations involving the differential operators based on the Volterra functional series. The validity of such representations needs to be examined. Here it is shown that for such representations to be effective, the spatiotemporal functions associated with the Volterra differential operators must be highly localized, or equivalently, widely extended in the transform space. This is achieved by exploiting Delta-function expansions, leading in a natural way to polynomial differential operators. The Four-vector Minkowski space is used throughout, facilitating general results and compact notation.
AB - Macroscopic Maxwell's theory for electrodynamics is an indeterminate set of coupled, vector, partial differential equations. This infrastructure requires the supplement of constitutive equations. Recently a general framework has been suggested, taking into account dispersion, inhomogeneity and nonlinearity, in which the constitutive equations are posited as differential equations involving the differential operators based on the Volterra functional series. The validity of such representations needs to be examined. Here it is shown that for such representations to be effective, the spatiotemporal functions associated with the Volterra differential operators must be highly localized, or equivalently, widely extended in the transform space. This is achieved by exploiting Delta-function expansions, leading in a natural way to polynomial differential operators. The Four-vector Minkowski space is used throughout, facilitating general results and compact notation.
UR - http://www.scopus.com/inward/record.url?scp=0036425183&partnerID=8YFLogxK
U2 - 10.1117/12.472972
DO - 10.1117/12.472972
M3 - Conference article
AN - SCOPUS:0036425183
SN - 0277-786X
VL - 4806
SP - 81
EP - 91
JO - Proceedings of SPIE - The International Society for Optical Engineering
JF - Proceedings of SPIE - The International Society for Optical Engineering
T2 - Complex Mediums III: Beyond Linear Isotropic Dielectrics
Y2 - 8 July 2002 through 10 July 2002
ER -