Abstract
The recent application of pseudo-differential operator and functional integral methods to the factored scalar Helmholtz equation has yielded extended parabolic wave theories and corresponding path integral solutions for a large variety of acoustic wave propagation problems. These known techniques are applied here to the full vector electromagnetic problem resulting in a new first-order Weyl pseudo-differential equation, which is recognized as an extended parabolic wave equation. Perturbation treatments of the Weyl composition equation for the operator symbol matrix yield high-frequency and other asymptotic wave theories. Unlike the scalar Helmholtz equation case, the one-way vector EM equation (and a scalar analogue provided by the Klein-Gordon equation of relativistic physics) require the solution of a generalized quadratic operator equation. While these operator solutions do not have a simple formal representation as in the straightforward square root case, they are conveniently constructed in the Weyl pseudo-differential operator calculus.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. Fishman, J.J. McCoy, and S.C. Wales, Factorization and path integration of the Helmholtz equation: numerical algorithms, J. Acoust. Soc. Am. 81:1355 (1987).
M. A. Leontovich and V.A. Fock, Solution of the problem of propagation of electromagnetic waves along the earth’s surface by the method of parabolic equations, J. Phys. USSR 10:13 (1946).
M. Lax, W. H. Louisell, and W. B. McKnight, From Maxwell to paraxial wave optics, Phys. Rev. 11:1365 (1975).
R. I. Brent, W. L. Siegmann, and M. J. Jacobson, Parabolic approximations for atmospheric propagation of EM waves, including the terrestrial magnetic field, to appear in Radio Science 25. (1990).
J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill Book Company, New York, 1964).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Brent, R.I., Fishman, L. (1991). Derivation of Extended Parabolic Theories for Vector Electromagnetic Wave Propagation. In: Bertoni, H.L., Felsen, L.B. (eds) Directions in Electromagnetic Wave Modeling. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3677-6_5
Download citation
DOI: https://doi.org/10.1007/978-1-4899-3677-6_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-3679-0
Online ISBN: 978-1-4899-3677-6
eBook Packages: Springer Book Archive