Derivation of Extended Parabolic Theories for Vector Electromagnetic Wave Propagation
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.
Unable to display preview. Download preview PDF.
- 4).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).Google Scholar
- 5).J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill Book Company, New York, 1964).Google Scholar