Abstract
Geometrical diffraction theory uses ray tracing techniques to calculate diffraction and other properties of the electromagnetic field generally considered characteristically wave like. We here study this dualism of the classical electromagnetic field so as to distinguish those aspects of quantum dualism that arise simply as properties of oscillatory integrals and those that may have deeper origins. By a series of transformations the solutions of certain optics problems are reduced to the evaluation of a Feynman path integral and the known semiclassical approximations for the path integral provide a justification for the geometrical diffraction theory. Particular attention is paid to the problem of edge diffraction and for a half plane barrier a closed form solution is obtained. A classical variational principle for barrier penetration is also presented.
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
J.B. Keller, A Geometrical Theory of Diffraction in “Calculus of Variations and its Applications”, Proceedings of a Symposium in Applied Mathematics”, ed. L.M. Graves, McGraw, N ew York, 1958.
R.G. Kouyoumjian, The Geometrical Theory of Diffraction and its Application, in “Numerical and Asymptotic Techniques in Electromagnetics”, ed. R. Mittra, Springer-Verlag, Topics in Applied Physics, Vol. 3, Springer, Berlin, 1975.
A.J.W. Sommerfeld, “Optics”, Academic Press, New York 1954.
L.S. Schulman, “Techniques and Applications of Path Integration”, Wiley, New York 1981.
C. Morette (DeWitt), On the Definition and Approximation of Feynmans Path Integrals, Phys. Rev. 81, 848 (1952).
R.M. Lewis and J. Boersma, Uniform Asymptotic Theory of Edge Diffraction, J. Math. Phys. 10, 2291 (1969).
S.W. Lee, Path Integrals for Solving some Electromagnetic Edge Diffraction Problems, J. Math. Phys. 19, 1414 (1978).
M.C. Gutzwiller, Phase-Integral Approximation in Momentum Space and Bound States of an Atom, J. Math. Phys. 8, 1979 (1967).
N. Bleistein and K.A. Handelsman, “Asymptotic Expansions of Integrals”, Holt, Rinehart and Winston, New York, 1975.
D.W. McLaughlin, Complex Time, Contour Independent Path Integrals, and Barrier Penetration, J. Math. Phys. 13, 1099 (1972).
M. Buttiker and R. Landauer, Traversal Time for Tunneling, IBM preprint, 1982.
L.S. Schulman, Exact Time-Dependent Green’s Function for the Half-Plane Barrier, Phys. Lev. Lett. 49, 599 (1982).
See also R.S. Longhurst, “Geometrical and Physical Optics,” Longmans, Green and Co. London 1957; p. 439. I thank Michael Berry for bringing this reference to my attention.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 D. Reidel Publishing Company
About this chapter
Cite this chapter
Schulman, L.S. (1984). Ray Optics for Diffraction: A Useful Paradox in a Path Integral Context. In: Diner, S., Fargue, D., Lochak, G., Selleri, F. (eds) The Wave-Particle Dualism. Fundamental Theories of Physics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6286-6_13
Download citation
DOI: https://doi.org/10.1007/978-94-009-6286-6_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6288-0
Online ISBN: 978-94-009-6286-6
eBook Packages: Springer Book Archive